amd/TTT-Bench
TTT-Bench: A Benchmark for Evaluating Reasoning Ability with Simple and Novel Tic-Tac-Toe-style Games 📃 Paper | 🤗 Dataset | 🌐 Website We introduce TTT-Bench, a new benchmark specifically created to evaluate the reasoning capability of LRMs through a suite of simple and novel two-player Tic-Tac-Toe-style games. Although trivial for humans, these games require basic strategic reasoning, including predicting an opponent's intentions and understanding spatial configurations.… See the full description on the dataset page: https://huggingface.co/datasets/amd/TTT-Bench.
1113
1[2 {3 "problem": "Alice and Bob are playing a game on two adjacent cubes. ABCD forms the top rectangle in the first cube and BIJC forms the top rectangle in the second cube. EFGH forms the bottom rectangle in the first cube and FKLG forms the bottom rectangle in the second cube. AE is an edge, BF is an edge, CG is an edge, DH is an edge, IK is an edge, and JL is an edge. Note that vertices B,C,G,F are shared by the two cubes. Alice and Bob plays a game where they take turns to put stickers on the vertices of the cubes that have not been occupied. Alice plays white stickers. Bob plays black stickers. The person who has four stickers on the same plane on either cube wins. Alice first places a white stone at F. Then Bob places a black stone at A. Then Alice places a white stone at K. Then Bob places a black stone at J. Then Alice places a white stone at L. Where should Bob play next?",4 "solution": "G",5 "is_unique_solution": true,6 "verdict": "blocked",7 "next_player": "Bob",8 "currect_board_visualization": "...*------*------B\n../|...../|...../|\n./.|..../.|..../.|\nB------*------*..|\n|..*---|--*...|..W\n|./....|./....|./\n|/.....|/.....|/\n*------W------W\n",9 "board_visualization": "...D------C------J\n../|...../|...../|\n./.|..../.|..../.|\nA------B------I..|\n|..H---|--G...|..L\n|./....|./....|./\n|/.....|/.....|/\nE------F------K\n",10 "problem_number": 011 },12 {13 "problem": "Alice and Bob are playing a game on two adjacent cubes. ABCD forms the top rectangle in the first cube and BIJC forms the top rectangle in the second cube. EFGH forms the bottom rectangle in the first cube and FKLG forms the bottom rectangle in the second cube. AE is an edge, BF is an edge, CG is an edge, DH is an edge, IK is an edge, and JL is an edge. Note that vertices B,C,G,F are shared by the two cubes. Alice and Bob plays a game where they take turns to put stickers on the vertices of the cubes that have not been occupied. Alice plays white stickers. Bob plays black stickers. The person who has four stickers on the same plane on either cube wins. Alice first places a white stone at C. Then Bob places a black stone at H. Then Alice places a white stone at F. Then Bob places a black stone at L. Then Alice places a white stone at G. Where should Bob play next?",14 "solution": "B",15 "is_unique_solution": true,16 "verdict": "blocked",17 "next_player": "Bob",18 "currect_board_visualization": "...*------W------*\n../|...../|...../|\n./.|..../.|..../.|\n*------*------*..|\n|..B---|--W...|..B\n|./....|./....|./\n|/.....|/.....|/\n*------W------*\n",19 "board_visualization": "...D------C------J\n../|...../|...../|\n./.|..../.|..../.|\nA------B------I..|\n|..H---|--G...|..L\n|./....|./....|./\n|/.....|/.....|/\nE------F------K\n",20 "problem_number": 121 },22 {23 "problem": "Alice and Bob are playing a game on two adjacent cubes. ABCD forms the top rectangle in the first cube and BIJC forms the top rectangle in the second cube. EFGH forms the bottom rectangle in the first cube and FKLG forms the bottom rectangle in the second cube. AE is an edge, BF is an edge, CG is an edge, DH is an edge, IK is an edge, and JL is an edge. Note that vertices B,C,G,F are shared by the two cubes. Alice and Bob plays a game where they take turns to put stickers on the vertices of the cubes that have not been occupied. Alice plays white stickers. Bob plays black stickers. The person who has four stickers on the same plane on either cube wins. Alice first places a white stone at A. Then Bob places a black stone at E. Then Alice places a white stone at B. Then Bob places a black stone at H. Then Alice places a white stone at C. Where should Bob play next?",24 "solution": "D",25 "is_unique_solution": true,26 "verdict": "blocked",27 "next_player": "Bob",28 "currect_board_visualization": "...*------W------*\n../|...../|...../|\n./.|..../.|..../.|\nW------W------*..|\n|..B---|--*...|..*\n|./....|./....|./\n|/.....|/.....|/\nB------*------*\n",29 "board_visualization": "...D------C------J\n../|...../|...../|\n./.|..../.|..../.|\nA------B------I..|\n|..H---|--G...|..L\n|./....|./....|./\n|/.....|/.....|/\nE------F------K\n",30 "problem_number": 231 },32 {33 "problem": "Alice and Bob are playing a game on two adjacent cubes. ABCD forms the top rectangle in the first cube and BIJC forms the top rectangle in the second cube. EFGH forms the bottom rectangle in the first cube and FKLG forms the bottom rectangle in the second cube. AE is an edge, BF is an edge, CG is an edge, DH is an edge, IK is an edge, and JL is an edge. Note that vertices B,C,G,F are shared by the two cubes. Alice and Bob plays a game where they take turns to put stickers on the vertices of the cubes that have not been occupied. Alice plays white stickers. Bob plays black stickers. The person who has four stickers on the same plane on either cube wins. Alice first places a white stone at G. Then Bob places a black stone at C. Then Alice places a white stone at I. Then Bob places a black stone at D. Then Alice places a white stone at L. Where should Bob play next?",34 "solution": "B",35 "is_unique_solution": true,36 "verdict": "blocked",37 "next_player": "Bob",38 "currect_board_visualization": "...B------B------*\n../|...../|...../|\n./.|..../.|..../.|\n*------*------W..|\n|..*---|--W...|..W\n|./....|./....|./\n|/.....|/.....|/\n*------*------*\n",39 "board_visualization": "...D------C------J\n../|...../|...../|\n./.|..../.|..../.|\nA------B------I..|\n|..H---|--G...|..L\n|./....|./....|./\n|/.....|/.....|/\nE------F------K\n",40 "problem_number": 341 },42 {43 "problem": "Alice and Bob are playing a game on two adjacent cubes. ABCD forms the top rectangle in the first cube and BIJC forms the top rectangle in the second cube. EFGH forms the bottom rectangle in the first cube and FKLG forms the bottom rectangle in the second cube. AE is an edge, BF is an edge, CG is an edge, DH is an edge, IK is an edge, and JL is an edge. Note that vertices B,C,G,F are shared by the two cubes. Alice and Bob plays a game where they take turns to put stickers on the vertices of the cubes that have not been occupied. Alice plays white stickers. Bob plays black stickers. The person who has four stickers on the same plane on either cube wins. Alice first places a white stone at C. Then Bob places a black stone at D. Then Alice places a white stone at E. Then Bob places a black stone at I. Then Alice places a white stone at H. Where should Bob play next?",44 "solution": "B",45 "is_unique_solution": true,46 "verdict": "blocked",47 "next_player": "Bob",48 "currect_board_visualization": "...B------W------*\n../|...../|...../|\n./.|..../.|..../.|\n*------*------B..|\n|..W---|--*...|..*\n|./....|./....|./\n|/.....|/.....|/\nW------*------*\n",49 "board_visualization": "...D------C------J\n../|...../|...../|\n./.|..../.|..../.|\nA------B------I..|\n|..H---|--G...|..L\n|./....|./....|./\n|/.....|/.....|/\nE------F------K\n",50 "problem_number": 451 },52 {53 "problem": "Alice and Bob are playing a game on two adjacent cubes. ABCD forms the top rectangle in the first cube and BIJC forms the top rectangle in the second cube. EFGH forms the bottom rectangle in the first cube and FKLG forms the bottom rectangle in the second cube. AE is an edge, BF is an edge, CG is an edge, DH is an edge, IK is an edge, and JL is an edge. Note that vertices B,C,G,F are shared by the two cubes. Alice and Bob plays a game where they take turns to put stickers on the vertices of the cubes that have not been occupied. Alice plays white stickers. Bob plays black stickers. The person who has four stickers on the same plane on either cube wins. Alice first places a white stone at A. Then Bob places a black stone at B. Then Alice places a white stone at C. Then Bob places a black stone at L. Then Alice places a white stone at E. Where should Bob play next?",54 "solution": "G",55 "is_unique_solution": true,56 "verdict": "blocked",57 "next_player": "Bob",58 "currect_board_visualization": "...*------W------*\n../|...../|...../|\n./.|..../.|..../.|\nW------B------*..|\n|..*---|--*...|..B\n|./....|./....|./\n|/.....|/.....|/\nW------*------*\n",59 "board_visualization": "...D------C------J\n../|...../|...../|\n./.|..../.|..../.|\nA------B------I..|\n|..H---|--G...|..L\n|./....|./....|./\n|/.....|/.....|/\nE------F------K\n",60 "problem_number": 561 },62 {63 "problem": "Alice and Bob are playing a game on two adjacent cubes. ABCD forms the top rectangle in the first cube and BIJC forms the top rectangle in the second cube. EFGH forms the bottom rectangle in the first cube and FKLG forms the bottom rectangle in the second cube. AE is an edge, BF is an edge, CG is an edge, DH is an edge, IK is an edge, and JL is an edge. Note that vertices B,C,G,F are shared by the two cubes. Alice and Bob plays a game where they take turns to put stickers on the vertices of the cubes that have not been occupied. Alice plays white stickers. Bob plays black stickers. The person who has four stickers on the same plane on either cube wins. Alice first places a white stone at A. Then Bob places a black stone at E. Then Alice places a white stone at B. Then Bob places a black stone at F. Then Alice places a white stone at D. Where should Bob play next?",64 "solution": "C",65 "is_unique_solution": true,66 "verdict": "blocked",67 "next_player": "Bob",68 "currect_board_visualization": "...W------*------*\n../|...../|...../|\n./.|..../.|..../.|\nW------W------*..|\n|..*---|--*...|..*\n|./....|./....|./\n|/.....|/.....|/\nB------B------*\n",69 "board_visualization": "...D------C------J\n../|...../|...../|\n./.|..../.|..../.|\nA------B------I..|\n|..H---|--G...|..L\n|./....|./....|./\n|/.....|/.....|/\nE------F------K\n",70 "problem_number": 671 },72 {73 "problem": "Alice and Bob are playing a game on two adjacent cubes. ABCD forms the top rectangle in the first cube and BIJC forms the top rectangle in the second cube. EFGH forms the bottom rectangle in the first cube and FKLG forms the bottom rectangle in the second cube. AE is an edge, BF is an edge, CG is an edge, DH is an edge, IK is an edge, and JL is an edge. Note that vertices B,C,G,F are shared by the two cubes. Alice and Bob plays a game where they take turns to put stickers on the vertices of the cubes that have not been occupied. Alice plays white stickers. Bob plays black stickers. The person who has four stickers on the same plane on either cube wins. Alice first places a white stone at E. Then Bob places a black stone at B. Then Alice places a white stone at F. Then Bob places a black stone at J. Then Alice places a white stone at G. Where should Bob play next?",74 "solution": "H",75 "is_unique_solution": true,76 "verdict": "blocked",77 "next_player": "Bob",78 "currect_board_visualization": "...*------*------B\n../|...../|...../|\n./.|..../.|..../.|\n*------B------*..|\n|..*---|--W...|..*\n|./....|./....|./\n|/.....|/.....|/\nW------W------*\n",79 "board_visualization": "...D------C------J\n../|...../|...../|\n./.|..../.|..../.|\nA------B------I..|\n|..H---|--G...|..L\n|./....|./....|./\n|/.....|/.....|/\nE------F------K\n",80 "problem_number": 781 },82 {83 "problem": "Alice and Bob are playing a game on two adjacent cubes. ABCD forms the top rectangle in the first cube and BIJC forms the top rectangle in the second cube. EFGH forms the bottom rectangle in the first cube and FKLG forms the bottom rectangle in the second cube. AE is an edge, BF is an edge, CG is an edge, DH is an edge, IK is an edge, and JL is an edge. Note that vertices B,C,G,F are shared by the two cubes. Alice and Bob plays a game where they take turns to put stickers on the vertices of the cubes that have not been occupied. Alice plays white stickers. Bob plays black stickers. The person who has four stickers on the same plane on either cube wins. Alice first places a white stone at B. Then Bob places a black stone at K. Then Alice places a white stone at C. Then Bob places a black stone at L. Then Alice places a white stone at D. Where should Bob play next?",84 "solution": "A",85 "is_unique_solution": true,86 "verdict": "blocked",87 "next_player": "Bob",88 "currect_board_visualization": "...W------W------*\n../|...../|...../|\n./.|..../.|..../.|\n*------W------*..|\n|..*---|--*...|..B\n|./....|./....|./\n|/.....|/.....|/\n*------*------B\n",89 "board_visualization": "...D------C------J\n../|...../|...../|\n./.|..../.|..../.|\nA------B------I..|\n|..H---|--G...|..L\n|./....|./....|./\n|/.....|/.....|/\nE------F------K\n",90 "problem_number": 891 },92 {93 "problem": "Alice and Bob are playing a game on two adjacent cubes. ABCD forms the top rectangle in the first cube and BIJC forms the top rectangle in the second cube. EFGH forms the bottom rectangle in the first cube and FKLG forms the bottom rectangle in the second cube. AE is an edge, BF is an edge, CG is an edge, DH is an edge, IK is an edge, and JL is an edge. Note that vertices B,C,G,F are shared by the two cubes. Alice and Bob plays a game where they take turns to put stickers on the vertices of the cubes that have not been occupied. Alice plays white stickers. Bob plays black stickers. The person who has four stickers on the same plane on either cube wins. Alice first places a white stone at A. Then Bob places a black stone at G. Then Alice places a white stone at E. Then Bob places a black stone at K. Then Alice places a white stone at F. Where should Bob play next?",94 "solution": "B",95 "is_unique_solution": true,96 "verdict": "blocked",97 "next_player": "Bob",98 "currect_board_visualization": "...*------*------*\n../|...../|...../|\n./.|..../.|..../.|\nW------*------*..|\n|..*---|--B...|..*\n|./....|./....|./\n|/.....|/.....|/\nW------W------B\n",99 "board_visualization": "...D------C------J\n../|...../|...../|\n./.|..../.|..../.|\nA------B------I..|\n|..H---|--G...|..L\n|./....|./....|./\n|/.....|/.....|/\nE------F------K\n",100 "problem_number": 9101 },102 {103 "problem": "Alice and Bob are playing a game on two adjacent cubes. ABCD forms the top rectangle in the first cube and BIJC forms the top rectangle in the second cube. EFGH forms the bottom rectangle in the first cube and FKLG forms the bottom rectangle in the second cube. AE is an edge, BF is an edge, CG is an edge, DH is an edge, IK is an edge, and JL is an edge. Note that vertices B,C,G,F are shared by the two cubes. Alice and Bob plays a game where they take turns to put stickers on the vertices of the cubes that have not been occupied. Alice plays white stickers. Bob plays black stickers. The person who has four stickers on the same plane on either cube wins. Alice first places a white stone at G. Then Bob places a black stone at F. Then Alice places a white stone at H. Then Bob places a black stone at J. Then Alice places a white stone at K. Then Bob places a black stone at L. Where should Alice play next?",104 "solution": "B",105 "is_unique_solution": true,106 "verdict": "blocked",107 "next_player": "Alice",108 "currect_board_visualization": "...*------*------B\n../|...../|...../|\n./.|..../.|..../.|\n*------*------*..|\n|..W---|--W...|..B\n|./....|./....|./\n|/.....|/.....|/\n*------B------W\n",109 "board_visualization": "...D------C------J\n../|...../|...../|\n./.|..../.|..../.|\nA------B------I..|\n|..H---|--G...|..L\n|./....|./....|./\n|/.....|/.....|/\nE------F------K\n",110 "problem_number": 10111 },112 {113 "problem": "Alice and Bob are playing a game on two adjacent cubes. ABCD forms the top rectangle in the first cube and BIJC forms the top rectangle in the second cube. EFGH forms the bottom rectangle in the first cube and FKLG forms the bottom rectangle in the second cube. AE is an edge, BF is an edge, CG is an edge, DH is an edge, IK is an edge, and JL is an edge. Note that vertices B,C,G,F are shared by the two cubes. Alice and Bob plays a game where they take turns to put stickers on the vertices of the cubes that have not been occupied. Alice plays white stickers. Bob plays black stickers. The person who has four stickers on the same plane on either cube wins. Alice first places a white stone at A. Then Bob places a black stone at B. Then Alice places a white stone at D. Then Bob places a black stone at C. Then Alice places a white stone at K. Then Bob places a black stone at J. Where should Alice play next?",114 "solution": "I",115 "is_unique_solution": true,116 "verdict": "blocked",117 "next_player": "Alice",118 "currect_board_visualization": "...W------B------B\n../|...../|...../|\n./.|..../.|..../.|\nW------B------*..|\n|..*---|--*...|..*\n|./....|./....|./\n|/.....|/.....|/\n*------*------W\n",119 "board_visualization": "...D------C------J\n../|...../|...../|\n./.|..../.|..../.|\nA------B------I..|\n|..H---|--G...|..L\n|./....|./....|./\n|/.....|/.....|/\nE------F------K\n",120 "problem_number": 11121 },122 {123 "problem": "Alice and Bob are playing a game on two adjacent cubes. ABCD forms the top rectangle in the first cube and BIJC forms the top rectangle in the second cube. EFGH forms the bottom rectangle in the first cube and FKLG forms the bottom rectangle in the second cube. AE is an edge, BF is an edge, CG is an edge, DH is an edge, IK is an edge, and JL is an edge. Note that vertices B,C,G,F are shared by the two cubes. Alice and Bob plays a game where they take turns to put stickers on the vertices of the cubes that have not been occupied. Alice plays white stickers. Bob plays black stickers. The person who has four stickers on the same plane on either cube wins. Alice first places a white stone at A. Then Bob places a black stone at C. Then Alice places a white stone at F. Then Bob places a black stone at G. Then Alice places a white stone at K. Then Bob places a black stone at J. Where should Alice play next?",124 "solution": "L",125 "is_unique_solution": true,126 "verdict": "blocked",127 "next_player": "Alice",128 "currect_board_visualization": "...*------B------B\n../|...../|...../|\n./.|..../.|..../.|\nW------*------*..|\n|..*---|--B...|..*\n|./....|./....|./\n|/.....|/.....|/\n*------W------W\n",129 "board_visualization": "...D------C------J\n../|...../|...../|\n./.|..../.|..../.|\nA------B------I..|\n|..H---|--G...|..L\n|./....|./....|./\n|/.....|/.....|/\nE------F------K\n",130 "problem_number": 12131 },132 {133 "problem": "Alice and Bob are playing a game on two adjacent cubes. ABCD forms the top rectangle in the first cube and BIJC forms the top rectangle in the second cube. EFGH forms the bottom rectangle in the first cube and FKLG forms the bottom rectangle in the second cube. AE is an edge, BF is an edge, CG is an edge, DH is an edge, IK is an edge, and JL is an edge. Note that vertices B,C,G,F are shared by the two cubes. Alice and Bob plays a game where they take turns to put stickers on the vertices of the cubes that have not been occupied. Alice plays white stickers. Bob plays black stickers. The person who has four stickers on the same plane on either cube wins. Alice first places a white stone at C. Then Bob places a black stone at B. Then Alice places a white stone at D. Then Bob places a black stone at E. Then Alice places a white stone at J. Then Bob places a black stone at F. Where should Alice play next?",134 "solution": "A",135 "is_unique_solution": true,136 "verdict": "blocked",137 "next_player": "Alice",138 "currect_board_visualization": "...W------W------W\n../|...../|...../|\n./.|..../.|..../.|\n*------B------*..|\n|..*---|--*...|..*\n|./....|./....|./\n|/.....|/.....|/\nB------B------*\n",139 "board_visualization": "...D------C------J\n../|...../|...../|\n./.|..../.|..../.|\nA------B------I..|\n|..H---|--G...|..L\n|./....|./....|./\n|/.....|/.....|/\nE------F------K\n",140 "problem_number": 13141 },142 {143 "problem": "Alice and Bob are playing a game on two adjacent cubes. ABCD forms the top rectangle in the first cube and BIJC forms the top rectangle in the second cube. EFGH forms the bottom rectangle in the first cube and FKLG forms the bottom rectangle in the second cube. AE is an edge, BF is an edge, CG is an edge, DH is an edge, IK is an edge, and JL is an edge. Note that vertices B,C,G,F are shared by the two cubes. Alice and Bob plays a game where they take turns to put stickers on the vertices of the cubes that have not been occupied. Alice plays white stickers. Bob plays black stickers. The person who has four stickers on the same plane on either cube wins. Alice first places a white stone at H. Then Bob places a black stone at B. Then Alice places a white stone at I. Then Bob places a black stone at C. Then Alice places a white stone at J. Then Bob places a black stone at F. Where should Alice play next?",144 "solution": "G",145 "is_unique_solution": true,146 "verdict": "blocked",147 "next_player": "Alice",148 "currect_board_visualization": "...*------B------W\n../|...../|...../|\n./.|..../.|..../.|\n*------B------W..|\n|..W---|--*...|..*\n|./....|./....|./\n|/.....|/.....|/\n*------B------*\n",149 "board_visualization": "...D------C------J\n../|...../|...../|\n./.|..../.|..../.|\nA------B------I..|\n|..H---|--G...|..L\n|./....|./....|./\n|/.....|/.....|/\nE------F------K\n",150 "problem_number": 14151 },152 {153 "problem": "Alice and Bob are playing a game on two adjacent cubes. ABCD forms the top rectangle in the first cube and BIJC forms the top rectangle in the second cube. EFGH forms the bottom rectangle in the first cube and FKLG forms the bottom rectangle in the second cube. AE is an edge, BF is an edge, CG is an edge, DH is an edge, IK is an edge, and JL is an edge. Note that vertices B,C,G,F are shared by the two cubes. Alice and Bob plays a game where they take turns to put stickers on the vertices of the cubes that have not been occupied. Alice plays white stickers. Bob plays black stickers. The person who has four stickers on the same plane on either cube wins. Alice first places a white stone at F. Then Bob places a black stone at G. Then Alice places a white stone at H. Then Bob places a black stone at I. Then Alice places a white stone at K. Then Bob places a black stone at L. Where should Alice play next?",154 "solution": "B",155 "is_unique_solution": true,156 "verdict": "blocked",157 "next_player": "Alice",158 "currect_board_visualization": "...*------*------*\n../|...../|...../|\n./.|..../.|..../.|\n*------*------B..|\n|..W---|--B...|..B\n|./....|./....|./\n|/.....|/.....|/\n*------W------W\n",159 "board_visualization": "...D------C------J\n../|...../|...../|\n./.|..../.|..../.|\nA------B------I..|\n|..H---|--G...|..L\n|./....|./....|./\n|/.....|/.....|/\nE------F------K\n",160 "problem_number": 15161 },162 {163 "problem": "Alice and Bob are playing a game on two adjacent cubes. ABCD forms the top rectangle in the first cube and BIJC forms the top rectangle in the second cube. EFGH forms the bottom rectangle in the first cube and FKLG forms the bottom rectangle in the second cube. AE is an edge, BF is an edge, CG is an edge, DH is an edge, IK is an edge, and JL is an edge. Note that vertices B,C,G,F are shared by the two cubes. Alice and Bob plays a game where they take turns to put stickers on the vertices of the cubes that have not been occupied. Alice plays white stickers. Bob plays black stickers. The person who has four stickers on the same plane on either cube wins. Alice first places a white stone at D. Then Bob places a black stone at C. Then Alice places a white stone at G. Then Bob places a black stone at J. Then Alice places a white stone at H. Then Bob places a black stone at K. Where should Alice play next?",164 "solution": "F",165 "is_unique_solution": true,166 "verdict": "blocked",167 "next_player": "Alice",168 "currect_board_visualization": "...W------B------B\n../|...../|...../|\n./.|..../.|..../.|\n*------*------*..|\n|..W---|--W...|..*\n|./....|./....|./\n|/.....|/.....|/\n*------*------B\n",169 "board_visualization": "...D------C------J\n../|...../|...../|\n./.|..../.|..../.|\nA------B------I..|\n|..H---|--G...|..L\n|./....|./....|./\n|/.....|/.....|/\nE------F------K\n",170 "problem_number": 16171 },172 {173 "problem": "Alice and Bob are playing a game on two adjacent cubes. ABCD forms the top rectangle in the first cube and BIJC forms the top rectangle in the second cube. EFGH forms the bottom rectangle in the first cube and FKLG forms the bottom rectangle in the second cube. AE is an edge, BF is an edge, CG is an edge, DH is an edge, IK is an edge, and JL is an edge. Note that vertices B,C,G,F are shared by the two cubes. Alice and Bob plays a game where they take turns to put stickers on the vertices of the cubes that have not been occupied. Alice plays white stickers. Bob plays black stickers. The person who has four stickers on the same plane on either cube wins. Alice first places a white stone at E. Then Bob places a black stone at A. Then Alice places a white stone at H. Then Bob places a black stone at C. Then Alice places a white stone at K. Then Bob places a black stone at D. Where should Alice play next?",174 "solution": "B",175 "is_unique_solution": true,176 "verdict": "blocked",177 "next_player": "Alice",178 "currect_board_visualization": "...B------B------*\n../|...../|...../|\n./.|..../.|..../.|\nB------*------*..|\n|..W---|--*...|..*\n|./....|./....|./\n|/.....|/.....|/\nW------*------W\n",179 "board_visualization": "...D------C------J\n../|...../|...../|\n./.|..../.|..../.|\nA------B------I..|\n|..H---|--G...|..L\n|./....|./....|./\n|/.....|/.....|/\nE------F------K\n",180 "problem_number": 17181 },182 {183 "problem": "Alice and Bob are playing a game on two adjacent cubes. ABCD forms the top rectangle in the first cube and BIJC forms the top rectangle in the second cube. EFGH forms the bottom rectangle in the first cube and FKLG forms the bottom rectangle in the second cube. AE is an edge, BF is an edge, CG is an edge, DH is an edge, IK is an edge, and JL is an edge. Note that vertices B,C,G,F are shared by the two cubes. Alice and Bob plays a game where they take turns to put stickers on the vertices of the cubes that have not been occupied. Alice plays white stickers. Bob plays black stickers. The person who has four stickers on the same plane on either cube wins. Alice first places a white stone at A. Then Bob places a black stone at D. Then Alice places a white stone at I. Then Bob places a black stone at E. Then Alice places a white stone at J. Then Bob places a black stone at F. Where should Alice play next?",184 "solution": "C",185 "is_unique_solution": true,186 "verdict": "blocked",187 "next_player": "Alice",188 "currect_board_visualization": "...B------*------W\n../|...../|...../|\n./.|..../.|..../.|\nW------*------W..|\n|..*---|--*...|..*\n|./....|./....|./\n|/.....|/.....|/\nB------B------*\n",189 "board_visualization": "...D------C------J\n../|...../|...../|\n./.|..../.|..../.|\nA------B------I..|\n|..H---|--G...|..L\n|./....|./....|./\n|/.....|/.....|/\nE------F------K\n",190 "problem_number": 18191 },192 {193 "problem": "Alice and Bob are playing a game on two adjacent cubes. ABCD forms the top rectangle in the first cube and BIJC forms the top rectangle in the second cube. EFGH forms the bottom rectangle in the first cube and FKLG forms the bottom rectangle in the second cube. AE is an edge, BF is an edge, CG is an edge, DH is an edge, IK is an edge, and JL is an edge. Note that vertices B,C,G,F are shared by the two cubes. Alice and Bob plays a game where they take turns to put stickers on the vertices of the cubes that have not been occupied. Alice plays white stickers. Bob plays black stickers. The person who has four stickers on the same plane on either cube wins. Alice first places a white stone at A. Then Bob places a black stone at E. Then Alice places a white stone at C. Then Bob places a black stone at G. Then Alice places a white stone at K. Then Bob places a black stone at H. Where should Alice play next?",194 "solution": "F",195 "is_unique_solution": true,196 "verdict": "blocked",197 "next_player": "Alice",198 "currect_board_visualization": "...*------W------*\n../|...../|...../|\n./.|..../.|..../.|\nW------*------*..|\n|..B---|--B...|..*\n|./....|./....|./\n|/.....|/.....|/\nB------*------W\n",199 "board_visualization": "...D------C------J\n../|...../|...../|\n./.|..../.|..../.|\nA------B------I..|\n|..H---|--G...|..L\n|./....|./....|./\n|/.....|/.....|/\nE------F------K\n",200 "problem_number": 19201 },202 {203 "problem": "Alice and Bob are playing a game on two adjacent cubes. ABCD forms the top rectangle in the first cube and BIJC forms the top rectangle in the second cube. EFGH forms the bottom rectangle in the first cube and FKLG forms the bottom rectangle in the second cube. AE is an edge, BF is an edge, CG is an edge, DH is an edge, IK is an edge, and JL is an edge. Note that vertices B,C,G,F are shared by the two cubes. Alice and Bob plays a game where they take turns to put stickers on the vertices of the cubes that have not been occupied. Alice plays white stickers. Bob plays black stickers. The person who has four stickers on the same plane on either cube wins. Alice first places a white stone at A. Then Bob places a black stone at B. Then Alice places a white stone at C. Then Bob places a black stone at I. Then Alice places a white stone at E. Then Bob places a black stone at K. Where should Alice play next?",204 "solution": "G",205 "is_unique_solution": true,206 "verdict": "win",207 "next_player": "Alice",208 "currect_board_visualization": "...*------W------*\n../|...../|...../|\n./.|..../.|..../.|\nW------B------B..|\n|..*---|--*...|..*\n|./....|./....|./\n|/.....|/.....|/\nW------*------B\n",209 "board_visualization": "...D------C------J\n../|...../|...../|\n./.|..../.|..../.|\nA------B------I..|\n|..H---|--G...|..L\n|./....|./....|./\n|/.....|/.....|/\nE------F------K\n",210 "problem_number": 20211 },212 {213 "problem": "Alice and Bob are playing a game on two adjacent cubes. ABCD forms the top rectangle in the first cube and BIJC forms the top rectangle in the second cube. EFGH forms the bottom rectangle in the first cube and FKLG forms the bottom rectangle in the second cube. AE is an edge, BF is an edge, CG is an edge, DH is an edge, IK is an edge, and JL is an edge. Note that vertices B,C,G,F are shared by the two cubes. Alice and Bob plays a game where they take turns to put stickers on the vertices of the cubes that have not been occupied. Alice plays white stickers. Bob plays black stickers. The person who has four stickers on the same plane on either cube wins. Alice first places a white stone at B. Then Bob places a black stone at D. Then Alice places a white stone at C. Then Bob places a black stone at H. Then Alice places a white stone at K. Then Bob places a black stone at I. Where should Alice play next?",214 "solution": "L",215 "is_unique_solution": true,216 "verdict": "win",217 "next_player": "Alice",218 "currect_board_visualization": "...B------W------*\n../|...../|...../|\n./.|..../.|..../.|\n*------W------B..|\n|..B---|--*...|..*\n|./....|./....|./\n|/.....|/.....|/\n*------*------W\n",219 "board_visualization": "...D------C------J\n../|...../|...../|\n./.|..../.|..../.|\nA------B------I..|\n|..H---|--G...|..L\n|./....|./....|./\n|/.....|/.....|/\nE------F------K\n",220 "problem_number": 21221 },222 {223 "problem": "Alice and Bob are playing a game on two adjacent cubes. ABCD forms the top rectangle in the first cube and BIJC forms the top rectangle in the second cube. EFGH forms the bottom rectangle in the first cube and FKLG forms the bottom rectangle in the second cube. AE is an edge, BF is an edge, CG is an edge, DH is an edge, IK is an edge, and JL is an edge. Note that vertices B,C,G,F are shared by the two cubes. Alice and Bob plays a game where they take turns to put stickers on the vertices of the cubes that have not been occupied. Alice plays white stickers. Bob plays black stickers. The person who has four stickers on the same plane on either cube wins. Alice first places a white stone at D. Then Bob places a black stone at C. Then Alice places a white stone at F. Then Bob places a black stone at E. Then Alice places a white stone at H. Then Bob places a black stone at K. Where should Alice play next?",224 "solution": "B",225 "is_unique_solution": true,226 "verdict": "win",227 "next_player": "Alice",228 "currect_board_visualization": "...W------B------*\n../|...../|...../|\n./.|..../.|..../.|\n*------*------*..|\n|..W---|--*...|..*\n|./....|./....|./\n|/.....|/.....|/\nB------W------B\n",229 "board_visualization": "...D------C------J\n../|...../|...../|\n./.|..../.|..../.|\nA------B------I..|\n|..H---|--G...|..L\n|./....|./....|./\n|/.....|/.....|/\nE------F------K\n",230 "problem_number": 22231 },232 {233 "problem": "Alice and Bob are playing a game on two adjacent cubes. ABCD forms the top rectangle in the first cube and BIJC forms the top rectangle in the second cube. EFGH forms the bottom rectangle in the first cube and FKLG forms the bottom rectangle in the second cube. AE is an edge, BF is an edge, CG is an edge, DH is an edge, IK is an edge, and JL is an edge. Note that vertices B,C,G,F are shared by the two cubes. Alice and Bob plays a game where they take turns to put stickers on the vertices of the cubes that have not been occupied. Alice plays white stickers. Bob plays black stickers. The person who has four stickers on the same plane on either cube wins. Alice first places a white stone at B. Then Bob places a black stone at C. Then Alice places a white stone at F. Then Bob places a black stone at E. Then Alice places a white stone at J. Then Bob places a black stone at G. Where should Alice play next?",234 "solution": "L",235 "is_unique_solution": true,236 "verdict": "win",237 "next_player": "Alice",238 "currect_board_visualization": "...*------B------W\n../|...../|...../|\n./.|..../.|..../.|\n*------W------*..|\n|..*---|--B...|..*\n|./....|./....|./\n|/.....|/.....|/\nB------W------*\n",239 "board_visualization": "...D------C------J\n../|...../|...../|\n./.|..../.|..../.|\nA------B------I..|\n|..H---|--G...|..L\n|./....|./....|./\n|/.....|/.....|/\nE------F------K\n",240 "problem_number": 23241 },242 {243 "problem": "Alice and Bob are playing a game on two adjacent cubes. ABCD forms the top rectangle in the first cube and BIJC forms the top rectangle in the second cube. EFGH forms the bottom rectangle in the first cube and FKLG forms the bottom rectangle in the second cube. AE is an edge, BF is an edge, CG is an edge, DH is an edge, IK is an edge, and JL is an edge. Note that vertices B,C,G,F are shared by the two cubes. Alice and Bob plays a game where they take turns to put stickers on the vertices of the cubes that have not been occupied. Alice plays white stickers. Bob plays black stickers. The person who has four stickers on the same plane on either cube wins. Alice first places a white stone at G. Then Bob places a black stone at E. Then Alice places a white stone at I. Then Bob places a black stone at J. Then Alice places a white stone at K. Then Bob places a black stone at L. Where should Alice play next?",244 "solution": "C",245 "is_unique_solution": true,246 "verdict": "win",247 "next_player": "Alice",248 "currect_board_visualization": "...*------*------B\n../|...../|...../|\n./.|..../.|..../.|\n*------*------W..|\n|..*---|--W...|..B\n|./....|./....|./\n|/.....|/.....|/\nB------*------W\n",249 "board_visualization": "...D------C------J\n../|...../|...../|\n./.|..../.|..../.|\nA------B------I..|\n|..H---|--G...|..L\n|./....|./....|./\n|/.....|/.....|/\nE------F------K\n",250 "problem_number": 24251 },252 {253 "problem": "Alice and Bob are playing a game on two adjacent cubes. ABCD forms the top rectangle in the first cube and BIJC forms the top rectangle in the second cube. EFGH forms the bottom rectangle in the first cube and FKLG forms the bottom rectangle in the second cube. AE is an edge, BF is an edge, CG is an edge, DH is an edge, IK is an edge, and JL is an edge. Note that vertices B,C,G,F are shared by the two cubes. Alice and Bob plays a game where they take turns to put stickers on the vertices of the cubes that have not been occupied. Alice plays white stickers. Bob plays black stickers. The person who has four stickers on the same plane on either cube wins. Alice first places a white stone at F. Then Bob places a black stone at A. Then Alice places a white stone at J. Then Bob places a black stone at H. Then Alice places a white stone at K. Then Bob places a black stone at L. Where should Alice play next?",254 "solution": "C",255 "is_unique_solution": true,256 "verdict": "win",257 "next_player": "Alice",258 "currect_board_visualization": "...*------*------W\n../|...../|...../|\n./.|..../.|..../.|\nB------*------*..|\n|..B---|--*...|..B\n|./....|./....|./\n|/.....|/.....|/\n*------W------W\n",259 "board_visualization": "...D------C------J\n../|...../|...../|\n./.|..../.|..../.|\nA------B------I..|\n|..H---|--G...|..L\n|./....|./....|./\n|/.....|/.....|/\nE------F------K\n",260 "problem_number": 25261 },262 {263 "problem": "Alice and Bob are playing a game on two adjacent cubes. ABCD forms the top rectangle in the first cube and BIJC forms the top rectangle in the second cube. EFGH forms the bottom rectangle in the first cube and FKLG forms the bottom rectangle in the second cube. AE is an edge, BF is an edge, CG is an edge, DH is an edge, IK is an edge, and JL is an edge. Note that vertices B,C,G,F are shared by the two cubes. Alice and Bob plays a game where they take turns to put stickers on the vertices of the cubes that have not been occupied. Alice plays white stickers. Bob plays black stickers. The person who has four stickers on the same plane on either cube wins. Alice first places a white stone at D. Then Bob places a black stone at B. Then Alice places a white stone at E. Then Bob places a black stone at I. Then Alice places a white stone at H. Then Bob places a black stone at K. Where should Alice play next?",264 "solution": "A",265 "is_unique_solution": true,266 "verdict": "win",267 "next_player": "Alice",268 "currect_board_visualization": "...W------*------*\n../|...../|...../|\n./.|..../.|..../.|\n*------B------B..|\n|..W---|--*...|..*\n|./....|./....|./\n|/.....|/.....|/\nW------*------B\n",269 "board_visualization": "...D------C------J\n../|...../|...../|\n./.|..../.|..../.|\nA------B------I..|\n|..H---|--G...|..L\n|./....|./....|./\n|/.....|/.....|/\nE------F------K\n",270 "problem_number": 26271 },272 {273 "problem": "Alice and Bob are playing a game on two adjacent cubes. ABCD forms the top rectangle in the first cube and BIJC forms the top rectangle in the second cube. EFGH forms the bottom rectangle in the first cube and FKLG forms the bottom rectangle in the second cube. AE is an edge, BF is an edge, CG is an edge, DH is an edge, IK is an edge, and JL is an edge. Note that vertices B,C,G,F are shared by the two cubes. Alice and Bob plays a game where they take turns to put stickers on the vertices of the cubes that have not been occupied. Alice plays white stickers. Bob plays black stickers. The person who has four stickers on the same plane on either cube wins. Alice first places a white stone at E. Then Bob places a black stone at C. Then Alice places a white stone at F. Then Bob places a black stone at D. Then Alice places a white stone at G. Then Bob places a black stone at K. Where should Alice play next?",274 "solution": "H",275 "is_unique_solution": true,276 "verdict": "win",277 "next_player": "Alice",278 "currect_board_visualization": "...B------B------*\n../|...../|...../|\n./.|..../.|..../.|\n*------*------*..|\n|..*---|--W...|..*\n|./....|./....|./\n|/.....|/.....|/\nW------W------B\n",279 "board_visualization": "...D------C------J\n../|...../|...../|\n./.|..../.|..../.|\nA------B------I..|\n|..H---|--G...|..L\n|./....|./....|./\n|/.....|/.....|/\nE------F------K\n",280 "problem_number": 27281 },282 {283 "problem": "Alice and Bob are playing a game on two adjacent cubes. ABCD forms the top rectangle in the first cube and BIJC forms the top rectangle in the second cube. EFGH forms the bottom rectangle in the first cube and FKLG forms the bottom rectangle in the second cube. AE is an edge, BF is an edge, CG is an edge, DH is an edge, IK is an edge, and JL is an edge. Note that vertices B,C,G,F are shared by the two cubes. Alice and Bob plays a game where they take turns to put stickers on the vertices of the cubes that have not been occupied. Alice plays white stickers. Bob plays black stickers. The person who has four stickers on the same plane on either cube wins. Alice first places a white stone at F. Then Bob places a black stone at A. Then Alice places a white stone at I. Then Bob places a black stone at D. Then Alice places a white stone at K. Then Bob places a black stone at H. Where should Alice play next?",284 "solution": "B",285 "is_unique_solution": true,286 "verdict": "win",287 "next_player": "Alice",288 "currect_board_visualization": "...B------*------*\n../|...../|...../|\n./.|..../.|..../.|\nB------*------W..|\n|..B---|--*...|..*\n|./....|./....|./\n|/.....|/.....|/\n*------W------W\n",289 "board_visualization": "...D------C------J\n../|...../|...../|\n./.|..../.|..../.|\nA------B------I..|\n|..H---|--G...|..L\n|./....|./....|./\n|/.....|/.....|/\nE------F------K\n",290 "problem_number": 28291 },292 {293 "problem": "Alice and Bob are playing a game on two adjacent cubes. ABCD forms the top rectangle in the first cube and BIJC forms the top rectangle in the second cube. EFGH forms the bottom rectangle in the first cube and FKLG forms the bottom rectangle in the second cube. AE is an edge, BF is an edge, CG is an edge, DH is an edge, IK is an edge, and JL is an edge. Note that vertices B,C,G,F are shared by the two cubes. Alice and Bob plays a game where they take turns to put stickers on the vertices of the cubes that have not been occupied. Alice plays white stickers. Bob plays black stickers. The person who has four stickers on the same plane on either cube wins. Alice first places a white stone at A. Then Bob places a black stone at C. Then Alice places a white stone at E. Then Bob places a black stone at I. Then Alice places a white stone at H. Then Bob places a black stone at J. Where should Alice play next?",294 "solution": "D",295 "is_unique_solution": true,296 "verdict": "win",297 "next_player": "Alice",298 "currect_board_visualization": "...*------B------B\n../|...../|...../|\n./.|..../.|..../.|\nW------*------B..|\n|..W---|--*...|..*\n|./....|./....|./\n|/.....|/.....|/\nW------*------*\n",299 "board_visualization": "...D------C------J\n../|...../|...../|\n./.|..../.|..../.|\nA------B------I..|\n|..H---|--G...|..L\n|./....|./....|./\n|/.....|/.....|/\nE------F------K\n",300 "problem_number": 29301 },302 {303 "problem": "Alice and Bob are playing a game on two adjacent cubes. ABCD forms the top rectangle in the first cube and BIJC forms the top rectangle in the second cube. EFGH forms the bottom rectangle in the first cube and FKLG forms the bottom rectangle in the second cube. AE is an edge, BF is an edge, CG is an edge, DH is an edge, IK is an edge, and JL is an edge. Note that vertices B,C,G,F are shared by the two cubes. Alice and Bob plays a game where they take turns to put stickers on the vertices of the cubes that have not been occupied. Alice plays white stickers. Bob plays black stickers. The person who has four stickers on the same plane on either cube wins. Alice first places a white stone at E. Then Bob places a black stone at A. Then Alice places a white stone at G. Then Bob places a black stone at D. Then Alice places a white stone at J. Then Bob places a black stone at L. Where should Alice play next?",304 "solution": "F",305 "is_unique_solution": true,306 "verdict": "fork",307 "next_player": "Alice",308 "currect_board_visualization": "...B------*------W\n../|...../|...../|\n./.|..../.|..../.|\nB------*------*..|\n|..*---|--W...|..B\n|./....|./....|./\n|/.....|/.....|/\nW------*------*\n",309 "board_visualization": "...D------C------J\n../|...../|...../|\n./.|..../.|..../.|\nA------B------I..|\n|..H---|--G...|..L\n|./....|./....|./\n|/.....|/.....|/\nE------F------K\n",310 "problem_number": 30311 },312 {313 "problem": "Alice and Bob are playing a game on two adjacent cubes. ABCD forms the top rectangle in the first cube and BIJC forms the top rectangle in the second cube. EFGH forms the bottom rectangle in the first cube and FKLG forms the bottom rectangle in the second cube. AE is an edge, BF is an edge, CG is an edge, DH is an edge, IK is an edge, and JL is an edge. Note that vertices B,C,G,F are shared by the two cubes. Alice and Bob plays a game where they take turns to put stickers on the vertices of the cubes that have not been occupied. Alice plays white stickers. Bob plays black stickers. The person who has four stickers on the same plane on either cube wins. Alice first places a white stone at D. Then Bob places a black stone at A. Then Alice places a white stone at F. Then Bob places a black stone at G. Then Alice places a white stone at J. Then Bob places a black stone at K. Where should Alice play next?",314 "solution": "B",315 "is_unique_solution": true,316 "verdict": "fork",317 "next_player": "Alice",318 "currect_board_visualization": "...W------*------W\n../|...../|...../|\n./.|..../.|..../.|\nB------*------*..|\n|..*---|--B...|..*\n|./....|./....|./\n|/.....|/.....|/\n*------W------B\n",319 "board_visualization": "...D------C------J\n../|...../|...../|\n./.|..../.|..../.|\nA------B------I..|\n|..H---|--G...|..L\n|./....|./....|./\n|/.....|/.....|/\nE------F------K\n",320 "problem_number": 31321 },322 {323 "problem": "Alice and Bob are playing a game on two adjacent cubes. ABCD forms the top rectangle in the first cube and BIJC forms the top rectangle in the second cube. EFGH forms the bottom rectangle in the first cube and FKLG forms the bottom rectangle in the second cube. AE is an edge, BF is an edge, CG is an edge, DH is an edge, IK is an edge, and JL is an edge. Note that vertices B,C,G,F are shared by the two cubes. Alice and Bob plays a game where they take turns to put stickers on the vertices of the cubes that have not been occupied. Alice plays white stickers. Bob plays black stickers. The person who has four stickers on the same plane on either cube wins. Alice first places a white stone at C. Then Bob places a black stone at E. Then Alice places a white stone at D. Then Bob places a black stone at H. Then Alice places a white stone at J. Then Bob places a black stone at L. Where should Alice play next?",324 "solution": "B",325 "is_unique_solution": true,326 "verdict": "fork",327 "next_player": "Alice",328 "currect_board_visualization": "...W------W------W\n../|...../|...../|\n./.|..../.|..../.|\n*------*------*..|\n|..B---|--*...|..B\n|./....|./....|./\n|/.....|/.....|/\nB------*------*\n",329 "board_visualization": "...D------C------J\n../|...../|...../|\n./.|..../.|..../.|\nA------B------I..|\n|..H---|--G...|..L\n|./....|./....|./\n|/.....|/.....|/\nE------F------K\n",330 "problem_number": 32331 },332 {333 "problem": "Alice and Bob are playing a game on two adjacent cubes. ABCD forms the top rectangle in the first cube and BIJC forms the top rectangle in the second cube. EFGH forms the bottom rectangle in the first cube and FKLG forms the bottom rectangle in the second cube. AE is an edge, BF is an edge, CG is an edge, DH is an edge, IK is an edge, and JL is an edge. Note that vertices B,C,G,F are shared by the two cubes. Alice and Bob plays a game where they take turns to put stickers on the vertices of the cubes that have not been occupied. Alice plays white stickers. Bob plays black stickers. The person who has four stickers on the same plane on either cube wins. Alice first places a white stone at E. Then Bob places a black stone at A. Then Alice places a white stone at G. Then Bob places a black stone at K. Then Alice places a white stone at J. Then Bob places a black stone at L. Where should Alice play next?",334 "solution": "F",335 "is_unique_solution": true,336 "verdict": "fork",337 "next_player": "Alice",338 "currect_board_visualization": "...*------*------W\n../|...../|...../|\n./.|..../.|..../.|\nB------*------*..|\n|..*---|--W...|..B\n|./....|./....|./\n|/.....|/.....|/\nW------*------B\n",339 "board_visualization": "...D------C------J\n../|...../|...../|\n./.|..../.|..../.|\nA------B------I..|\n|..H---|--G...|..L\n|./....|./....|./\n|/.....|/.....|/\nE------F------K\n",340 "problem_number": 33341 },342 {343 "problem": "Alice and Bob are playing a game on two adjacent cubes. ABCD forms the top rectangle in the first cube and BIJC forms the top rectangle in the second cube. EFGH forms the bottom rectangle in the first cube and FKLG forms the bottom rectangle in the second cube. AE is an edge, BF is an edge, CG is an edge, DH is an edge, IK is an edge, and JL is an edge. Note that vertices B,C,G,F are shared by the two cubes. Alice and Bob plays a game where they take turns to put stickers on the vertices of the cubes that have not been occupied. Alice plays white stickers. Bob plays black stickers. The person who has four stickers on the same plane on either cube wins. Alice first places a white stone at C. Then Bob places a black stone at D. Then Alice places a white stone at G. Then Bob places a black stone at E. Then Alice places a white stone at H. Then Bob places a black stone at I. Where should Alice play next?",344 "solution": "B",345 "is_unique_solution": true,346 "verdict": "fork",347 "next_player": "Alice",348 "currect_board_visualization": "...B------W------*\n../|...../|...../|\n./.|..../.|..../.|\n*------*------B..|\n|..W---|--W...|..*\n|./....|./....|./\n|/.....|/.....|/\nB------*------*\n",349 "board_visualization": "...D------C------J\n../|...../|...../|\n./.|..../.|..../.|\nA------B------I..|\n|..H---|--G...|..L\n|./....|./....|./\n|/.....|/.....|/\nE------F------K\n",350 "problem_number": 34351 },352 {353 "problem": "Alice and Bob are playing a game on two adjacent cubes. ABCD forms the top rectangle in the first cube and BIJC forms the top rectangle in the second cube. EFGH forms the bottom rectangle in the first cube and FKLG forms the bottom rectangle in the second cube. AE is an edge, BF is an edge, CG is an edge, DH is an edge, IK is an edge, and JL is an edge. Note that vertices B,C,G,F are shared by the two cubes. Alice and Bob plays a game where they take turns to put stickers on the vertices of the cubes that have not been occupied. Alice plays white stickers. Bob plays black stickers. The person who has four stickers on the same plane on either cube wins. Alice first places a white stone at E. Then Bob places a black stone at D. Then Alice places a white stone at G. Then Bob places a black stone at F. Then Alice places a white stone at I. Then Bob places a black stone at L. Where should Alice play next?",354 "solution": "C",355 "is_unique_solution": true,356 "verdict": "fork",357 "next_player": "Alice",358 "currect_board_visualization": "...B------*------*\n../|...../|...../|\n./.|..../.|..../.|\n*------*------W..|\n|..*---|--W...|..B\n|./....|./....|./\n|/.....|/.....|/\nW------B------*\n",359 "board_visualization": "...D------C------J\n../|...../|...../|\n./.|..../.|..../.|\nA------B------I..|\n|..H---|--G...|..L\n|./....|./....|./\n|/.....|/.....|/\nE------F------K\n",360 "problem_number": 35361 },362 {363 "problem": "Alice and Bob are playing a game on two adjacent cubes. ABCD forms the top rectangle in the first cube and BIJC forms the top rectangle in the second cube. EFGH forms the bottom rectangle in the first cube and FKLG forms the bottom rectangle in the second cube. AE is an edge, BF is an edge, CG is an edge, DH is an edge, IK is an edge, and JL is an edge. Note that vertices B,C,G,F are shared by the two cubes. Alice and Bob plays a game where they take turns to put stickers on the vertices of the cubes that have not been occupied. Alice plays white stickers. Bob plays black stickers. The person who has four stickers on the same plane on either cube wins. Alice first places a white stone at E. Then Bob places a black stone at D. Then Alice places a white stone at F. Then Bob places a black stone at G. Then Alice places a white stone at H. Then Bob places a black stone at L. Where should Alice play next?",364 "solution": "B",365 "is_unique_solution": true,366 "verdict": "fork",367 "next_player": "Alice",368 "currect_board_visualization": "...B------*------*\n../|...../|...../|\n./.|..../.|..../.|\n*------*------*..|\n|..W---|--B...|..B\n|./....|./....|./\n|/.....|/.....|/\nW------W------*\n",369 "board_visualization": "...D------C------J\n../|...../|...../|\n./.|..../.|..../.|\nA------B------I..|\n|..H---|--G...|..L\n|./....|./....|./\n|/.....|/.....|/\nE------F------K\n",370 "problem_number": 36371 },372 {373 "problem": "Alice and Bob are playing a game on two adjacent cubes. ABCD forms the top rectangle in the first cube and BIJC forms the top rectangle in the second cube. EFGH forms the bottom rectangle in the first cube and FKLG forms the bottom rectangle in the second cube. AE is an edge, BF is an edge, CG is an edge, DH is an edge, IK is an edge, and JL is an edge. Note that vertices B,C,G,F are shared by the two cubes. Alice and Bob plays a game where they take turns to put stickers on the vertices of the cubes that have not been occupied. Alice plays white stickers. Bob plays black stickers. The person who has four stickers on the same plane on either cube wins. Alice first places a white stone at F. Then Bob places a black stone at A. Then Alice places a white stone at H. Then Bob places a black stone at B. Then Alice places a white stone at K. Then Bob places a black stone at I. Where should Alice play next?",374 "solution": "G",375 "is_unique_solution": true,376 "verdict": "fork",377 "next_player": "Alice",378 "currect_board_visualization": "...*------*------*\n../|...../|...../|\n./.|..../.|..../.|\nB------B------B..|\n|..W---|--*...|..*\n|./....|./....|./\n|/.....|/.....|/\n*------W------W\n",379 "board_visualization": "...D------C------J\n../|...../|...../|\n./.|..../.|..../.|\nA------B------I..|\n|..H---|--G...|..L\n|./....|./....|./\n|/.....|/.....|/\nE------F------K\n",380 "problem_number": 37381 },382 {383 "problem": "Alice and Bob are playing a game on two adjacent cubes. ABCD forms the top rectangle in the first cube and BIJC forms the top rectangle in the second cube. EFGH forms the bottom rectangle in the first cube and FKLG forms the bottom rectangle in the second cube. AE is an edge, BF is an edge, CG is an edge, DH is an edge, IK is an edge, and JL is an edge. Note that vertices B,C,G,F are shared by the two cubes. Alice and Bob plays a game where they take turns to put stickers on the vertices of the cubes that have not been occupied. Alice plays white stickers. Bob plays black stickers. The person who has four stickers on the same plane on either cube wins. Alice first places a white stone at I. Then Bob places a black stone at G. Then Alice places a white stone at K. Then Bob places a black stone at H. Then Alice places a white stone at L. Then Bob places a black stone at J. Where should Alice play next?",384 "solution": "B",385 "is_unique_solution": true,386 "verdict": "fork",387 "next_player": "Alice",388 "currect_board_visualization": "...*------*------B\n../|...../|...../|\n./.|..../.|..../.|\n*------*------W..|\n|..B---|--B...|..W\n|./....|./....|./\n|/.....|/.....|/\n*------*------W\n",389 "board_visualization": "...D------C------J\n../|...../|...../|\n./.|..../.|..../.|\nA------B------I..|\n|..H---|--G...|..L\n|./....|./....|./\n|/.....|/.....|/\nE------F------K\n",390 "problem_number": 38391 },392 {393 "problem": "Alice and Bob are playing a game on two adjacent cubes. ABCD forms the top rectangle in the first cube and BIJC forms the top rectangle in the second cube. EFGH forms the bottom rectangle in the first cube and FKLG forms the bottom rectangle in the second cube. AE is an edge, BF is an edge, CG is an edge, DH is an edge, IK is an edge, and JL is an edge. Note that vertices B,C,G,F are shared by the two cubes. Alice and Bob plays a game where they take turns to put stickers on the vertices of the cubes that have not been occupied. Alice plays white stickers. Bob plays black stickers. The person who has four stickers on the same plane on either cube wins. Alice first places a white stone at C. Then Bob places a black stone at F. Then Alice places a white stone at D. Then Bob places a black stone at H. Then Alice places a white stone at K. Then Bob places a black stone at J. Where should Alice play next?",394 "solution": "B",395 "is_unique_solution": true,396 "verdict": "fork",397 "next_player": "Alice",398 "currect_board_visualization": "...W------W------B\n../|...../|...../|\n./.|..../.|..../.|\n*------*------*..|\n|..B---|--*...|..*\n|./....|./....|./\n|/.....|/.....|/\n*------B------W\n",399 "board_visualization": "...D------C------J\n../|...../|...../|\n./.|..../.|..../.|\nA------B------I..|\n|..H---|--G...|..L\n|./....|./....|./\n|/.....|/.....|/\nE------F------K\n",400 "problem_number": 39401 },402 {403 "problem": "Alice and Bob are playing a game on two adjacent cubes. ABCD forms the top rectangle in the first cube and BIJC forms the top rectangle in the second cube. EFGH forms the bottom rectangle in the first cube and FKLG forms the bottom rectangle in the second cube. AE is an edge, BF is an edge, CG is an edge, DH is an edge, IK is an edge, and JL is an edge. Note that vertices B,C,G,F are shared by the two cubes. Alice and Bob plays a game where they take turns to put stickers on the vertices of the cubes that have not been occupied. Alice plays white stickers. Bob plays black stickers. The person who has four stickers on the same plane on either cube wins. Alice first places a white stone at D. Then Bob places a black stone at E. Then Alice places a white stone at F. Then Bob places a black stone at J. Then Alice places a white stone at I. Then Bob places a black stone at L. Then Alice places a white stone at K. Where should Bob play next?",404 "solution": "B",405 "is_unique_solution": true,406 "verdict": "blocked",407 "next_player": "Bob",408 "currect_board_visualization": "...W------*------B\n../|...../|...../|\n./.|..../.|..../.|\n*------*------W..|\n|..*---|--*...|..B\n|./....|./....|./\n|/.....|/.....|/\nB------W------W\n",409 "board_visualization": "...D------C------J\n../|...../|...../|\n./.|..../.|..../.|\nA------B------I..|\n|..H---|--G...|..L\n|./....|./....|./\n|/.....|/.....|/\nE------F------K\n",410 "problem_number": 40411 },412 {413 "problem": "Alice and Bob are playing a game on two adjacent cubes. ABCD forms the top rectangle in the first cube and BIJC forms the top rectangle in the second cube. EFGH forms the bottom rectangle in the first cube and FKLG forms the bottom rectangle in the second cube. AE is an edge, BF is an edge, CG is an edge, DH is an edge, IK is an edge, and JL is an edge. Note that vertices B,C,G,F are shared by the two cubes. Alice and Bob plays a game where they take turns to put stickers on the vertices of the cubes that have not been occupied. Alice plays white stickers. Bob plays black stickers. The person who has four stickers on the same plane on either cube wins. Alice first places a white stone at A. Then Bob places a black stone at G. Then Alice places a white stone at B. Then Bob places a black stone at I. Then Alice places a white stone at C. Then Bob places a black stone at K. Then Alice places a white stone at L. Where should Bob play next?",414 "solution": "D",415 "is_unique_solution": true,416 "verdict": "blocked",417 "next_player": "Bob",418 "currect_board_visualization": "...*------W------*\n../|...../|...../|\n./.|..../.|..../.|\nW------W------B..|\n|..*---|--B...|..W\n|./....|./....|./\n|/.....|/.....|/\n*------*------B\n",419 "board_visualization": "...D------C------J\n../|...../|...../|\n./.|..../.|..../.|\nA------B------I..|\n|..H---|--G...|..L\n|./....|./....|./\n|/.....|/.....|/\nE------F------K\n",420 "problem_number": 41421 },422 {423 "problem": "Alice and Bob are playing a game on two adjacent cubes. ABCD forms the top rectangle in the first cube and BIJC forms the top rectangle in the second cube. EFGH forms the bottom rectangle in the first cube and FKLG forms the bottom rectangle in the second cube. AE is an edge, BF is an edge, CG is an edge, DH is an edge, IK is an edge, and JL is an edge. Note that vertices B,C,G,F are shared by the two cubes. Alice and Bob plays a game where they take turns to put stickers on the vertices of the cubes that have not been occupied. Alice plays white stickers. Bob plays black stickers. The person who has four stickers on the same plane on either cube wins. Alice first places a white stone at C. Then Bob places a black stone at B. Then Alice places a white stone at H. Then Bob places a black stone at E. Then Alice places a white stone at J. Then Bob places a black stone at G. Then Alice places a white stone at K. Where should Bob play next?",424 "solution": "F",425 "is_unique_solution": true,426 "verdict": "blocked",427 "next_player": "Bob",428 "currect_board_visualization": "...*------W------W\n../|...../|...../|\n./.|..../.|..../.|\n*------B------*..|\n|..W---|--B...|..*\n|./....|./....|./\n|/.....|/.....|/\nB------*------W\n",429 "board_visualization": "...D------C------J\n../|...../|...../|\n./.|..../.|..../.|\nA------B------I..|\n|..H---|--G...|..L\n|./....|./....|./\n|/.....|/.....|/\nE------F------K\n",430 "problem_number": 42431 },432 {433 "problem": "Alice and Bob are playing a game on two adjacent cubes. ABCD forms the top rectangle in the first cube and BIJC forms the top rectangle in the second cube. EFGH forms the bottom rectangle in the first cube and FKLG forms the bottom rectangle in the second cube. AE is an edge, BF is an edge, CG is an edge, DH is an edge, IK is an edge, and JL is an edge. Note that vertices B,C,G,F are shared by the two cubes. Alice and Bob plays a game where they take turns to put stickers on the vertices of the cubes that have not been occupied. Alice plays white stickers. Bob plays black stickers. The person who has four stickers on the same plane on either cube wins. Alice first places a white stone at C. Then Bob places a black stone at A. Then Alice places a white stone at E. Then Bob places a black stone at F. Then Alice places a white stone at I. Then Bob places a black stone at L. Then Alice places a white stone at K. Where should Bob play next?",434 "solution": "G",435 "is_unique_solution": true,436 "verdict": "blocked",437 "next_player": "Bob",438 "currect_board_visualization": "...*------W------*\n../|...../|...../|\n./.|..../.|..../.|\nB------*------W..|\n|..*---|--*...|..B\n|./....|./....|./\n|/.....|/.....|/\nW------B------W\n",439 "board_visualization": "...D------C------J\n../|...../|...../|\n./.|..../.|..../.|\nA------B------I..|\n|..H---|--G...|..L\n|./....|./....|./\n|/.....|/.....|/\nE------F------K\n",440 "problem_number": 43441 },442 {443 "problem": "Alice and Bob are playing a game on two adjacent cubes. ABCD forms the top rectangle in the first cube and BIJC forms the top rectangle in the second cube. EFGH forms the bottom rectangle in the first cube and FKLG forms the bottom rectangle in the second cube. AE is an edge, BF is an edge, CG is an edge, DH is an edge, IK is an edge, and JL is an edge. Note that vertices B,C,G,F are shared by the two cubes. Alice and Bob plays a game where they take turns to put stickers on the vertices of the cubes that have not been occupied. Alice plays white stickers. Bob plays black stickers. The person who has four stickers on the same plane on either cube wins. Alice first places a white stone at C. Then Bob places a black stone at D. Then Alice places a white stone at E. Then Bob places a black stone at H. Then Alice places a white stone at I. Then Bob places a black stone at K. Then Alice places a white stone at J. Where should Bob play next?",444 "solution": "B",445 "is_unique_solution": true,446 "verdict": "blocked",447 "next_player": "Bob",448 "currect_board_visualization": "...B------W------W\n../|...../|...../|\n./.|..../.|..../.|\n*------*------W..|\n|..B---|--*...|..*\n|./....|./....|./\n|/.....|/.....|/\nW------*------B\n",449 "board_visualization": "...D------C------J\n../|...../|...../|\n./.|..../.|..../.|\nA------B------I..|\n|..H---|--G...|..L\n|./....|./....|./\n|/.....|/.....|/\nE------F------K\n",450 "problem_number": 44451 },452 {453 "problem": "Alice and Bob are playing a game on two adjacent cubes. ABCD forms the top rectangle in the first cube and BIJC forms the top rectangle in the second cube. EFGH forms the bottom rectangle in the first cube and FKLG forms the bottom rectangle in the second cube. AE is an edge, BF is an edge, CG is an edge, DH is an edge, IK is an edge, and JL is an edge. Note that vertices B,C,G,F are shared by the two cubes. Alice and Bob plays a game where they take turns to put stickers on the vertices of the cubes that have not been occupied. Alice plays white stickers. Bob plays black stickers. The person who has four stickers on the same plane on either cube wins. Alice first places a white stone at C. Then Bob places a black stone at A. Then Alice places a white stone at E. Then Bob places a black stone at F. Then Alice places a white stone at J. Then Bob places a black stone at H. Then Alice places a white stone at L. Where should Bob play next?",454 "solution": "G",455 "is_unique_solution": true,456 "verdict": "blocked",457 "next_player": "Bob",458 "currect_board_visualization": "...*------W------W\n../|...../|...../|\n./.|..../.|..../.|\nB------*------*..|\n|..B---|--*...|..W\n|./....|./....|./\n|/.....|/.....|/\nW------B------*\n",459 "board_visualization": "...D------C------J\n../|...../|...../|\n./.|..../.|..../.|\nA------B------I..|\n|..H---|--G...|..L\n|./....|./....|./\n|/.....|/.....|/\nE------F------K\n",460 "problem_number": 45461 },462 {463 "problem": "Alice and Bob are playing a game on two adjacent cubes. ABCD forms the top rectangle in the first cube and BIJC forms the top rectangle in the second cube. EFGH forms the bottom rectangle in the first cube and FKLG forms the bottom rectangle in the second cube. AE is an edge, BF is an edge, CG is an edge, DH is an edge, IK is an edge, and JL is an edge. Note that vertices B,C,G,F are shared by the two cubes. Alice and Bob plays a game where they take turns to put stickers on the vertices of the cubes that have not been occupied. Alice plays white stickers. Bob plays black stickers. The person who has four stickers on the same plane on either cube wins. Alice first places a white stone at F. Then Bob places a black stone at B. Then Alice places a white stone at G. Then Bob places a black stone at D. Then Alice places a white stone at H. Then Bob places a black stone at K. Then Alice places a white stone at L. Where should Bob play next?",464 "solution": "E",465 "is_unique_solution": true,466 "verdict": "blocked",467 "next_player": "Bob",468 "currect_board_visualization": "...B------*------*\n../|...../|...../|\n./.|..../.|..../.|\n*------B------*..|\n|..W---|--W...|..W\n|./....|./....|./\n|/.....|/.....|/\n*------W------B\n",469 "board_visualization": "...D------C------J\n../|...../|...../|\n./.|..../.|..../.|\nA------B------I..|\n|..H---|--G...|..L\n|./....|./....|./\n|/.....|/.....|/\nE------F------K\n",470 "problem_number": 46471 },472 {473 "problem": "Alice and Bob are playing a game on two adjacent cubes. ABCD forms the top rectangle in the first cube and BIJC forms the top rectangle in the second cube. EFGH forms the bottom rectangle in the first cube and FKLG forms the bottom rectangle in the second cube. AE is an edge, BF is an edge, CG is an edge, DH is an edge, IK is an edge, and JL is an edge. Note that vertices B,C,G,F are shared by the two cubes. Alice and Bob plays a game where they take turns to put stickers on the vertices of the cubes that have not been occupied. Alice plays white stickers. Bob plays black stickers. The person who has four stickers on the same plane on either cube wins. Alice first places a white stone at C. Then Bob places a black stone at A. Then Alice places a white stone at E. Then Bob places a black stone at F. Then Alice places a white stone at H. Then Bob places a black stone at L. Then Alice places a white stone at J. Where should Bob play next?",474 "solution": "B",475 "is_unique_solution": true,476 "verdict": "blocked",477 "next_player": "Bob",478 "currect_board_visualization": "...*------W------W\n../|...../|...../|\n./.|..../.|..../.|\nB------*------*..|\n|..W---|--*...|..B\n|./....|./....|./\n|/.....|/.....|/\nW------B------*\n",479 "board_visualization": "...D------C------J\n../|...../|...../|\n./.|..../.|..../.|\nA------B------I..|\n|..H---|--G...|..L\n|./....|./....|./\n|/.....|/.....|/\nE------F------K\n",480 "problem_number": 47481 },482 {483 "problem": "Alice and Bob are playing a game on two adjacent cubes. ABCD forms the top rectangle in the first cube and BIJC forms the top rectangle in the second cube. EFGH forms the bottom rectangle in the first cube and FKLG forms the bottom rectangle in the second cube. AE is an edge, BF is an edge, CG is an edge, DH is an edge, IK is an edge, and JL is an edge. Note that vertices B,C,G,F are shared by the two cubes. Alice and Bob plays a game where they take turns to put stickers on the vertices of the cubes that have not been occupied. Alice plays white stickers. Bob plays black stickers. The person who has four stickers on the same plane on either cube wins. Alice first places a white stone at F. Then Bob places a black stone at B. Then Alice places a white stone at G. Then Bob places a black stone at I. Then Alice places a white stone at H. Then Bob places a black stone at L. Then Alice places a white stone at K. Where should Bob play next?",484 "solution": "E",485 "is_unique_solution": true,486 "verdict": "blocked",487 "next_player": "Bob",488 "currect_board_visualization": "...*------*------*\n../|...../|...../|\n./.|..../.|..../.|\n*------B------B..|\n|..W---|--W...|..B\n|./....|./....|./\n|/.....|/.....|/\n*------W------W\n",489 "board_visualization": "...D------C------J\n../|...../|...../|\n./.|..../.|..../.|\nA------B------I..|\n|..H---|--G...|..L\n|./....|./....|./\n|/.....|/.....|/\nE------F------K\n",490 "problem_number": 48491 },492 {493 "problem": "Alice and Bob are playing a game on two adjacent cubes. ABCD forms the top rectangle in the first cube and BIJC forms the top rectangle in the second cube. EFGH forms the bottom rectangle in the first cube and FKLG forms the bottom rectangle in the second cube. AE is an edge, BF is an edge, CG is an edge, DH is an edge, IK is an edge, and JL is an edge. Note that vertices B,C,G,F are shared by the two cubes. Alice and Bob plays a game where they take turns to put stickers on the vertices of the cubes that have not been occupied. Alice plays white stickers. Bob plays black stickers. The person who has four stickers on the same plane on either cube wins. Alice first places a white stone at D. Then Bob places a black stone at A. Then Alice places a white stone at E. Then Bob places a black stone at B. Then Alice places a white stone at F. Then Bob places a black stone at K. Then Alice places a white stone at L. Where should Bob play next?",494 "solution": "C",495 "is_unique_solution": true,496 "verdict": "blocked",497 "next_player": "Bob",498 "currect_board_visualization": "...W------*------*\n../|...../|...../|\n./.|..../.|..../.|\nB------B------*..|\n|..*---|--*...|..W\n|./....|./....|./\n|/.....|/.....|/\nW------W------B\n",499 "board_visualization": "...D------C------J\n../|...../|...../|\n./.|..../.|..../.|\nA------B------I..|\n|..H---|--G...|..L\n|./....|./....|./\n|/.....|/.....|/\nE------F------K\n",500 "problem_number": 49501 },502 {503 "problem": "Alice and Bob are playing a game on two adjacent cubes. ABCD forms the top rectangle in the first cube and BIJC forms the top rectangle in the second cube. EFGH forms the bottom rectangle in the first cube and FKLG forms the bottom rectangle in the second cube. AE is an edge, BF is an edge, CG is an edge, DH is an edge, IK is an edge, and JL is an edge. Note that vertices B,C,G,F are shared by the two cubes. Alice and Bob plays a game where they take turns to put stickers on the vertices of the cubes that have not been occupied. Alice plays white stickers. Bob plays black stickers. The person who has four stickers on the same plane on either cube wins. Alice first places a white stone at A. Then Bob places a black stone at F. Then Alice places a white stone at D. Then Bob places a black stone at I. Then Alice places a white stone at G. Then Bob places a black stone at K. Then Alice places a white stone at L. Where should Bob play next?",504 "solution": "B",505 "is_unique_solution": true,506 "verdict": "win",507 "next_player": "Bob",508 "currect_board_visualization": "...W------*------*\n../|...../|...../|\n./.|..../.|..../.|\nW------*------B..|\n|..*---|--W...|..W\n|./....|./....|./\n|/.....|/.....|/\n*------B------B\n",509 "board_visualization": "...D------C------J\n../|...../|...../|\n./.|..../.|..../.|\nA------B------I..|\n|..H---|--G...|..L\n|./....|./....|./\n|/.....|/.....|/\nE------F------K\n",510 "problem_number": 50511 },512 {513 "problem": "Alice and Bob are playing a game on two adjacent cubes. ABCD forms the top rectangle in the first cube and BIJC forms the top rectangle in the second cube. EFGH forms the bottom rectangle in the first cube and FKLG forms the bottom rectangle in the second cube. AE is an edge, BF is an edge, CG is an edge, DH is an edge, IK is an edge, and JL is an edge. Note that vertices B,C,G,F are shared by the two cubes. Alice and Bob plays a game where they take turns to put stickers on the vertices of the cubes that have not been occupied. Alice plays white stickers. Bob plays black stickers. The person who has four stickers on the same plane on either cube wins. Alice first places a white stone at A. Then Bob places a black stone at F. Then Alice places a white stone at C. Then Bob places a black stone at I. Then Alice places a white stone at D. Then Bob places a black stone at K. Then Alice places a white stone at H. Where should Bob play next?",514 "solution": "B",515 "is_unique_solution": true,516 "verdict": "win",517 "next_player": "Bob",518 "currect_board_visualization": "...W------W------*\n../|...../|...../|\n./.|..../.|..../.|\nW------*------B..|\n|..W---|--*...|..*\n|./....|./....|./\n|/.....|/.....|/\n*------B------B\n",519 "board_visualization": "...D------C------J\n../|...../|...../|\n./.|..../.|..../.|\nA------B------I..|\n|..H---|--G...|..L\n|./....|./....|./\n|/.....|/.....|/\nE------F------K\n",520 "problem_number": 51521 },522 {523 "problem": "Alice and Bob are playing a game on two adjacent cubes. ABCD forms the top rectangle in the first cube and BIJC forms the top rectangle in the second cube. EFGH forms the bottom rectangle in the first cube and FKLG forms the bottom rectangle in the second cube. AE is an edge, BF is an edge, CG is an edge, DH is an edge, IK is an edge, and JL is an edge. Note that vertices B,C,G,F are shared by the two cubes. Alice and Bob plays a game where they take turns to put stickers on the vertices of the cubes that have not been occupied. Alice plays white stickers. Bob plays black stickers. The person who has four stickers on the same plane on either cube wins. Alice first places a white stone at C. Then Bob places a black stone at A. Then Alice places a white stone at F. Then Bob places a black stone at D. Then Alice places a white stone at G. Then Bob places a black stone at H. Then Alice places a white stone at I. Where should Bob play next?",524 "solution": "E",525 "is_unique_solution": true,526 "verdict": "win",527 "next_player": "Bob",528 "currect_board_visualization": "...B------W------*\n../|...../|...../|\n./.|..../.|..../.|\nB------*------W..|\n|..B---|--W...|..*\n|./....|./....|./\n|/.....|/.....|/\n*------W------*\n",529 "board_visualization": "...D------C------J\n../|...../|...../|\n./.|..../.|..../.|\nA------B------I..|\n|..H---|--G...|..L\n|./....|./....|./\n|/.....|/.....|/\nE------F------K\n",530 "problem_number": 52531 },532 {533 "problem": "Alice and Bob are playing a game on two adjacent cubes. ABCD forms the top rectangle in the first cube and BIJC forms the top rectangle in the second cube. EFGH forms the bottom rectangle in the first cube and FKLG forms the bottom rectangle in the second cube. AE is an edge, BF is an edge, CG is an edge, DH is an edge, IK is an edge, and JL is an edge. Note that vertices B,C,G,F are shared by the two cubes. Alice and Bob plays a game where they take turns to put stickers on the vertices of the cubes that have not been occupied. Alice plays white stickers. Bob plays black stickers. The person who has four stickers on the same plane on either cube wins. Alice first places a white stone at H. Then Bob places a black stone at A. Then Alice places a white stone at I. Then Bob places a black stone at C. Then Alice places a white stone at K. Then Bob places a black stone at E. Then Alice places a white stone at L. Where should Bob play next?",534 "solution": "G",535 "is_unique_solution": true,536 "verdict": "win",537 "next_player": "Bob",538 "currect_board_visualization": "...*------B------*\n../|...../|...../|\n./.|..../.|..../.|\nB------*------W..|\n|..W---|--*...|..W\n|./....|./....|./\n|/.....|/.....|/\nB------*------W\n",539 "board_visualization": "...D------C------J\n../|...../|...../|\n./.|..../.|..../.|\nA------B------I..|\n|..H---|--G...|..L\n|./....|./....|./\n|/.....|/.....|/\nE------F------K\n",540 "problem_number": 53541 },542 {543 "problem": "Alice and Bob are playing a game on two adjacent cubes. ABCD forms the top rectangle in the first cube and BIJC forms the top rectangle in the second cube. EFGH forms the bottom rectangle in the first cube and FKLG forms the bottom rectangle in the second cube. AE is an edge, BF is an edge, CG is an edge, DH is an edge, IK is an edge, and JL is an edge. Note that vertices B,C,G,F are shared by the two cubes. Alice and Bob plays a game where they take turns to put stickers on the vertices of the cubes that have not been occupied. Alice plays white stickers. Bob plays black stickers. The person who has four stickers on the same plane on either cube wins. Alice first places a white stone at E. Then Bob places a black stone at B. Then Alice places a white stone at H. Then Bob places a black stone at G. Then Alice places a white stone at J. Then Bob places a black stone at I. Then Alice places a white stone at K. Where should Bob play next?",544 "solution": "L",545 "is_unique_solution": true,546 "verdict": "win",547 "next_player": "Bob",548 "currect_board_visualization": "...*------*------W\n../|...../|...../|\n./.|..../.|..../.|\n*------B------B..|\n|..W---|--B...|..*\n|./....|./....|./\n|/.....|/.....|/\nW------*------W\n",549 "board_visualization": "...D------C------J\n../|...../|...../|\n./.|..../.|..../.|\nA------B------I..|\n|..H---|--G...|..L\n|./....|./....|./\n|/.....|/.....|/\nE------F------K\n",550 "problem_number": 54551 },552 {553 "problem": "Alice and Bob are playing a game on two adjacent cubes. ABCD forms the top rectangle in the first cube and BIJC forms the top rectangle in the second cube. EFGH forms the bottom rectangle in the first cube and FKLG forms the bottom rectangle in the second cube. AE is an edge, BF is an edge, CG is an edge, DH is an edge, IK is an edge, and JL is an edge. Note that vertices B,C,G,F are shared by the two cubes. Alice and Bob plays a game where they take turns to put stickers on the vertices of the cubes that have not been occupied. Alice plays white stickers. Bob plays black stickers. The person who has four stickers on the same plane on either cube wins. Alice first places a white stone at D. Then Bob places a black stone at C. Then Alice places a white stone at E. Then Bob places a black stone at G. Then Alice places a white stone at F. Then Bob places a black stone at K. Then Alice places a white stone at H. Where should Bob play next?",554 "solution": "I",555 "is_unique_solution": true,556 "verdict": "win",557 "next_player": "Bob",558 "currect_board_visualization": "...W------B------*\n../|...../|...../|\n./.|..../.|..../.|\n*------*------*..|\n|..W---|--B...|..*\n|./....|./....|./\n|/.....|/.....|/\nW------W------B\n",559 "board_visualization": "...D------C------J\n../|...../|...../|\n./.|..../.|..../.|\nA------B------I..|\n|..H---|--G...|..L\n|./....|./....|./\n|/.....|/.....|/\nE------F------K\n",560 "problem_number": 55561 },562 {563 "problem": "Alice and Bob are playing a game on two adjacent cubes. ABCD forms the top rectangle in the first cube and BIJC forms the top rectangle in the second cube. EFGH forms the bottom rectangle in the first cube and FKLG forms the bottom rectangle in the second cube. AE is an edge, BF is an edge, CG is an edge, DH is an edge, IK is an edge, and JL is an edge. Note that vertices B,C,G,F are shared by the two cubes. Alice and Bob plays a game where they take turns to put stickers on the vertices of the cubes that have not been occupied. Alice plays white stickers. Bob plays black stickers. The person who has four stickers on the same plane on either cube wins. Alice first places a white stone at A. Then Bob places a black stone at F. Then Alice places a white stone at C. Then Bob places a black stone at J. Then Alice places a white stone at E. Then Bob places a black stone at L. Then Alice places a white stone at I. Where should Bob play next?",564 "solution": "B",565 "is_unique_solution": true,566 "verdict": "win",567 "next_player": "Bob",568 "currect_board_visualization": "...*------W------B\n../|...../|...../|\n./.|..../.|..../.|\nW------*------W..|\n|..*---|--*...|..B\n|./....|./....|./\n|/.....|/.....|/\nW------B------*\n",569 "board_visualization": "...D------C------J\n../|...../|...../|\n./.|..../.|..../.|\nA------B------I..|\n|..H---|--G...|..L\n|./....|./....|./\n|/.....|/.....|/\nE------F------K\n",570 "problem_number": 56571 },572 {573 "problem": "Alice and Bob are playing a game on two adjacent cubes. ABCD forms the top rectangle in the first cube and BIJC forms the top rectangle in the second cube. EFGH forms the bottom rectangle in the first cube and FKLG forms the bottom rectangle in the second cube. AE is an edge, BF is an edge, CG is an edge, DH is an edge, IK is an edge, and JL is an edge. Note that vertices B,C,G,F are shared by the two cubes. Alice and Bob plays a game where they take turns to put stickers on the vertices of the cubes that have not been occupied. Alice plays white stickers. Bob plays black stickers. The person who has four stickers on the same plane on either cube wins. Alice first places a white stone at G. Then Bob places a black stone at A. Then Alice places a white stone at I. Then Bob places a black stone at D. Then Alice places a white stone at K. Then Bob places a black stone at H. Then Alice places a white stone at L. Where should Bob play next?",574 "solution": "E",575 "is_unique_solution": true,576 "verdict": "win",577 "next_player": "Bob",578 "currect_board_visualization": "...B------*------*\n../|...../|...../|\n./.|..../.|..../.|\nB------*------W..|\n|..B---|--W...|..W\n|./....|./....|./\n|/.....|/.....|/\n*------*------W\n",579 "board_visualization": "...D------C------J\n../|...../|...../|\n./.|..../.|..../.|\nA------B------I..|\n|..H---|--G...|..L\n|./....|./....|./\n|/.....|/.....|/\nE------F------K\n",580 "problem_number": 57581 },582 {583 "problem": "Alice and Bob are playing a game on two adjacent cubes. ABCD forms the top rectangle in the first cube and BIJC forms the top rectangle in the second cube. EFGH forms the bottom rectangle in the first cube and FKLG forms the bottom rectangle in the second cube. AE is an edge, BF is an edge, CG is an edge, DH is an edge, IK is an edge, and JL is an edge. Note that vertices B,C,G,F are shared by the two cubes. Alice and Bob plays a game where they take turns to put stickers on the vertices of the cubes that have not been occupied. Alice plays white stickers. Bob plays black stickers. The person who has four stickers on the same plane on either cube wins. Alice first places a white stone at C. Then Bob places a black stone at B. Then Alice places a white stone at G. Then Bob places a black stone at I. Then Alice places a white stone at H. Then Bob places a black stone at K. Then Alice places a white stone at J. Where should Bob play next?",584 "solution": "F",585 "is_unique_solution": true,586 "verdict": "win",587 "next_player": "Bob",588 "currect_board_visualization": "...*------W------W\n../|...../|...../|\n./.|..../.|..../.|\n*------B------B..|\n|..W---|--W...|..*\n|./....|./....|./\n|/.....|/.....|/\n*------*------B\n",589 "board_visualization": "...D------C------J\n../|...../|...../|\n./.|..../.|..../.|\nA------B------I..|\n|..H---|--G...|..L\n|./....|./....|./\n|/.....|/.....|/\nE------F------K\n",590 "problem_number": 58591 },592 {593 "problem": "Alice and Bob are playing a game on two adjacent cubes. ABCD forms the top rectangle in the first cube and BIJC forms the top rectangle in the second cube. EFGH forms the bottom rectangle in the first cube and FKLG forms the bottom rectangle in the second cube. AE is an edge, BF is an edge, CG is an edge, DH is an edge, IK is an edge, and JL is an edge. Note that vertices B,C,G,F are shared by the two cubes. Alice and Bob plays a game where they take turns to put stickers on the vertices of the cubes that have not been occupied. Alice plays white stickers. Bob plays black stickers. The person who has four stickers on the same plane on either cube wins. Alice first places a white stone at A. Then Bob places a black stone at C. Then Alice places a white stone at D. Then Bob places a black stone at G. Then Alice places a white stone at J. Then Bob places a black stone at I. Then Alice places a white stone at L. Where should Bob play next?",594 "solution": "K",595 "is_unique_solution": true,596 "verdict": "win",597 "next_player": "Bob",598 "currect_board_visualization": "...W------B------W\n../|...../|...../|\n./.|..../.|..../.|\nW------*------B..|\n|..*---|--B...|..W\n|./....|./....|./\n|/.....|/.....|/\n*------*------*\n",599 "board_visualization": "...D------C------J\n../|...../|...../|\n./.|..../.|..../.|\nA------B------I..|\n|..H---|--G...|..L\n|./....|./....|./\n|/.....|/.....|/\nE------F------K\n",600 "problem_number": 59601 },602 {603 "problem": "Alice and Bob are playing a game on two adjacent cubes. ABCD forms the top rectangle in the first cube and BIJC forms the top rectangle in the second cube. EFGH forms the bottom rectangle in the first cube and FKLG forms the bottom rectangle in the second cube. AE is an edge, BF is an edge, CG is an edge, DH is an edge, IK is an edge, and JL is an edge. Note that vertices B,C,G,F are shared by the two cubes. Alice and Bob plays a game where they take turns to put stickers on the vertices of the cubes that have not been occupied. Alice plays white stickers. Bob plays black stickers. The person who has four stickers on the same plane on either cube wins. Alice first places a white stone at B. Then Bob places a black stone at A. Then Alice places a white stone at G. Then Bob places a black stone at C. Then Alice places a white stone at J. Then Bob places a black stone at E. Then Alice places a white stone at K. Where should Bob play next?",604 "solution": "D",605 "is_unique_solution": true,606 "verdict": "fork",607 "next_player": "Bob",608 "currect_board_visualization": "...*------B------W\n../|...../|...../|\n./.|..../.|..../.|\nB------W------*..|\n|..*---|--W...|..*\n|./....|./....|./\n|/.....|/.....|/\nB------*------W\n",609 "board_visualization": "...D------C------J\n../|...../|...../|\n./.|..../.|..../.|\nA------B------I..|\n|..H---|--G...|..L\n|./....|./....|./\n|/.....|/.....|/\nE------F------K\n",610 "problem_number": 60611 },612 {613 "problem": "Alice and Bob are playing a game on two adjacent cubes. ABCD forms the top rectangle in the first cube and BIJC forms the top rectangle in the second cube. EFGH forms the bottom rectangle in the first cube and FKLG forms the bottom rectangle in the second cube. AE is an edge, BF is an edge, CG is an edge, DH is an edge, IK is an edge, and JL is an edge. Note that vertices B,C,G,F are shared by the two cubes. Alice and Bob plays a game where they take turns to put stickers on the vertices of the cubes that have not been occupied. Alice plays white stickers. Bob plays black stickers. The person who has four stickers on the same plane on either cube wins. Alice first places a white stone at D. Then Bob places a black stone at C. Then Alice places a white stone at G. Then Bob places a black stone at E. Then Alice places a white stone at I. Then Bob places a black stone at F. Then Alice places a white stone at K. Where should Bob play next?",614 "solution": "B",615 "is_unique_solution": true,616 "verdict": "fork",617 "next_player": "Bob",618 "currect_board_visualization": "...W------B------*\n../|...../|...../|\n./.|..../.|..../.|\n*------*------W..|\n|..*---|--W...|..*\n|./....|./....|./\n|/.....|/.....|/\nB------B------W\n",619 "board_visualization": "...D------C------J\n../|...../|...../|\n./.|..../.|..../.|\nA------B------I..|\n|..H---|--G...|..L\n|./....|./....|./\n|/.....|/.....|/\nE------F------K\n",620 "problem_number": 61621 },622 {623 "problem": "Alice and Bob are playing a game on two adjacent cubes. ABCD forms the top rectangle in the first cube and BIJC forms the top rectangle in the second cube. EFGH forms the bottom rectangle in the first cube and FKLG forms the bottom rectangle in the second cube. AE is an edge, BF is an edge, CG is an edge, DH is an edge, IK is an edge, and JL is an edge. Note that vertices B,C,G,F are shared by the two cubes. Alice and Bob plays a game where they take turns to put stickers on the vertices of the cubes that have not been occupied. Alice plays white stickers. Bob plays black stickers. The person who has four stickers on the same plane on either cube wins. Alice first places a white stone at D. Then Bob places a black stone at B. Then Alice places a white stone at E. Then Bob places a black stone at F. Then Alice places a white stone at G. Then Bob places a black stone at L. Then Alice places a white stone at J. Where should Bob play next?",624 "solution": "K",625 "is_unique_solution": true,626 "verdict": "fork",627 "next_player": "Bob",628 "currect_board_visualization": "...W------*------W\n../|...../|...../|\n./.|..../.|..../.|\n*------B------*..|\n|..*---|--W...|..B\n|./....|./....|./\n|/.....|/.....|/\nW------B------*\n",629 "board_visualization": "...D------C------J\n../|...../|...../|\n./.|..../.|..../.|\nA------B------I..|\n|..H---|--G...|..L\n|./....|./....|./\n|/.....|/.....|/\nE------F------K\n",630 "problem_number": 62631 },632 {633 "problem": "Alice and Bob are playing a game on two adjacent cubes. ABCD forms the top rectangle in the first cube and BIJC forms the top rectangle in the second cube. EFGH forms the bottom rectangle in the first cube and FKLG forms the bottom rectangle in the second cube. AE is an edge, BF is an edge, CG is an edge, DH is an edge, IK is an edge, and JL is an edge. Note that vertices B,C,G,F are shared by the two cubes. Alice and Bob plays a game where they take turns to put stickers on the vertices of the cubes that have not been occupied. Alice plays white stickers. Bob plays black stickers. The person who has four stickers on the same plane on either cube wins. Alice first places a white stone at C. Then Bob places a black stone at A. Then Alice places a white stone at H. Then Bob places a black stone at E. Then Alice places a white stone at I. Then Bob places a black stone at G. Then Alice places a white stone at K. Where should Bob play next?",634 "solution": "F",635 "is_unique_solution": true,636 "verdict": "fork",637 "next_player": "Bob",638 "currect_board_visualization": "...*------W------*\n../|...../|...../|\n./.|..../.|..../.|\nB------*------W..|\n|..W---|--B...|..*\n|./....|./....|./\n|/.....|/.....|/\nB------*------W\n",639 "board_visualization": "...D------C------J\n../|...../|...../|\n./.|..../.|..../.|\nA------B------I..|\n|..H---|--G...|..L\n|./....|./....|./\n|/.....|/.....|/\nE------F------K\n",640 "problem_number": 63641 },642 {643 "problem": "Alice and Bob are playing a game on two adjacent cubes. ABCD forms the top rectangle in the first cube and BIJC forms the top rectangle in the second cube. EFGH forms the bottom rectangle in the first cube and FKLG forms the bottom rectangle in the second cube. AE is an edge, BF is an edge, CG is an edge, DH is an edge, IK is an edge, and JL is an edge. Note that vertices B,C,G,F are shared by the two cubes. Alice and Bob plays a game where they take turns to put stickers on the vertices of the cubes that have not been occupied. Alice plays white stickers. Bob plays black stickers. The person who has four stickers on the same plane on either cube wins. Alice first places a white stone at A. Then Bob places a black stone at E. Then Alice places a white stone at D. Then Bob places a black stone at F. Then Alice places a white stone at I. Then Bob places a black stone at L. Then Alice places a white stone at J. Where should Bob play next?",644 "solution": "G",645 "is_unique_solution": true,646 "verdict": "fork",647 "next_player": "Bob",648 "currect_board_visualization": "...W------*------W\n../|...../|...../|\n./.|..../.|..../.|\nW------*------W..|\n|..*---|--*...|..B\n|./....|./....|./\n|/.....|/.....|/\nB------B------*\n",649 "board_visualization": "...D------C------J\n../|...../|...../|\n./.|..../.|..../.|\nA------B------I..|\n|..H---|--G...|..L\n|./....|./....|./\n|/.....|/.....|/\nE------F------K\n",650 "problem_number": 64651 },652 {653 "problem": "Alice and Bob are playing a game on two adjacent cubes. ABCD forms the top rectangle in the first cube and BIJC forms the top rectangle in the second cube. EFGH forms the bottom rectangle in the first cube and FKLG forms the bottom rectangle in the second cube. AE is an edge, BF is an edge, CG is an edge, DH is an edge, IK is an edge, and JL is an edge. Note that vertices B,C,G,F are shared by the two cubes. Alice and Bob plays a game where they take turns to put stickers on the vertices of the cubes that have not been occupied. Alice plays white stickers. Bob plays black stickers. The person who has four stickers on the same plane on either cube wins. Alice first places a white stone at D. Then Bob places a black stone at F. Then Alice places a white stone at E. Then Bob places a black stone at G. Then Alice places a white stone at I. Then Bob places a black stone at H. Then Alice places a white stone at J. Where should Bob play next?",654 "solution": "B",655 "is_unique_solution": true,656 "verdict": "fork",657 "next_player": "Bob",658 "currect_board_visualization": "...W------*------W\n../|...../|...../|\n./.|..../.|..../.|\n*------*------W..|\n|..B---|--B...|..*\n|./....|./....|./\n|/.....|/.....|/\nW------B------*\n",659 "board_visualization": "...D------C------J\n../|...../|...../|\n./.|..../.|..../.|\nA------B------I..|\n|..H---|--G...|..L\n|./....|./....|./\n|/.....|/.....|/\nE------F------K\n",660 "problem_number": 65661 },662 {663 "problem": "Alice and Bob are playing a game on two adjacent cubes. ABCD forms the top rectangle in the first cube and BIJC forms the top rectangle in the second cube. EFGH forms the bottom rectangle in the first cube and FKLG forms the bottom rectangle in the second cube. AE is an edge, BF is an edge, CG is an edge, DH is an edge, IK is an edge, and JL is an edge. Note that vertices B,C,G,F are shared by the two cubes. Alice and Bob plays a game where they take turns to put stickers on the vertices of the cubes that have not been occupied. Alice plays white stickers. Bob plays black stickers. The person who has four stickers on the same plane on either cube wins. Alice first places a white stone at D. Then Bob places a black stone at A. Then Alice places a white stone at H. Then Bob places a black stone at F. Then Alice places a white stone at J. Then Bob places a black stone at I. Then Alice places a white stone at L. Where should Bob play next?",664 "solution": "B",665 "is_unique_solution": true,666 "verdict": "fork",667 "next_player": "Bob",668 "currect_board_visualization": "...W------*------W\n../|...../|...../|\n./.|..../.|..../.|\nB------*------B..|\n|..W---|--*...|..W\n|./....|./....|./\n|/.....|/.....|/\n*------B------*\n",669 "board_visualization": "...D------C------J\n../|...../|...../|\n./.|..../.|..../.|\nA------B------I..|\n|..H---|--G...|..L\n|./....|./....|./\n|/.....|/.....|/\nE------F------K\n",670 "problem_number": 66671 },672 {673 "problem": "Alice and Bob are playing a game on two adjacent cubes. ABCD forms the top rectangle in the first cube and BIJC forms the top rectangle in the second cube. EFGH forms the bottom rectangle in the first cube and FKLG forms the bottom rectangle in the second cube. AE is an edge, BF is an edge, CG is an edge, DH is an edge, IK is an edge, and JL is an edge. Note that vertices B,C,G,F are shared by the two cubes. Alice and Bob plays a game where they take turns to put stickers on the vertices of the cubes that have not been occupied. Alice plays white stickers. Bob plays black stickers. The person who has four stickers on the same plane on either cube wins. Alice first places a white stone at A. Then Bob places a black stone at D. Then Alice places a white stone at H. Then Bob places a black stone at F. Then Alice places a white stone at I. Then Bob places a black stone at G. Then Alice places a white stone at L. Where should Bob play next?",674 "solution": "C",675 "is_unique_solution": true,676 "verdict": "fork",677 "next_player": "Bob",678 "currect_board_visualization": "...B------*------*\n../|...../|...../|\n./.|..../.|..../.|\nW------*------W..|\n|..W---|--B...|..W\n|./....|./....|./\n|/.....|/.....|/\n*------B------*\n",679 "board_visualization": "...D------C------J\n../|...../|...../|\n./.|..../.|..../.|\nA------B------I..|\n|..H---|--G...|..L\n|./....|./....|./\n|/.....|/.....|/\nE------F------K\n",680 "problem_number": 67681 },682 {683 "problem": "Alice and Bob are playing a game on two adjacent cubes. ABCD forms the top rectangle in the first cube and BIJC forms the top rectangle in the second cube. EFGH forms the bottom rectangle in the first cube and FKLG forms the bottom rectangle in the second cube. AE is an edge, BF is an edge, CG is an edge, DH is an edge, IK is an edge, and JL is an edge. Note that vertices B,C,G,F are shared by the two cubes. Alice and Bob plays a game where they take turns to put stickers on the vertices of the cubes that have not been occupied. Alice plays white stickers. Bob plays black stickers. The person who has four stickers on the same plane on either cube wins. Alice first places a white stone at B. Then Bob places a black stone at C. Then Alice places a white stone at D. Then Bob places a black stone at F. Then Alice places a white stone at E. Then Bob places a black stone at G. Then Alice places a white stone at K. Where should Bob play next?",684 "solution": "J",685 "is_unique_solution": true,686 "verdict": "fork",687 "next_player": "Bob",688 "currect_board_visualization": "...W------B------*\n../|...../|...../|\n./.|..../.|..../.|\n*------W------*..|\n|..*---|--B...|..*\n|./....|./....|./\n|/.....|/.....|/\nW------B------W\n",689 "board_visualization": "...D------C------J\n../|...../|...../|\n./.|..../.|..../.|\nA------B------I..|\n|..H---|--G...|..L\n|./....|./....|./\n|/.....|/.....|/\nE------F------K\n",690 "problem_number": 68691 },692 {693 "problem": "Alice and Bob are playing a game on two adjacent cubes. ABCD forms the top rectangle in the first cube and BIJC forms the top rectangle in the second cube. EFGH forms the bottom rectangle in the first cube and FKLG forms the bottom rectangle in the second cube. AE is an edge, BF is an edge, CG is an edge, DH is an edge, IK is an edge, and JL is an edge. Note that vertices B,C,G,F are shared by the two cubes. Alice and Bob plays a game where they take turns to put stickers on the vertices of the cubes that have not been occupied. Alice plays white stickers. Bob plays black stickers. The person who has four stickers on the same plane on either cube wins. Alice first places a white stone at C. Then Bob places a black stone at B. Then Alice places a white stone at H. Then Bob places a black stone at F. Then Alice places a white stone at J. Then Bob places a black stone at G. Then Alice places a white stone at K. Where should Bob play next?",694 "solution": "A",695 "is_unique_solution": true,696 "verdict": "fork",697 "next_player": "Bob",698 "currect_board_visualization": "...*------W------W\n../|...../|...../|\n./.|..../.|..../.|\n*------B------*..|\n|..W---|--B...|..*\n|./....|./....|./\n|/.....|/.....|/\n*------B------W\n",699 "board_visualization": "...D------C------J\n../|...../|...../|\n./.|..../.|..../.|\nA------B------I..|\n|..H---|--G...|..L\n|./....|./....|./\n|/.....|/.....|/\nE------F------K\n",700 "problem_number": 69701 },702 {703 "problem": "Alice and Bob are playing a game on two adjacent cubes. ABCD forms the top rectangle in the first cube and BIJC forms the top rectangle in the second cube. EFGH forms the bottom rectangle in the first cube and FKLG forms the bottom rectangle in the second cube. AE is an edge, BF is an edge, CG is an edge, DH is an edge, IK is an edge, and JL is an edge. Note that vertices B,C,G,F are shared by the two cubes. Alice and Bob plays a game where they take turns to put stickers on the vertices of the cubes that have not been occupied. Alice plays white stickers. Bob plays black stickers. The person who has four stickers on the same plane on either cube wins. Alice first places a white stone at B. Then Bob places a black stone at G. Then Alice places a white stone at C. Then Bob places a black stone at H. Then Alice places a white stone at E. Then Bob places a black stone at I. Where should Alice play next?",704 "solution": "A, D, F",705 "is_unique_solution": false,706 "verdict": "fork",707 "next_player": "Alice",708 "currect_board_visualization": "...*------W------*\n../|...../|...../|\n./.|..../.|..../.|\n*------W------B..|\n|..B---|--B...|..*\n|./....|./....|./\n|/.....|/.....|/\nW------*------*\n",709 "board_visualization": "...D------C------J\n../|...../|...../|\n./.|..../.|..../.|\nA------B------I..|\n|..H---|--G...|..L\n|./....|./....|./\n|/.....|/.....|/\nE------F------K\n",710 "problem_number": 70711 },712 {713 "problem": "Alice and Bob are playing a game on two adjacent cubes. ABCD forms the top rectangle in the first cube and BIJC forms the top rectangle in the second cube. EFGH forms the bottom rectangle in the first cube and FKLG forms the bottom rectangle in the second cube. AE is an edge, BF is an edge, CG is an edge, DH is an edge, IK is an edge, and JL is an edge. Note that vertices B,C,G,F are shared by the two cubes. Alice and Bob plays a game where they take turns to put stickers on the vertices of the cubes that have not been occupied. Alice plays white stickers. Bob plays black stickers. The person who has four stickers on the same plane on either cube wins. Alice first places a white stone at F. Then Bob places a black stone at H. Then Alice places a white stone at G. Then Bob places a black stone at I. Then Alice places a white stone at L. Then Bob places a black stone at K. Where should Alice play next?",714 "solution": "B, C, J",715 "is_unique_solution": false,716 "verdict": "fork",717 "next_player": "Alice",718 "currect_board_visualization": "...*------*------*\n../|...../|...../|\n./.|..../.|..../.|\n*------*------B..|\n|..B---|--W...|..W\n|./....|./....|./\n|/.....|/.....|/\n*------W------B\n",719 "board_visualization": "...D------C------J\n../|...../|...../|\n./.|..../.|..../.|\nA------B------I..|\n|..H---|--G...|..L\n|./....|./....|./\n|/.....|/.....|/\nE------F------K\n",720 "problem_number": 71721 },722 {723 "problem": "Alice and Bob are playing a game on two adjacent cubes. ABCD forms the top rectangle in the first cube and BIJC forms the top rectangle in the second cube. EFGH forms the bottom rectangle in the first cube and FKLG forms the bottom rectangle in the second cube. AE is an edge, BF is an edge, CG is an edge, DH is an edge, IK is an edge, and JL is an edge. Note that vertices B,C,G,F are shared by the two cubes. Alice and Bob plays a game where they take turns to put stickers on the vertices of the cubes that have not been occupied. Alice plays white stickers. Bob plays black stickers. The person who has four stickers on the same plane on either cube wins. Alice first places a white stone at G. Then Bob places a black stone at E. Then Alice places a white stone at K. Then Bob places a black stone at F. Then Alice places a white stone at L. Then Bob places a black stone at J. Where should Alice play next?",724 "solution": "B, C, I",725 "is_unique_solution": false,726 "verdict": "fork",727 "next_player": "Alice",728 "currect_board_visualization": "...*------*------B\n../|...../|...../|\n./.|..../.|..../.|\n*------*------*..|\n|..*---|--W...|..W\n|./....|./....|./\n|/.....|/.....|/\nB------B------W\n",729 "board_visualization": "...D------C------J\n../|...../|...../|\n./.|..../.|..../.|\nA------B------I..|\n|..H---|--G...|..L\n|./....|./....|./\n|/.....|/.....|/\nE------F------K\n",730 "problem_number": 72731 },732 {733 "problem": "Alice and Bob are playing a game on two adjacent cubes. ABCD forms the top rectangle in the first cube and BIJC forms the top rectangle in the second cube. EFGH forms the bottom rectangle in the first cube and FKLG forms the bottom rectangle in the second cube. AE is an edge, BF is an edge, CG is an edge, DH is an edge, IK is an edge, and JL is an edge. Note that vertices B,C,G,F are shared by the two cubes. Alice and Bob plays a game where they take turns to put stickers on the vertices of the cubes that have not been occupied. Alice plays white stickers. Bob plays black stickers. The person who has four stickers on the same plane on either cube wins. Alice first places a white stone at D. Then Bob places a black stone at C. Then Alice places a white stone at E. Then Bob places a black stone at I. Then Alice places a white stone at G. Then Bob places a black stone at L. Where should Alice play next?",734 "solution": "A, F, H",735 "is_unique_solution": false,736 "verdict": "fork",737 "next_player": "Alice",738 "currect_board_visualization": "...W------B------*\n../|...../|...../|\n./.|..../.|..../.|\n*------*------B..|\n|..*---|--W...|..B\n|./....|./....|./\n|/.....|/.....|/\nW------*------*\n",739 "board_visualization": "...D------C------J\n../|...../|...../|\n./.|..../.|..../.|\nA------B------I..|\n|..H---|--G...|..L\n|./....|./....|./\n|/.....|/.....|/\nE------F------K\n",740 "problem_number": 73741 },742 {743 "problem": "Alice and Bob are playing a game on two adjacent cubes. ABCD forms the top rectangle in the first cube and BIJC forms the top rectangle in the second cube. EFGH forms the bottom rectangle in the first cube and FKLG forms the bottom rectangle in the second cube. AE is an edge, BF is an edge, CG is an edge, DH is an edge, IK is an edge, and JL is an edge. Note that vertices B,C,G,F are shared by the two cubes. Alice and Bob plays a game where they take turns to put stickers on the vertices of the cubes that have not been occupied. Alice plays white stickers. Bob plays black stickers. The person who has four stickers on the same plane on either cube wins. Alice first places a white stone at A. Then Bob places a black stone at E. Then Alice places a white stone at B. Then Bob places a black stone at H. Then Alice places a white stone at F. Then Bob places a black stone at K. Where should Alice play next?",744 "solution": "C, D, G",745 "is_unique_solution": false,746 "verdict": "fork",747 "next_player": "Alice",748 "currect_board_visualization": "...*------*------*\n../|...../|...../|\n./.|..../.|..../.|\nW------W------*..|\n|..B---|--*...|..*\n|./....|./....|./\n|/.....|/.....|/\nB------W------B\n",749 "board_visualization": "...D------C------J\n../|...../|...../|\n./.|..../.|..../.|\nA------B------I..|\n|..H---|--G...|..L\n|./....|./....|./\n|/.....|/.....|/\nE------F------K\n",750 "problem_number": 74751 },752 {753 "problem": "Alice and Bob are playing a game on two adjacent cubes. ABCD forms the top rectangle in the first cube and BIJC forms the top rectangle in the second cube. EFGH forms the bottom rectangle in the first cube and FKLG forms the bottom rectangle in the second cube. AE is an edge, BF is an edge, CG is an edge, DH is an edge, IK is an edge, and JL is an edge. Note that vertices B,C,G,F are shared by the two cubes. Alice and Bob plays a game where they take turns to put stickers on the vertices of the cubes that have not been occupied. Alice plays white stickers. Bob plays black stickers. The person who has four stickers on the same plane on either cube wins. Alice first places a white stone at C. Then Bob places a black stone at A. Then Alice places a white stone at F. Then Bob places a black stone at G. Then Alice places a white stone at H. Then Bob places a black stone at K. Where should Alice play next?",754 "solution": "B, D, E",755 "is_unique_solution": false,756 "verdict": "fork",757 "next_player": "Alice",758 "currect_board_visualization": "...*------W------*\n../|...../|...../|\n./.|..../.|..../.|\nB------*------*..|\n|..W---|--B...|..*\n|./....|./....|./\n|/.....|/.....|/\n*------W------B\n",759 "board_visualization": "...D------C------J\n../|...../|...../|\n./.|..../.|..../.|\nA------B------I..|\n|..H---|--G...|..L\n|./....|./....|./\n|/.....|/.....|/\nE------F------K\n",760 "problem_number": 75761 },762 {763 "problem": "Alice and Bob are playing a game on two adjacent cubes. ABCD forms the top rectangle in the first cube and BIJC forms the top rectangle in the second cube. EFGH forms the bottom rectangle in the first cube and FKLG forms the bottom rectangle in the second cube. AE is an edge, BF is an edge, CG is an edge, DH is an edge, IK is an edge, and JL is an edge. Note that vertices B,C,G,F are shared by the two cubes. Alice and Bob plays a game where they take turns to put stickers on the vertices of the cubes that have not been occupied. Alice plays white stickers. Bob plays black stickers. The person who has four stickers on the same plane on either cube wins. Alice first places a white stone at B. Then Bob places a black stone at A. Then Alice places a white stone at G. Then Bob places a black stone at D. Then Alice places a white stone at J. Then Bob places a black stone at F. Where should Alice play next?",764 "solution": "C, I, L",765 "is_unique_solution": false,766 "verdict": "fork",767 "next_player": "Alice",768 "currect_board_visualization": "...B------*------W\n../|...../|...../|\n./.|..../.|..../.|\nB------W------*..|\n|..*---|--W...|..*\n|./....|./....|./\n|/.....|/.....|/\n*------B------*\n",769 "board_visualization": "...D------C------J\n../|...../|...../|\n./.|..../.|..../.|\nA------B------I..|\n|..H---|--G...|..L\n|./....|./....|./\n|/.....|/.....|/\nE------F------K\n",770 "problem_number": 76771 },772 {773 "problem": "Alice and Bob are playing a game on two adjacent cubes. ABCD forms the top rectangle in the first cube and BIJC forms the top rectangle in the second cube. EFGH forms the bottom rectangle in the first cube and FKLG forms the bottom rectangle in the second cube. AE is an edge, BF is an edge, CG is an edge, DH is an edge, IK is an edge, and JL is an edge. Note that vertices B,C,G,F are shared by the two cubes. Alice and Bob plays a game where they take turns to put stickers on the vertices of the cubes that have not been occupied. Alice plays white stickers. Bob plays black stickers. The person who has four stickers on the same plane on either cube wins. Alice first places a white stone at B. Then Bob places a black stone at A. Then Alice places a white stone at J. Then Bob places a black stone at F. Then Alice places a white stone at K. Then Bob places a black stone at H. Where should Alice play next?",774 "solution": "C, I, L",775 "is_unique_solution": false,776 "verdict": "fork",777 "next_player": "Alice",778 "currect_board_visualization": "...*------*------W\n../|...../|...../|\n./.|..../.|..../.|\nB------W------*..|\n|..B---|--*...|..*\n|./....|./....|./\n|/.....|/.....|/\n*------B------W\n",779 "board_visualization": "...D------C------J\n../|...../|...../|\n./.|..../.|..../.|\nA------B------I..|\n|..H---|--G...|..L\n|./....|./....|./\n|/.....|/.....|/\nE------F------K\n",780 "problem_number": 77781 },782 {783 "problem": "Alice and Bob are playing a game on two adjacent cubes. ABCD forms the top rectangle in the first cube and BIJC forms the top rectangle in the second cube. EFGH forms the bottom rectangle in the first cube and FKLG forms the bottom rectangle in the second cube. AE is an edge, BF is an edge, CG is an edge, DH is an edge, IK is an edge, and JL is an edge. Note that vertices B,C,G,F are shared by the two cubes. Alice and Bob plays a game where they take turns to put stickers on the vertices of the cubes that have not been occupied. Alice plays white stickers. Bob plays black stickers. The person who has four stickers on the same plane on either cube wins. Alice first places a white stone at D. Then Bob places a black stone at A. Then Alice places a white stone at F. Then Bob places a black stone at E. Then Alice places a white stone at G. Then Bob places a black stone at I. Where should Alice play next?",784 "solution": "B, C, H",785 "is_unique_solution": false,786 "verdict": "fork",787 "next_player": "Alice",788 "currect_board_visualization": "...W------*------*\n../|...../|...../|\n./.|..../.|..../.|\nB------*------B..|\n|..*---|--W...|..*\n|./....|./....|./\n|/.....|/.....|/\nB------W------*\n",789 "board_visualization": "...D------C------J\n../|...../|...../|\n./.|..../.|..../.|\nA------B------I..|\n|..H---|--G...|..L\n|./....|./....|./\n|/.....|/.....|/\nE------F------K\n",790 "problem_number": 78791 },792 {793 "problem": "Alice and Bob are playing a game on two adjacent cubes. ABCD forms the top rectangle in the first cube and BIJC forms the top rectangle in the second cube. EFGH forms the bottom rectangle in the first cube and FKLG forms the bottom rectangle in the second cube. AE is an edge, BF is an edge, CG is an edge, DH is an edge, IK is an edge, and JL is an edge. Note that vertices B,C,G,F are shared by the two cubes. Alice and Bob plays a game where they take turns to put stickers on the vertices of the cubes that have not been occupied. Alice plays white stickers. Bob plays black stickers. The person who has four stickers on the same plane on either cube wins. Alice first places a white stone at A. Then Bob places a black stone at D. Then Alice places a white stone at C. Then Bob places a black stone at J. Then Alice places a white stone at H. Then Bob places a black stone at K. Where should Alice play next?",794 "solution": "B, E, G",795 "is_unique_solution": false,796 "verdict": "fork",797 "next_player": "Alice",798 "currect_board_visualization": "...B------W------B\n../|...../|...../|\n./.|..../.|..../.|\nW------*------*..|\n|..W---|--*...|..*\n|./....|./....|./\n|/.....|/.....|/\n*------*------B\n",799 "board_visualization": "...D------C------J\n../|...../|...../|\n./.|..../.|..../.|\nA------B------I..|\n|..H---|--G...|..L\n|./....|./....|./\n|/.....|/.....|/\nE------F------K\n",800 "problem_number": 79801 },802 {803 "problem": "Alice and Bob are playing a game on two adjacent cubes. ABCD forms the top rectangle in the first cube and BIJC forms the top rectangle in the second cube. EFGH forms the bottom rectangle in the first cube and FKLG forms the bottom rectangle in the second cube. AE is an edge, BF is an edge, CG is an edge, DH is an edge, IK is an edge, and JL is an edge. Note that vertices B,C,G,F are shared by the two cubes. Alice and Bob plays a game where they take turns to put stickers on the vertices of the cubes that have not been occupied. Alice plays white stickers. Bob plays black stickers. The person who has four stickers on the same plane on either cube wins. Alice first places a white stone at B. Then Bob places a black stone at A. Then Alice places a white stone at H. Then Bob places a black stone at E. Then Alice places a white stone at J. Then Bob places a black stone at F. Then Alice places a white stone at K. Where should Bob play next?",804 "solution": "C, D, G",805 "is_unique_solution": false,806 "verdict": "fork",807 "next_player": "Bob",808 "currect_board_visualization": "...*------*------W\n../|...../|...../|\n./.|..../.|..../.|\nB------W------*..|\n|..W---|--*...|..*\n|./....|./....|./\n|/.....|/.....|/\nB------B------W\n",809 "board_visualization": "...D------C------J\n../|...../|...../|\n./.|..../.|..../.|\nA------B------I..|\n|..H---|--G...|..L\n|./....|./....|./\n|/.....|/.....|/\nE------F------K\n",810 "problem_number": 80811 },812 {813 "problem": "Alice and Bob are playing a game on two adjacent cubes. ABCD forms the top rectangle in the first cube and BIJC forms the top rectangle in the second cube. EFGH forms the bottom rectangle in the first cube and FKLG forms the bottom rectangle in the second cube. AE is an edge, BF is an edge, CG is an edge, DH is an edge, IK is an edge, and JL is an edge. Note that vertices B,C,G,F are shared by the two cubes. Alice and Bob plays a game where they take turns to put stickers on the vertices of the cubes that have not been occupied. Alice plays white stickers. Bob plays black stickers. The person who has four stickers on the same plane on either cube wins. Alice first places a white stone at C. Then Bob places a black stone at B. Then Alice places a white stone at E. Then Bob places a black stone at F. Then Alice places a white stone at H. Then Bob places a black stone at I. Then Alice places a white stone at K. Where should Bob play next?",814 "solution": "G, J, L",815 "is_unique_solution": false,816 "verdict": "fork",817 "next_player": "Bob",818 "currect_board_visualization": "...*------W------*\n../|...../|...../|\n./.|..../.|..../.|\n*------B------B..|\n|..W---|--*...|..*\n|./....|./....|./\n|/.....|/.....|/\nW------B------W\n",819 "board_visualization": "...D------C------J\n../|...../|...../|\n./.|..../.|..../.|\nA------B------I..|\n|..H---|--G...|..L\n|./....|./....|./\n|/.....|/.....|/\nE------F------K\n",820 "problem_number": 81821 },822 {823 "problem": "Alice and Bob are playing a game on two adjacent cubes. ABCD forms the top rectangle in the first cube and BIJC forms the top rectangle in the second cube. EFGH forms the bottom rectangle in the first cube and FKLG forms the bottom rectangle in the second cube. AE is an edge, BF is an edge, CG is an edge, DH is an edge, IK is an edge, and JL is an edge. Note that vertices B,C,G,F are shared by the two cubes. Alice and Bob plays a game where they take turns to put stickers on the vertices of the cubes that have not been occupied. Alice plays white stickers. Bob plays black stickers. The person who has four stickers on the same plane on either cube wins. Alice first places a white stone at A. Then Bob places a black stone at C. Then Alice places a white stone at H. Then Bob places a black stone at F. Then Alice places a white stone at I. Then Bob places a black stone at K. Then Alice places a white stone at J. Where should Bob play next?",824 "solution": "B, G, L",825 "is_unique_solution": false,826 "verdict": "fork",827 "next_player": "Bob",828 "currect_board_visualization": "...*------B------W\n../|...../|...../|\n./.|..../.|..../.|\nW------*------W..|\n|..W---|--*...|..*\n|./....|./....|./\n|/.....|/.....|/\n*------B------B\n",829 "board_visualization": "...D------C------J\n../|...../|...../|\n./.|..../.|..../.|\nA------B------I..|\n|..H---|--G...|..L\n|./....|./....|./\n|/.....|/.....|/\nE------F------K\n",830 "problem_number": 82831 },832 {833 "problem": "Alice and Bob are playing a game on two adjacent cubes. ABCD forms the top rectangle in the first cube and BIJC forms the top rectangle in the second cube. EFGH forms the bottom rectangle in the first cube and FKLG forms the bottom rectangle in the second cube. AE is an edge, BF is an edge, CG is an edge, DH is an edge, IK is an edge, and JL is an edge. Note that vertices B,C,G,F are shared by the two cubes. Alice and Bob plays a game where they take turns to put stickers on the vertices of the cubes that have not been occupied. Alice plays white stickers. Bob plays black stickers. The person who has four stickers on the same plane on either cube wins. Alice first places a white stone at D. Then Bob places a black stone at E. Then Alice places a white stone at F. Then Bob places a black stone at G. Then Alice places a white stone at K. Then Bob places a black stone at H. Then Alice places a white stone at L. Where should Bob play next?",834 "solution": "A, B, C",835 "is_unique_solution": false,836 "verdict": "fork",837 "next_player": "Bob",838 "currect_board_visualization": "...W------*------*\n../|...../|...../|\n./.|..../.|..../.|\n*------*------*..|\n|..B---|--B...|..W\n|./....|./....|./\n|/.....|/.....|/\nB------W------W\n",839 "board_visualization": "...D------C------J\n../|...../|...../|\n./.|..../.|..../.|\nA------B------I..|\n|..H---|--G...|..L\n|./....|./....|./\n|/.....|/.....|/\nE------F------K\n",840 "problem_number": 83841 },842 {843 "problem": "Alice and Bob are playing a game on two adjacent cubes. ABCD forms the top rectangle in the first cube and BIJC forms the top rectangle in the second cube. EFGH forms the bottom rectangle in the first cube and FKLG forms the bottom rectangle in the second cube. AE is an edge, BF is an edge, CG is an edge, DH is an edge, IK is an edge, and JL is an edge. Note that vertices B,C,G,F are shared by the two cubes. Alice and Bob plays a game where they take turns to put stickers on the vertices of the cubes that have not been occupied. Alice plays white stickers. Bob plays black stickers. The person who has four stickers on the same plane on either cube wins. Alice first places a white stone at D. Then Bob places a black stone at A. Then Alice places a white stone at H. Then Bob places a black stone at C. Then Alice places a white stone at I. Then Bob places a black stone at F. Then Alice places a white stone at K. Where should Bob play next?",844 "solution": "B, E, G",845 "is_unique_solution": false,846 "verdict": "fork",847 "next_player": "Bob",848 "currect_board_visualization": "...W------B------*\n../|...../|...../|\n./.|..../.|..../.|\nB------*------W..|\n|..W---|--*...|..*\n|./....|./....|./\n|/.....|/.....|/\n*------B------W\n",849 "board_visualization": "...D------C------J\n../|...../|...../|\n./.|..../.|..../.|\nA------B------I..|\n|..H---|--G...|..L\n|./....|./....|./\n|/.....|/.....|/\nE------F------K\n",850 "problem_number": 84851 },852 {853 "problem": "Alice and Bob are playing a game on two adjacent cubes. ABCD forms the top rectangle in the first cube and BIJC forms the top rectangle in the second cube. EFGH forms the bottom rectangle in the first cube and FKLG forms the bottom rectangle in the second cube. AE is an edge, BF is an edge, CG is an edge, DH is an edge, IK is an edge, and JL is an edge. Note that vertices B,C,G,F are shared by the two cubes. Alice and Bob plays a game where they take turns to put stickers on the vertices of the cubes that have not been occupied. Alice plays white stickers. Bob plays black stickers. The person who has four stickers on the same plane on either cube wins. Alice first places a white stone at A. Then Bob places a black stone at B. Then Alice places a white stone at F. Then Bob places a black stone at G. Then Alice places a white stone at H. Then Bob places a black stone at K. Then Alice places a white stone at J. Where should Bob play next?",854 "solution": "C, I, L",855 "is_unique_solution": false,856 "verdict": "fork",857 "next_player": "Bob",858 "currect_board_visualization": "...*------*------W\n../|...../|...../|\n./.|..../.|..../.|\nW------B------*..|\n|..W---|--B...|..*\n|./....|./....|./\n|/.....|/.....|/\n*------W------B\n",859 "board_visualization": "...D------C------J\n../|...../|...../|\n./.|..../.|..../.|\nA------B------I..|\n|..H---|--G...|..L\n|./....|./....|./\n|/.....|/.....|/\nE------F------K\n",860 "problem_number": 85861 },862 {863 "problem": "Alice and Bob are playing a game on two adjacent cubes. ABCD forms the top rectangle in the first cube and BIJC forms the top rectangle in the second cube. EFGH forms the bottom rectangle in the first cube and FKLG forms the bottom rectangle in the second cube. AE is an edge, BF is an edge, CG is an edge, DH is an edge, IK is an edge, and JL is an edge. Note that vertices B,C,G,F are shared by the two cubes. Alice and Bob plays a game where they take turns to put stickers on the vertices of the cubes that have not been occupied. Alice plays white stickers. Bob plays black stickers. The person who has four stickers on the same plane on either cube wins. Alice first places a white stone at E. Then Bob places a black stone at B. Then Alice places a white stone at H. Then Bob places a black stone at D. Then Alice places a white stone at I. Then Bob places a black stone at G. Then Alice places a white stone at K. Where should Bob play next?",864 "solution": "A, C, F",865 "is_unique_solution": false,866 "verdict": "fork",867 "next_player": "Bob",868 "currect_board_visualization": "...B------*------*\n../|...../|...../|\n./.|..../.|..../.|\n*------B------W..|\n|..W---|--B...|..*\n|./....|./....|./\n|/.....|/.....|/\nW------*------W\n",869 "board_visualization": "...D------C------J\n../|...../|...../|\n./.|..../.|..../.|\nA------B------I..|\n|..H---|--G...|..L\n|./....|./....|./\n|/.....|/.....|/\nE------F------K\n",870 "problem_number": 86871 },872 {873 "problem": "Alice and Bob are playing a game on two adjacent cubes. ABCD forms the top rectangle in the first cube and BIJC forms the top rectangle in the second cube. EFGH forms the bottom rectangle in the first cube and FKLG forms the bottom rectangle in the second cube. AE is an edge, BF is an edge, CG is an edge, DH is an edge, IK is an edge, and JL is an edge. Note that vertices B,C,G,F are shared by the two cubes. Alice and Bob plays a game where they take turns to put stickers on the vertices of the cubes that have not been occupied. Alice plays white stickers. Bob plays black stickers. The person who has four stickers on the same plane on either cube wins. Alice first places a white stone at D. Then Bob places a black stone at C. Then Alice places a white stone at E. Then Bob places a black stone at F. Then Alice places a white stone at G. Then Bob places a black stone at L. Then Alice places a white stone at I. Where should Bob play next?",874 "solution": "B, J, K",875 "is_unique_solution": false,876 "verdict": "fork",877 "next_player": "Bob",878 "currect_board_visualization": "...W------B------*\n../|...../|...../|\n./.|..../.|..../.|\n*------*------W..|\n|..*---|--W...|..B\n|./....|./....|./\n|/.....|/.....|/\nW------B------*\n",879 "board_visualization": "...D------C------J\n../|...../|...../|\n./.|..../.|..../.|\nA------B------I..|\n|..H---|--G...|..L\n|./....|./....|./\n|/.....|/.....|/\nE------F------K\n",880 "problem_number": 87881 },882 {883 "problem": "Alice and Bob are playing a game on two adjacent cubes. ABCD forms the top rectangle in the first cube and BIJC forms the top rectangle in the second cube. EFGH forms the bottom rectangle in the first cube and FKLG forms the bottom rectangle in the second cube. AE is an edge, BF is an edge, CG is an edge, DH is an edge, IK is an edge, and JL is an edge. Note that vertices B,C,G,F are shared by the two cubes. Alice and Bob plays a game where they take turns to put stickers on the vertices of the cubes that have not been occupied. Alice plays white stickers. Bob plays black stickers. The person who has four stickers on the same plane on either cube wins. Alice first places a white stone at A. Then Bob places a black stone at B. Then Alice places a white stone at E. Then Bob places a black stone at G. Then Alice places a white stone at I. Then Bob places a black stone at J. Then Alice places a white stone at K. Where should Bob play next?",884 "solution": "C, F, L",885 "is_unique_solution": false,886 "verdict": "fork",887 "next_player": "Bob",888 "currect_board_visualization": "...*------*------B\n../|...../|...../|\n./.|..../.|..../.|\nW------B------W..|\n|..*---|--B...|..*\n|./....|./....|./\n|/.....|/.....|/\nW------*------W\n",889 "board_visualization": "...D------C------J\n../|...../|...../|\n./.|..../.|..../.|\nA------B------I..|\n|..H---|--G...|..L\n|./....|./....|./\n|/.....|/.....|/\nE------F------K\n",890 "problem_number": 88891 },892 {893 "problem": "Alice and Bob are playing a game on two adjacent cubes. ABCD forms the top rectangle in the first cube and BIJC forms the top rectangle in the second cube. EFGH forms the bottom rectangle in the first cube and FKLG forms the bottom rectangle in the second cube. AE is an edge, BF is an edge, CG is an edge, DH is an edge, IK is an edge, and JL is an edge. Note that vertices B,C,G,F are shared by the two cubes. Alice and Bob plays a game where they take turns to put stickers on the vertices of the cubes that have not been occupied. Alice plays white stickers. Bob plays black stickers. The person who has four stickers on the same plane on either cube wins. Alice first places a white stone at D. Then Bob places a black stone at B. Then Alice places a white stone at H. Then Bob places a black stone at E. Then Alice places a white stone at J. Then Bob places a black stone at G. Then Alice places a white stone at K. Where should Bob play next?",894 "solution": "A, C, F",895 "is_unique_solution": false,896 "verdict": "fork",897 "next_player": "Bob",898 "currect_board_visualization": "...W------*------W\n../|...../|...../|\n./.|..../.|..../.|\n*------B------*..|\n|..W---|--B...|..*\n|./....|./....|./\n|/.....|/.....|/\nB------*------W\n",899 "board_visualization": "...D------C------J\n../|...../|...../|\n./.|..../.|..../.|\nA------B------I..|\n|..H---|--G...|..L\n|./....|./....|./\n|/.....|/.....|/\nE------F------K\n",900 "problem_number": 89901 }902]