Parallel-Reasoning/countdown_problems
0101
1[2 {3 "nums": [4 6,5 88,6 41,7 388 ],9 "target": 79,10 "solution": [11 "88-6=82",12 "41-38=3",13 "82-3=79"14 ],15 "optimal_path": "Current State: 79:[6, 88, 41, 38], Operations: []\nExploring Operation: 88-6=82, Resulting Numbers: [41, 38, 82]\nGenerated Node #2: [41, 38, 82] from Operation: 88-6=82\nCurrent State: 79:[41, 38, 82], Operations: ['88-6=82']\nExploring Operation: 41-38=3, Resulting Numbers: [82, 3]\nGenerated Node #3: [82, 3] from Operation: 41-38=3\nCurrent State: 79:[82, 3], Operations: ['88-6=82', '41-38=3']\nExploring Operation: 82-3=79, Resulting Numbers: [79]\n79,79 equal: Goal Reached\n",16 "start_size": 417 },18 {19 "nums": [20 37,21 62,22 80,23 8824 ],25 "target": 91,26 "solution": [27 "37+62=99",28 "88-80=8",29 "99-8=91"30 ],31 "optimal_path": "Current State: 91:[37, 62, 80, 88], Operations: []\nExploring Operation: 37+62=99, Resulting Numbers: [80, 88, 99]\nGenerated Node #2: [80, 88, 99] from Operation: 37+62=99\nCurrent State: 91:[80, 88, 99], Operations: ['37+62=99']\nExploring Operation: 88-80=8, Resulting Numbers: [99, 8]\nGenerated Node #3: [99, 8] from Operation: 88-80=8\nCurrent State: 91:[99, 8], Operations: ['37+62=99', '88-80=8']\nExploring Operation: 99-8=91, Resulting Numbers: [91]\n91,91 equal: Goal Reached\n",32 "start_size": 433 },34 {35 "nums": [36 34,37 57,38 24,39 8040 ],41 "target": 81,42 "solution": [43 "57-34=23",44 "24+80=104",45 "104-23=81"46 ],47 "optimal_path": "Current State: 81:[34, 57, 24, 80], Operations: []\nExploring Operation: 57-34=23, Resulting Numbers: [24, 80, 23]\nGenerated Node #2: [24, 80, 23] from Operation: 57-34=23\nCurrent State: 81:[24, 80, 23], Operations: ['57-34=23']\nExploring Operation: 24+80=104, Resulting Numbers: [23, 104]\nGenerated Node #3: [23, 104] from Operation: 24+80=104\nCurrent State: 81:[23, 104], Operations: ['57-34=23', '24+80=104']\nExploring Operation: 104-23=81, Resulting Numbers: [81]\n81,81 equal: Goal Reached\n",48 "start_size": 449 },50 {51 "nums": [52 41,53 63,54 31,55 6356 ],57 "target": 73,58 "solution": [59 "41+31=72",60 "63/63=1",61 "72+1=73"62 ],63 "optimal_path": "Current State: 73:[41, 63, 31, 63], Operations: []\nExploring Operation: 41+31=72, Resulting Numbers: [63, 63, 72]\nGenerated Node #2: [63, 63, 72] from Operation: 41+31=72\nCurrent State: 73:[63, 63, 72], Operations: ['41+31=72']\nExploring Operation: 63/63=1, Resulting Numbers: [72, 1]\nGenerated Node #3: [72, 1] from Operation: 63/63=1\nCurrent State: 73:[72, 1], Operations: ['41+31=72', '63/63=1']\nExploring Operation: 72+1=73, Resulting Numbers: [73]\n73,73 equal: Goal Reached\n",64 "start_size": 465 },66 {67 "nums": [68 94,69 47,70 28,71 9472 ],73 "target": 58,74 "solution": [75 "94*28=2632",76 "94+2632=2726",77 "2726/47=58"78 ],79 "optimal_path": "Current State: 58:[94, 47, 28, 94], Operations: []\nExploring Operation: 94*28=2632, Resulting Numbers: [47, 2632]\nGenerated Node #2: [47, 2632] from Operation: 94*28=2632\nCurrent State: 58:[47, 2632], Operations: ['94*28=2632']\nExploring Operation: 94+2632=2726, Resulting Numbers: [47, 2726]\nGenerated Node #3: [47, 2726] from Operation: 94+2632=2726\nCurrent State: 58:[47, 2726], Operations: ['94*28=2632', '94+2632=2726']\nExploring Operation: 2726/47=58, Resulting Numbers: [58]\n58,58 equal: Goal Reached\n",80 "start_size": 481 },82 {83 "nums": [84 4,85 31,86 22,87 5588 ],89 "target": 41,90 "solution": [91 "4*55=220",92 "220/22=10",93 "31+10=41"94 ],95 "optimal_path": "Current State: 41:[4, 31, 22, 55], Operations: []\nExploring Operation: 4*55=220, Resulting Numbers: [31, 22, 220]\nGenerated Node #2: [31, 22, 220] from Operation: 4*55=220\nCurrent State: 41:[31, 22, 220], Operations: ['4*55=220']\nExploring Operation: 220/22=10, Resulting Numbers: [31, 10]\nGenerated Node #3: [31, 10] from Operation: 220/22=10\nCurrent State: 41:[31, 10], Operations: ['4*55=220', '220/22=10']\nExploring Operation: 31+10=41, Resulting Numbers: [41]\n41,41 equal: Goal Reached\n",96 "start_size": 497 },98 {99 "nums": [100 33,101 92,102 82,103 30104 ],105 "target": 54,106 "solution": [107 "33*82=2706",108 "92*30=2760",109 "2760-2706=54"110 ],111 "optimal_path": "Current State: 54:[33, 92, 82, 30], Operations: []\nExploring Operation: 33*82=2706, Resulting Numbers: [92, 30, 2706]\nGenerated Node #2: [92, 30, 2706] from Operation: 33*82=2706\nCurrent State: 54:[92, 30, 2706], Operations: ['33*82=2706']\nExploring Operation: 92*30=2760, Resulting Numbers: [2706, 2760]\nGenerated Node #3: [2706, 2760] from Operation: 92*30=2760\nCurrent State: 54:[2706, 2760], Operations: ['33*82=2706', '92*30=2760']\nExploring Operation: 2760-2706=54, Resulting Numbers: [54]\n54,54 equal: Goal Reached\n",112 "start_size": 4113 },114 {115 "nums": [116 91,117 58,118 80,119 91120 ],121 "target": 22,122 "solution": [123 "91+58=149",124 "80+91=171",125 "171-149=22"126 ],127 "optimal_path": "Current State: 22:[91, 58, 80, 91], Operations: []\nExploring Operation: 91+58=149, Resulting Numbers: [80, 149]\nGenerated Node #2: [80, 149] from Operation: 91+58=149\nCurrent State: 22:[80, 149], Operations: ['91+58=149']\nExploring Operation: 80+91=171, Resulting Numbers: [149, 171]\nGenerated Node #3: [149, 171] from Operation: 80+91=171\nCurrent State: 22:[149, 171], Operations: ['91+58=149', '80+91=171']\nExploring Operation: 171-149=22, Resulting Numbers: [22]\n22,22 equal: Goal Reached\n",128 "start_size": 4129 },130 {131 "nums": [132 18,133 24,134 27,135 36136 ],137 "target": 69,138 "solution": [139 "24-18=6",140 "27+36=63",141 "6+63=69"142 ],143 "optimal_path": "Current State: 69:[18, 24, 27, 36], Operations: []\nExploring Operation: 24-18=6, Resulting Numbers: [27, 36, 6]\nGenerated Node #2: [27, 36, 6] from Operation: 24-18=6\nCurrent State: 69:[27, 36, 6], Operations: ['24-18=6']\nExploring Operation: 27+36=63, Resulting Numbers: [6, 63]\nGenerated Node #3: [6, 63] from Operation: 27+36=63\nCurrent State: 69:[6, 63], Operations: ['24-18=6', '27+36=63']\nExploring Operation: 6+63=69, Resulting Numbers: [69]\n69,69 equal: Goal Reached\n",144 "start_size": 4145 },146 {147 "nums": [148 39,149 24,150 6,151 68152 ],153 "target": 22,154 "solution": [155 "39-24=15",156 "6*15=90",157 "90-68=22"158 ],159 "optimal_path": "Current State: 22:[39, 24, 6, 68], Operations: []\nExploring Operation: 39-24=15, Resulting Numbers: [6, 68, 15]\nGenerated Node #2: [6, 68, 15] from Operation: 39-24=15\nCurrent State: 22:[6, 68, 15], Operations: ['39-24=15']\nExploring Operation: 6*15=90, Resulting Numbers: [68, 90]\nGenerated Node #3: [68, 90] from Operation: 6*15=90\nCurrent State: 22:[68, 90], Operations: ['39-24=15', '6*15=90']\nExploring Operation: 90-68=22, Resulting Numbers: [22]\n22,22 equal: Goal Reached\n",160 "start_size": 4161 },162 {163 "nums": [164 49,165 38,166 74,167 76168 ],169 "target": 23,170 "solution": [171 "74-49=25",172 "76/38=2",173 "25-2=23"174 ],175 "optimal_path": "Current State: 23:[49, 38, 74, 76], Operations: []\nExploring Operation: 74-49=25, Resulting Numbers: [38, 76, 25]\nGenerated Node #2: [38, 76, 25] from Operation: 74-49=25\nCurrent State: 23:[38, 76, 25], Operations: ['74-49=25']\nExploring Operation: 76/38=2, Resulting Numbers: [25, 2]\nGenerated Node #3: [25, 2] from Operation: 76/38=2\nCurrent State: 23:[25, 2], Operations: ['74-49=25', '76/38=2']\nExploring Operation: 25-2=23, Resulting Numbers: [23]\n23,23 equal: Goal Reached\n",176 "start_size": 4177 },178 {179 "nums": [180 79,181 17,182 80,183 93184 ],185 "target": 77,186 "solution": [187 "79+17=96",188 "80+93=173",189 "173-96=77"190 ],191 "optimal_path": "Current State: 77:[79, 17, 80, 93], Operations: []\nExploring Operation: 79+17=96, Resulting Numbers: [80, 93, 96]\nGenerated Node #2: [80, 93, 96] from Operation: 79+17=96\nCurrent State: 77:[80, 93, 96], Operations: ['79+17=96']\nExploring Operation: 80+93=173, Resulting Numbers: [96, 173]\nGenerated Node #3: [96, 173] from Operation: 80+93=173\nCurrent State: 77:[96, 173], Operations: ['79+17=96', '80+93=173']\nExploring Operation: 173-96=77, Resulting Numbers: [77]\n77,77 equal: Goal Reached\n",192 "start_size": 4193 },194 {195 "nums": [196 64,197 60,198 15,199 71200 ],201 "target": 68,202 "solution": [203 "64+60=124",204 "71-15=56",205 "124-56=68"206 ],207 "optimal_path": "Current State: 68:[64, 60, 15, 71], Operations: []\nExploring Operation: 64+60=124, Resulting Numbers: [15, 71, 124]\nGenerated Node #2: [15, 71, 124] from Operation: 64+60=124\nCurrent State: 68:[15, 71, 124], Operations: ['64+60=124']\nExploring Operation: 71-15=56, Resulting Numbers: [124, 56]\nGenerated Node #3: [124, 56] from Operation: 71-15=56\nCurrent State: 68:[124, 56], Operations: ['64+60=124', '71-15=56']\nExploring Operation: 124-56=68, Resulting Numbers: [68]\n68,68 equal: Goal Reached\n",208 "start_size": 4209 },210 {211 "nums": [212 76,213 93,214 52,215 90216 ],217 "target": 95,218 "solution": [219 "90-52=38",220 "76/38=2",221 "93+2=95"222 ],223 "optimal_path": "Current State: 95:[76, 93, 52, 90], Operations: []\nExploring Operation: 90-52=38, Resulting Numbers: [76, 93, 38]\nGenerated Node #2: [76, 93, 38] from Operation: 90-52=38\nCurrent State: 95:[76, 93, 38], Operations: ['90-52=38']\nExploring Operation: 76/38=2, Resulting Numbers: [93, 2]\nGenerated Node #3: [93, 2] from Operation: 76/38=2\nCurrent State: 95:[93, 2], Operations: ['90-52=38', '76/38=2']\nExploring Operation: 93+2=95, Resulting Numbers: [95]\n95,95 equal: Goal Reached\n",224 "start_size": 4225 },226 {227 "nums": [228 97,229 11,230 20,231 8232 ],233 "target": 11,234 "solution": [235 "97+11=108",236 "108-20=88",237 "88/8=11"238 ],239 "optimal_path": "Current State: 11:[97, 11, 20, 8], Operations: []\nExploring Operation: 97+11=108, Resulting Numbers: [20, 8, 108]\nGenerated Node #2: [20, 8, 108] from Operation: 97+11=108\nCurrent State: 11:[20, 8, 108], Operations: ['97+11=108']\nExploring Operation: 108-20=88, Resulting Numbers: [8, 88]\nGenerated Node #3: [8, 88] from Operation: 108-20=88\nCurrent State: 11:[8, 88], Operations: ['97+11=108', '108-20=88']\nExploring Operation: 88/8=11, Resulting Numbers: [11]\n11,11 equal: Goal Reached\n",240 "start_size": 4241 },242 {243 "nums": [244 17,245 4,246 80,247 85248 ],249 "target": 82,250 "solution": [251 "17+85=102",252 "80/4=20",253 "102-20=82"254 ],255 "optimal_path": "Current State: 82:[17, 4, 80, 85], Operations: []\nExploring Operation: 17+85=102, Resulting Numbers: [4, 80, 102]\nGenerated Node #2: [4, 80, 102] from Operation: 17+85=102\nCurrent State: 82:[4, 80, 102], Operations: ['17+85=102']\nExploring Operation: 80/4=20, Resulting Numbers: [102, 20]\nGenerated Node #3: [102, 20] from Operation: 80/4=20\nCurrent State: 82:[102, 20], Operations: ['17+85=102', '80/4=20']\nExploring Operation: 102-20=82, Resulting Numbers: [82]\n82,82 equal: Goal Reached\n",256 "start_size": 4257 },258 {259 "nums": [260 92,261 75,262 46,263 29264 ],265 "target": 23,266 "solution": [267 "92/46=2",268 "75-29=46",269 "46/2=23"270 ],271 "optimal_path": "Current State: 23:[92, 75, 46, 29], Operations: []\nExploring Operation: 92/46=2, Resulting Numbers: [75, 29, 2]\nGenerated Node #2: [75, 29, 2] from Operation: 92/46=2\nCurrent State: 23:[75, 29, 2], Operations: ['92/46=2']\nExploring Operation: 75-29=46, Resulting Numbers: [2, 46]\nGenerated Node #3: [2, 46] from Operation: 75-29=46\nCurrent State: 23:[2, 46], Operations: ['92/46=2', '75-29=46']\nExploring Operation: 46/2=23, Resulting Numbers: [23]\n23,23 equal: Goal Reached\n",272 "start_size": 4273 },274 {275 "nums": [276 70,277 24,278 5,279 22280 ],281 "target": 60,282 "solution": [283 "70/5=14",284 "24+22=46",285 "14+46=60"286 ],287 "optimal_path": "Current State: 60:[70, 24, 5, 22], Operations: []\nExploring Operation: 70/5=14, Resulting Numbers: [24, 22, 14]\nGenerated Node #2: [24, 22, 14] from Operation: 70/5=14\nCurrent State: 60:[24, 22, 14], Operations: ['70/5=14']\nExploring Operation: 24+22=46, Resulting Numbers: [14, 46]\nGenerated Node #3: [14, 46] from Operation: 24+22=46\nCurrent State: 60:[14, 46], Operations: ['70/5=14', '24+22=46']\nExploring Operation: 14+46=60, Resulting Numbers: [60]\n60,60 equal: Goal Reached\n",288 "start_size": 4289 },290 {291 "nums": [292 91,293 52,294 50,295 45296 ],297 "target": 13,298 "solution": [299 "91-50=41",300 "45-41=4",301 "52/4=13"302 ],303 "optimal_path": "Current State: 13:[91, 52, 50, 45], Operations: []\nExploring Operation: 91-50=41, Resulting Numbers: [52, 45, 41]\nGenerated Node #2: [52, 45, 41] from Operation: 91-50=41\nCurrent State: 13:[52, 45, 41], Operations: ['91-50=41']\nExploring Operation: 45-41=4, Resulting Numbers: [52, 4]\nGenerated Node #3: [52, 4] from Operation: 45-41=4\nCurrent State: 13:[52, 4], Operations: ['91-50=41', '45-41=4']\nExploring Operation: 52/4=13, Resulting Numbers: [13]\n13,13 equal: Goal Reached\n",304 "start_size": 4305 },306 {307 "nums": [308 82,309 95,310 21,311 80312 ],313 "target": 53,314 "solution": [315 "82-80=2",316 "21*2=42",317 "95-42=53"318 ],319 "optimal_path": "Current State: 53:[82, 95, 21, 80], Operations: []\nExploring Operation: 82-80=2, Resulting Numbers: [95, 21, 2]\nGenerated Node #2: [95, 21, 2] from Operation: 82-80=2\nCurrent State: 53:[95, 21, 2], Operations: ['82-80=2']\nExploring Operation: 21*2=42, Resulting Numbers: [95, 42]\nGenerated Node #3: [95, 42] from Operation: 21*2=42\nCurrent State: 53:[95, 42], Operations: ['82-80=2', '21*2=42']\nExploring Operation: 95-42=53, Resulting Numbers: [53]\n53,53 equal: Goal Reached\n",320 "start_size": 4321 },322 {323 "nums": [324 68,325 21,326 23,327 29328 ],329 "target": 83,330 "solution": [331 "68+21=89",332 "29-23=6",333 "89-6=83"334 ],335 "optimal_path": "Current State: 83:[68, 21, 23, 29], Operations: []\nExploring Operation: 68+21=89, Resulting Numbers: [23, 29, 89]\nGenerated Node #2: [23, 29, 89] from Operation: 68+21=89\nCurrent State: 83:[23, 29, 89], Operations: ['68+21=89']\nExploring Operation: 29-23=6, Resulting Numbers: [89, 6]\nGenerated Node #3: [89, 6] from Operation: 29-23=6\nCurrent State: 83:[89, 6], Operations: ['68+21=89', '29-23=6']\nExploring Operation: 89-6=83, Resulting Numbers: [83]\n83,83 equal: Goal Reached\n",336 "start_size": 4337 },338 {339 "nums": [340 40,341 95,342 70,343 75344 ],345 "target": 60,346 "solution": [347 "95-40=55",348 "75-70=5",349 "55+5=60"350 ],351 "optimal_path": "Current State: 60:[40, 95, 70, 75], Operations: []\nExploring Operation: 95-40=55, Resulting Numbers: [70, 75, 55]\nGenerated Node #2: [70, 75, 55] from Operation: 95-40=55\nCurrent State: 60:[70, 75, 55], Operations: ['95-40=55']\nExploring Operation: 75-70=5, Resulting Numbers: [55, 5]\nGenerated Node #3: [55, 5] from Operation: 75-70=5\nCurrent State: 60:[55, 5], Operations: ['95-40=55', '75-70=5']\nExploring Operation: 55+5=60, Resulting Numbers: [60]\n60,60 equal: Goal Reached\n",352 "start_size": 4353 },354 {355 "nums": [356 42,357 13,358 70,359 28360 ],361 "target": 17,362 "solution": [363 "42*13=546",364 "546-70=476",365 "476/28=17"366 ],367 "optimal_path": "Current State: 17:[42, 13, 70, 28], Operations: []\nExploring Operation: 42*13=546, Resulting Numbers: [70, 28, 546]\nGenerated Node #2: [70, 28, 546] from Operation: 42*13=546\nCurrent State: 17:[70, 28, 546], Operations: ['42*13=546']\nExploring Operation: 546-70=476, Resulting Numbers: [28, 476]\nGenerated Node #3: [28, 476] from Operation: 546-70=476\nCurrent State: 17:[28, 476], Operations: ['42*13=546', '546-70=476']\nExploring Operation: 476/28=17, Resulting Numbers: [17]\n17,17 equal: Goal Reached\n",368 "start_size": 4369 },370 {371 "nums": [372 87,373 34,374 71,375 2376 ],377 "target": 90,378 "solution": [379 "87+71=158",380 "34*2=68",381 "158-68=90"382 ],383 "optimal_path": "Current State: 90:[87, 34, 71, 2], Operations: []\nExploring Operation: 87+71=158, Resulting Numbers: [34, 2, 158]\nGenerated Node #2: [34, 2, 158] from Operation: 87+71=158\nCurrent State: 90:[34, 2, 158], Operations: ['87+71=158']\nExploring Operation: 34*2=68, Resulting Numbers: [158, 68]\nGenerated Node #3: [158, 68] from Operation: 34*2=68\nCurrent State: 90:[158, 68], Operations: ['87+71=158', '34*2=68']\nExploring Operation: 158-68=90, Resulting Numbers: [90]\n90,90 equal: Goal Reached\n",384 "start_size": 4385 },386 {387 "nums": [388 65,389 85,390 26,391 72392 ],393 "target": 67,394 "solution": [395 "85-72=13",396 "26/13=2",397 "65+2=67"398 ],399 "optimal_path": "Current State: 67:[65, 85, 26, 72], Operations: []\nExploring Operation: 85-72=13, Resulting Numbers: [65, 26, 13]\nGenerated Node #2: [65, 26, 13] from Operation: 85-72=13\nCurrent State: 67:[65, 26, 13], Operations: ['85-72=13']\nExploring Operation: 26/13=2, Resulting Numbers: [65, 2]\nGenerated Node #3: [65, 2] from Operation: 26/13=2\nCurrent State: 67:[65, 2], Operations: ['85-72=13', '26/13=2']\nExploring Operation: 65+2=67, Resulting Numbers: [67]\n67,67 equal: Goal Reached\n",400 "start_size": 4401 },402 {403 "nums": [404 81,405 32,406 96,407 48408 ],409 "target": 17,410 "solution": [411 "32*96=3072",412 "3072/48=64",413 "81-64=17"414 ],415 "optimal_path": "Current State: 17:[81, 32, 96, 48], Operations: []\nExploring Operation: 32*96=3072, Resulting Numbers: [81, 48, 3072]\nGenerated Node #2: [81, 48, 3072] from Operation: 32*96=3072\nCurrent State: 17:[81, 48, 3072], Operations: ['32*96=3072']\nExploring Operation: 3072/48=64, Resulting Numbers: [81, 64]\nGenerated Node #3: [81, 64] from Operation: 3072/48=64\nCurrent State: 17:[81, 64], Operations: ['32*96=3072', '3072/48=64']\nExploring Operation: 81-64=17, Resulting Numbers: [17]\n17,17 equal: Goal Reached\n",416 "start_size": 4417 },418 {419 "nums": [420 43,421 81,422 49,423 28424 ],425 "target": 17,426 "solution": [427 "81-43=38",428 "49-28=21",429 "38-21=17"430 ],431 "optimal_path": "Current State: 17:[43, 81, 49, 28], Operations: []\nExploring Operation: 81-43=38, Resulting Numbers: [49, 28, 38]\nGenerated Node #2: [49, 28, 38] from Operation: 81-43=38\nCurrent State: 17:[49, 28, 38], Operations: ['81-43=38']\nExploring Operation: 49-28=21, Resulting Numbers: [38, 21]\nGenerated Node #3: [38, 21] from Operation: 49-28=21\nCurrent State: 17:[38, 21], Operations: ['81-43=38', '49-28=21']\nExploring Operation: 38-21=17, Resulting Numbers: [17]\n17,17 equal: Goal Reached\n",432 "start_size": 4433 },434 {435 "nums": [436 3,437 70,438 90,439 14440 ],441 "target": 46,442 "solution": [443 "90-70=20",444 "3*20=60",445 "60-14=46"446 ],447 "optimal_path": "Current State: 46:[3, 70, 90, 14], Operations: []\nExploring Operation: 90-70=20, Resulting Numbers: [3, 14, 20]\nGenerated Node #2: [3, 14, 20] from Operation: 90-70=20\nCurrent State: 46:[3, 14, 20], Operations: ['90-70=20']\nExploring Operation: 3*20=60, Resulting Numbers: [14, 60]\nGenerated Node #3: [14, 60] from Operation: 3*20=60\nCurrent State: 46:[14, 60], Operations: ['90-70=20', '3*20=60']\nExploring Operation: 60-14=46, Resulting Numbers: [46]\n46,46 equal: Goal Reached\n",448 "start_size": 4449 },450 {451 "nums": [452 64,453 62,454 16,455 41456 ],457 "target": 27,458 "solution": [459 "64-62=2",460 "41-16=25",461 "2+25=27"462 ],463 "optimal_path": "Current State: 27:[64, 62, 16, 41], Operations: []\nExploring Operation: 64-62=2, Resulting Numbers: [16, 41, 2]\nGenerated Node #2: [16, 41, 2] from Operation: 64-62=2\nCurrent State: 27:[16, 41, 2], Operations: ['64-62=2']\nExploring Operation: 41-16=25, Resulting Numbers: [2, 25]\nGenerated Node #3: [2, 25] from Operation: 41-16=25\nCurrent State: 27:[2, 25], Operations: ['64-62=2', '41-16=25']\nExploring Operation: 2+25=27, Resulting Numbers: [27]\n27,27 equal: Goal Reached\n",464 "start_size": 4465 },466 {467 "nums": [468 48,469 6,470 49,471 3472 ],473 "target": 17,474 "solution": [475 "49-48=1",476 "6*3=18",477 "18-1=17"478 ],479 "optimal_path": "Current State: 17:[48, 6, 49, 3], Operations: []\nExploring Operation: 49-48=1, Resulting Numbers: [6, 3, 1]\nGenerated Node #2: [6, 3, 1] from Operation: 49-48=1\nCurrent State: 17:[6, 3, 1], Operations: ['49-48=1']\nExploring Operation: 6*3=18, Resulting Numbers: [1, 18]\nGenerated Node #3: [1, 18] from Operation: 6*3=18\nCurrent State: 17:[1, 18], Operations: ['49-48=1', '6*3=18']\nExploring Operation: 18-1=17, Resulting Numbers: [17]\n17,17 equal: Goal Reached\n",480 "start_size": 4481 },482 {483 "nums": [484 4,485 91,486 96,487 95488 ],489 "target": 95,490 "solution": [491 "4+91=95",492 "96-95=1",493 "95*1=95"494 ],495 "optimal_path": "Current State: 95:[4, 91, 96, 95], Operations: []\nExploring Operation: 4+91=95, Resulting Numbers: [96, 95, 95]\nGenerated Node #2: [96, 95, 95] from Operation: 4+91=95\nCurrent State: 95:[96, 95, 95], Operations: ['4+91=95']\nExploring Operation: 96-95=1, Resulting Numbers: [1]\n1,95 equal: Goal Reached\nExploring Operation: 95*1=95, Resulting Numbers: [95]\n95,95 equal: Goal Reached\n",496 "start_size": 4497 },498 {499 "nums": [500 48,501 4,502 60,503 85504 ],505 "target": 69,506 "solution": [507 "48-4=44",508 "85-60=25",509 "44+25=69"510 ],511 "optimal_path": "Current State: 69:[48, 4, 60, 85], Operations: []\nExploring Operation: 48-4=44, Resulting Numbers: [60, 85, 44]\nGenerated Node #2: [60, 85, 44] from Operation: 48-4=44\nCurrent State: 69:[60, 85, 44], Operations: ['48-4=44']\nExploring Operation: 85-60=25, Resulting Numbers: [44, 25]\nGenerated Node #3: [44, 25] from Operation: 85-60=25\nCurrent State: 69:[44, 25], Operations: ['48-4=44', '85-60=25']\nExploring Operation: 44+25=69, Resulting Numbers: [69]\n69,69 equal: Goal Reached\n",512 "start_size": 4513 },514 {515 "nums": [516 96,517 96,518 48,519 8520 ],521 "target": 72,522 "solution": [523 "96+96=192",524 "192/8=24",525 "48+24=72"526 ],527 "optimal_path": "Current State: 72:[96, 96, 48, 8], Operations: []\nExploring Operation: 96+96=192, Resulting Numbers: [48, 8, 192]\nGenerated Node #2: [48, 8, 192] from Operation: 96+96=192\nCurrent State: 72:[48, 8, 192], Operations: ['96+96=192']\nExploring Operation: 192/8=24, Resulting Numbers: [48, 24]\nGenerated Node #3: [48, 24] from Operation: 192/8=24\nCurrent State: 72:[48, 24], Operations: ['96+96=192', '192/8=24']\nExploring Operation: 48+24=72, Resulting Numbers: [72]\n72,72 equal: Goal Reached\n",528 "start_size": 4529 },530 {531 "nums": [532 64,533 37,534 16,535 31536 ],537 "target": 24,538 "solution": [539 "64/16=4",540 "37-31=6",541 "4*6=24"542 ],543 "optimal_path": "Current State: 24:[64, 37, 16, 31], Operations: []\nExploring Operation: 64/16=4, Resulting Numbers: [37, 31, 4]\nGenerated Node #2: [37, 31, 4] from Operation: 64/16=4\nCurrent State: 24:[37, 31, 4], Operations: ['64/16=4']\nExploring Operation: 37-31=6, Resulting Numbers: [4, 6]\nGenerated Node #3: [4, 6] from Operation: 37-31=6\nCurrent State: 24:[4, 6], Operations: ['64/16=4', '37-31=6']\nExploring Operation: 4*6=24, Resulting Numbers: [24]\n24,24 equal: Goal Reached\n",544 "start_size": 4545 },546 {547 "nums": [548 78,549 17,550 26,551 90552 ],553 "target": 76,554 "solution": [555 "78/26=3",556 "90-17=73",557 "3+73=76"558 ],559 "optimal_path": "Current State: 76:[78, 17, 26, 90], Operations: []\nExploring Operation: 78/26=3, Resulting Numbers: [17, 90, 3]\nGenerated Node #2: [17, 90, 3] from Operation: 78/26=3\nCurrent State: 76:[17, 90, 3], Operations: ['78/26=3']\nExploring Operation: 90-17=73, Resulting Numbers: [3, 73]\nGenerated Node #3: [3, 73] from Operation: 90-17=73\nCurrent State: 76:[3, 73], Operations: ['78/26=3', '90-17=73']\nExploring Operation: 3+73=76, Resulting Numbers: [76]\n76,76 equal: Goal Reached\n",560 "start_size": 4561 },562 {563 "nums": [564 8,565 68,566 74,567 42568 ],569 "target": 90,570 "solution": [571 "74-68=6",572 "8*6=48",573 "42+48=90"574 ],575 "optimal_path": "Current State: 90:[8, 68, 74, 42], Operations: []\nExploring Operation: 74-68=6, Resulting Numbers: [8, 42, 6]\nGenerated Node #2: [8, 42, 6] from Operation: 74-68=6\nCurrent State: 90:[8, 42, 6], Operations: ['74-68=6']\nExploring Operation: 8*6=48, Resulting Numbers: [42, 48]\nGenerated Node #3: [42, 48] from Operation: 8*6=48\nCurrent State: 90:[42, 48], Operations: ['74-68=6', '8*6=48']\nExploring Operation: 42+48=90, Resulting Numbers: [90]\n90,90 equal: Goal Reached\n",576 "start_size": 4577 },578 {579 "nums": [580 32,581 60,582 34,583 36584 ],585 "target": 94,586 "solution": [587 "32+60=92",588 "36-34=2",589 "92+2=94"590 ],591 "optimal_path": "Current State: 94:[32, 60, 34, 36], Operations: []\nExploring Operation: 32+60=92, Resulting Numbers: [34, 36, 92]\nGenerated Node #2: [34, 36, 92] from Operation: 32+60=92\nCurrent State: 94:[34, 36, 92], Operations: ['32+60=92']\nExploring Operation: 36-34=2, Resulting Numbers: [92, 2]\nGenerated Node #3: [92, 2] from Operation: 36-34=2\nCurrent State: 94:[92, 2], Operations: ['32+60=92', '36-34=2']\nExploring Operation: 92+2=94, Resulting Numbers: [94]\n94,94 equal: Goal Reached\n",592 "start_size": 4593 },594 {595 "nums": [596 37,597 65,598 84,599 57600 ],601 "target": 19,602 "solution": [603 "65-37=28",604 "84/28=3",605 "57/3=19"606 ],607 "optimal_path": "Current State: 19:[37, 65, 84, 57], Operations: []\nExploring Operation: 65-37=28, Resulting Numbers: [84, 57, 28]\nGenerated Node #2: [84, 57, 28] from Operation: 65-37=28\nCurrent State: 19:[84, 57, 28], Operations: ['65-37=28']\nExploring Operation: 84/28=3, Resulting Numbers: [57, 3]\nGenerated Node #3: [57, 3] from Operation: 84/28=3\nCurrent State: 19:[57, 3], Operations: ['65-37=28', '84/28=3']\nExploring Operation: 57/3=19, Resulting Numbers: [19]\n19,19 equal: Goal Reached\n",608 "start_size": 4609 },610 {611 "nums": [612 96,613 94,614 64,615 17616 ],617 "target": 49,618 "solution": [619 "96-94=2",620 "64-17=47",621 "2+47=49"622 ],623 "optimal_path": "Current State: 49:[96, 94, 64, 17], Operations: []\nExploring Operation: 96-94=2, Resulting Numbers: [64, 17, 2]\nGenerated Node #2: [64, 17, 2] from Operation: 96-94=2\nCurrent State: 49:[64, 17, 2], Operations: ['96-94=2']\nExploring Operation: 64-17=47, Resulting Numbers: [2, 47]\nGenerated Node #3: [2, 47] from Operation: 64-17=47\nCurrent State: 49:[2, 47], Operations: ['96-94=2', '64-17=47']\nExploring Operation: 2+47=49, Resulting Numbers: [49]\n49,49 equal: Goal Reached\n",624 "start_size": 4625 },626 {627 "nums": [628 33,629 6,630 44,631 82632 ],633 "target": 90,634 "solution": [635 "6*44=264",636 "264/33=8",637 "82+8=90"638 ],639 "optimal_path": "Current State: 90:[33, 6, 44, 82], Operations: []\nExploring Operation: 6*44=264, Resulting Numbers: [33, 82, 264]\nGenerated Node #2: [33, 82, 264] from Operation: 6*44=264\nCurrent State: 90:[33, 82, 264], Operations: ['6*44=264']\nExploring Operation: 264/33=8, Resulting Numbers: [82, 8]\nGenerated Node #3: [82, 8] from Operation: 264/33=8\nCurrent State: 90:[82, 8], Operations: ['6*44=264', '264/33=8']\nExploring Operation: 82+8=90, Resulting Numbers: [90]\n90,90 equal: Goal Reached\n",640 "start_size": 4641 },642 {643 "nums": [644 98,645 63,646 12,647 82648 ],649 "target": 45,650 "solution": [651 "82-12=70",652 "63*70=4410",653 "4410/98=45"654 ],655 "optimal_path": "Current State: 45:[98, 63, 12, 82], Operations: []\nExploring Operation: 82-12=70, Resulting Numbers: [98, 63, 70]\nGenerated Node #2: [98, 63, 70] from Operation: 82-12=70\nCurrent State: 45:[98, 63, 70], Operations: ['82-12=70']\nExploring Operation: 63*70=4410, Resulting Numbers: [98, 4410]\nGenerated Node #3: [98, 4410] from Operation: 63*70=4410\nCurrent State: 45:[98, 4410], Operations: ['82-12=70', '63*70=4410']\nExploring Operation: 4410/98=45, Resulting Numbers: [45]\n45,45 equal: Goal Reached\n",656 "start_size": 4657 },658 {659 "nums": [660 94,661 48,662 5,663 33664 ],665 "target": 84,666 "solution": [667 "94-48=46",668 "5+33=38",669 "46+38=84"670 ],671 "optimal_path": "Current State: 84:[94, 48, 5, 33], Operations: []\nExploring Operation: 94-48=46, Resulting Numbers: [5, 33, 46]\nGenerated Node #2: [5, 33, 46] from Operation: 94-48=46\nCurrent State: 84:[5, 33, 46], Operations: ['94-48=46']\nExploring Operation: 5+33=38, Resulting Numbers: [46, 38]\nGenerated Node #3: [46, 38] from Operation: 5+33=38\nCurrent State: 84:[46, 38], Operations: ['94-48=46', '5+33=38']\nExploring Operation: 46+38=84, Resulting Numbers: [84]\n84,84 equal: Goal Reached\n",672 "start_size": 4673 },674 {675 "nums": [676 4,677 72,678 74,679 8680 ],681 "target": 34,682 "solution": [683 "4*8=32",684 "74-72=2",685 "32+2=34"686 ],687 "optimal_path": "Current State: 34:[4, 72, 74, 8], Operations: []\nExploring Operation: 4*8=32, Resulting Numbers: [72, 74, 32]\nGenerated Node #2: [72, 74, 32] from Operation: 4*8=32\nCurrent State: 34:[72, 74, 32], Operations: ['4*8=32']\nExploring Operation: 74-72=2, Resulting Numbers: [32, 2]\nGenerated Node #3: [32, 2] from Operation: 74-72=2\nCurrent State: 34:[32, 2], Operations: ['4*8=32', '74-72=2']\nExploring Operation: 32+2=34, Resulting Numbers: [34]\n34,34 equal: Goal Reached\n",688 "start_size": 4689 },690 {691 "nums": [692 24,693 45,694 77,695 56696 ],697 "target": 31,698 "solution": [699 "56-45=11",700 "77/11=7",701 "24+7=31"702 ],703 "optimal_path": "Current State: 31:[24, 45, 77, 56], Operations: []\nExploring Operation: 56-45=11, Resulting Numbers: [24, 77, 11]\nGenerated Node #2: [24, 77, 11] from Operation: 56-45=11\nCurrent State: 31:[24, 77, 11], Operations: ['56-45=11']\nExploring Operation: 77/11=7, Resulting Numbers: [24, 7]\nGenerated Node #3: [24, 7] from Operation: 77/11=7\nCurrent State: 31:[24, 7], Operations: ['56-45=11', '77/11=7']\nExploring Operation: 24+7=31, Resulting Numbers: [31]\n31,31 equal: Goal Reached\n",704 "start_size": 4705 },706 {707 "nums": [708 66,709 63,710 15,711 71712 ],713 "target": 66,714 "solution": [715 "66-63=3",716 "15/3=5",717 "71-5=66"718 ],719 "optimal_path": "Current State: 66:[66, 63, 15, 71], Operations: []\nExploring Operation: 66-63=3, Resulting Numbers: [15, 71, 3]\nGenerated Node #2: [15, 71, 3] from Operation: 66-63=3\nCurrent State: 66:[15, 71, 3], Operations: ['66-63=3']\nExploring Operation: 15/3=5, Resulting Numbers: [71, 5]\nGenerated Node #3: [71, 5] from Operation: 15/3=5\nCurrent State: 66:[71, 5], Operations: ['66-63=3', '15/3=5']\nExploring Operation: 71-5=66, Resulting Numbers: [66]\n66,66 equal: Goal Reached\n",720 "start_size": 4721 },722 {723 "nums": [724 87,725 3,726 30,727 82728 ],729 "target": 22,730 "solution": [731 "87+3=90",732 "30+82=112",733 "112-90=22"734 ],735 "optimal_path": "Current State: 22:[87, 3, 30, 82], Operations: []\nExploring Operation: 87+3=90, Resulting Numbers: [30, 82, 90]\nGenerated Node #2: [30, 82, 90] from Operation: 87+3=90\nCurrent State: 22:[30, 82, 90], Operations: ['87+3=90']\nExploring Operation: 30+82=112, Resulting Numbers: [90, 112]\nGenerated Node #3: [90, 112] from Operation: 30+82=112\nCurrent State: 22:[90, 112], Operations: ['87+3=90', '30+82=112']\nExploring Operation: 112-90=22, Resulting Numbers: [22]\n22,22 equal: Goal Reached\n",736 "start_size": 4737 },738 {739 "nums": [740 57,741 99,742 56,743 22744 ],745 "target": 78,746 "solution": [747 "57+99=156",748 "56+22=78",749 "156-78=78"750 ],751 "optimal_path": "Current State: 78:[57, 99, 56, 22], Operations: []\nExploring Operation: 57+99=156, Resulting Numbers: [56, 22, 156]\nGenerated Node #2: [56, 22, 156] from Operation: 57+99=156\nCurrent State: 78:[56, 22, 156], Operations: ['57+99=156']\nExploring Operation: 56+22=78, Resulting Numbers: [156, 78]\nGenerated Node #3: [156, 78] from Operation: 56+22=78\nCurrent State: 78:[156, 78], Operations: ['57+99=156', '56+22=78']\nExploring Operation: 156-78=78, Resulting Numbers: [78]\n78,78 equal: Goal Reached\n",752 "start_size": 4753 },754 {755 "nums": [756 30,757 46,758 10,759 11760 ],761 "target": 75,762 "solution": [763 "30+46=76",764 "11-10=1",765 "76-1=75"766 ],767 "optimal_path": "Current State: 75:[30, 46, 10, 11], Operations: []\nExploring Operation: 30+46=76, Resulting Numbers: [10, 11, 76]\nGenerated Node #2: [10, 11, 76] from Operation: 30+46=76\nCurrent State: 75:[10, 11, 76], Operations: ['30+46=76']\nExploring Operation: 11-10=1, Resulting Numbers: [76, 1]\nGenerated Node #3: [76, 1] from Operation: 11-10=1\nCurrent State: 75:[76, 1], Operations: ['30+46=76', '11-10=1']\nExploring Operation: 76-1=75, Resulting Numbers: [75]\n75,75 equal: Goal Reached\n",768 "start_size": 4769 },770 {771 "nums": [772 83,773 37,774 27,775 67776 ],777 "target": 48,778 "solution": [779 "83-37=46",780 "27+67=94",781 "94-46=48"782 ],783 "optimal_path": "Current State: 48:[83, 37, 27, 67], Operations: []\nExploring Operation: 83-37=46, Resulting Numbers: [27, 67, 46]\nGenerated Node #2: [27, 67, 46] from Operation: 83-37=46\nCurrent State: 48:[27, 67, 46], Operations: ['83-37=46']\nExploring Operation: 27+67=94, Resulting Numbers: [46, 94]\nGenerated Node #3: [46, 94] from Operation: 27+67=94\nCurrent State: 48:[46, 94], Operations: ['83-37=46', '27+67=94']\nExploring Operation: 94-46=48, Resulting Numbers: [48]\n48,48 equal: Goal Reached\n",784 "start_size": 4785 },786 {787 "nums": [788 39,789 37,790 11,791 16792 ],793 "target": 88,794 "solution": [795 "39-37=2",796 "11*16=176",797 "176/2=88"798 ],799 "optimal_path": "Current State: 88:[39, 37, 11, 16], Operations: []\nExploring Operation: 39-37=2, Resulting Numbers: [11, 16, 2]\nGenerated Node #2: [11, 16, 2] from Operation: 39-37=2\nCurrent State: 88:[11, 16, 2], Operations: ['39-37=2']\nExploring Operation: 11*16=176, Resulting Numbers: [2, 176]\nGenerated Node #3: [2, 176] from Operation: 11*16=176\nCurrent State: 88:[2, 176], Operations: ['39-37=2', '11*16=176']\nExploring Operation: 176/2=88, Resulting Numbers: [88]\n88,88 equal: Goal Reached\n",800 "start_size": 4801 },802 {803 "nums": [804 77,805 86,806 97,807 2808 ],809 "target": 23,810 "solution": [811 "97-77=20",812 "86/2=43",813 "43-20=23"814 ],815 "optimal_path": "Current State: 23:[77, 86, 97, 2], Operations: []\nExploring Operation: 97-77=20, Resulting Numbers: [86, 2, 20]\nGenerated Node #2: [86, 2, 20] from Operation: 97-77=20\nCurrent State: 23:[86, 2, 20], Operations: ['97-77=20']\nExploring Operation: 86/2=43, Resulting Numbers: [20, 43]\nGenerated Node #3: [20, 43] from Operation: 86/2=43\nCurrent State: 23:[20, 43], Operations: ['97-77=20', '86/2=43']\nExploring Operation: 43-20=23, Resulting Numbers: [23]\n23,23 equal: Goal Reached\n",816 "start_size": 4817 },818 {819 "nums": [820 28,821 67,822 30,823 18824 ],825 "target": 70,826 "solution": [827 "28-18=10",828 "30/10=3",829 "67+3=70"830 ],831 "optimal_path": "Current State: 70:[28, 67, 30, 18], Operations: []\nExploring Operation: 28-18=10, Resulting Numbers: [67, 30, 10]\nGenerated Node #2: [67, 30, 10] from Operation: 28-18=10\nCurrent State: 70:[67, 30, 10], Operations: ['28-18=10']\nExploring Operation: 30/10=3, Resulting Numbers: [67, 3]\nGenerated Node #3: [67, 3] from Operation: 30/10=3\nCurrent State: 70:[67, 3], Operations: ['28-18=10', '30/10=3']\nExploring Operation: 67+3=70, Resulting Numbers: [70]\n70,70 equal: Goal Reached\n",832 "start_size": 4833 },834 {835 "nums": [836 68,837 38,838 47,839 27840 ],841 "target": 65,842 "solution": [843 "47-38=9",844 "27/9=3",845 "68-3=65"846 ],847 "optimal_path": "Current State: 65:[68, 38, 47, 27], Operations: []\nExploring Operation: 47-38=9, Resulting Numbers: [68, 27, 9]\nGenerated Node #2: [68, 27, 9] from Operation: 47-38=9\nCurrent State: 65:[68, 27, 9], Operations: ['47-38=9']\nExploring Operation: 27/9=3, Resulting Numbers: [68, 3]\nGenerated Node #3: [68, 3] from Operation: 27/9=3\nCurrent State: 65:[68, 3], Operations: ['47-38=9', '27/9=3']\nExploring Operation: 68-3=65, Resulting Numbers: [65]\n65,65 equal: Goal Reached\n",848 "start_size": 4849 },850 {851 "nums": [852 76,853 33,854 24,855 18856 ],857 "target": 38,858 "solution": [859 "33-24=9",860 "76*9=684",861 "684/18=38"862 ],863 "optimal_path": "Current State: 38:[76, 33, 24, 18], Operations: []\nExploring Operation: 33-24=9, Resulting Numbers: [76, 18, 9]\nGenerated Node #2: [76, 18, 9] from Operation: 33-24=9\nCurrent State: 38:[76, 18, 9], Operations: ['33-24=9']\nExploring Operation: 76*9=684, Resulting Numbers: [18, 684]\nGenerated Node #3: [18, 684] from Operation: 76*9=684\nCurrent State: 38:[18, 684], Operations: ['33-24=9', '76*9=684']\nExploring Operation: 684/18=38, Resulting Numbers: [38]\n38,38 equal: Goal Reached\n",864 "start_size": 4865 },866 {867 "nums": [868 99,869 35,870 9,871 67872 ],873 "target": 43,874 "solution": [875 "99/9=11",876 "67-35=32",877 "11+32=43"878 ],879 "optimal_path": "Current State: 43:[99, 35, 9, 67], Operations: []\nExploring Operation: 99/9=11, Resulting Numbers: [35, 67, 11]\nGenerated Node #2: [35, 67, 11] from Operation: 99/9=11\nCurrent State: 43:[35, 67, 11], Operations: ['99/9=11']\nExploring Operation: 67-35=32, Resulting Numbers: [11, 32]\nGenerated Node #3: [11, 32] from Operation: 67-35=32\nCurrent State: 43:[11, 32], Operations: ['99/9=11', '67-35=32']\nExploring Operation: 11+32=43, Resulting Numbers: [43]\n43,43 equal: Goal Reached\n",880 "start_size": 4881 },882 {883 "nums": [884 93,885 10,886 89,887 9888 ],889 "target": 23,890 "solution": [891 "93+10=103",892 "89-9=80",893 "103-80=23"894 ],895 "optimal_path": "Current State: 23:[93, 10, 89, 9], Operations: []\nExploring Operation: 93+10=103, Resulting Numbers: [89, 9, 103]\nGenerated Node #2: [89, 9, 103] from Operation: 93+10=103\nCurrent State: 23:[89, 9, 103], Operations: ['93+10=103']\nExploring Operation: 89-9=80, Resulting Numbers: [103, 80]\nGenerated Node #3: [103, 80] from Operation: 89-9=80\nCurrent State: 23:[103, 80], Operations: ['93+10=103', '89-9=80']\nExploring Operation: 103-80=23, Resulting Numbers: [23]\n23,23 equal: Goal Reached\n",896 "start_size": 4897 },898 {899 "nums": [900 69,901 92,902 92,903 60904 ],905 "target": 12,906 "solution": [907 "92*60=5520",908 "5520/69=80",909 "92-80=12"910 ],911 "optimal_path": "Current State: 12:[69, 92, 92, 60], Operations: []\nExploring Operation: 92*60=5520, Resulting Numbers: [69, 5520]\nGenerated Node #2: [69, 5520] from Operation: 92*60=5520\nCurrent State: 12:[69, 5520], Operations: ['92*60=5520']\nExploring Operation: 5520/69=80, Resulting Numbers: [80]\n80,12 equal: Goal Reached\nExploring Operation: 92-80=12, Resulting Numbers: [12]\n12,12 equal: Goal Reached\n",912 "start_size": 4913 },914 {915 "nums": [916 25,917 2,918 88,919 80920 ],921 "target": 97,922 "solution": [923 "88-25=63",924 "2*80=160",925 "160-63=97"926 ],927 "optimal_path": "Current State: 97:[25, 2, 88, 80], Operations: []\nExploring Operation: 88-25=63, Resulting Numbers: [2, 80, 63]\nGenerated Node #2: [2, 80, 63] from Operation: 88-25=63\nCurrent State: 97:[2, 80, 63], Operations: ['88-25=63']\nExploring Operation: 2*80=160, Resulting Numbers: [63, 160]\nGenerated Node #3: [63, 160] from Operation: 2*80=160\nCurrent State: 97:[63, 160], Operations: ['88-25=63', '2*80=160']\nExploring Operation: 160-63=97, Resulting Numbers: [97]\n97,97 equal: Goal Reached\n",928 "start_size": 4929 },930 {931 "nums": [932 68,933 35,934 46,935 75936 ],937 "target": 77,938 "solution": [939 "75-68=7",940 "46-35=11",941 "7*11=77"942 ],943 "optimal_path": "Current State: 77:[68, 35, 46, 75], Operations: []\nExploring Operation: 75-68=7, Resulting Numbers: [35, 46, 7]\nGenerated Node #2: [35, 46, 7] from Operation: 75-68=7\nCurrent State: 77:[35, 46, 7], Operations: ['75-68=7']\nExploring Operation: 46-35=11, Resulting Numbers: [7, 11]\nGenerated Node #3: [7, 11] from Operation: 46-35=11\nCurrent State: 77:[7, 11], Operations: ['75-68=7', '46-35=11']\nExploring Operation: 7*11=77, Resulting Numbers: [77]\n77,77 equal: Goal Reached\n",944 "start_size": 4945 },946 {947 "nums": [948 33,949 90,950 76,951 9952 ],953 "target": 10,954 "solution": [955 "90-33=57",956 "76-9=67",957 "67-57=10"958 ],959 "optimal_path": "Current State: 10:[33, 90, 76, 9], Operations: []\nExploring Operation: 90-33=57, Resulting Numbers: [76, 9, 57]\nGenerated Node #2: [76, 9, 57] from Operation: 90-33=57\nCurrent State: 10:[76, 9, 57], Operations: ['90-33=57']\nExploring Operation: 76-9=67, Resulting Numbers: [57, 67]\nGenerated Node #3: [57, 67] from Operation: 76-9=67\nCurrent State: 10:[57, 67], Operations: ['90-33=57', '76-9=67']\nExploring Operation: 67-57=10, Resulting Numbers: [10]\n10,10 equal: Goal Reached\n",960 "start_size": 4961 },962 {963 "nums": [964 82,965 39,966 78,967 44968 ],969 "target": 77,970 "solution": [971 "82-39=43",972 "78-44=34",973 "43+34=77"974 ],975 "optimal_path": "Current State: 77:[82, 39, 78, 44], Operations: []\nExploring Operation: 82-39=43, Resulting Numbers: [78, 44, 43]\nGenerated Node #2: [78, 44, 43] from Operation: 82-39=43\nCurrent State: 77:[78, 44, 43], Operations: ['82-39=43']\nExploring Operation: 78-44=34, Resulting Numbers: [43, 34]\nGenerated Node #3: [43, 34] from Operation: 78-44=34\nCurrent State: 77:[43, 34], Operations: ['82-39=43', '78-44=34']\nExploring Operation: 43+34=77, Resulting Numbers: [77]\n77,77 equal: Goal Reached\n",976 "start_size": 4977 },978 {979 "nums": [980 84,981 35,982 84,983 3984 ],985 "target": 70,986 "solution": [987 "84/84=1",988 "3-1=2",989 "35*2=70"990 ],991 "optimal_path": "Current State: 70:[84, 35, 84, 3], Operations: []\nExploring Operation: 84/84=1, Resulting Numbers: [35, 3, 1]\nGenerated Node #2: [35, 3, 1] from Operation: 84/84=1\nCurrent State: 70:[35, 3, 1], Operations: ['84/84=1']\nExploring Operation: 3-1=2, Resulting Numbers: [35, 2]\nGenerated Node #3: [35, 2] from Operation: 3-1=2\nCurrent State: 70:[35, 2], Operations: ['84/84=1', '3-1=2']\nExploring Operation: 35*2=70, Resulting Numbers: [70]\n70,70 equal: Goal Reached\n",992 "start_size": 4993 },994 {995 "nums": [996 33,997 77,998 73,999 471000 ],1001 "target": 10,1002 "solution": [1003 "33+77=110",1004 "73+47=120",1005 "120-110=10"1006 ],1007 "optimal_path": "Current State: 10:[33, 77, 73, 47], Operations: []\nExploring Operation: 33+77=110, Resulting Numbers: [73, 47, 110]\nGenerated Node #2: [73, 47, 110] from Operation: 33+77=110\nCurrent State: 10:[73, 47, 110], Operations: ['33+77=110']\nExploring Operation: 73+47=120, Resulting Numbers: [110, 120]\nGenerated Node #3: [110, 120] from Operation: 73+47=120\nCurrent State: 10:[110, 120], Operations: ['33+77=110', '73+47=120']\nExploring Operation: 120-110=10, Resulting Numbers: [10]\n10,10 equal: Goal Reached\n",1008 "start_size": 41009 },1010 {1011 "nums": [1012 3,1013 52,1014 43,1015 341016 ],1017 "target": 43,1018 "solution": [1019 "3*43=129",1020 "52+34=86",1021 "129-86=43"1022 ],1023 "optimal_path": "Current State: 43:[3, 52, 43, 34], Operations: []\nExploring Operation: 3*43=129, Resulting Numbers: [52, 34, 129]\nGenerated Node #2: [52, 34, 129] from Operation: 3*43=129\nCurrent State: 43:[52, 34, 129], Operations: ['3*43=129']\nExploring Operation: 52+34=86, Resulting Numbers: [129, 86]\nGenerated Node #3: [129, 86] from Operation: 52+34=86\nCurrent State: 43:[129, 86], Operations: ['3*43=129', '52+34=86']\nExploring Operation: 129-86=43, Resulting Numbers: [43]\n43,43 equal: Goal Reached\n",1024 "start_size": 41025 },1026 {1027 "nums": [1028 36,1029 79,1030 10,1031 941032 ],1033 "target": 41,1034 "solution": [1035 "79-36=43",1036 "94-10=84",1037 "84-43=41"1038 ],1039 "optimal_path": "Current State: 41:[36, 79, 10, 94], Operations: []\nExploring Operation: 79-36=43, Resulting Numbers: [10, 94, 43]\nGenerated Node #2: [10, 94, 43] from Operation: 79-36=43\nCurrent State: 41:[10, 94, 43], Operations: ['79-36=43']\nExploring Operation: 94-10=84, Resulting Numbers: [43, 84]\nGenerated Node #3: [43, 84] from Operation: 94-10=84\nCurrent State: 41:[43, 84], Operations: ['79-36=43', '94-10=84']\nExploring Operation: 84-43=41, Resulting Numbers: [41]\n41,41 equal: Goal Reached\n",1040 "start_size": 41041 },1042 {1043 "nums": [1044 28,1045 43,1046 90,1047 691048 ],1049 "target": 92,1050 "solution": [1051 "28+43=71",1052 "90-69=21",1053 "71+21=92"1054 ],1055 "optimal_path": "Current State: 92:[28, 43, 90, 69], Operations: []\nExploring Operation: 28+43=71, Resulting Numbers: [90, 69, 71]\nGenerated Node #2: [90, 69, 71] from Operation: 28+43=71\nCurrent State: 92:[90, 69, 71], Operations: ['28+43=71']\nExploring Operation: 90-69=21, Resulting Numbers: [71, 21]\nGenerated Node #3: [71, 21] from Operation: 90-69=21\nCurrent State: 92:[71, 21], Operations: ['28+43=71', '90-69=21']\nExploring Operation: 71+21=92, Resulting Numbers: [92]\n92,92 equal: Goal Reached\n",1056 "start_size": 41057 },1058 {1059 "nums": [1060 49,1061 37,1062 35,1063 61064 ],1065 "target": 70,1066 "solution": [1067 "49-37=12",1068 "35*12=420",1069 "420/6=70"1070 ],1071 "optimal_path": "Current State: 70:[49, 37, 35, 6], Operations: []\nExploring Operation: 49-37=12, Resulting Numbers: [35, 6, 12]\nGenerated Node #2: [35, 6, 12] from Operation: 49-37=12\nCurrent State: 70:[35, 6, 12], Operations: ['49-37=12']\nExploring Operation: 35*12=420, Resulting Numbers: [6, 420]\nGenerated Node #3: [6, 420] from Operation: 35*12=420\nCurrent State: 70:[6, 420], Operations: ['49-37=12', '35*12=420']\nExploring Operation: 420/6=70, Resulting Numbers: [70]\n70,70 equal: Goal Reached\n",1072 "start_size": 41073 },1074 {1075 "nums": [1076 16,1077 66,1078 99,1079 441080 ],1081 "target": 60,1082 "solution": [1083 "66+99=165",1084 "16*165=2640",1085 "2640/44=60"1086 ],1087 "optimal_path": "Current State: 60:[16, 66, 99, 44], Operations: []\nExploring Operation: 66+99=165, Resulting Numbers: [16, 44, 165]\nGenerated Node #2: [16, 44, 165] from Operation: 66+99=165\nCurrent State: 60:[16, 44, 165], Operations: ['66+99=165']\nExploring Operation: 16*165=2640, Resulting Numbers: [44, 2640]\nGenerated Node #3: [44, 2640] from Operation: 16*165=2640\nCurrent State: 60:[44, 2640], Operations: ['66+99=165', '16*165=2640']\nExploring Operation: 2640/44=60, Resulting Numbers: [60]\n60,60 equal: Goal Reached\n",1088 "start_size": 41089 },1090 {1091 "nums": [1092 82,1093 3,1094 80,1095 901096 ],1097 "target": 13,1098 "solution": [1099 "90-82=8",1100 "80/8=10",1101 "3+10=13"1102 ],1103 "optimal_path": "Current State: 13:[82, 3, 80, 90], Operations: []\nExploring Operation: 90-82=8, Resulting Numbers: [3, 80, 8]\nGenerated Node #2: [3, 80, 8] from Operation: 90-82=8\nCurrent State: 13:[3, 80, 8], Operations: ['90-82=8']\nExploring Operation: 80/8=10, Resulting Numbers: [3, 10]\nGenerated Node #3: [3, 10] from Operation: 80/8=10\nCurrent State: 13:[3, 10], Operations: ['90-82=8', '80/8=10']\nExploring Operation: 3+10=13, Resulting Numbers: [13]\n13,13 equal: Goal Reached\n",1104 "start_size": 41105 },1106 {1107 "nums": [1108 51,1109 97,1110 9,1111 851112 ],1113 "target": 72,1114 "solution": [1115 "51+97=148",1116 "85-9=76",1117 "148-76=72"1118 ],1119 "optimal_path": "Current State: 72:[51, 97, 9, 85], Operations: []\nExploring Operation: 51+97=148, Resulting Numbers: [9, 85, 148]\nGenerated Node #2: [9, 85, 148] from Operation: 51+97=148\nCurrent State: 72:[9, 85, 148], Operations: ['51+97=148']\nExploring Operation: 85-9=76, Resulting Numbers: [148, 76]\nGenerated Node #3: [148, 76] from Operation: 85-9=76\nCurrent State: 72:[148, 76], Operations: ['51+97=148', '85-9=76']\nExploring Operation: 148-76=72, Resulting Numbers: [72]\n72,72 equal: Goal Reached\n",1120 "start_size": 41121 },1122 {1123 "nums": [1124 57,1125 93,1126 66,1127 311128 ],1129 "target": 53,1130 "solution": [1131 "57+93=150",1132 "66+31=97",1133 "150-97=53"1134 ],1135 "optimal_path": "Current State: 53:[57, 93, 66, 31], Operations: []\nExploring Operation: 57+93=150, Resulting Numbers: [66, 31, 150]\nGenerated Node #2: [66, 31, 150] from Operation: 57+93=150\nCurrent State: 53:[66, 31, 150], Operations: ['57+93=150']\nExploring Operation: 66+31=97, Resulting Numbers: [150, 97]\nGenerated Node #3: [150, 97] from Operation: 66+31=97\nCurrent State: 53:[150, 97], Operations: ['57+93=150', '66+31=97']\nExploring Operation: 150-97=53, Resulting Numbers: [53]\n53,53 equal: Goal Reached\n",1136 "start_size": 41137 },1138 {1139 "nums": [1140 31,1141 84,1142 44,1143 291144 ],1145 "target": 68,1146 "solution": [1147 "84-31=53",1148 "44-29=15",1149 "53+15=68"1150 ],1151 "optimal_path": "Current State: 68:[31, 84, 44, 29], Operations: []\nExploring Operation: 84-31=53, Resulting Numbers: [44, 29, 53]\nGenerated Node #2: [44, 29, 53] from Operation: 84-31=53\nCurrent State: 68:[44, 29, 53], Operations: ['84-31=53']\nExploring Operation: 44-29=15, Resulting Numbers: [53, 15]\nGenerated Node #3: [53, 15] from Operation: 44-29=15\nCurrent State: 68:[53, 15], Operations: ['84-31=53', '44-29=15']\nExploring Operation: 53+15=68, Resulting Numbers: [68]\n68,68 equal: Goal Reached\n",1152 "start_size": 41153 },1154 {1155 "nums": [1156 9,1157 95,1158 61,1159 411160 ],1161 "target": 67,1162 "solution": [1163 "95-41=54",1164 "54/9=6",1165 "61+6=67"1166 ],1167 "optimal_path": "Current State: 67:[9, 95, 61, 41], Operations: []\nExploring Operation: 95-41=54, Resulting Numbers: [9, 61, 54]\nGenerated Node #2: [9, 61, 54] from Operation: 95-41=54\nCurrent State: 67:[9, 61, 54], Operations: ['95-41=54']\nExploring Operation: 54/9=6, Resulting Numbers: [61, 6]\nGenerated Node #3: [61, 6] from Operation: 54/9=6\nCurrent State: 67:[61, 6], Operations: ['95-41=54', '54/9=6']\nExploring Operation: 61+6=67, Resulting Numbers: [67]\n67,67 equal: Goal Reached\n",1168 "start_size": 41169 },1170 {1171 "nums": [1172 65,1173 48,1174 14,1175 171176 ],1177 "target": 49,1178 "solution": [1179 "17-14=3",1180 "48/3=16",1181 "65-16=49"1182 ],1183 "optimal_path": "Current State: 49:[65, 48, 14, 17], Operations: []\nExploring Operation: 17-14=3, Resulting Numbers: [65, 48, 3]\nGenerated Node #2: [65, 48, 3] from Operation: 17-14=3\nCurrent State: 49:[65, 48, 3], Operations: ['17-14=3']\nExploring Operation: 48/3=16, Resulting Numbers: [65, 16]\nGenerated Node #3: [65, 16] from Operation: 48/3=16\nCurrent State: 49:[65, 16], Operations: ['17-14=3', '48/3=16']\nExploring Operation: 65-16=49, Resulting Numbers: [49]\n49,49 equal: Goal Reached\n",1184 "start_size": 41185 },1186 {1187 "nums": [1188 73,1189 94,1190 26,1191 171192 ],1193 "target": 19,1194 "solution": [1195 "73-26=47",1196 "94/47=2",1197 "17+2=19"1198 ],1199 "optimal_path": "Current State: 19:[73, 94, 26, 17], Operations: []\nExploring Operation: 73-26=47, Resulting Numbers: [94, 17, 47]\nGenerated Node #2: [94, 17, 47] from Operation: 73-26=47\nCurrent State: 19:[94, 17, 47], Operations: ['73-26=47']\nExploring Operation: 94/47=2, Resulting Numbers: [17, 2]\nGenerated Node #3: [17, 2] from Operation: 94/47=2\nCurrent State: 19:[17, 2], Operations: ['73-26=47', '94/47=2']\nExploring Operation: 17+2=19, Resulting Numbers: [19]\n19,19 equal: Goal Reached\n",1200 "start_size": 4