Emulated-Inc/countdown-arithmetic-training-pool

Countdown arithmetic training pool

Arithmetic puzzles of the Countdown kind: a handful of source numbers, a target, and the job of writing an expression over the four operations that reaches the target, using each source number at most once and not having to use them all. A set generated for this pool and three public datasets read at the pinned revisions named below, laid out twice. Train on either layer or on both.

pool.jsonl

Every source rewritten into one shape, 7708159 rows, one JSON object per line, with these fields.

4823720 of the rows carry an expression. Each one was checked by running it through a parser that reads it as an integer expression over + - * / and parentheses, confirming that the numbers it uses are a sub-multiset of that row's own source numbers, that every division in it is exact, and that its value equals the target. Nothing else was kept. A null solution means no expression its source offered survived that check, which for the two large sets is usually a row whose own solver reported a near miss rather than a hit, so it is not evidence that the puzzle has no answer. Checking an attempt is a few lines of code and needs no answer key, so a row without a solution is still a usable prompt if you can solve it or are willing to train against a checker.

Rows are deduplicated on the puzzle itself, the sorted multiset of the numbers together with the target, keeping the first source that carries it in the order of the sections below. Rows whose target is one of their own source numbers are not in this file, since that puzzle is answered by copying a number down.

The category field is the draw size and the target band, where a target up to 99 is small, up to 499 medium and above that large. How the rows and the expressions fall across it is worth reading before sampling, because the two are not spread the same way at all.

sources/

The same data untouched, 8000072 rows, one directory per source. The three downloaded sets hold the files at the paths, in the parquet format and with the columns their own repositories publish, and the generated set is one jsonl file. Nothing here was renamed, reshaped, reordered or deduplicated. Use this layer if you want a field the rewritten one drops, such as the near-miss value and the distance to it in the two large sets, or the human solve rates and solve times in the Game of 24 set.

The sources

sources/generated

Puzzles drawn under the rules of the televised game, every one proved solvable by an exhaustive search that also wrote down the expression it found. Generated for this pool under seed 20260913, file puzzles.jsonl. 1000000 rows here, of which 1000000 also appear in pool.jsonl and 1000000 of those carry an expression. Provenance class rule-generated, licence cc-by-4.0. Its own fields are id, numbers, target, solution, category.

Worth knowing. One generator drew all of it, so it is one distribution rather than a survey of puzzle styles, and its draw sizes and target bands follow the weights recorded in the manifest rather than a uniform spread.

sources/countdown_numbers_6

Six-number puzzles drawn under the rules of the televised game, two tiles of each number from 1 to 10 and one tile each of 25, 50, 75 and 100, with a target and the expression its own solver found. From alexjackson17/countdown-numbers-6-gr at revision bea976bae5c3942cfa43b1a7d99f3a360f6c8a0b, files data/train-00000-of-00001.parquet, data/test-00000-of-00001.parquet. 999290 rows here, of which 742968 also appear in pool.jsonl and 637681 of those carry an expression. Provenance class rule-generated, licence mit. Its own fields are starting for the source numbers, target, closest for the value its solver reached, expression for the expression that reaches that value, delta for the distance between the two, score for the points the televised game would award, size for the count of source numbers.

Worth knowing. Its solver is not exhaustive. Of 300 rows sampled from its test file whose delta is not zero, meaning its solver reported a near miss rather than a hit, an exhaustive search reaches the target exactly on 183. So a row without an expression here is a row whose expression that solver did not find, and not a puzzle that has no answer.

sources/countdown_numbers_3_8

Puzzles of three to eight source numbers drawn uniformly from 1 to 100 rather than from the televised tile pool, a million of each size, with a target and the expression its own solver found. From alexjackson17/countdown-numbers-3-8 at revision e5edf4837453cba34c2a0ccf4fff9b6f9e6c9d0f, files data/train-00000-of-00002.parquet, data/train-00001-of-00002.parquet, data/test-00000-of-00001.parquet. 5999521 rows here, of which 5964234 also appear in pool.jsonl and 3185095 of those carry an expression. Provenance class rule-generated, licence mit. Its own fields are the same columns as the six-number set.

Worth knowing. Its draws are uniform over 1 to 100, so most of them cannot occur in the televised game, and its sizes run to eight numbers. The same non-exhaustive solver applies.

sources/game_of_24

The complete enumeration of four-card Game of 24 hands collected from 4nums.com, each with every expression that reaches 24 and with the solve rate and the solve times of more than six million real attempts since 2012. From nlile/24-game at revision 0106b176e4648061d60c32ddb85ac0816699652d, files data/train-00000-of-00001.parquet. 1261 rows here, of which 957 also appear in pool.jsonl and 944 of those carry an expression. Provenance class collected, licence apache-2.0. Its own fields are numbers for the four cards, solutions for every expression reaching 24, solvable, amt and meantime and stdtime for human solve times in seconds, solved_rate for the share of human attempts that succeeded.

Worth knowing. The puzzle enumeration itself is mechanical. What is collected from people is the difficulty metadata, which only the raw layer keeps, since the rewritten rows hold one shape for every source. The target is always 24 and the cards are 1 to 13.

Provenance and licences

No Countdown corpus written by people exists, and this pool does not pretend otherwise. Three of the four sources were produced by a program that samples numbers and a target and then solves the draw, which is the provenance class rule-generated, and they are almost all of the rows. The fourth, the Game of 24 enumeration, is classed collected because the set is a real artefact of people playing: its ranking, its solve rates and its solve times aggregate more than six million attempts recorded since 2012, and those columns are in its directory under sources/. The puzzles in it were enumerated mechanically all the same. No row anywhere in the pool was written by a language model.

The pool as a whole is offered under cc-by-4.0. The sources themselves are mit for the two large sets, apache-2.0 for the Game of 24 set and cc-by-4.0 for the generated set, and every rewritten row carries its own in the licence field while each directory under sources/ is one source, so a subset under a single licence can be selected. Attribution goes to Alex Jackson for the two Countdown sets and their generator, to the maintainers of nlile/24-game and to 4nums.com for the Game of 24 enumeration and its human statistics.

Filtering

168 rows were removed before publication, from both layers alike, because their puzzle, the sorted numbers together with the target, matched one in a held-out list: 68 against a list that is not distributed here, and 100 against the hands ranked 901 to 1000 in the published 4nums.com difficulty ranking, a band that is widely reserved. Nothing else was filtered: no draw size, no target band and no difficulty was selected for or against, so the pool still holds the seven and eight number draws and the targets outside the usual range that its larger source carries, and the category field is how to select what you want.