Datasets:
Tasks:
Reinforcement Learning
Modalities:
Text
Formats:
json
Languages:
English
Size:
10K - 100K
License:
task_id stringlengths 8 8 | family stringclasses 1
value | split stringclasses 1
value | description stringlengths 73 96 | reward stringclasses 1
value | sample_instances listlengths 1 1 |
|---|---|---|---|---|---|
math-q01 | math | train | One fixed algebra question (polynomials__coefficient_named); the same question on every reset. | binary: 1 only for exactly {"value": ...} equal to the exact answer (graded by answer kind) | [
{
"seed": 0,
"kind": "rational",
"files": {
"brief.md": "# Question\n\nExpress (3 + 4 - 6)*(-o - 2 + 2)*(2847*o + 3344*o - 83*o + 463*o) as r*o + h + w*o**2 and give w.\n\n# What to submit\n\nSubmit exactly {\"value\": ...} where the value is the exact answer: an integer or terminating decimal as ... |
math-q02 | math | train | One fixed calculus question (polynomials__compose); the same question on every reset. | binary: 1 only for exactly {"value": ...} equal to the exact answer (graded by answer kind) | [
{
"seed": 0,
"kind": "expression",
"files": {
"brief.md": "# Question\n\nLet y(p) = -15*p. Let t(q) = 1 - 11204*q**2. Determine t(y(f)).\n\n# What to submit\n\nSubmit exactly {\"value\": ...} where the value is a polynomial expression string in the variable(s) used by the question, written with * ... |
math-q03 | math | train | One fixed compare question (comparison__closest_composed); the same question on every reset. | binary: 1 only for exactly {"value": ...} equal to the exact answer (graded by answer kind) | [
{
"seed": 0,
"kind": "choice",
"files": {
"brief.md": "# Question\n\nLet t = 0.2538 + -0.0538. Which is the nearest to t? (a) 0.1 (b) 2 (c) -0.2 (d) 37\n\n# What to submit\n\nSubmit exactly {\"value\": ...} where the value is the letter of the correct option as a string, such as \"c\".\nOnly t... |
math-q04 | math | train | One fixed count question (count__divisibility); the same question on every reset. | binary: 1 only for exactly {"value": ...} equal to the exact answer (graded by answer kind) | [
{
"seed": 0,
"kind": "rational",
"files": {
"brief.md": "# Question\n\nHow many integers from 1 to 1758 inclusive are divisible by 5 or 7 but not by 14?\n\n# What to submit\n\nSubmit exactly {\"value\": ...} where the value is the exact answer: an integer or terminating decimal as a JSON number, o... |
math-q05 | math | train | One fixed logic question (logic__seating); the same question on every reset. | binary: 1 only for exactly {"value": ...} equal to the exact answer (graded by answer kind) | [
{
"seed": 0,
"kind": "rational",
"files": {
"brief.md": "# Question\n\n4 people, Ava, Ben, Cal and Dee, sit in a row of seats numbered 1 to 4 from left to right.\nBen is somewhere left of Ava.\nDee sits at one of the two ends.\nCal sits at one of the two ends.\nExactly one person sits between Dee ... |
math-q06 | math | train | One fixed numbers question (numbers__gcd); the same question on every reset. | binary: 1 only for exactly {"value": ...} equal to the exact answer (graded by answer kind) | [
{
"seed": 0,
"kind": "rational",
"files": {
"brief.md": "# Question\n\nCalculate the greatest common divisor of 397086 and 3230.\n\n# What to submit\n\nSubmit exactly {\"value\": ...} where the value is the exact answer: an integer or terminating decimal as a JSON number, or a fraction as a string... |
math-q07 | math | train | One fixed prob question (probability__swr_p_sequence); the same question on every reset. | binary: 1 only for exactly {"value": ...} equal to the exact answer (graded by answer kind) | [
{
"seed": 0,
"kind": "rational",
"files": {
"brief.md": "# Question\n\nCalculate prob of sequence twjt when four letters picked without replacement from {q: 2, d: 1, r: 1, w: 3, j: 1, t: 12}.\n\n# What to submit\n\nSubmit exactly {\"value\": ...} where the value is the exact answer: an integer or ... |
math-q08 | math | train | One fixed algebra question (polynomials__evaluate_composed); the same question on every reset. | binary: 1 only for exactly {"value": ...} equal to the exact answer (graded by answer kind) | [
{
"seed": 0,
"kind": "rational",
"files": {
"brief.md": "# Question\n\nLet m be (0 + 0 + -1)/1. Let f be 5*4/((-4)/m). Let y(r) = f*r**3 - r**3 - r - 3*r**2 - 5*r**3 + 3. Determine y(-2).\n\n# What to submit\n\nSubmit exactly {\"value\": ...} where the value is the exact answer: an integer or term... |
math-q09 | math | train | One fixed calculus question (polynomials__compose); the same question on every reset. | binary: 1 only for exactly {"value": ...} equal to the exact answer (graded by answer kind) | [
{
"seed": 0,
"kind": "expression",
"files": {
"brief.md": "# Question\n\nLet w(t) = 237*t. Let f(r) = 30 - 5 - 25 - r**2. Determine f(w(a)).\n\n# What to submit\n\nSubmit exactly {\"value\": ...} where the value is a polynomial expression string in the variable(s) used by the question, written wit... |
math-q10 | math | train | One fixed compare question (comparison__kth_biggest_composed); the same question on every reset. | binary: 1 only for exactly {"value": ...} equal to the exact answer (graded by answer kind) | [
{
"seed": 0,
"kind": "name",
"files": {
"brief.md": "# Question\n\nLet k = -0.18 + 0.48. Let w = -6 + 9. What is the third smallest value in w, 0.059, k?\n\n# What to submit\n\nSubmit exactly {\"value\": ...} where the value is the value or variable name exactly as it appears in the question, as a... |
math-q11 | math | train | One fixed count question (count__derangements); the same question on every reset. | binary: 1 only for exactly {"value": ...} equal to the exact answer (graded by answer kind) | [
{
"seed": 0,
"kind": "rational",
"files": {
"brief.md": "# Question\n\n6 people each put a hat in a box and then each draws one hat at random. In how many of the possible draws do exactly 0 people get their own hat back?\n\n# What to submit\n\nSubmit exactly {\"value\": ...} where the value is the... |
math-q12 | math | train | One fixed logic question (logic__power_mod); the same question on every reset. | binary: 1 only for exactly {"value": ...} equal to the exact answer (graded by answer kind) | [
{
"seed": 0,
"kind": "rational",
"files": {
"brief.md": "# Question\n\nWhat is the remainder when 18**118 is divided by 96?\n\n# What to submit\n\nSubmit exactly {\"value\": ...} where the value is the exact answer: an integer or terminating decimal as a JSON number, or a fraction as a string such... |
math-q13 | math | train | One fixed numbers question (numbers__gcd); the same question on every reset. | binary: 1 only for exactly {"value": ...} equal to the exact answer (graded by answer kind) | [
{
"seed": 0,
"kind": "rational",
"files": {
"brief.md": "# Question\n\nWhat is the highest common factor of 580591 and 11?\n\n# What to submit\n\nSubmit exactly {\"value\": ...} where the value is the exact answer: an integer or terminating decimal as a JSON number, or a fraction as a string such ... |
math-q14 | math | train | One fixed algebra question (algebra__linear_2d); the same question on every reset. | binary: 1 only for exactly {"value": ...} equal to the exact answer (graded by answer kind) | [
{
"seed": 0,
"kind": "rational",
"files": {
"brief.md": "# Question\n\nSolve 5*i - 19 = 3*h, -15 = -3*i + 4*h - h for i.\n\n# What to submit\n\nSubmit exactly {\"value\": ...} where the value is the exact answer: an integer or terminating decimal as a JSON number, or a fraction as a string such as... |
math-q15 | math | train | One fixed compare question (comparison__kth_biggest); the same question on every reset. | binary: 1 only for exactly {"value": ...} equal to the exact answer (graded by answer kind) | [
{
"seed": 0,
"kind": "choice",
"files": {
"brief.md": "# Question\n\nWhich is the third smallest value? (a) -1/131 (b) -1/21 (c) 0 (d) -1/4\n\n# What to submit\n\nSubmit exactly {\"value\": ...} where the value is the letter of the correct option as a string, such as \"c\".\nOnly the exact ans... |
math-q16 | math | train | One fixed count question (count__lattice_paths); the same question on every reset. | binary: 1 only for exactly {"value": ...} equal to the exact answer (graded by answer kind) | [
{
"seed": 0,
"kind": "rational",
"files": {
"brief.md": "# Question\n\nA path moves from (0, 0) to (5, 3) using unit steps right (+1, 0) or up (0, +1). How many such paths avoid the point (4, 2)?\n\n# What to submit\n\nSubmit exactly {\"value\": ...} where the value is the exact answer: an integer... |
math-q17 | math | train | One fixed logic question (logic__knights_who); the same question on every reset. | binary: 1 only for exactly {"value": ...} equal to the exact answer (graded by answer kind) | [
{
"seed": 0,
"kind": "boolean",
"files": {
"brief.md": "# Question\n\nOn an island, knights always tell the truth and knaves always lie. Ava, Ben and Cal are each a knight or a knave.\nAva says: \"Cal and I are the same kind.\"\nBen says: \"Exactly 2 of us are knights.\"\nCal says: \"Exactly 1 of ... |
math-q18 | math | train | One fixed numbers question (numbers__gcd_composed); the same question on every reset. | binary: 1 only for exactly {"value": ...} equal to the exact answer (graded by answer kind) | [
{
"seed": 0,
"kind": "rational",
"files": {
"brief.md": "# Question\n\nLet y be (-1)/3*(-2 + -10). Let f(j) = -j**3 + 3*j**2 + 4*j + 2. Let k be f(y). Suppose 0 = 3*u + 2*c - 14, c - 10 = -0*u - k*u. Calculate the greatest common factor of u and 3.\n\n# What to submit\n\nSubmit exactly {\"value\":... |
math-q19 | math | train | One fixed algebra question (algebra__linear_1d_composed); the same question on every reset. | binary: 1 only for exactly {"value": ...} equal to the exact answer (graded by answer kind) | [
{
"seed": 0,
"kind": "rational",
"files": {
"brief.md": "# Question\n\nLet y(f) = f**3 + 10*f**2 - f. Let p be y(-11). Let w = p - -122. Solve 6*k = 2*k + w for k.\n\n# What to submit\n\nSubmit exactly {\"value\": ...} where the value is the exact answer: an integer or terminating decimal as a JSO... |
math-q20 | math | train | One fixed compare question (comparison__closest_composed); the same question on every reset. | binary: 1 only for exactly {"value": ...} equal to the exact answer (graded by answer kind) | [
{
"seed": 0,
"kind": "choice",
"files": {
"brief.md": "# Question\n\nLet o = -2691 + 2690.7. Which is the closest to 0.1? (a) o (b) 6 (c) 3 (d) 0\n\n# What to submit\n\nSubmit exactly {\"value\": ...} where the value is the letter of the correct option as a string, such as \"c\".\nOnly the exa... |
math-q21 | math | train | One fixed count question (count__dice); the same question on every reset. | binary: 1 only for exactly {"value": ...} equal to the exact answer (graded by answer kind) | [
{
"seed": 0,
"kind": "rational",
"files": {
"brief.md": "# Question\n\n3 fair 6-sided dice (faces 1 to 6) are rolled. What is the probability that the product is even?\n\n# What to submit\n\nSubmit exactly {\"value\": ...} where the value is the exact answer: an integer or terminating decimal as a... |
math-q22 | math | train | One fixed logic question (logic__shortest_path); the same question on every reset. | binary: 1 only for exactly {"value": ...} equal to the exact answer (graded by answer kind) | [
{
"seed": 0,
"kind": "rational",
"files": {
"brief.md": "# Question\n\nRoads (two-way) with their lengths: A-B 6, A-C 6, A-E 6, B-D 8, B-E 3. What is the length of the shortest route from A to E?\n\n# What to submit\n\nSubmit exactly {\"value\": ...} where the value is the exact answer: an integer... |
math-q23 | math | train | One fixed numbers question (numbers__is_prime_composed); the same question on every reset. | binary: 1 only for exactly {"value": ...} equal to the exact answer (graded by answer kind) | [
{
"seed": 0,
"kind": "boolean",
"files": {
"brief.md": "# Question\n\nLet p be 330/77 + 4/(-14). Suppose 2*r + 8 - 111 = j, 0 = -p*r - 5*j + 185. Let t = 199 - r. Is t prime?\n\n# What to submit\n\nSubmit exactly {\"value\": ...} where the value is true or false (JSON booleans, not strings).\nOnly... |
math-q24 | math | train | One fixed algebra question (algebra__sequence_next_term); the same question on every reset. | binary: 1 only for exactly {"value": ...} equal to the exact answer (graded by answer kind) | [
{
"seed": 0,
"kind": "rational",
"files": {
"brief.md": "# Question\n\nWhat comes next: 15892319, 15892318, 15892317?\n\n# What to submit\n\nSubmit exactly {\"value\": ...} where the value is the exact answer: an integer or terminating decimal as a JSON number, or a fraction as a string such as \"... |
math-q25 | math | train | One fixed compare question (comparison__kth_biggest); the same question on every reset. | binary: 1 only for exactly {"value": ...} equal to the exact answer (graded by answer kind) | [
{
"seed": 0,
"kind": "rational",
"files": {
"brief.md": "# Question\n\nWhat is the second smallest value in -0.5, -0.043171, 5, 25, -1?\n\n# What to submit\n\nSubmit exactly {\"value\": ...} where the value is the exact answer: an integer or terminating decimal as a JSON number, or a fraction as a... |
math-q26 | math | train | One fixed count question (count__arrangements); the same question on every reset. | binary: 1 only for exactly {"value": ...} equal to the exact answer (graded by answer kind) | [
{
"seed": 0,
"kind": "rational",
"files": {
"brief.md": "# Question\n\nHow many distinct arrangements of the letters of BANANA have no two N's next to each other?\n\n# What to submit\n\nSubmit exactly {\"value\": ...} where the value is the exact answer: an integer or terminating decimal as a JSON... |
math-q27 | math | train | One fixed logic question (logic__knights_count); the same question on every reset. | binary: 1 only for exactly {"value": ...} equal to the exact answer (graded by answer kind) | [
{
"seed": 0,
"kind": "rational",
"files": {
"brief.md": "# Question\n\nOn an island, knights always tell the truth and knaves always lie. Ava, Ben and Cal are each a knight or a knave.\nAva says: \"Ben and I are the same kind.\"\nBen says: \"Cal and I are different kinds.\"\nCal says: \"Exactly 1 ... |
math-q28 | math | train | One fixed numbers question (numbers__place_value_composed); the same question on every reset. | binary: 1 only for exactly {"value": ...} equal to the exact answer (graded by answer kind) | [
{
"seed": 0,
"kind": "rational",
"files": {
"brief.md": "# Question\n\nLet h = -122 - -192. Let a = h - 20. What is the tens digit of a?\n\n# What to submit\n\nSubmit exactly {\"value\": ...} where the value is the exact answer: an integer or terminating decimal as a JSON number, or a fraction as ... |
math-q29 | math | train | One fixed algebra question (algebra__sequence_nth_term); the same question on every reset. | binary: 1 only for exactly {"value": ...} equal to the exact answer (graded by answer kind) | [
{
"seed": 0,
"kind": "expression",
"files": {
"brief.md": "# Question\n\nWhat is the x'th term of 374288, 374291, 374294?\n\n# What to submit\n\nSubmit exactly {\"value\": ...} where the value is a polynomial expression string in the variable(s) used by the question, written with * and ** (no impl... |
math-q30 | math | train | One fixed compare question (comparison__pair_composed); the same question on every reset. | binary: 1 only for exactly {"value": ...} equal to the exact answer (graded by answer kind) | [
{
"seed": 0,
"kind": "name",
"files": {
"brief.md": "# Question\n\nLet p = -3.66 - -3.36. Let h be 2/(-5) - 2/(-30). Which is greater: p or h?\n\n# What to submit\n\nSubmit exactly {\"value\": ...} where the value is the value or variable name exactly as it appears in the question, as a string, su... |
math-q31 | math | train | One fixed count question (count__derangements); the same question on every reset. | binary: 1 only for exactly {"value": ...} equal to the exact answer (graded by answer kind) | [
{
"seed": 0,
"kind": "rational",
"files": {
"brief.md": "# Question\n\n5 people each put a hat in a box and then each draws one hat at random. In how many of the possible draws do exactly 1 people get their own hat back?\n\n# What to submit\n\nSubmit exactly {\"value\": ...} where the value is the... |
math-q32 | math | train | One fixed logic question (logic__recurrence); the same question on every reset. | binary: 1 only for exactly {"value": ...} equal to the exact answer (graded by answer kind) | [
{
"seed": 0,
"kind": "rational",
"files": {
"brief.md": "# Question\n\nA sequence has a(0) = 1, a(1) = 1 and a(n) = -3*a(n-1) + 1*a(n-2) for n >= 2. What is a(9)?\n\n# What to submit\n\nSubmit exactly {\"value\": ...} where the value is the exact answer: an integer or terminating decimal as a JSON... |
Evidence Desk: fixed exact mathematics
OpenEnv environment for the OpenEnv Arena. This version spends the whole training run on one domain, mathematics and formal reasoning, using 32 fixed questions: one task per question, identical on every reset. The arena plays each training step as several episodes of one task, so every comparison group is attempts at the same problem rather than different problems of different difficulty.
Tasks
math-q01 to math-q32, listed in data/math_fixed.jsonl with their exact
answers. They span algebra (6), comparison (6), counting (6), logic (6),
number theory (5), calculus (2) and probability (1). They were chosen from 88
candidates (one per question-bank cell plus generated counting and logic
puzzles) by screening the untrained Qwen3.8-27B in bf16 with four attempts
each, keeping questions solved sometimes but not always (closest to even odds
first, balanced by area).
The larger bank data/math_bank.jsonl (24,800 questions over 62
module/difficulty cells) is the pool the questions were drawn from; the
environment also serves it through the per-area tasks math-arith to
math-logic, which this submission does not train on. Counting and logic
answers come from exhaustive search, and puzzles are kept only when the answer
is unique.
Interaction
One JSON action per turn: calc (an arithmetic expression), submit the answer
object, open a file or finish. The question is shown at reset. An optional
work field holds scratch reasoning and is ignored. Episodes end on submit,
finish or after 14 calls.
Reward
Binary and exact: 1 only for exactly {"value": ...} equal to the reference.
Grading depends on the answer kind: rationals compare as exact fractions
("-7/12" or a terminating decimal), polynomial expressions by identity at
random integer points, prime factors and orderings as lists, true/false as
JSON booleans, option letters, base-n strings and clock times as strings.
tasks.jsonl lists each task with its instance.
Data and licences
Bank questions were generated locally with
DeepMind mathematics_dataset
1.0.1 (Apache-2.0, Copyright 2019 DeepMind Technologies Limited); see
data/deepmind_math_LICENSE.txt and data/math_manifest.json. Counting and
logic questions are our own generators. Held-out question types are not
published or shipped.
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