id stringlengths 6 8 | alias stringlengths 24 50 | problem stringlengths 24 5.03k | answer int64 -16,384 80.2B | graph stringlengths 0 6.44k | domain stringclasses 4
values | secondary_domain stringclasses 4
values | goal stringclasses 4
values | evaluator_id stringclasses 1
value | root_lemma stringclasses 89
values | lemma_paths listlengths 0 5 | recipe_id stringlengths 0 6 | seed_template_id stringclasses 96
values | ending_id stringclasses 13
values | olympiad_level int64 2 9 | num_spawns int64 0 3 ⌀ | lemma_set listlengths 1 7 ⌀ | num_lemmas int64 1 7 ⌀ | generation_time float64 0 43.9 | created_at stringlengths 27 27 | verification dict | problem_hash stringlengths 6 6 | parent_id stringlengths 0 6 | variant stringclasses 3
values | license stringclasses 1
value | llm_solvers listlengths 1 13 ⌀ | solution_status int64 0 2 ⌀ | lemma_applicability listlengths 0 12 | irt_difficulty dict |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
8859d7 | algebra_poly_eval_v1_784195855_2589 | Let $$
A = \sum_{k=1}^{3} \phi(k) \left\lfloor \frac{3}{k} \right\rfloor,$$ where $\phi$ denotes Euler's totient function. Define $$
x = \frac{A \cdot 6^5 - 67 \cdot 6^4 + 20 \cdot 6^3 - 95 \cdot 6^2 - 35 \cdot 6 - 99}{-5}.$$ Compute the value of $Q = |x|$. | 7,917 | graphs = [
Graph(
let={
"_n": Const(3),
"x": Const(6),
"result": Div(Sum(Mul(Summation(var="k", start=Const(1), end=Const(3), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Ref("_n"), Var("k"))))), Pow(Ref("x"), Const(5))), Mul(Const(-67), Pow(Ref("x"), Const(4))), Mul(Const(20... | NT | null | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | algebra_poly_eval_v1 | null | 4 | 0 | [
"K2"
] | 1 | 0.003 | 2026-02-08T05:53:53.302390Z | {
"verified": true,
"answer": 7917,
"timestamp": "2026-02-08T05:53:53.304897Z"
} | 46a2fe | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 157,
"completion_tokens": 810
},
"timestamp": "2026-02-12T16:06:03.156Z",
"answer": 7917
},
{
... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
}
] | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
5caf63 | lin_form_endings_v1_655260480_6147 | Let $a = 28$ and $b = 70$. Define $k = 413$ and let $d = \gcd(a, b)$. Compute $m = \left\lfloor \frac{k}{\gcd(k, d)} \right\rfloor$. Let $s = 14728 \cdot m$. Find the remainder when $s$ is divided by 58819. | 45,486 | graphs = [
Graph(
let={
"a_coeff": Const(28),
"b_coeff": Const(70),
"k_val": Const(413),
"step": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"_inner_result": Floor(Div(Ref("k_val"), GCD(a=Ref("k_val"), b=Ref("step")))),
"_scale_k": Const(1... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 4 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T18:51:27.935664Z | {
"verified": true,
"answer": 45486,
"timestamp": "2026-02-08T18:51:27.936515Z"
} | a2d65f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 126,
"completion_tokens": 1260
},
"timestamp": "2026-02-18T20:03:27.563Z",
"answer": 45486
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
bd05d5 | modular_sum_quadratic_residues_v1_349078426_1736 | Let $p$ be the number of ordered pairs of positive odd integers $(x_1, x_2)$ such that $x_1 + x_2 = 482$. Compute
$$
\frac{p(p-1)}{4}.
$$ | 14,460 | graphs = [
Graph(
let={
"_n": Const(4),
"p": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2")), Con... | NT | null | SUM | sympy | COMB1 | [
"COMB1"
] | 567f58 | modular_sum_quadratic_residues_v1 | null | 3 | 0 | [
"COMB1"
] | 1 | 0.002 | 2026-02-08T13:53:53.301413Z | {
"verified": true,
"answer": 14460,
"timestamp": "2026-02-08T13:53:53.303725Z"
} | 8530b4 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 112,
"completion_tokens": 541
},
"timestamp": "2026-02-16T05:09:34.844Z",
"answer": 14460
},
{
"id": 11,
... | 2 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
d95d08 | comb_count_partitions_v1_1470522791_258 | Let $m = 6$ and $n = 9$. Define $S$ as the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = m$. Let $P$ be the set of all products $xy$ where $(x, y) \in S$. Let $N = \sum_{k=1}^{\max P} \phi(k) \left\lfloor \frac{n}{k} \right\rfloor$, where $\phi$ denotes Euler's totient function. Compute the ... | 89,134 | graphs = [
Graph(
let={
"_m": Const(6),
"_n": Const(9),
"n": Summation(var="k", start=Const(1), end=MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var(... | NT | COMB | COUNT | sympy | B1 | [
"B1/K2"
] | ebd04c | comb_count_partitions_v1 | null | 5 | 0 | [
"B1",
"K2"
] | 2 | 0.003 | 2026-02-08T12:55:51.112683Z | {
"verified": true,
"answer": 89134,
"timestamp": "2026-02-08T12:55:51.116147Z"
} | 610443 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 172,
"completion_tokens": 1085
},
"timestamp": "2026-02-15T07:29:11.850Z",
"answer": 89134
},
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K2",
"status": "ok_later"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
2ce4b6 | comb_bell_compute_v1_397696148_2830 | Let $n$ be the number of nonnegative integers $j$ such that $0 \leq j \leq 36865$ and the binomial coefficient $\binom{36865}{j}$ is odd. Compute the Bell number $B_n$, which counts the number of partitions of a set of $n$ elements. Find the value of $15753 - B_n$. | 11,613 | graphs = [
Graph(
let={
"_n": Const(36865),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Ref("_n")), Eq(Mod(value=Binom(n=Const(36865), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')),
"r... | COMB | null | COMPUTE | sympy | V8 | [
"V8"
] | 86348e | comb_bell_compute_v1 | null | 7 | 0 | [
"V8"
] | 1 | 0.001 | 2026-02-08T14:06:12.921691Z | {
"verified": true,
"answer": 11613,
"timestamp": "2026-02-08T14:06:12.922808Z"
} | 81b410 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 190,
"completion_tokens": 614
},
"timestamp": "2026-02-24T19:50:36.416Z",
"answer": 11613
},
{
"i... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
... | {
"lo": -2.43,
"mid": 1.2,
"hi": 4.84
} | ||
c0ce9a | nt_min_with_divisor_count_v1_865884756_4965 | Let $n$ be the smallest positive integer such that $n \leq 33856$ and the number of positive divisors of $n$ is exactly 8. Find the value of $n$. | 24 | graphs = [
Graph(
let={
"upper": Const(33856),
"div_count": Const(8),
"result": MinOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(NumDivisors(n=Var("n")), Ref("div_count"))))),
},
goal=Ref("res... | NT | null | EXTREMUM | sympy | C2 | [
"VIETA_SUM",
"ONE_PHI_1"
] | 92db82 | nt_min_with_divisor_count_v1 | null | 4 | 0 | [
"C2",
"ONE_PHI_1",
"VIETA_SUM"
] | 3 | 4.418 | 2026-02-08T18:18:06.879787Z | {
"verified": true,
"answer": 24,
"timestamp": "2026-02-08T18:18:11.298048Z"
} | 50f6a5 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 88,
"completion_tokens": 1268
},
"timestamp": "2026-02-18T15:53:29.594Z",
"answer": 24
},
{
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "ONE_PHI_1",
"status": "ok"
},
{
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
be6749 | comb_factorial_compute_v1_1419126231_114 | Let $n$ be the minimum value of $19b^3 - 15a^2b - 33ab^2 + 37a^3$ over all ordered pairs $(a, b)$ of positive integers with $1 \leq a \leq 23$ and $1 \leq b \leq \left|\{ v \geq 1 : v \leq 689 \text{ and } v = 41b'^2 - 74ab' + 34a'^2 \text{ for some integers } a', b' \in [1,5] \}\right|$. Let $Q = n!$. Compute $Q$. | 40,320 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(37),
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(23)), Geq(Var("b"), Const(1)), Leq(Var("b"), CountOverSet(set=Solu... | COMB | null | COMPUTE | sympy | QF_PSD_DISTINCT | [
"QF_PSD_DISTINCT/POLY3_MIN"
] | 77024c | comb_factorial_compute_v1 | null | 5 | 0 | [
"POLY3_MIN",
"QF_PSD_DISTINCT"
] | 2 | 0.004 | 2026-02-25T09:38:40.695116Z | {
"verified": true,
"answer": 40320,
"timestamp": "2026-02-25T09:38:40.698712Z"
} | e72223 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 253,
"completion_tokens": 7316
},
"timestamp": "2026-03-30T07:06:32.086Z",
"answer": 40320
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "POLY3_MIN",
"status": "ok_later"
},
{
"lemma": "QF_PSD_DI... | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | ||
f8bf95 | nt_count_gcd_equals_v1_458359167_2629 | Let $n = 2$ and $k = 318$. Let $d$ be the smallest integer greater than or equal to $n$ that divides $8783743$. Let $U = 17711$. Let $r$ be the number of positive integers $n'$ such that $1 \leq n' \leq U$ and $\gcd(n', k) = d$. Compute the remainder when $44121 \cdot r$ is divided by $59153$. | 46,885 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": Const(17711),
"k": Const(318),
"d": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(8783743))))),
"result": CountOverSet(set... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | nt_count_gcd_equals_v1 | null | 3 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 1.357 | 2026-02-08T06:23:01.646073Z | {
"verified": true,
"answer": 46885,
"timestamp": "2026-02-08T06:23:03.002676Z"
} | 0b0df0 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 146,
"completion_tokens": 1831
},
"timestamp": "2026-02-13T03:14:42.073Z",
"answer": 46885
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
9f7031 | v1_endings_v1_677425708_1121 | Let $ n = 66487 $. Let $ v_5(n!) $ denote the largest integer $ k $ such that $ 5^k $ divides $ n! $, and let $ v_7(n!) $ denote the largest integer $ k $ such that $ 7^k $ divides $ n! $. Let $ a $ be the remainder when $ v_5(n!) $ is divided by 1000, and let $ b $ be the remainder when $ v_7(n!) $ is divided by 100. ... | 61,877 | graphs = [
Graph(
let={
"n_val": Const(66487),
"p1_val": Const(5),
"p2_val": Const(7),
"n_fact": Factorial(Ref("n_val")),
"vp1": MaxKDivides(target=Ref("n_fact"), base=Ref("p1_val")),
"vp2": MaxKDivides(target=Ref("n_fact"), base=Ref("p... | NT | null | COMPUTE | sympy | V1 | [
"V1"
] | dae96f | v1_endings_v1 | null | 5 | null | [
"V1"
] | 1 | 0 | 2026-02-08T04:00:17.496400Z | {
"verified": true,
"answer": 61877,
"timestamp": "2026-02-08T04:00:17.496877Z"
} | 0d9b9f | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 227,
"completion_tokens": 1245
},
"timestamp": "2026-02-09T15:56:41.903Z",
"answer": 61877
},
{
"... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K5",
"status": "same_pattern_wrong"
},
{
"lemma": "MOD_ADD",
"statu... | {
"lo": -6.5,
"mid": -0.2,
"hi": 6.11
} | ||
1b98a4 | modular_mod_compute_v1_1125832087_1290 | Compute the remainder when $-23104$ is divided by $14641$. | 6,178 | graphs = [
Graph(
let={
"a": Const(-23104),
"m": Const(14641),
"result": Mod(value=Ref("a"), modulus=Ref("m")),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | modular_mod_compute_v1 | null | 2 | 0 | [
"LIN_FORM"
] | 1 | 0.009 | 2026-02-08T03:40:29.387861Z | {
"verified": true,
"answer": 6178,
"timestamp": "2026-02-08T03:40:29.396841Z"
} | 254528 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 126,
"completion_tokens": 468
},
"timestamp": "2026-02-10T15:22:45.003Z",
"answer": 6178
},
{
"id... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
ea31b6 | diophantine_sum_product_min_v1_48377204_1601 | Let $S = 26$. Let $P$ be the number of integers $t$ such that $10 \leq t \leq 186$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 48$, $1 \leq b \leq 6$, and $t = 3a + 7b$. Let $M$ be the maximum value of $xy$ over all pairs of positive integers $(x, y)$ such that $x + y = 10$. Determine the value of... | 11 | graphs = [
Graph(
let={
"S": Const(26),
"P": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=48)), Geq(left=Var(n... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM",
"B1"
] | 2f9b70 | diophantine_sum_product_min_v1 | null | 6 | 0 | [
"B1",
"LIN_FORM"
] | 2 | 0.014 | 2026-02-08T16:15:13.091032Z | {
"verified": true,
"answer": 11,
"timestamp": "2026-02-08T16:15:13.105053Z"
} | 766a12 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 189,
"completion_tokens": 5497
},
"timestamp": "2026-02-16T23:33:56.760Z",
"answer": 11
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
4f14a9 | nt_gcd_compute_v1_168721529_1711 | Let $a = 986193$ and $b = 1593081$. Define $d = \gcd(a, b)$. Let $\phi(n)$ denote Euler's totient function and $\tau(n)$ denote the number of positive divisors of $n$. Compute the remainder when
$$
d + \phi\left(|d| + \phi(1)\right) + \tau\left(|d| + \phi(2)\right)
$$
is divided by $84396$. | 28,865 | graphs = [
Graph(
let={
"a": Const(986193),
"b": Const(1593081),
"result": GCD(a=Ref("a"), b=Ref("b")),
"Q": Mod(value=Sum(Ref("result"), EulerPhi(n=Sum(Abs(arg=Ref(name='result')), EulerPhi(n=Const(1)))), NumDivisors(n=Sum(Abs(arg=Ref(name='result')), EulerPh... | NT | null | COMPUTE | sympy | ONE_PHI_1 | [
"ONE_PHI_1",
"ONE_PHI_2"
] | a76f7e | nt_gcd_compute_v1 | null | 3 | 0 | [
"ONE_PHI_1",
"ONE_PHI_2"
] | 2 | 0.004 | 2026-02-08T13:53:29.536287Z | {
"verified": true,
"answer": 28865,
"timestamp": "2026-02-08T13:53:29.540416Z"
} | 56e0f2 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 215,
"completion_tokens": 1809
},
"timestamp": "2026-02-09T20:39:42.282Z",
"answer": 28865
},
{
"... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "ONE_PHI_1",
"stat... | {
"lo": -6.5,
"mid": -0.2,
"hi": 6.11
} | ||
80dbfd | nt_count_divisible_v1_1742523217_5512 | Let $m$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that
\[pq=6,\quad \gcd(p,q)=1,\quad\text{and}\quad p<q.\]
Let $n=337$, let $U=81796$, and let $d=11$.
Let $R$ be the number of integers $t$ with $1\le t\le U$ such that $d\mid t$.
Let $M$ be the smallest integer $k$ with... | 44,177 | graphs = [
Graph(
let={
"_c": Const(2008),
"_m": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=6)), Eq(left=GCD(a=Var(name='p'), b=Var(name=... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/MIN_PRIME_FACTOR",
"MAX_PRIME_BELOW"
] | aedac7 | nt_count_divisible_v1 | two_moduli | 6 | 0 | [
"COPRIME_PAIRS",
"MAX_PRIME_BELOW",
"MIN_PRIME_FACTOR"
] | 3 | 3.248 | 2026-02-08T11:02:18.574697Z | {
"verified": true,
"answer": 44177,
"timestamp": "2026-02-08T11:02:21.822974Z"
} | 8441cb | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 215,
"completion_tokens": 1281
},
"timestamp": "2026-02-14T10:15:56.196Z",
"answer": 44177
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status"... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
99d3e5 | lin_form_endings_v1_1742523217_3510 | Let $a = 40$ and $b = 70$. Define $d = \gcd(a, b)$. Let $k = 64$ and compute $g = \gcd(k, d)$. Define $r = \left\lfloor \frac{k}{g} \right\rfloor$. Multiply $r$ by $9227$, and let the result be $s$. Compute the remainder when $s$ is divided by $77410$. | 63,034 | graphs = [
Graph(
let={
"a_coeff": Const(40),
"b_coeff": Const(70),
"k_val": Const(64),
"step": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"_inner_result": Floor(Div(Ref("k_val"), GCD(a=Ref("k_val"), b=Ref("step")))),
"_scale_k": Const(92... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 3 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T05:55:29.672459Z | {
"verified": true,
"answer": 63034,
"timestamp": "2026-02-08T05:55:29.672977Z"
} | 13e116 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 164,
"completion_tokens": 393
},
"timestamp": "2026-02-11T23:21:53.941Z",
"answer": 63862
},
{
"id": 11... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
2b71e4 | nt_lcm_compute_v1_971394319_805 | Let $a$ be the minimum value of $x + y$ over all ordered pairs of positive integers $(x, y)$ such that $xy = 2193361$. Let $b = 1971$. Define $L$ to be the least common multiple of $a$ and $b$. Let $c = 6000$ and $n = 2$. Compute the sum $\sum_{i=0}^{d-1} \left( \text{the } i\text{-th decimal digit of } L \right) \cdot... | 6,747 | graphs = [
Graph(
let={
"_n": Const(2),
"a": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(2193361)))), expr=Sum(Var("x"), Var("y")))),... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_lcm_compute_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.002 | 2026-02-08T13:19:09.790976Z | {
"verified": true,
"answer": 6747,
"timestamp": "2026-02-08T13:19:09.793141Z"
} | 900dfa | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 202,
"completion_tokens": 1863
},
"timestamp": "2026-02-15T12:54:45.716Z",
"answer": 6747
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
88cd3f_n | comb_count_surjections_v1_1218484723_7021 | A game show has 5 distinct prizes to distribute among 4 identical bonus chests, with no chest left empty. The number of ways to assign the prizes is $S(5,4)$, and the total configuration count is scaled by $4!$ to account for chest labeling. Let $M$ be this total. The final prize multiplier is the remainder when $41479... | 70,800 | COMB | null | COUNT | sympy | STARS_BARS | [
"STARS_BARS",
"ONE_FACTORIAL_0"
] | 71b4f8 | comb_count_surjections_v1 | null | 2 | null | [
"ONE_FACTORIAL_0",
"STARS_BARS"
] | 2 | 0.008 | 2026-02-25T08:26:40.229395Z | null | 8877cf | 88cd3f | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 204,
"completion_tokens": 1299
},
"timestamp": "2026-03-31T02:06:00.288Z",
"answer": 70800
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "ONE_FACTORIAL_0",
"status": "ok"
},
{
"lemma": "STARS_BA... | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | |
d849c5 | alg_qf_psd_orbit_v1_601307018_3193 | Let $M$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 20$ such that $25b^2 - 18ab + 10a^2 \le 4885$. Let $S$ be the set of ordered pairs $(a2, b2)$ with $1 \le a2, b2 \le 40$ satisfying $-18a2b2 + 25b2^2 + 10a2^2 \le 3904$, and let $N = |S|$. Let $Q$ be the number of ordered pairs $(... | 5 | graphs = [
Graph(
let={
"_m": Const(3904),
"_n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(20)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(20)), Leq(Sum(Mul(Const(25), Pow(Var("b"), Const(2)))... | ALG | null | COUNT | sympy | LIN_FORM | [
"QF_PSD_COUNT_LEQ/QF_PSD_COUNT_LEQ"
] | cbd80a | alg_qf_psd_orbit_v1 | null | 7 | 0 | [
"LIN_FORM",
"QF_PSD_COUNT_LEQ"
] | 2 | 2.832 | 2026-03-10T03:45:14.853505Z | {
"verified": true,
"answer": 5,
"timestamp": "2026-03-10T03:45:17.685181Z"
} | 5be3ab | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 292,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T07:49:27.631Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
}
] | {
"lo": 1.23,
"mid": 4.27,
"hi": 6.7
} | ||
03e703 | antilemma_product_of_sums_v1_124444284_248 | Let $S_1$ be the sum of $k$ over all ordered pairs $(k, j)$ where $k$ ranges from 1 to 8 and $j$ ranges from 1 to 5. Let $d_{\text{min}}$ be the smallest divisor of 1001 that is at least 2. Define $S_2$ to be the sum of all nonnegative integers $j \leq 7$ for which the binomial coefficient $\binom{d_{\text{min}}}{j}$ i... | 10,013 | graphs = [
Graph(
let={
"_n": Const(1001),
"S1": SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("k"), Var("_j")]), condition=Const(1), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(8)), right=IntegerRange(start=Const(1), end=Const(5)))), expr... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR",
"PRODUCT_OF_SUMS"
] | 4fd6ac | antilemma_product_of_sums_v1 | null | 6 | 0 | [
"MIN_PRIME_FACTOR",
"PRODUCT_OF_SUMS"
] | 2 | 0.003 | 2026-02-08T03:06:13.473419Z | {
"verified": true,
"answer": 10013,
"timestamp": "2026-02-08T03:06:13.476089Z"
} | 9f1023 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 299,
"completion_tokens": 1104
},
"timestamp": "2026-02-09T15:07:34.154Z",
"answer": 10013
},
{
"... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "PRODUCT_OF_SUMS",
"statu... | {
"lo": -6.51,
"mid": -0.32,
"hi": 5.36
} | ||
a55beb | geo_count_lattice_rect_v1_1978505735_6306 | Compute the number of lattice points in the rectangle $[0, 128] \times [0, 302]$, including the boundary. | 39,087 | graphs = [
Graph(
let={
"a": Const(128),
"b": Const(302),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 2 | 0 | null | null | 0.001 | 2026-02-08T19:33:09.674219Z | {
"verified": true,
"answer": 39087,
"timestamp": "2026-02-08T19:33:09.674922Z"
} | 4ad48e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 76,
"completion_tokens": 497
},
"timestamp": "2026-02-25T01:26:34.226Z",
"answer": 39087
},
{
... | 1 | [] | {
"lo": -8.48,
"mid": -5.37,
"hi": -3.03
} | ||||
67de60 | nt_count_divisible_and_v1_1915831931_545 | Let $d_1 = 6$. Define $p$ to be a positive integer such that there exists a positive integer $q$ with $p \cdot q = 5880$, $\gcd(p, q) = 1$, and $p < q$. Let $d_2$ be the number of such integers $p$. Let $U = 53688$. Define $n$ to be an integer satisfying $1 \leq n \leq U$, $d_1$ divides $n$, and $d_2$ divides $n$. Let ... | 13,347 | graphs = [
Graph(
let={
"_n": Const(60358),
"upper": Const(53688),
"d1": Const(6),
"d2": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')),... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_count_divisible_and_v1 | null | 6 | 0 | [
"COPRIME_PAIRS"
] | 1 | 3.31 | 2026-02-08T15:31:03.760413Z | {
"verified": true,
"answer": 13347,
"timestamp": "2026-02-08T15:31:07.070635Z"
} | af5897 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 193,
"completion_tokens": 2317
},
"timestamp": "2026-02-16T08:50:24.460Z",
"answer": 13347
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V5",
"s... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
dd2207 | nt_min_coprime_above_v1_655260480_4728 | Let $r$ be the sum of the solutions to the equation $x^2 - 493x - 1988 = 0$. Find the smallest integer $n$ such that $40000 < n \leq 40503$ and $\gcd(n, r) = 1$. Let $Q$ be the Bell number corresponding to the remainder when the absolute value of this $n$ is divided by $11$. Compute $Q$. | 203 | graphs = [
Graph(
let={
"start": Const(40000),
"upper": Const(40503),
"modulus": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Const(2)), Mul(Const(-493), Var("x")), Const(-1988)), Const(0)))),
"result": MinOverSet(set=SolutionsSet(v... | NT | COMB | EXTREMUM | sympy | VIETA_SUM | [
"VIETA_SUM"
] | b33a7a | nt_min_coprime_above_v1 | null | 5 | 0 | [
"VIETA_SUM"
] | 1 | 0.073 | 2026-02-08T18:05:06.561116Z | {
"verified": true,
"answer": 203,
"timestamp": "2026-02-08T18:05:06.633781Z"
} | 72798a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 138,
"completion_tokens": 1210
},
"timestamp": "2026-02-18T13:57:20.083Z",
"answer": 203
},
{
... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "VIETA_SUM",
"status": "ok"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
9c4cb0 | nt_count_divisors_in_range_v1_677425708_2693 | Let $n = 166320$. Let $a$ be the smallest integer $d \geq 2$ that divides $55190041$. Let $b = 11880$. Determine the number of positive divisors $d$ of $n$ such that $a \leq d \leq b$. | 133 | graphs = [
Graph(
let={
"n": Const(166320),
"a": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(55190041))))),
"b": Const(11880),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), c... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | nt_count_divisors_in_range_v1 | null | 4 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.106 | 2026-02-08T05:12:07.849965Z | {
"verified": true,
"answer": 133,
"timestamp": "2026-02-08T05:12:07.955733Z"
} | 2a0397 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 176,
"completion_tokens": 6240
},
"timestamp": "2026-02-11T23:04:41.956Z",
"answer": 133
},
{
"i... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
afe561 | diophantine_fbi2_count_v1_865884756_3605 | Let $n$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 6760000$. Let $k = 60$ and $m = 6$. Let $T$ be the set of all positive integers $k_1$ such that $1 \leq k_1 \leq n$ and $240$ divides $k_1$, and let $t$ be the number of elements in $T$. Determine the number of ... | 2 | graphs = [
Graph(
let={
"_c": Const(65),
"_m": Const(6),
"_n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(6760000)))), e... | NT | null | COUNT | sympy | B3 | [
"B3/C2",
"C2/C2"
] | 67f475 | diophantine_fbi2_count_v1 | null | 7 | 0 | [
"B3",
"C2"
] | 2 | 0.011 | 2026-02-08T17:30:57.250919Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-02-08T17:30:57.261619Z"
} | 181cc3 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 193,
"completion_tokens": 1671
},
"timestamp": "2026-02-18T03:33:17.341Z",
"answer": 2
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MA... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
dcaad5 | comb_bell_compute_v1_151522320_1975 | Let $k_{\text{max}}$ be the largest integer $k$ such that $2^k \leq 39341198735$. Let $n$ be the number of positive integers $n'$ such that $1 \leq n' \leq 72$, $6$ divides $n'$, and $\gcd(n', k_{\text{max}}) = 1$. Compute the $n$th Bell number, which counts the number of partitions of a set of size $n$. Find the value... | 21,147 | graphs = [
Graph(
let={
"_m": Const(6),
"_n": MaxOverSet(set=SolutionsSet(var=Var("k"), condition=Leq(Pow(Const(2), Var("k")), Const(39341198735)))),
"n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(72)), Divides(... | NT | COMB | COMPUTE | sympy | MAX_VAL | [
"MAX_VAL/C5"
] | 33e5b1 | comb_bell_compute_v1 | null | 7 | 0 | [
"C5",
"MAX_VAL"
] | 2 | 0.002 | 2026-02-08T04:29:46.218674Z | {
"verified": true,
"answer": 21147,
"timestamp": "2026-02-08T04:29:46.220831Z"
} | 6f546f | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 225,
"completion_tokens": 1026
},
"timestamp": "2026-02-10T16:49:38.015Z",
"answer": 21147
},
{
... | 1 | [
{
"lemma": "C5",
"status": "ok_later"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "same_pattern_wrong"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "ok"
... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
f0c2c8 | antilemma_cartesian_v1_655260480_4103 | Let $x$ be the number of ordered pairs $(a,b)$ such that $1 \leq a \leq 21$ and $1 \leq b \leq 42$. Let $m = x + 2$. The Fibonacci entry point modulo $m$ is defined as the smallest positive integer $k$ such that the $k$th Fibonacci number $F_k$ is divisible by $m$. Find the value of this entry point. | 126 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(21)), right=IntegerRange(start=Const(1), end=Const(42)))),
"Q": FibonacciEntryPoint(modulus=Sum(Abs(arg=Ref(name='x')), Const(value=2))),
},
goal=Ref("Q"),
)... | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | antilemma_cartesian_v1 | null | 2 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.008 | 2026-02-08T17:43:35.224343Z | {
"verified": true,
"answer": 126,
"timestamp": "2026-02-08T17:43:35.232686Z"
} | 31cfd3 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 138,
"completion_tokens": 1395
},
"timestamp": "2026-02-18T07:43:46.370Z",
"answer": 126
},
{
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
... | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||
128a3c | comb_sum_binomial_row_v1_1218484723_7659 | Let $n$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 15$ such that $17a^4 + 68a^3b + 102a^2b^2 + 68ab^3 + 17b^4 = 1114112$. Compute $2^n$. | 32,768 | graphs = [
Graph(
let={
"_n": Const(17),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(15)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(15)), Eq(Sum(Mul(Ref("_n"), Pow(Var("b"), Const(4))), Mu... | COMB | null | SUM | sympy | POLY_ORBIT_HENSEL | [
"POLY4_COUNT"
] | 861d91 | comb_sum_binomial_row_v1 | null | 3 | 0 | [
"POLY4_COUNT",
"POLY_ORBIT_HENSEL"
] | 2 | 0.357 | 2026-02-25T09:07:11.779829Z | {
"verified": true,
"answer": 32768,
"timestamp": "2026-02-25T09:07:12.136915Z"
} | 559d72 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 188,
"completion_tokens": 643
},
"timestamp": "2026-03-30T05:45:59.785Z",
"answer": 32768
},
{
"i... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "POLY4_COUNT",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": ... | {
"lo": -6.2,
"mid": -2.87,
"hi": 0.44
} | ||
988585 | alg_sum_powers_v1_1218484723_2035 | Let $M$ be the largest positive divisor of $25060027$ that is at most $5003$. Let $P = \min\{ x + y : x, y > 0,\ xy = 772641 \}$. Compute $\left( \sum_{k=1}^{P} k^3 \right) \bmod M$. | 4,726 | graphs = [
Graph(
let={
"_m": Const(3),
"_n": MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Leq(Var("d"), Const(5003)), Divides(divisor=Var("d"), dividend=Const(25060027))))),
"result": Mod(value=Summation(var="k", start=Const(1), end=Mi... | NT | null | COMPUTE | sympy | MAX_DIVISOR | [
"MAX_DIVISOR/B3"
] | 51e324 | alg_sum_powers_v1 | null | 5 | 0 | [
"B3",
"MAX_DIVISOR"
] | 2 | 0.07 | 2026-02-25T03:43:49.386095Z | {
"verified": true,
"answer": 4726,
"timestamp": "2026-02-25T03:43:49.455878Z"
} | c11f7f | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 184,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T02:41:37.552Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemm... | {
"lo": 1.14,
"mid": 4.13,
"hi": 6.32
} | ||
4c8e2c | modular_min_linear_v1_1742523217_234 | Let $a = 81921$, $b = 61383$, and $m = 86499$. Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 72$, $\gcd(p, q) = 1$, and $p < q$. Let $\phi$ denote Euler's totient function evaluated at the number of elements in $S$. Determine the value of the smallest inte... | 988 | graphs = [
Graph(
let={
"a": Const(81921),
"b": Const(61383),
"m": Const(86499),
"result": MinOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), EulerPhi(n=CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')),... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/ONE_PHI_2"
] | 761f00 | modular_min_linear_v1 | null | 6 | 0 | [
"COPRIME_PAIRS",
"ONE_PHI_2"
] | 2 | 6.73 | 2026-02-08T02:56:26.069749Z | {
"verified": true,
"answer": 988,
"timestamp": "2026-02-08T02:56:32.799445Z"
} | 97c6c7 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 248,
"completion_tokens": 4029
},
"timestamp": "2026-02-09T15:18:09.279Z",
"answer": 988
},
{
"id... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "ONE_PHI_2",
... | {
"lo": -6.51,
"mid": -0.31,
"hi": 5.43
} | ||
3564b1 | nt_min_crt_v1_865884756_2389 | Let $a = 0$, $b = 10$, $m = 5$, and $k = 11$. Let $u = \sum_{k_2=1}^4 k_2$ and define $s = \sum_{k_1=1}^u k_1$. Let $r$ be the smallest positive integer $n$ such that $n \leq s$, $n \equiv a \pmod{m}$, and $n \equiv b \pmod{k}$. Compute the remainder when $91661 \cdot r$ is divided by $87980$.
Find the value of this e... | 36,810 | graphs = [
Graph(
let={
"_n": Const(87980),
"m": Const(5),
"k": Const(11),
"a": Const(0),
"b": Const(10),
"upper": Summation(var="k1", start=Const(1), end=Summation(var="k2", start=Const(1), end=Const(4), expr=Var("k2")), expr=Var("k1")... | NT | null | EXTREMUM | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC/SUM_ARITHMETIC"
] | 2a57af | nt_min_crt_v1 | null | 4 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.008 | 2026-02-08T16:43:41.327248Z | {
"verified": true,
"answer": 36810,
"timestamp": "2026-02-08T16:43:41.334831Z"
} | 4673e3 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 176,
"completion_tokens": 650
},
"timestamp": "2026-02-17T11:00:58.839Z",
"answer": 36810
},
{... | 1 | [
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
3dc37f | antilemma_cartesian_v1_2051736721_1816 | Let $x$ be the number of ordered pairs $(a, b)$ such that $1 \leq a \leq 36$ and $1 \leq b \leq 37$.\\
Let $y$ be the number of ordered pairs $(c, d)$ such that $1 \leq c \leq 7$ and $1 \leq d \leq 11$.\\
Compute the remainder when $y - x$ is divided by $74245$. | 72,990 | graphs = [
Graph(
let={
"_n": Const(74245),
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(36)), right=IntegerRange(start=Const(1), end=Const(37)))),
"Q": Mod(value=Sub(CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1),... | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN",
"COUNT_CARTESIAN"
] | f9c395 | antilemma_cartesian_v1 | negation_mod | 2 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.002 | 2026-02-08T16:13:10.037915Z | {
"verified": true,
"answer": 72990,
"timestamp": "2026-02-08T16:13:10.039894Z"
} | cc3bff | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 214,
"completion_tokens": 507
},
"timestamp": "2026-02-24T20:24:52.645Z",
"answer": 72990
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status":... | {
"lo": -6.4,
"mid": -4.13,
"hi": -2.01
} | ||
3ec33b | nt_count_divisors_in_range_v1_2051736721_557 | Let $n = 45360$. Let $A$ be the set of all divisors $d$ of $n$ such that $40 \le d \le 2169$, where $2169$ is the number of ordered pairs $(i,j)$ with $1 \le i \le 9$ and $1 \le j \le 241$. Let $r = |A|$. Compute $\sum_{k=1}^{r} \tau(k)$, where $\tau(k)$ denotes the number of positive divisors of $k$. | 263 | graphs = [
Graph(
let={
"n": Const(45360),
"a": Const(40),
"b": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(9)), right=IntegerRange(start=Const(1), end=Const(241)))),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condi... | NT | null | COUNT | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | nt_count_divisors_in_range_v1 | null | 4 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.041 | 2026-02-08T15:31:35.609726Z | {
"verified": true,
"answer": 263,
"timestamp": "2026-02-08T15:31:35.651193Z"
} | 3cea0b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 159,
"completion_tokens": 3659
},
"timestamp": "2026-02-16T09:03:32.639Z",
"answer": 263
},
{
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
1a1d4f | diophantine_product_count_v1_717093673_2879 | Let $k = 240$ and let $u$ be the number of ordered pairs $(i, j)$ of positive integers with $1 \leq i \leq 15$ and $1 \leq j \leq 16$ such that $\gcd(i, j) = 1$. Determine the number of positive integers $x$ such that $1 \leq x \leq u$, $x$ divides $k$, and $\frac{k}{x} \leq u$. | 18 | graphs = [
Graph(
let={
"k": Const(240),
"upper": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(GCD(a=Var("i"), b=Var("j")), Const(1)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(15)), right=IntegerRange(start=Const(1), ... | NT | null | COUNT | sympy | COUNT_COPRIME_GRID | [
"COUNT_COPRIME_GRID"
] | 20ec03 | diophantine_product_count_v1 | null | 5 | 0 | [
"COUNT_COPRIME_GRID"
] | 1 | 0.279 | 2026-02-08T17:15:29.090981Z | {
"verified": true,
"answer": 18,
"timestamp": "2026-02-08T17:15:29.370018Z"
} | 8ef8a5 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 145,
"completion_tokens": 2000
},
"timestamp": "2026-02-17T23:05:35.522Z",
"answer": 18
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status":... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
0d912d | nt_count_coprime_v1_677425708_2573 | Let $k$ be the smallest integer $d \geq 2$ that divides 2021. Let $\text{upper} = 21609$. Compute the number of positive integers $n$ such that $1 \leq n \leq \text{upper}$ and $\gcd(n, k) = 1$. | 21,107 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": Const(21609),
"k": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(2021))))),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), cond... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | nt_count_coprime_v1 | null | 4 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 1.922 | 2026-02-08T05:07:35.225892Z | {
"verified": true,
"answer": 21107,
"timestamp": "2026-02-08T05:07:37.148200Z"
} | e6c91c | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 180,
"completion_tokens": 831
},
"timestamp": "2026-02-11T22:57:43.589Z",
"answer": 21107
},
{
"... | 1 | [
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
c28886 | antilemma_k3_v1_1915831931_1153 | Let $n = 86687$. Define $x$ to be the sum of Euler's totient function $\phi(d)$ over all positive divisors $d$ of $n$. Let $c = 73396$. Compute the remainder when $c \cdot x$ is divided by $84847$. | 57,063 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=86687), var='d', expr=EulerPhi(n=Var(name='d'))),
"_c": Const(73396),
"Q": Mod(value=Mul(Ref("_c"), Ref("x")), modulus=Const(84847)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T15:54:51.411405Z | {
"verified": true,
"answer": 57063,
"timestamp": "2026-02-08T15:54:51.412169Z"
} | fdaaab | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 108,
"completion_tokens": 1135
},
"timestamp": "2026-02-16T16:33:11.118Z",
"answer": 57063
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
7b2b65 | comb_factorial_compute_v1_677425708_3299 | Let $n$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 205800$, $\gcd(p, q) = 1$, and $p < q$. Let $c = 49695$. Compute the remainder when $c \cdot n!$ is divided by 58288. | 52,400 | graphs = [
Graph(
let={
"_n": Const(58288),
"n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=205800)), Eq(left=GCD(a=Var(name='p'), b=Var(... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_factorial_compute_v1 | null | 6 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.006 | 2026-02-08T05:38:19.203604Z | {
"verified": true,
"answer": 52400,
"timestamp": "2026-02-08T05:38:19.209790Z"
} | f0679a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 124,
"completion_tokens": 4925
},
"timestamp": "2026-02-12T12:16:02.374Z",
"answer": 52400
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
5d7fa5 | diophantine_fbi2_min_v1_1520064083_5999 | Let $A$ be the set of all prime numbers $n$ such that $2 \leq n \leq 501$. Let $u$ be the number of elements $n$ in $A$ for which the sum of the decimal digits of $n$ is odd. Determine the smallest positive integer $d$ such that $5 \leq d \leq u$, $d$ divides $240$, and $\frac{240}{d} \geq 4$. Let this value be $r$. Co... | 11 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(4),
"k": Const(240),
"upper": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_m")),... | NT | null | EXTREMUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW/L3B"
] | 5f10c3 | diophantine_fbi2_min_v1 | null | 6 | 0 | [
"L3B",
"MAX_PRIME_BELOW"
] | 2 | 0.012 | 2026-02-08T07:46:13.035289Z | {
"verified": true,
"answer": 11,
"timestamp": "2026-02-08T07:46:13.047562Z"
} | 05cf47 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 212,
"completion_tokens": 2183
},
"timestamp": "2026-02-13T12:16:18.010Z",
"answer": 11
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3B",
"status": "ok_later"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
5497bc | alg_poly4_sum_v1_601307018_9995 | Let $p_{\max}$ be the largest prime $n$ such that $2 \le n \le 452$. Compute the remainder when $$\sum_{a=1}^{p_{\max}} \sum_{b=1}^{449} (82a^4 - 212a^3b + 222a^2b^2 - 92ab^3 + 17b^4)$$ is divided by $86303$. | 61,155 | graphs = [
Graph(
let={
"_n": Const(86303),
"result": Mod(value=SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), L... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | alg_poly4_sum_v1 | null | 5 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.84 | 2026-03-10T10:26:16.853785Z | {
"verified": true,
"answer": 61155,
"timestamp": "2026-03-10T10:26:17.693824Z"
} | 74d2f7 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 202,
"completion_tokens": 9885
},
"timestamp": "2026-04-19T12:46:05.341Z",
"answer": 61155
},
{
... | 1 | [
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "... | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
48b7d6 | v1_endings_v1_1874849503_361 | Let $n = 31966$ and $p = 5$. Let $v_p(n!)$ denote the largest integer $k$ such that $p^k$ divides $n!$. Compute the value of $v_p(n!) - \left\lfloor \log_p n \right\rfloor$. | 7,983 | graphs = [
Graph(
let={
"n_val": Const(31966),
"p_val": Const(5),
"n_fact": Factorial(Ref("n_val")),
"vp_fact": MaxKDivides(target=Ref("n_fact"), base=Ref("p_val")),
"log_p_n": Floor(Log(left=Ref(name='n_val'), right=Ref(name='p_val'))),
... | NT | null | COMPUTE | sympy | V1 | [
"V1"
] | dae96f | v1_endings_v1 | null | 3 | null | [
"V1"
] | 1 | 0.001 | 2026-02-08T12:58:04.329697Z | {
"verified": true,
"answer": 7983,
"timestamp": "2026-02-08T12:58:04.330438Z"
} | bc2d1f | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 176,
"completion_tokens": 832
},
"timestamp": "2026-02-09T16:10:02.207Z",
"answer": 7983
},
{
"id... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K5",
"status": "same_pattern_wrong"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V1",
"status": "ok"
},
{
"lemma": "V5",
"status":... | {
"lo": -6.5,
"mid": -0.2,
"hi": 6.11
} | ||
e7ab02 | comb_binomial_compute_v1_865884756_6481 | Let $n = 13$. Let $k$ be the smallest integer $d$ such that $d \geq 2$ and $d$ divides $2695$. Compute $\binom{n}{k}$. | 1,287 | graphs = [
Graph(
let={
"_n": Const(2),
"n": Const(13),
"k": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(2695))))),
"result": Binom(n=Ref("n"), k=Ref("k")),
},
goal=... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | comb_binomial_compute_v1 | null | 3 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.002 | 2026-02-08T19:13:39.056366Z | {
"verified": true,
"answer": 1287,
"timestamp": "2026-02-08T19:13:39.058280Z"
} | 75ae7f | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 104,
"completion_tokens": 752
},
"timestamp": "2026-02-16T18:36:20.022Z",
"answer": 1287
},
{
"id": 11,
... | 2 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V7",
... | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
9791f0 | antilemma_k3_v1_48377204_3047 | Let $m = 83841$ and $n = 27714$. Define $x$ to be the sum of $\phi(d)$ over all positive divisors $d$ of $n$, where $\phi$ is Euler's totient function. Let $S$ be the sum of all real solutions $x_1$ to the equation $x_1^2 - 7690x_1 - 605904 = 0$. Compute the remainder when $S \cdot x$ is divided by $m$. | 80,679 | graphs = [
Graph(
let={
"_m": Const(83841),
"_n": Const(27714),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Mod(value=Mul(SumOverSet(set=SolutionsSet(var=Var("x1"), condition=Eq(Sum(Pow(Var("x1"), Const(2)), Mul(Const(... | NT | COMB | COMPUTE | sympy | K13 | [
"VIETA_SUM",
"IDENTITY_MUL_ZERO",
"K3"
] | 23907a | antilemma_k3_v1 | affine_mod | 3 | 0 | [
"IDENTITY_MUL_ZERO",
"K13",
"K3",
"VIETA_SUM"
] | 4 | 0.004 | 2026-02-08T17:08:48.561804Z | {
"verified": true,
"answer": 80679,
"timestamp": "2026-02-08T17:08:48.565427Z"
} | ed4706 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 153,
"completion_tokens": 2159
},
"timestamp": "2026-02-17T20:33:04.744Z",
"answer": 80679
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "IDENTITY_MUL_ZERO",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "M... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
3caba0 | modular_min_linear_v1_1742523217_3246 | Let $a = 19115$ and $m = 52046$. Let $b$ be the number of integers $n$ with $1 \leq n \leq 16561$ such that the sum of the decimal digits of $n$ is odd. Determine the smallest positive integer $x$ such that $1 \leq x \leq m$ and
$$
a \cdot x \equiv b \pmod{m}.
$$ | 12,999 | graphs = [
Graph(
let={
"_n": Const(2),
"a": Const(19115),
"b": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(16561)), Eq(Mod(value=DigitSum(Var("n")), modulus=Ref("_n")), Const(1))))),
"m": Const(52046)... | NT | null | EXTREMUM | sympy | L3B | [
"L3B"
] | cc148f | modular_min_linear_v1 | null | 6 | 0 | [
"L3B"
] | 1 | 2.097 | 2026-02-08T05:44:53.080736Z | {
"verified": true,
"answer": 12999,
"timestamp": "2026-02-08T05:44:55.177239Z"
} | 6aed46 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 137,
"completion_tokens": 5061
},
"timestamp": "2026-02-12T13:35:22.836Z",
"answer": 12999
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3B",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
... | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
21a603 | comb_binomial_compute_v1_1978505735_7446 | Let $m$ be the maximum value of $x_1 y_1$ over all ordered pairs $(x_1, y_1)$ of positive integers such that $x_1 + y_1 = 14$. Let $n$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = m$. Compute $\binom{n}{7}$. | 3,432 | graphs = [
Graph(
let={
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var(... | ALG | COMB | COMPUTE | sympy | B1 | [
"B1/B3"
] | 80b49d | comb_binomial_compute_v1 | null | 3 | 0 | [
"B1",
"B3"
] | 2 | 0.003 | 2026-02-08T20:16:19.100003Z | {
"verified": true,
"answer": 3432,
"timestamp": "2026-02-08T20:16:19.102991Z"
} | 4b24ba | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 134,
"completion_tokens": 1149
},
"timestamp": "2026-02-25T01:54:19.772Z",
"answer": 3432
},
{... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -8.48,
"mid": -5.37,
"hi": -3.03
} | ||
c1250a | sequence_fibonacci_compute_v1_677425708_828 | Let $n$ be the largest prime number satisfying $2 \leq n \leq 23$. Compute the remainder when $73181$ times the $n$th Fibonacci number is divided by $82064$. | 2,397 | graphs = [
Graph(
let={
"_n": Const(2),
"n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Const(23)), IsPrime(Var("n"))))),
"result": Fibonacci(arg=Ref(name='n')),
"Q": Mod(value=Mul(Const(73181), Ref("result"... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | sequence_fibonacci_compute_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.001 | 2026-02-08T03:47:34.857115Z | {
"verified": true,
"answer": 2397,
"timestamp": "2026-02-08T03:47:34.858450Z"
} | c3a2ec | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 159,
"completion_tokens": 3564
},
"timestamp": "2026-02-09T13:30:34.899Z",
"answer": 2397
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
}
] | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
a8949f | antilemma_product_of_sums_v1_168721529_715 | Let $S_1$ be the set of all ordered pairs $(k,\_j)$ with $1 \leq k \leq 8$ and $1 \leq \_j \leq 4$. Let $a$ be the sum of all values of $k$ as $(k,\_j)$ ranges over $S_1$. Let $S_2$ be the set of all ordered pairs $(i,j)$ with $1 \leq i \leq 9$ and $1 \leq j \leq 5$. Let $b$ be the sum of all values of $ij$ as $(i,j)$ ... | 44,027 | graphs = [
Graph(
let={
"x": Mul(SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("k"), Var("_j")]), condition=Const(1), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(8)), right=IntegerRange(start=Const(1), end=Const(4)))), expr=Var("k"))), SumOverSet(set=... | NT | null | COMPUTE | sympy | PRODUCT_OF_SUMS | [
"PRODUCT_OF_SUMS"
] | f2b2b0 | antilemma_product_of_sums_v1 | null | 2 | 0 | [
"PRODUCT_OF_SUMS"
] | 1 | 0.001 | 2026-02-08T13:12:38.105927Z | {
"verified": true,
"answer": 44027,
"timestamp": "2026-02-08T13:12:38.106827Z"
} | e8fc7f | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 285,
"completion_tokens": 744
},
"timestamp": "2026-02-09T08:16:21.512Z",
"answer": 44027
},
{
"i... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "PRODUCT_OF_SUMS",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}... | {
"lo": -6.69,
"mid": -2.39,
"hi": 1.83
} | ||
bee470 | diophantine_fbi2_count_v1_1248542787_729 | Let $k = 360$. Compute the number of integers $d$ such that $3 \leq d \leq 107$, $d$ divides $k$, $\frac{k}{d} \geq 3$, and
$$
\frac{k}{d} \leq \text{the number of integers } n \text{ with } 1 \leq n \leq 539 \text{ such that } n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{5}.
$$
Let $c = 26549$. Find the rema... | 78,462 | graphs = [
Graph(
let={
"k": Const(360),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(3)), Leq(Var("d"), Const(107)), Divides(divisor=Var("d"), dividend=Ref("k")), Geq(Div(Ref("k"), Var("d")), Const(3)), Leq(Div(Ref("k"), Var("d")), CountOve... | NT | null | COUNT | sympy | L3C | [
"L3C"
] | 73f8b0 | diophantine_fbi2_count_v1 | null | 5 | 0 | [
"L3C"
] | 1 | 0.008 | 2026-02-08T03:21:21.946816Z | {
"verified": true,
"answer": 78462,
"timestamp": "2026-02-08T03:21:21.955081Z"
} | 1494bf | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 256,
"completion_tokens": 2990
},
"timestamp": "2026-02-09T20:26:54.437Z",
"answer": 78462
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"s... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
97b16b | comb_count_partitions_v1_1742523217_1029 | Let $n$ be the number of integers $t$ with $18 \leq t \leq 116$ such that there exist positive integers $a$ and $b$ with $1 \leq a \leq 4$, $1 \leq b \leq 15$, and $t = 14a + 4b$. Let $P(n)$ denote the number of integer partitions of $n$. Compute the remainder when $27565 \cdot P(n)$ is divided by $56416$. | 39,195 | graphs = [
Graph(
let={
"_n": Const(56416),
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=4)), Geq(left=Va... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_count_partitions_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T03:23:49.101019Z | {
"verified": true,
"answer": 39195,
"timestamp": "2026-02-08T03:23:49.102597Z"
} | 4de946 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 220,
"completion_tokens": 32373
},
"timestamp": "2026-02-23T22:15:55.843Z",
"answer": 39195
},
{
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": ... | {
"lo": 1.97,
"mid": 4.36,
"hi": 6.69
} | ||
8343d2 | geo_count_lattice_rect_v1_1918700295_3343 | Compute the number of lattice points in the rectangle $[0, 225] \times [0, 186]$, including its boundary. | 42,262 | graphs = [
Graph(
let={
"a": Const(225),
"b": Const(186),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0 | 2026-02-08T08:32:42.521947Z | {
"verified": true,
"answer": 42262,
"timestamp": "2026-02-08T08:32:42.522325Z"
} | 61dd5e | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 139,
"completion_tokens": 319
},
"timestamp": "2026-02-24T09:41:58.889Z",
"answer": 42262
},
{
"i... | 1 | [] | {
"lo": -3.84,
"mid": -1.67,
"hi": 1.32
} | ||||
f8f32a | comb_count_derangements_v1_349078426_1169 | Let $n$ be the number of positive integers less than or equal to 17 whose digit sum is even. Compute the subfactorial of $n$. | 14,833 | graphs = [
Graph(
let={
"_n": Const(17),
"n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_n")), Eq(Mod(value=DigitSum(Var("n")), modulus=Const(2)), Const(0))))),
"result": Subfactorial(arg=Ref(name='n')),
... | COMB | null | COUNT | sympy | L3B | [
"L3B"
] | cc148f | comb_count_derangements_v1 | null | 3 | 0 | [
"L3B"
] | 1 | 0.002 | 2026-02-08T13:27:14.762387Z | {
"verified": true,
"answer": 14833,
"timestamp": "2026-02-08T13:27:14.764205Z"
} | 372d17 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 142,
"completion_tokens": 733
},
"timestamp": "2026-02-24T18:22:59.958Z",
"answer": 14833
},
{
"i... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "L3B",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"sta... | {
"lo": -4.92,
"mid": -2.91,
"hi": -0.68
} | ||
f9d17c | comb_count_derangements_v1_397696148_798 | Let $n$ be the smallest integer $d$ such that $d \geq 2$ and $d$ divides $41503$. Compute the subfactorial of $n$. | 1,854 | graphs = [
Graph(
let={
"_n": Const(2),
"n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(41503))))),
"result": Subfactorial(arg=Ref(name='n')),
},
goal=Ref("result"),
)
] | NT | COMB | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | comb_count_derangements_v1 | null | 2 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.001 | 2026-02-08T11:44:28.692786Z | {
"verified": true,
"answer": 1854,
"timestamp": "2026-02-08T11:44:28.693735Z"
} | e66cba | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 85,
"completion_tokens": 791
},
"timestamp": "2026-02-14T18:06:35.620Z",
"answer": 1854
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
df70e4 | diophantine_fbi2_min_v1_784195855_7092 | Let $k$ be the number of positive integers $n \leq 19$ such that the sum of the digits of $n$ is odd. Let $d$ be the smallest integer $d$ with $2 \leq d \leq 20$ such that $d$ divides $k$ and $\frac{k}{d} \geq 4$. Compute the remainder when $71922 \cdot d$ is divided by $90677$. | 53,167 | graphs = [
Graph(
let={
"k": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(19)), Eq(Mod(value=DigitSum(Var("n")), modulus=Const(2)), Const(1))))),
"upper": Const(20),
"result": MinOverSet(set=SolutionsSet(var=Var("d... | NT | null | EXTREMUM | sympy | L3B | [
"L3B"
] | cc148f | diophantine_fbi2_min_v1 | null | 4 | 0 | [
"L3B"
] | 1 | 0.004 | 2026-02-08T09:05:09.508153Z | {
"verified": true,
"answer": 53167,
"timestamp": "2026-02-08T09:05:09.512401Z"
} | cb291d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 139,
"completion_tokens": 844
},
"timestamp": "2026-02-14T00:11:36.260Z",
"answer": 53167
},
{... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "L3B",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
155088 | alg_poly3_min_v1_1218484723_2782 | Let $M$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 30$ such that $13a^2 - 2ab + 2b^2 \le 832$. Let $Q$ be the minimum value of
$$
13552a_1^3 + 43560a_1^{k} b_1 + 13068a_1b_1^2 + 13068b_1^3
$$
over all positive integers $a_1, b_1$ with $1 \le a_1 \le M$, $1 \le b_1 \le 134$, where
... | 83,248 | graphs = [
Graph(
let={
"_m": Const(14),
"_n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(30)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(30)), Leq(Sum(Mul(Const(13), Pow(Var("a"), Const(2))), ... | ALG | null | COMPUTE | sympy | QF_PSD_COUNT_LEQ | [
"QF_PSD_COUNT_LEQ/QF_PSD_MIN"
] | 7f6761 | alg_poly3_min_v1 | null | 6 | 0 | [
"QF_PSD_COUNT_LEQ",
"QF_PSD_MIN"
] | 2 | 0.046 | 2026-02-25T04:29:40.148757Z | {
"verified": true,
"answer": 83248,
"timestamp": "2026-02-25T04:29:40.195001Z"
} | fe9909 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 332,
"completion_tokens": 6126
},
"timestamp": "2026-03-29T06:32:14.714Z",
"answer": 83248
},
{
"... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
},
{
"lemma": "QF_PSD_MIN",
"status": "ok_later"
}
] | {
"lo": -4.26,
"mid": -1.8,
"hi": 1.26
} | ||
a6040f | nt_count_intersection_v1_153355830_2359 | Let $N = 20000$. Define $a$ to be the number of integers $t$ with $5 \leq t \leq 15$ such that there exist positive integers $a', b'$ with $1 \leq a' \leq 3$, $1 \leq b' \leq 3$, and $t = 2a' + 3b'$. Let $b = 14$. Define $S$ to be the set of all positive integers $n \leq N$ such that $a$ divides $n$ and $\gcd(n, b) = 1... | 952 | graphs = [
Graph(
let={
"N": Const(20000),
"a": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=3)), Geq(left=Var... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_count_intersection_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 1.029 | 2026-02-08T07:04:50.294383Z | {
"verified": true,
"answer": 952,
"timestamp": "2026-02-08T07:04:51.323815Z"
} | a70cf6 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 185,
"completion_tokens": 1150
},
"timestamp": "2026-02-13T07:42:28.243Z",
"answer": 1905
},
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
6b8cbe | antilemma_k3_v1_865884756_5091 | Compute the sum
$$
\sum_{d \mid 23481} \phi(d),
$$
where $\phi$ denotes Euler's totient function. | 23,481 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=23481), var='d', expr=EulerPhi(n=Var(name='d'))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0 | 2026-02-08T18:22:40.204652Z | {
"verified": true,
"answer": 23481,
"timestamp": "2026-02-08T18:22:40.204994Z"
} | b8460f | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 95,
"completion_tokens": 319
},
"timestamp": "2026-02-16T12:18:47.703Z",
"answer": 23481
},
{
"id": 11,
... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
96f3cf | alg_poly4_sum_v1_1218484723_731 | Let $P = \max\{ n : n \geq 2, n \leq 339, n \text{ is prime} \}$. Find the remainder when $\sum_{a=1}^{198} \sum_{b=1}^{198} \left( P a^4 + 296a^3b + 600a^2b^2 + 32ab^3 + 32b^4 \right)$ is divided by $54704$. | 21,906 | graphs = [
Graph(
let={
"_n": Const(339),
"result": Mod(value=SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(198)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(198)))), expr=Sum(Mul(MaxO... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | alg_poly4_sum_v1 | null | 5 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.091 | 2026-02-25T02:28:02.135059Z | {
"verified": true,
"answer": 21906,
"timestamp": "2026-02-25T02:28:02.225857Z"
} | 42c86a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 211,
"completion_tokens": 32768
},
"timestamp": "2026-03-10T01:21:55.015Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": 3.81,
"mid": 5.7,
"hi": 7.82
} | ||
db4a65 | comb_binomial_compute_v1_601307018_2852 | Let $n$ be the number of integers $v$ in the range $72 \leq v \leq 1800$ for which there exist integers $a, b \in \{1, 2, 3, 4, 5\}$ such that $32a \cdot b + 32b^2 + 8a^2 = v$. Let $M = \binom{n}{6}$. Find the remainder when $44121M$ is divided by $70880$. | 11,796 | graphs = [
Graph(
let={
"_n": Const(70880),
"n": CountOverSet(set=SolutionsSet(var=Var("v"), condition=And(Geq(Var("v"), Const(72)), Leq(Var("v"), Const(1800)), Exists(var=Tuple(elements=[Var(name='a'), Var(name='b')]), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq... | COMB | null | COMPUTE | sympy | QF_PSD_DISTINCT | [
"QF_PSD_DISTINCT"
] | a8f9cb | comb_binomial_compute_v1 | null | 4 | 0 | [
"QF_PSD_DISTINCT"
] | 1 | 0.004 | 2026-03-10T03:28:56.789124Z | {
"verified": true,
"answer": 11796,
"timestamp": "2026-03-10T03:28:56.792903Z"
} | 0c03cd | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 219,
"completion_tokens": 2563
},
"timestamp": "2026-03-29T06:40:59.595Z",
"answer": 11796
},
{
"... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "QF_PSD_DISTINCT",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
... | {
"lo": -2.46,
"mid": 1.23,
"hi": 4.93
} | ||
f4fb01 | algebra_quadratic_discriminant_v1_1520064083_8423 | Let $a = -9$ and $c = 10$. Let $b$ be the number of nonnegative integers $j$ such that $0 \le j \le 321$ and $\binom{k}{j}$ is odd, where $k$ is the number of prime numbers $n$ satisfying $2 \le n \le 2131$. Compute $b^2 - 4ac$. | 424 | graphs = [
Graph(
let={
"_n": Const(2),
"a": Const(-9),
"b": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(321)), Eq(Mod(value=Binom(n=CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)... | NT | null | COMPUTE | sympy | COUNT_PRIMES | [
"COUNT_PRIMES/V8"
] | e03b9d | algebra_quadratic_discriminant_v1 | null | 6 | 0 | [
"COUNT_PRIMES",
"V8"
] | 2 | 0.002 | 2026-02-08T10:10:33.404048Z | {
"verified": true,
"answer": 424,
"timestamp": "2026-02-08T10:10:33.406329Z"
} | 394345 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 132,
"completion_tokens": 1705
},
"timestamp": "2026-02-14T06:41:34.499Z",
"answer": 424
},
{
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
a1bfa6 | comb_count_partitions_v1_1874849503_105 | Let $n$ be the number of integers $t$ such that $12 \leq t \leq 75$ and there exist positive integers $a$, $b$ with $1 \leq a \leq 8$, $1 \leq b \leq 5$, and $t = 5a + 7b$. Let $r$ be the number of integer partitions of $n$. Find the remainder when $4 - r$ is divided by $76572$. | 39,238 | graphs = [
Graph(
let={
"_n": Const(76572),
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=8)), Geq(left=Va... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_count_partitions_v1 | null | 7 | 0 | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T12:48:43.572524Z | {
"verified": true,
"answer": 39238,
"timestamp": "2026-02-08T12:48:43.573870Z"
} | 5282d2 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 218,
"completion_tokens": 1484
},
"timestamp": "2026-02-09T13:51:07.258Z",
"answer": 39238
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": 1.15,
"mid": 4.18,
"hi": 6.61
} | ||
079ee0 | sequence_lucas_compute_v1_1439011603_348 | Let $n$ be the number of integers $t$ such that $28 \leq t \leq 58$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 4$, $1 \leq b \leq 6$, and $t = 5a + 3b + 20$. Compute the $n$-th Lucas number. | 64,079 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=4)), Geq(left=Var(name='b'), right=Const(value=1... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | sequence_lucas_compute_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.003 | 2026-02-08T15:25:28.658617Z | {
"verified": true,
"answer": 64079,
"timestamp": "2026-02-08T15:25:28.661234Z"
} | 599c63 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 128,
"completion_tokens": 1727
},
"timestamp": "2026-02-16T06:27:25.768Z",
"answer": 64079
},
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
f5cf0f | nt_lcm_compute_v1_1353956133_558 | Let $a$ be the largest prime number less than or equal to $2372$. Let $b = 1647$. Define $\text{result}$ to be the least common multiple of $a$ and $b$. Let $Q$ be the remainder when $\text{result}$ is divided by $88959$. Compute $Q$. | 79,800 | graphs = [
Graph(
let={
"_n": Const(2),
"a": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Const(2372)), IsPrime(Var("n"))))),
"b": Const(1647),
"result": LCM(a=Ref("a"), b=Ref("b")),
"Q": Mod(value... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | nt_lcm_compute_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.001 | 2026-02-08T11:31:24.915964Z | {
"verified": true,
"answer": 79800,
"timestamp": "2026-02-08T11:31:24.917171Z"
} | 4ae74e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 117,
"completion_tokens": 1091
},
"timestamp": "2026-02-14T17:46:33.223Z",
"answer": 79800
},
... | 1 | [
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
5152a9 | comb_count_permutations_fixed_v1_2051736721_5584 | Let $n = 9$ and $k = \sum_{i=1}^{2} \phi(i) \cdot \left\lfloor \frac{2}{i} \right\rfloor$, where $\phi$ is Euler's totient function. Compute $\binom{n}{k} \cdot !(n - k)$, where $!m$ denotes the number of derangements of $m$ elements. | 22,260 | graphs = [
Graph(
let={
"_n": Const(2),
"n": Const(9),
"k": Summation(var="k1", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k1")), Floor(Div(Const(2), Var("k1"))))),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub(left=Ref(name='n... | NT | COMB | COUNT | sympy | K2 | [
"K2"
] | 6897ab | comb_count_permutations_fixed_v1 | null | 5 | 0 | [
"K2"
] | 1 | 0.002 | 2026-02-08T18:40:40.705058Z | {
"verified": true,
"answer": 22260,
"timestamp": "2026-02-08T18:40:40.706585Z"
} | b75ff1 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 131,
"completion_tokens": 1355
},
"timestamp": "2026-02-18T18:35:48.405Z",
"answer": 22260
},
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
b69996 | antilemma_k2_v1_2051736721_3356 | Let $S$ be the set of all integers $x$ such that
$$x^2-80x+1431=0.$$
Let $A$ be the sum of all elements of $S$.
Let
$$C=\sum_{d\mid 50} \varphi(d),$$
where $\varphi$ denotes Euler's totient function.
Define
$$N=\frac{80}{A}.$$
Let
$$x=\sum_{k=N}^{50} \varphi(k)\left\lfloor \frac{C}{k} \right\rfloor.$$
Compute $x$. | 1,275 | graphs = [
Graph(
let={
"_m": Const(1431),
"_n": Const(2),
"x": Summation(var="k", start=Div(Const(80), SumOverSet(set=SolutionsSet(var=Var("x1"), condition=Eq(Sum(Pow(Var("x1"), Ref("_n")), Mul(Const(-80), Var("x1")), Ref("_m")), Sub(Const(23), Const(23)))))), end=Const(... | NT | COMB | COMPUTE | sympy | VIETA_SUM | [
"VIETA_SUM/IDENTITY_DIV_SELF/K2",
"IDENTITY_SUB_SELF",
"K3/K2",
"K2"
] | 8f0b6c | antilemma_k2_v1 | null | 5 | 0 | [
"IDENTITY_DIV_SELF",
"IDENTITY_SUB_SELF",
"K2",
"K3",
"VIETA_SUM"
] | 5 | 0.006 | 2026-02-08T17:16:14.247407Z | {
"verified": true,
"answer": 1275,
"timestamp": "2026-02-08T17:16:14.253167Z"
} | 104439 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 165,
"completion_tokens": 925
},
"timestamp": "2026-02-17T22:54:13.489Z",
"answer": 1275
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "IDENTITY_DIV_SELF",
"status": "ok_later"
},
{
"lemma": "IDENTITY_SUB_SELF",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lem... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
f1bb2d | modular_mod_compute_v1_2051736721_3523 | Let $n = 100$. Consider the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = n$. Define $m$ to be the maximum value of $xy$ over all such pairs. Compute the remainder when $-64$ is divided by $m$. | 2,436 | graphs = [
Graph(
let={
"_n": Const(100),
"a": Const(-64),
"m": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Ref("_n")))), expr=... | NT | null | COMPUTE | sympy | B1 | [
"B1"
] | 5b950e | modular_mod_compute_v1 | null | 3 | 0 | [
"B1"
] | 1 | 0.002 | 2026-02-08T17:23:33.106108Z | {
"verified": true,
"answer": 2436,
"timestamp": "2026-02-08T17:23:33.107748Z"
} | 78af54 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 109,
"completion_tokens": 553
},
"timestamp": "2026-02-18T01:03:02.028Z",
"answer": 2436
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
49c75e | nt_min_crt_v1_151522320_2134 | Let $T$ be the set of all integers $t$ such that $7 \le t \le 20$ and there exist positive integers $a \le 5$ and $b \le 2$ for which $t = 2a + 5b$. Let $u = |T|$. Define $n$ to be the smallest positive integer such that $n \le u$, $n \equiv 2 \pmod{5}$, and $n \equiv 2 \pmod{11}$. Find the remainder when $|n|$ is divi... | 2 | graphs = [
Graph(
let={
"m": Const(5),
"k": Const(11),
"a": Const(2),
"b": Const(2),
"upper": Summation(var="k", start=Const(1), end=CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'),... | NT | null | EXTREMUM | sympy | MIN_PRIME_FACTOR | [
"LIN_FORM/SUM_ARITHMETIC"
] | 5a2696 | nt_min_crt_v1 | null | 5 | 0 | [
"LIN_FORM",
"MIN_PRIME_FACTOR",
"SUM_ARITHMETIC"
] | 3 | 0.164 | 2026-02-08T04:37:49.987698Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-02-08T04:37:50.151259Z"
} | addd88 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 239,
"completion_tokens": 813
},
"timestamp": "2026-02-11T21:38:30.647Z",
"answer": 2
},
{
"id":... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "SUM_ARIT... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
76fd1c | nt_count_divisors_in_range_v1_458359167_102 | Let $S$ be the set of all positive integers $t$ such that $5 \leq t \leq 35$ and there exist positive integers $a$, $b$ with $1 \leq a \leq 13$, $1 \leq b \leq 3$, and $t = 2a + 3b$. Let $m = 19$ and $n = 332640$. Let $a$ be the largest integer such that $19^a$ divides $19^{25}$. Let $b$ be the largest integer such tha... | 128 | graphs = [
Graph(
let={
"_m": Const(19),
"_n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=13)), Geq(left=Var... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/K13",
"K14"
] | 5e8c98 | nt_count_divisors_in_range_v1 | null | 4 | 0 | [
"K13",
"K14",
"LIN_FORM"
] | 3 | 0.128 | 2026-02-08T02:59:29.204108Z | {
"verified": true,
"answer": 128,
"timestamp": "2026-02-08T02:59:29.331688Z"
} | 82c428 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 3829,
"completion_tokens": 556
},
"timestamp": "2026-02-17T17:45:47.233Z",
"answer": 128
}
] | 2 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K13",
"status": "ok_later"
},
{
"lemma": "K14",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
... | {
"lo": -6.48,
"mid": 1.54,
"hi": 9.56
} | ||
03b2b7 | antilemma_cartesian_v1_784195855_2580 | Compute the remainder when $27 - (33 \times 43)$ is divided by $90663$. | 89,271 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(33)), right=IntegerRange(start=Const(1), end=Const(43)))),
"_c": Const(27),
"Q": Mod(value=Sub(Ref("_c"), Ref("x")), modulus=Const(90663)),
},
goal=R... | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | antilemma_cartesian_v1 | null | 2 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.001 | 2026-02-08T05:52:57.098353Z | {
"verified": true,
"answer": 89271,
"timestamp": "2026-02-08T05:52:57.099055Z"
} | a04332 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 131,
"completion_tokens": 317
},
"timestamp": "2026-02-24T04:47:08.995Z",
"answer": 89271
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.18,
"mid": -5,
"hi": -3.01
} | ||
4633e9 | comb_binomial_compute_v1_1218484723_1864 | Let $n$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 30$ such that $17a^4 + 68a^3b + 102a^2b^2 + 68ab^3 + 17b^4 = 860625$. Compute $\binom{n}{7}$. | 3,432 | graphs = [
Graph(
let={
"_n": Const(4),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(30)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(30)), Eq(Sum(Mul(Const(68), Var("a"), Pow(Var("b"), Const... | COMB | null | COMPUTE | sympy | POLY4_COUNT | [
"POLY4_COUNT"
] | 861d91 | comb_binomial_compute_v1 | null | 3 | 0 | [
"POLY4_COUNT"
] | 1 | 0.002 | 2026-02-25T03:33:16.241049Z | {
"verified": true,
"answer": 3432,
"timestamp": "2026-02-25T03:33:16.242711Z"
} | ca8eb1 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 191,
"completion_tokens": 1095
},
"timestamp": "2026-03-29T01:48:48.956Z",
"answer": 3432
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "POLY4_COUNT",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -4.26,
"mid": -1.81,
"hi": 1.23
} | ||
790b7a | alg_qf_psd_count_v1_1218484723_437 | Let $A = \min\left\{ 64a_1^3 + 152b_1^3 + 108a_1b_1^2 + 144a_1^2b_1 \mid a_1, b_1 \in \mathbb{Z}^+,\, 1 \leq a_1, b_1 \leq 11 \right\}$. Find the number of ordered pairs $(a, b)$ of positive integers with $1 \leq a \leq A$ and $1 \leq b \leq 468$ such that $$18b^2 - 42ab + 29a^2 = 232713.$$ | 11 | graphs = [
Graph(
let={
"_n": Const(108),
"result": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a1"), Var("b1")]), condition=And(Geq(Va... | ALG | null | COUNT | sympy | B3 | [
"POLY3_MIN"
] | e2e279 | alg_qf_psd_count_v1 | null | 5 | 0 | [
"B3",
"POLY3_MIN"
] | 2 | 4.265 | 2026-02-25T02:08:22.480918Z | {
"verified": true,
"answer": 11,
"timestamp": "2026-02-25T02:08:26.746015Z"
} | 45b98b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 260,
"completion_tokens": 12627
},
"timestamp": "2026-03-28T22:38:07.548Z",
"answer": 11
},
{
"id... | 1 | [
{
"lemma": "POLY3_MIN",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 1.22,
"mid": 3.76,
"hi": 5.73
} | ||
8082c9 | comb_factorial_compute_v1_677425708_1382 | Let $n$ be the number of positive integers $p$ such that there exists a positive integer $q$ with $p < q$, $\gcd(p, q) = 1$, and $p \cdot q = 6300$.
Let $f = n!$ denote the factorial of $n$. Compute the remainder when $68253 \cdot f$ is divided by 67742. | 9,952 | graphs = [
Graph(
let={
"_n": Const(67742),
"n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=6300)), Eq(left=GCD(a=Var(name='p'), b=Var(na... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_factorial_compute_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.002 | 2026-02-08T04:08:47.862772Z | {
"verified": true,
"answer": 9952,
"timestamp": "2026-02-08T04:08:47.864363Z"
} | f25472 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 196,
"completion_tokens": 2335
},
"timestamp": "2026-02-09T19:13:46.081Z",
"answer": 9952
},
{
"i... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.53,
"mid": 1.02,
"hi": 5.49
} | ||
98a33a | comb_factorial_compute_v1_1742523217_2846 | Let $n$ be the number of positive integers at most 15 that are relatively prime to 14. Compute $n!$. | 5,040 | graphs = [
Graph(
let={
"_n": Const(15),
"n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_n")), Eq(GCD(a=Var("n"), b=Const(14)), Const(1))))),
"result": Factorial(Ref("n")),
},
goal=Ref("result"),
... | NT | null | COMPUTE | sympy | C4 | [
"C4"
] | 08d162 | comb_factorial_compute_v1 | null | 3 | 0 | [
"C4"
] | 1 | 0.002 | 2026-02-08T05:24:46.284033Z | {
"verified": true,
"answer": 5040,
"timestamp": "2026-02-08T05:24:46.285704Z"
} | c7b6de | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 74,
"completion_tokens": 598
},
"timestamp": "2026-02-12T08:23:20.358Z",
"answer": 5040
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
}
] | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
c0f865 | antilemma_k2_v1_784195855_3218 | Let $m = 315$. For each positive divisor $d$ of $m$, let $\phi(d)$ denote Euler's totient function evaluated at $d$. Define $n$ to be the sum of $\phi(d)$ over all positive divisors $d$ of $m$. Compute
$$
\sum_{k=1}^{315} \phi(k) \left\lfloor \frac{n}{k} \right\rfloor.
$$ | 49,770 | graphs = [
Graph(
let={
"_m": Const(315),
"_n": SumOverDivisors(n=Const(value=315), var='d', expr=EulerPhi(n=Var(name='d'))),
"x": Summation(var="k", start=Const(1), end=Ref("_m"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Ref("_n"), Var("k"))))),
},
goal=R... | NT | COMB | COMPUTE | sympy | K3 | [
"K3/K2",
"K2"
] | c7f244 | antilemma_k2_v1 | null | 7 | 0 | [
"K2",
"K3"
] | 2 | 0.001 | 2026-02-08T06:18:11.963284Z | {
"verified": true,
"answer": 49770,
"timestamp": "2026-02-08T06:18:11.964014Z"
} | 008fab | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 135,
"completion_tokens": 971
},
"timestamp": "2026-02-12T22:22:41.957Z",
"answer": 49770
},
{... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V3",
"s... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
245a14 | geo_visible_lattice_v1_1353956133_94 | Let $n = 144$. A lattice point $(x, y)$ is visible from the origin if $\gcd(x, y) = 1$. Let $R$ be the number of visible lattice points $(x, y)$ with $1 \leq x, y \leq n$. Compute the remainder when $64833 \cdot R$ is divided by $96991$. | 80,096 | graphs = [
Graph(
let={
"n": Const(144),
"result": VisibleLatticePoints(n=Ref(name='n')),
"Q": Mod(value=Mul(Const(64833), Ref("result")), modulus=Const(96991)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 4 | 0 | null | null | 1.783 | 2026-02-08T11:18:21.189063Z | {
"verified": true,
"answer": 80096,
"timestamp": "2026-02-08T11:18:22.971672Z"
} | fab9d9 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 191,
"completion_tokens": 32768
},
"timestamp": "2026-02-24T13:21:07.007Z",
"answer": null
},
{
... | 1 | [] | {
"lo": 1.15,
"mid": 4.18,
"hi": 6.61
} | ||||
8acd58 | comb_binomial_compute_v1_124444284_2121 | Let $n = \sum_{k=1}^{5} \phi(k) \left\lfloor \frac{5}{k} \right\rfloor$, where $\phi$ denotes Euler's totient function. Let $k = 8$. Let $R = \binom{n}{k}$, and let $Q$ be the remainder when $44121 \cdot R$ is divided by 89783. Find the value of $Q$. | 24,789 | graphs = [
Graph(
let={
"_n": Const(5),
"n": Summation(var="k", start=Const(1), end=Const(5), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Ref("_n"), Var("k"))))),
"k": Const(8),
"result": Binom(n=Ref("n"), k=Ref("k")),
"Q": Mod(value=Mul(Const(44121),... | NT | null | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | comb_binomial_compute_v1 | null | 5 | 0 | [
"K2"
] | 1 | 0.003 | 2026-02-08T04:19:38.399108Z | {
"verified": true,
"answer": 24789,
"timestamp": "2026-02-08T04:19:38.401683Z"
} | fb7cd4 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 207,
"completion_tokens": 1248
},
"timestamp": "2026-02-10T16:32:04.979Z",
"answer": 24789
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
f55143 | modular_modexp_compute_v1_1742523217_1313 | Let $ m = 12 $. Define $ S $ to be the set of all positive integers $ p $ for which there exists a positive integer $ q $ such that $ p \cdot q = 216 $, $ \gcd(p, q) = 1 $, and $ p < q $. Let $ n = |S| $. Let $ a $ be the largest prime number $ r $ such that $ n \leq r \leq 12 $. Define $ T $ to be the set of all order... | 9,483 | graphs = [
Graph(
let={
"_m": Const(12),
"_n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=216)), Eq(left=GCD(a=Var(name='p'), b=Var(name=... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/MAX_PRIME_BELOW",
"B3"
] | fdc414 | modular_modexp_compute_v1 | null | 6 | 0 | [
"B3",
"COPRIME_PAIRS",
"MAX_PRIME_BELOW"
] | 3 | 0.003 | 2026-02-08T03:40:43.292070Z | {
"verified": true,
"answer": 9483,
"timestamp": "2026-02-08T03:40:43.295000Z"
} | 41f6b0 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 281,
"completion_tokens": 9170
},
"timestamp": "2026-02-23T21:10:18.415Z",
"answer": 9483
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
... | {
"lo": 1.96,
"mid": 5.23,
"hi": 8.52
} | ||
2fb169 | comb_bell_compute_v1_1742523217_529 | Let $m = 8456$. Let $T$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 17875984$. Let $s$ be the minimum value of $x + y$ over all such pairs. Let $j$ range over the nonnegative integers from 0 to $s$, inclusive. Let $n$ be the number of such $j$ for which $\binom{m}{j}$ is odd. Let $B_n$... | 54 | graphs = [
Graph(
let={
"_m": Const(8456),
"_n": Const(2),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(a... | NT | COMB | COMPUTE | sympy | LIN_FORM | [
"B3/V8"
] | 4fad5b | comb_bell_compute_v1 | null | 7 | 0 | [
"B3",
"LIN_FORM",
"V8"
] | 3 | 0.024 | 2026-02-08T03:06:47.476022Z | {
"verified": true,
"answer": 54,
"timestamp": "2026-02-08T03:06:47.500016Z"
} | d93350 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 270,
"completion_tokens": 3567
},
"timestamp": "2026-02-09T04:05:37.364Z",
"answer": 54
},
{
"id... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
... | {
"lo": 1.96,
"mid": 5.23,
"hi": 8.52
} | ||
967921 | alg_sym_quad_system_v1_601307018_5798 | Let $M$ be the sum of $a^5 + b^5 + c^5$ over all positive integers $a, b, c$ satisfying $a^2 + b^2 + c^2 = ab + bc + ca$ and $2a + 4b + 3c = 2349$, taken modulo the number of pairs $(a_1, b_1)$ with $1 \le a_1, b_1 \le 40$ such that $41a_1^2 - 12a_1b_1 + 20b_1^2 \le 34697$. Find the remainder when $44121M$ is divided b... | 31,732 | graphs = [
Graph(
let={
"_n": Const(2),
"result": Mod(value=SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b"), Var("c")]), condition=And(Eq(Sum(Pow(Var("a"), Const(2)), Pow(Var("b"), Const(2)), Pow(Var("c"), Const(2))), Sum(Mul(Var("a"), Var("b")), Mul... | ALG | null | COMPUTE | sympy | QF_PSD_COUNT_LEQ | [
"QF_PSD_COUNT_LEQ"
] | 009d0f | alg_sym_quad_system_v1 | null | 7 | 0 | [
"QF_PSD_COUNT_LEQ"
] | 1 | 0.023 | 2026-03-10T06:20:21.755401Z | {
"verified": true,
"answer": 31732,
"timestamp": "2026-03-10T06:20:21.778658Z"
} | 442af8 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 259,
"completion_tokens": 11317
},
"timestamp": "2026-04-19T02:57:03.494Z",
"answer": 31732
},
{
... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
}
] | {
"lo": 2.1,
"mid": 5.36,
"hi": 8.63
} | ||
fc7b6c | modular_sum_quadratic_residues_v1_458359167_1549 | Let $p = 401$. Let $S$ be the set of all positive integers $p$ such that there exists a positive integer $q$ satisfying $p \cdot q = 150$, $\gcd(p, q) = 1$, and $p < q$. Compute $\frac{p(p-1)}{|S|}$. | 40,100 | graphs = [
Graph(
let={
"p": Const(401),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value... | NT | null | SUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | modular_sum_quadratic_residues_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.001 | 2026-02-08T04:45:16.581484Z | {
"verified": true,
"answer": 40100,
"timestamp": "2026-02-08T04:45:16.582778Z"
} | 77a237 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 183,
"completion_tokens": 1389
},
"timestamp": "2026-02-11T21:52:01.129Z",
"answer": 40100
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V1",
"status": ... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
80e0bc | comb_count_partitions_v1_865884756_4030 | Let $T$ be the set of all integers $t$ such that $20 \leq t \leq 122$ and $t = 14a + 6b$ for some integers $a$ and $b$ with $1 \leq a \leq 4$ and $1 \leq b \leq 11$. Let $n$ be the number of elements in $T$. Compute the number of integer partitions of $n$. | 37,338 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=4)), Geq(left=Var(name='b'), right=Const(value=1... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_count_partitions_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.003 | 2026-02-08T17:43:02.888635Z | {
"verified": true,
"answer": 37338,
"timestamp": "2026-02-08T17:43:02.891331Z"
} | 52b4cb | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 139,
"completion_tokens": 1861
},
"timestamp": "2026-02-18T06:41:47.870Z",
"answer": 37338
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||
f66d60 | modular_count_residue_v1_458359167_1348 | Let $m = 7$. Define $n$ to be the number of prime numbers $p$ such that $2 \leq p \leq m$. Let $r$ be the maximum value of $xy$ over all pairs of positive integers $(x, y)$ such that $x + y = n$. Let $t$ range over integers from 18 to 51, and define $m'$ to be the number of values of $t$ for which there exist positive ... | 93,680 | graphs = [
Graph(
let={
"_m": Const(7),
"_n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_m")), IsPrime(Var("n"))))),
"upper": Const(34596),
"m": CountOverSet(set=SolutionsSet(var=Var("t"), condition=E... | NT | null | COUNT | sympy | COUNT_PRIMES | [
"COUNT_PRIMES/LIN_FORM/B1"
] | e80d65 | modular_count_residue_v1 | null | 5 | 0 | [
"B1",
"COUNT_PRIMES",
"LIN_FORM"
] | 3 | 1.426 | 2026-02-08T04:33:34.228946Z | {
"verified": true,
"answer": 93680,
"timestamp": "2026-02-08T04:33:35.654513Z"
} | 3e994e | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 299,
"completion_tokens": 1713
},
"timestamp": "2026-02-10T17:01:58.439Z",
"answer": 93680
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok_later"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},... | {
"lo": -3.49,
"mid": 1.84,
"hi": 7.55
} | ||
9427b4 | comb_binomial_compute_v1_1520064083_2928 | Let $n = 12$. Let $k$ be the sum of all real solutions $x$ to the equation $x^2 - 7x - 1548 = 0$. Compute $\binom{n}{k}$. | 792 | graphs = [
Graph(
let={
"n": Const(12),
"k": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Const(2)), Mul(Const(-7), Var("x")), Const(-1548)), Const(0)))),
"result": Binom(n=Ref("n"), k=Ref("k")),
},
goal=Ref("result"),
)
] | ALG | COMB | COMPUTE | sympy | VIETA_SUM | [
"VIETA_SUM"
] | b33a7a | comb_binomial_compute_v1 | null | 3 | 0 | [
"VIETA_SUM"
] | 1 | 0.002 | 2026-02-08T05:19:13.840760Z | {
"verified": true,
"answer": 792,
"timestamp": "2026-02-08T05:19:13.842623Z"
} | f8a478 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 160,
"completion_tokens": 574
},
"timestamp": "2026-02-24T03:16:18.216Z",
"answer": 792
},
{
"id"... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "VIETA_SUM",
"status": "ok"
}
] | {
"lo": -9.23,
"mid": -6.18,
"hi": -4.06
} | ||
9f3d81 | comb_catalan_compute_v1_168721529_374 | Let $T$ be the set of all positive integers $t$ such that $9 \le t \le 36$ and there exist positive integers $a$ and $b$ with $1 \le a \le 2$, $1 \le b \le 11$, and $t = 7a + 2b$. Let $N$ be the number of elements in $T$. Now consider the set of all ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x... | 58,786 | graphs = [
Graph(
let={
"_n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=2)), Geq(left=Var(name='b'), right=Const(value=... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/COMB1"
] | 268a62 | comb_catalan_compute_v1 | null | 7 | 0 | [
"COMB1",
"LIN_FORM"
] | 2 | 0.003 | 2026-02-08T13:00:53.618747Z | {
"verified": true,
"answer": 58786,
"timestamp": "2026-02-08T13:00:53.621290Z"
} | 34f7c1 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 251,
"completion_tokens": 1734
},
"timestamp": "2026-02-24T16:58:06.390Z",
"answer": 58786
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok_later"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status": "... | {
"lo": -2.77,
"mid": -0.49,
"hi": 2.44
} | ||
6b00ec | modular_inverse_v1_458359167_2017 | Let $a = \sum_{k=1}^{12} k$. Let $x$ be the smallest positive integer such that $1 \leq x \leq 112$ and $a \cdot x \equiv 1 \pmod{113}$. Compute the remainder when $5^{|x|} + 16129$ is divided by $99991$. | 45,395 | graphs = [
Graph(
let={
"a": Summation(var="k", start=Const(1), end=Const(12), expr=Var("k")),
"m": Const(113),
"upper": Const(112),
"result": MinOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), Const(1)), Leq(Var("x"), Ref("upper")), Eq(Mod(... | ALG | NT | EXTREMUM | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | modular_inverse_v1 | null | 6 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.016 | 2026-02-08T04:58:50.449045Z | {
"verified": true,
"answer": 45395,
"timestamp": "2026-02-08T04:58:50.465154Z"
} | d41c23 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 190,
"completion_tokens": 6887
},
"timestamp": "2026-02-11T22:33:16.740Z",
"answer": 45395
},
{
... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
65e8be | comb_count_permutations_fixed_v1_1520064083_990 | Let $n = 10$ and $k = 5$. Define $\text{result} = \binom{n}{k} \cdot !(n - k)$, where $!m$ denotes the number of derangements of $m$ objects. Let $c = 26393$ and let $Q$ be the remainder when $c \cdot \text{result}$ is divided by $93690$. Compute $Q$. | 51,714 | graphs = [
Graph(
let={
"n": Const(10),
"k": Const(5),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub(left=Ref(name='n'), right=Ref(name='k')))),
"_c": Const(26393),
"Q": Mod(value=Mul(Ref("_c"), Ref("result")), modulus=Const(936... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/MOBIUS_COPRIME"
] | d91cf7 | comb_count_permutations_fixed_v1 | null | 4 | 0 | [
"LIN_FORM",
"MOBIUS_COPRIME"
] | 2 | 0.073 | 2026-02-08T03:42:01.323261Z | {
"verified": true,
"answer": 51714,
"timestamp": "2026-02-08T03:42:01.395830Z"
} | d54754 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 203,
"completion_tokens": 1440
},
"timestamp": "2026-02-10T15:35:43.723Z",
"answer": 51714
},
{
"... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": ... | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
75e581 | comb_sum_binomial_mod_v1_1080341949_337 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 961$. Let $m$ be the minimum value of $x + y$ over all pairs in $S$. Compute the remainder when $\sum_{k=1}^{41} \binom{m}{k}$ is divided by $10567$. | 739 | graphs = [
Graph(
let={
"_n": Const(41),
"sum": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Binom(n=MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("... | ALG | COMB | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | comb_sum_binomial_mod_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.01 | 2026-02-08T13:25:48.429963Z | {
"verified": true,
"answer": 739,
"timestamp": "2026-02-08T13:25:48.439726Z"
} | 368748 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 186,
"completion_tokens": 32768
},
"timestamp": "2026-02-24T18:28:29.431Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 3.25,
"mid": 5.68,
"hi": 8.81
} | ||
d7cb65 | comb_count_surjections_v1_458359167_3854 | Let $n$ be the number of ordered pairs $(i, j)$ of positive integers such that $1 \leq i \leq 6$, $1 \leq j \leq 7$, and $i + j = 7$. Let $k = 4$. Define $\text{result} = k! \cdot S(n, k)$, where $S(n, k)$ denotes the Stirling number of the second kind. Compute $\text{result}$. | 1,560 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(7)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(6)), right=IntegerRange(start=Const(1), end=Const(7))))),
"k": Con... | COMB | null | COUNT | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | comb_count_surjections_v1 | null | 4 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.016 | 2026-02-08T11:23:52.975154Z | {
"verified": true,
"answer": 1560,
"timestamp": "2026-02-08T11:23:52.990899Z"
} | fc2f75 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 212,
"completion_tokens": 862
},
"timestamp": "2026-02-24T13:44:57.701Z",
"answer": 1560
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.84,
"mid": -1.67,
"hi": 1.32
} | ||
664d79 | modular_mod_compute_v1_677425708_3664 | Let $T = \sum_{k=1}^{10} k$, and let $a = \sum_{k=1}^{T} k$. Let $m = 4489$. Compute the remainder when $a$ is divided by $m$, then compute the remainder when $50457$ times that result is divided by $94421$. | 89,718 | graphs = [
Graph(
let={
"_n": Summation(var="k", start=Const(1), end=Const(10), expr=Var("k")),
"a": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Var("k")),
"m": Const(4489),
"result": Mod(value=Ref("a"), modulus=Ref("m")),
"_c": Const(50... | NT | null | COMPUTE | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC/SUM_ARITHMETIC"
] | 2a57af | modular_mod_compute_v1 | null | 2 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.001 | 2026-02-08T05:53:10.386517Z | {
"verified": true,
"answer": 89718,
"timestamp": "2026-02-08T05:53:10.387776Z"
} | 05db21 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 118,
"completion_tokens": 2030
},
"timestamp": "2026-02-12T15:53:50.606Z",
"answer": 89718
},
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
fffeca | modular_sum_quadratic_residues_v1_153355830_256 | Let $C = 4$. Let $m$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = C$. Let $n$ be the maximum value of $xy$ over all ordered pairs $(x, y)$ of positive integers such that $x + y = m$. Let $p$ be the number of integers $t$ with $9 \leq t \leq 369$ for which there ex... | 30,363 | graphs = [
Graph(
let={
"_c": Const(4),
"_m": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_c")))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | SUM | sympy | C3 | [
"B3/B1/LIN_FORM"
] | f992df | modular_sum_quadratic_residues_v1 | null | 6 | 0 | [
"B1",
"B3",
"C3",
"LIN_FORM"
] | 4 | 0.005 | 2026-02-08T02:59:23.447959Z | {
"verified": true,
"answer": 30363,
"timestamp": "2026-02-08T02:59:23.453271Z"
} | 22280d | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 257,
"completion_tokens": 9217
},
"timestamp": "2026-02-23T15:25:04.381Z",
"answer": 30363
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok_later"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lem... | {
"lo": 1.96,
"mid": 5.23,
"hi": 8.52
} | ||
7dc0b8_l | geo_visible_lattice_v1_1125832087_2450 | Let $n = 120$. Define $V$ to be the number of lattice points $(x, y)$ with $1 \leq x, y \leq n$ such that $\gcd(x, y) = 1$. Compute the remainder when $2304 - V$ is divided by $66189$. | 0 | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 5 | 0 | null | null | 0.305 | 2026-02-08T04:37:23.450336Z | {
"verified": false,
"answer": 59722,
"timestamp": "2026-02-08T04:37:23.755469Z"
} | 2d42e5 | 7dc0b8 | legacy_text | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 177,
"completion_tokens": 9230
},
"timestamp": "2026-02-24T01:15:24.825Z",
"answer": 59722
},
{
"... | 1 | [] | {
"lo": 1.97,
"mid": 4.36,
"hi": 6.69
} | |||
450860 | diophantine_fbi2_min_v1_784195855_10208 | Let $n = 317$, $k = 33$, and $u = 43$. Define $D$ as the set of all integers $d$ such that $3 \leq d \leq u$, $d$ divides $k$, and $\frac{k}{d} \geq 4$. Let $r$ be the smallest element of $D$. Let $p$ be the smallest prime divisor of $9720582149$. Compute $$r \bmod 317 + 7001 \cdot (r \bmod p).$$ | 21,006 | graphs = [
Graph(
let={
"_n": Const(317),
"k": Const(33),
"upper": Const(43),
"result": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(3)), Leq(Var("d"), Ref("upper")), Divides(divisor=Var("d"), dividend=Ref("k")), Geq(Div(Ref("k")... | NT | null | EXTREMUM | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | cffc20 | diophantine_fbi2_min_v1 | two_moduli | 4 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.005 | 2026-02-08T17:29:32.002546Z | {
"verified": true,
"answer": 21006,
"timestamp": "2026-02-08T17:29:32.007379Z"
} | 225b79 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 160,
"completion_tokens": 2440
},
"timestamp": "2026-02-18T03:17:18.891Z",
"answer": 21006
},
... | 1 | [
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
c25e88 | sequence_lucas_compute_v1_784195855_7424 | Let $S$ be the set of all positive integers $p$ such that there exists a positive integer $q$ with $pq = 6$, $\gcd(p, q) = 1$, and $p < q$. Let $\text{count}$ be the number of elements in $S$. Let $n$ be the largest prime number $n$ such that $\text{count} \leq n \leq 26$. Compute the $n$-th Lucas number. | 64,079 | graphs = [
Graph(
let={
"_n": Const(26),
"n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q'... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/MAX_PRIME_BELOW"
] | 2248fc | sequence_lucas_compute_v1 | null | 3 | 0 | [
"COPRIME_PAIRS",
"MAX_PRIME_BELOW"
] | 2 | 0.003 | 2026-02-08T09:16:59.357582Z | {
"verified": true,
"answer": 64079,
"timestamp": "2026-02-08T09:16:59.360581Z"
} | db4ba2 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 145,
"completion_tokens": 1079
},
"timestamp": "2026-02-14T02:32:08.151Z",
"answer": 64079
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "V... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
7d9e2f | alg_poly4_sum_v1_1218484723_1214 | Let $S$ be the set of integers $t$ expressible as $t = 9a + 6b$ for some integers $a, b$ with $1 \le a \le 1024$, $1 \le b \le 92$, and $15 \le t \le 9768$. Let $m = |S|$. Let $n$ be the number of integers $v$ with $13 \le v \le m$ for which there exist integers $a, b$ with $1 \le a, b \le 14$ such that $-6ab + 2a^2 + ... | 44,228 | graphs = [
Graph(
let={
"_m": Const(88478),
"_n": Const(17),
"result": Mod(value=SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(366)), Geq(Var("b"), Const(1)), Leq(Var("b"), C... | ALG | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/QF_PSD_DISTINCT"
] | e187db | alg_poly4_sum_v1 | null | 7 | 0 | [
"LIN_FORM",
"QF_PSD_DISTINCT"
] | 2 | 0.62 | 2026-02-25T02:59:36.607562Z | {
"verified": true,
"answer": 44228,
"timestamp": "2026-02-25T02:59:37.227501Z"
} | 3e6018 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 328,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T00:15:07.516Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_DISTINCT",
"status": "ok_later"
}
] | {
"lo": 4.76,
"mid": 6.79,
"hi": 9.83
} | ||
96c1c1 | nt_max_prime_below_v1_1520064083_1692 | Let $P$ be the number of positive integers $p$ for which there exists an integer $q$ such that $p \cdot q = 24$, $\gcd(p, q) = 1$, and $p < q$.
Let $S$ be the set of prime numbers $n$ such that
$$
\sum_{d \mid P} \phi(d) \leq n \leq 12544,
$$
defined over positive divisors $d$ of $P$, where $\phi$ denotes Euler's toti... | 12,541 | graphs = [
Graph(
let={
"_n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=24)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(value=1)), ... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/K3"
] | f9481c | nt_max_prime_below_v1 | null | 6 | 0 | [
"COPRIME_PAIRS",
"K3"
] | 2 | 0.617 | 2026-02-08T04:13:06.027049Z | {
"verified": true,
"answer": 12541,
"timestamp": "2026-02-08T04:13:06.643934Z"
} | 831c6f | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 236,
"completion_tokens": 1650
},
"timestamp": "2026-02-10T15:49:21.490Z",
"answer": 12541
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K3",
"status": "ok_later"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
712a2e | nt_lcm_compute_v1_458359167_1046 | Let $a$ be the largest prime number between $2$ and $2442$, inclusive. Let $b = 2271$, and let $\text{result} = \text{LCM}(a, b)$. Let $Q$ be the sum of $d_i \cdot (i+1)^2$ over all digits $d_i$ of $\text{result}$ (taken in base $10$, from right to left, starting with index $i=0$), plus $22201$. Compute $Q$. | 22,824 | graphs = [
Graph(
let={
"_n": Const(2),
"a": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Const(2442)), IsPrime(Var("n"))))),
"b": Const(2271),
"result": LCM(a=Ref("a"), b=Ref("b")),
"Q": Sum(Summa... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | nt_lcm_compute_v1 | null | 5 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.005 | 2026-02-08T04:14:47.119443Z | {
"verified": true,
"answer": 22824,
"timestamp": "2026-02-08T04:14:47.124353Z"
} | f95565 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 221,
"completion_tokens": 2401
},
"timestamp": "2026-02-10T15:54:08.297Z",
"answer": 22824
},
{
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
517747 | nt_count_divisible_v1_1520064083_5058 | Let $p$ and $q$ be positive integers such that $pq = 10187100$, $\gcd(p, q) = 1$, and $p < q$. Let $d$ be the number of such integers $p$. Let $S$ be the set of all positive integers $n$ such that $n \leq 51984$ and $n$ is divisible by $d$. Let $r = |S|$. Compute $r + \phi(r+1) + \tau(r+1)$, where $\phi$ denotes Euler'... | 4,465 | graphs = [
Graph(
let={
"upper": Const(51984),
"divisor": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=10187100)), Eq(left=GCD(a=Var(name='... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_count_divisible_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 2.918 | 2026-02-08T06:35:24.842396Z | {
"verified": true,
"answer": 4465,
"timestamp": "2026-02-08T06:35:27.760352Z"
} | decf3f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 177,
"completion_tokens": 1498
},
"timestamp": "2026-02-13T02:09:07.260Z",
"answer": 4465
},
{... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
3e9fa6 | geo_visible_lattice_v1_1520064083_7969 | Let $n = 89$. Define $P$ to be the number of visible lattice points $(x, y)$ such that $1 \le x, y \le n$. Compute the value of $43681 - P$. | 38,770 | graphs = [
Graph(
let={
"n": Const(89),
"result": VisibleLatticePoints(n=Ref(name='n')),
"Q": Sub(Const(43681), Ref("result")),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 5 | 0 | null | null | 0.533 | 2026-02-08T09:23:22.301824Z | {
"verified": true,
"answer": 38770,
"timestamp": "2026-02-08T09:23:22.835163Z"
} | 29437a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 157,
"completion_tokens": 4618
},
"timestamp": "2026-02-24T11:18:19.377Z",
"answer": 38770
},
{
"... | 1 | [] | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||||
5027d4 | comb_sum_binomial_mod_v1_458359167_3132 | Let $n_1 = 0$, and define $$u = \sum_{k=0}^{n_1} (-1)^k \binom{n_1}{k}.$$ Let $a = 2u$ and $b = 2$, and define $n = a + b$. Let $$h = \sum_{k=0}^{n} (-1)^k \binom{n}{k}.$$ Compute the remainder when $$\sum_{k=28}^{175} \binom{209}{k}$$ is divided by $10369 + h$. Let this remainder be $r$. Find the remainder when $32107... | 6,854 | graphs = [
Graph(
let={
"n1": Const(0),
"u": Summation(var="k", start=Const(0), end=Ref("n1"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n1"), k=Var("k")))),
"a": Mul(Const(2), Ref("u")),
"b": Const(2),
"n": Sum(Ref("a"), Ref("b")),
... | COMB | null | COMPUTE | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING"
] | c21569 | comb_sum_binomial_mod_v1 | null | 5 | 2 | [
"BINOMIAL_ALTERNATING"
] | 1 | 0.016 | 2026-02-08T06:59:19.174947Z | {
"verified": true,
"answer": 6854,
"timestamp": "2026-02-08T06:59:19.191380Z"
} | 2ff205 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 258,
"completion_tokens": 32768
},
"timestamp": "2026-02-24T07:31:28.490Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"stat... | {
"lo": 3.25,
"mid": 5.68,
"hi": 8.81
} | ||
d75930 | sequence_fibonacci_compute_v1_1978505735_7528 | Let $n$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 100$. Let $F_n$ denote the $n$th Fibonacci number, with $F_1 = F_2 = 1$ and $F_{k} = F_{k-1} + F_{k-2}$ for $k \geq 3$. Compute the remainder when $44121 \cdot F_n$ is divided by $89458$. | 46,677 | graphs = [
Graph(
let={
"_n": Const(100),
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_n")))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | sequence_fibonacci_compute_v1 | null | 3 | 0 | [
"B3"
] | 1 | 0.002 | 2026-02-08T20:18:15.836143Z | {
"verified": true,
"answer": 46677,
"timestamp": "2026-02-08T20:18:15.837818Z"
} | 3c13d1 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 154,
"completion_tokens": 1974
},
"timestamp": "2026-02-19T00:20:16.888Z",
"answer": 46677
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
240035 | nt_euler_phi_compute_v1_677425708_820 | Let $A$ be the set of all ordered pairs $(p,q)$ of positive integers such that $pq=36$, $\gcd(p,q)=1$, and $p<q$. Let $r$ be the number of positive integers $p$ for which there exists a positive integer $q$ with $(p,q)\in A$.
Let $B$ be the set of all integers $n$ such that $n\ge r$, $n\le 4$, and $n$ is prime, and as... | 73,170 | graphs = [
Graph(
let={
"_m": Const(73441),
"_n": Const(4),
"p": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/MAX_PRIME_BELOW/BIG_OMEGA_ONE",
"MOBIUS_SUM"
] | f3a19b | nt_euler_phi_compute_v1 | null | 6 | 2 | [
"BIG_OMEGA_ONE",
"COPRIME_PAIRS",
"MAX_PRIME_BELOW",
"MOBIUS_SUM"
] | 4 | 0.004 | 2026-02-08T03:46:53.086994Z | {
"verified": true,
"answer": 73170,
"timestamp": "2026-02-08T03:46:53.090541Z"
} | ec3935 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 347,
"completion_tokens": 2625
},
"timestamp": "2026-02-09T12:50:20.638Z",
"answer": 73170
},
{
"... | 1 | [
{
"lemma": "BIG_OMEGA_ONE",
"status": "ok_later"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELO... | {
"lo": -6.5,
"mid": -0.2,
"hi": 6.11
} | ||
25d938 | nt_count_divisible_and_v1_898971024_757 | Let $S$ be the set of all integers $n$ such that $1 \leq n \leq 29976$, $n$ is divisible by $6$, and the remainder when $n$ is divided by $8$ equals $\sum_{k=0}^{1} (-1)^k \binom{1}{k}$. Find the number of elements in $S$. | 1,249 | graphs = [
Graph(
let={
"upper": Const(29976),
"d1": Const(6),
"d2": Const(8),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(value=Var("n"), modulus=Ref("d1")), Const(0)), Eq(Mo... | COMB | null | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING"
] | c21569 | nt_count_divisible_and_v1 | null | 3 | 0 | [
"BINOMIAL_ALTERNATING"
] | 1 | 2.152 | 2026-02-08T15:37:54.381120Z | {
"verified": true,
"answer": 1249,
"timestamp": "2026-02-08T15:37:56.533510Z"
} | a59c49 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 192,
"completion_tokens": 607
},
"timestamp": "2026-02-24T18:25:22.495Z",
"answer": 1249
},
{
"i... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status"... | {
"lo": -8.52,
"mid": -5.43,
"hi": -3.2
} | ||
2a351e | modular_mod_compute_v1_784195855_2734 | Let $T$ be the set of all integers $t$ such that $10 \leq t \leq 1035$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 22$, $1 \leq b \leq 482$, and $$t = 3a + 2b + 5.$$ Compute the remainder when $59536$ is divided by the number of elements in $T$. | 144 | graphs = [
Graph(
let={
"a": Const(59536),
"m": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=22)), Geq(left=Va... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | modular_mod_compute_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.003 | 2026-02-08T05:57:12.231347Z | {
"verified": true,
"answer": 144,
"timestamp": "2026-02-08T05:57:12.234082Z"
} | c3aea1 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 141,
"completion_tokens": 4983
},
"timestamp": "2026-02-12T17:12:06.383Z",
"answer": 144
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
548e84_n | comb_count_derangements_v1_1419126231_1103 | A theater has $7$ actors, each assigned a unique costume. After a power outage, the costumes are returned such that no actor gets their own. In how many ways can this happen? Multiply that number by $73589$, then find the remainder when the result is divided by $77738$. | 3,816 | COMB | null | COUNT | sympy | SUM_GEOM | [
"SUM_GEOM"
] | 04214c | comb_count_derangements_v1 | null | 3 | null | [
"SUM_GEOM"
] | 1 | 0.001 | 2026-02-25T10:38:04.445507Z | null | a79d42 | 548e84 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 171,
"completion_tokens": 1014
},
"timestamp": "2026-03-31T04:17:42.506Z",
"answer": 3816
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "SUM_GEOM",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} |
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