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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
89c592 | antilemma_k3_v1_1915831931_3305 | Let $n = 16313$. Compute the sum
$$
\sum_{d \mid n} \phi(d),
$$
where $\phi(d)$ denotes Euler's totient function. Find the value of this sum. | 16,313 | graphs = [
Graph(
let={
"_n": Const(16313),
"x": SumOverDivisors(n=Ref(name='_n'), 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 | 0.001 | 2026-02-08T17:32:31.042119Z | {
"verified": true,
"answer": 16313,
"timestamp": "2026-02-08T17:32:31.042833Z"
} | cc7d6c | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 110,
"completion_tokens": 870
},
"timestamp": "2026-02-16T11:23:42.102Z",
"answer": 8072
},
{
"id": 11,
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
}
] | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
627c6f | nt_sum_divisors_mod_v1_784195855_8718 | Let $n = 20160$ and $M = 10957$. Define $\sigma$ to be the sum of all positive divisors of $n$. Let $r$ be the remainder when $\sigma$ is divided by $M$. Let $P$ be the set of all prime numbers $p$ such that $2 \leq p \leq 11$. Compute the Bell number $B_k$, where $k$ is the remainder when $|r|$ is divided by the maxim... | 4,140 | graphs = [
Graph(
let={
"n": Const(20160),
"M": Const(10957),
"sigma": SumDivisors(n=Ref("n")),
"result": Mod(value=Ref("sigma"), modulus=Ref("M")),
"Q": Bell(Mod(value=Abs(arg=Ref(name='result')), modulus=MaxOverSet(set=SolutionsSet(var=Var("n"), ... | NT | COMB | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | 88ea9c | nt_sum_divisors_mod_v1 | bell_mod | 6 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.004 | 2026-02-08T16:17:21.065335Z | {
"verified": true,
"answer": 4140,
"timestamp": "2026-02-08T16:17:21.069252Z"
} | 09c07b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 161,
"completion_tokens": 1215
},
"timestamp": "2026-02-17T01:04:07.344Z",
"answer": 4140
},
{... | 1 | [
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V1",
"statu... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
fa1045 | antilemma_k3_v1_1874849503_1032 | Compute the sum of $\phi(d)$ over all positive divisors $d$ of $61693$, where $\phi$ denotes Euler's totient function. | 61,693 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=61693), var='d', expr=EulerPhi(n=Var(name='d'))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K13 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K13",
"K3"
] | 2 | 0.002 | 2026-02-08T13:30:55.746695Z | {
"verified": true,
"answer": 61693,
"timestamp": "2026-02-08T13:30:55.748759Z"
} | 74a093 | 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": 1424
},
"timestamp": "2026-02-10T00:07:24.773Z",
"answer": 61693
},
{
"... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
c0f405 | algebra_poly_eval_v1_153355830_617 | Let $m = 4$, $n = 3$, and $x = 7$. Define
\[
Q = 4 \cdot 7^4 - 9 \cdot 7^p - 8 \cdot 7^2 + 7 + c,
\]
where $p$ is the largest prime number not exceeding $n$, and $c$ is the number of positive integers $p$ for which there exists a positive integer $q$ such that $p < q$, $pq = 17640$, and $\gcd(p, q) = 1$. Find the remai... | 27,595 | graphs = [
Graph(
let={
"_m": Const(4),
"_n": Const(3),
"x": Const(7),
"result": Sum(Mul(Ref("_m"), Pow(Ref("x"), Const(4))), Mul(Const(-9), Pow(Ref("x"), MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n"))... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW",
"COPRIME_PAIRS"
] | 05d703 | algebra_poly_eval_v1 | null | 5 | 0 | [
"COPRIME_PAIRS",
"MAX_PRIME_BELOW"
] | 2 | 0.004 | 2026-02-08T04:05:16.575676Z | {
"verified": true,
"answer": 27595,
"timestamp": "2026-02-08T04:05:16.580079Z"
} | 328ea4 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 255,
"completion_tokens": 2811
},
"timestamp": "2026-02-10T15:15:42.930Z",
"answer": 27595
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"stat... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
b0377d | comb_sum_binomial_row_v1_2051736721_47 | Let $n$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 24$. Compute $2^n$. | 4,096 | graphs = [
Graph(
let={
"_n": Const(24),
"n": 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")), Re... | NT | null | SUM | sympy | COMB1 | [
"COMB1"
] | 567f58 | comb_sum_binomial_row_v1 | null | 3 | 0 | [
"COMB1"
] | 1 | 0.003 | 2026-02-08T15:10:14.097741Z | {
"verified": true,
"answer": 4096,
"timestamp": "2026-02-08T15:10:14.100335Z"
} | 57bc8a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 89,
"completion_tokens": 461
},
"timestamp": "2026-02-16T01:07:33.862Z",
"answer": 4096
},
{
... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CON... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
0eb2eb | antilemma_v7_kummer_2080023795_116 | Let $ c = 11 $ and $ n = 3 $. Let $ m $ be the number of integers $ t $ with $ 27 \leq t \leq 2730 $ for which there exist positive integers $ a \leq 94 $ and $ b \leq 110 $ such that $ t = 15a + 12b $. Let $ k $ be the largest integer such that $ c^k $ divides $ 22264! $. Define $ x $ to be the largest integer such th... | 6 | graphs = [
Graph(
let={
"_c": Const(11),
"_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=94)), Geq(left=Var... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/V1/V7",
"V7"
] | 7ddbbb | antilemma_v7_kummer | null | 7 | 0 | [
"LIN_FORM",
"V1",
"V7"
] | 3 | 0.028 | 2026-02-08T11:34:00.226886Z | {
"verified": true,
"answer": 6,
"timestamp": "2026-02-08T11:34:00.254425Z"
} | 7bdd65 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 239,
"completion_tokens": 4200
},
"timestamp": "2026-02-10T05:28:31.936Z",
"answer": 3
},
{
"i... | 1 | [
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
... | {
"lo": 2.06,
"mid": 5.24,
"hi": 8.53
} | ||
6e3af1 | modular_inverse_v1_349078426_449 | Let $m$ be the largest prime number $n$ such that $2 \leq n \leq N$, where $N$ is the number of integers $t$ with $24 \leq t \leq 1013$ for which there exist positive integers $a \leq 309$ and $b \leq 14$ such that $t = 3a + 5b + 16$. Let $s$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ ... | 34,774 | graphs = [
Graph(
let={
"_n": Const(44121),
"a": Const(523),
"m": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM/MAX_PRIME_BELOW",
"B3"
] | 2a7052 | modular_inverse_v1 | null | 6 | 0 | [
"B3",
"LIN_FORM",
"MAX_PRIME_BELOW"
] | 3 | 0.045 | 2026-02-08T13:03:55.596008Z | {
"verified": true,
"answer": 34774,
"timestamp": "2026-02-08T13:03:55.641366Z"
} | 518a4c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 218,
"completion_tokens": 5960
},
"timestamp": "2026-02-15T09:25:54.971Z",
"answer": 34774
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
9016c6 | comb_bell_compute_v1_151522320_1394 | Let $t$ be an integer satisfying $8 \leq t \leq 400$. A value of $t$ is said to be representable if there exist integers $a$ and $b$ such that $1 \leq a \leq 11$, $1 \leq b \leq 115$, and $t = 5a + 3b$. Let $m = 385$ and let $n$ be the number of nonnegative integers $j$ with $0 \leq j \leq m$ such that $\binom{n}{j}$ i... | 4,140 | graphs = [
Graph(
let={
"_m": Const(385),
"_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=11)), Geq(left=Va... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/V8"
] | 654a7e | comb_bell_compute_v1 | null | 7 | 0 | [
"LIN_FORM",
"V8"
] | 2 | 0.005 | 2026-02-08T03:58:23.858138Z | {
"verified": true,
"answer": 4140,
"timestamp": "2026-02-08T03:58:23.862707Z"
} | f652cd | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 288,
"completion_tokens": 6240
},
"timestamp": "2026-02-11T16:12:06.305Z",
"answer": 190899322
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"statu... | {
"lo": 3.43,
"mid": 5.73,
"hi": 8.84
} | ||
daa5bc | antilemma_sum_primes_v1_784195855_2043 | Let $t = \sum_{d \mid 10} \mu(d)$ and $m = \sum_{d \mid 1} \mu(d)$. Let $n_0 = (2 + t) \cdot m$. Compute the sum of all prime numbers $n$ such that $n_0 \le n \le 3^k$, where $k$ is the largest integer for which $3^k$ divides $2^9 + 1^9$. | 5 | graphs = [
Graph(
let={
"_m": Const(2),
"n1": Const(10),
"t": SumOverDivisors(n=Ref(name='n1'), var='d', expr=MoebiusMu(n=Var(name='d'))),
"n": Const(1),
"m": SumOverDivisors(n=Ref(name='n'), var='d', expr=MoebiusMu(n=Var(name='d'))),
"... | NT | null | COMPUTE | sympy | B1 | [
"LTE_SUM/SUM_PRIMES",
"MOBIUS_SUM",
"SUM_PRIMES"
] | 9ee86c | antilemma_sum_primes_v1 | null | 5 | 2 | [
"B1",
"LTE_SUM",
"MOBIUS_SUM",
"SUM_PRIMES"
] | 4 | 0.01 | 2026-02-08T05:27:34.991780Z | {
"verified": true,
"answer": 5,
"timestamp": "2026-02-08T05:27:35.002212Z"
} | ad502e | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 197,
"completion_tokens": 460
},
"timestamp": "2026-02-18T16:48:08.816Z",
"answer": 5
}
] | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "ok"
},
{
"le... | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
9cf3a6 | diophantine_product_count_v1_1520064083_10268 | Let $n = 13916$. Let $k$ be the sum of all real solutions $x$ to the equation $x^2 - 240x + n = 0$. Let $T$ be the set of all integers $t$ such that $21 \leq t \leq 288$ and $t = 9a + 12b$ for some integers $a$, $b$ with $1 \leq a \leq 4$ and $1 \leq b \leq 21$. Let $u$ be the number of elements in $T$. Determine the n... | 16 | graphs = [
Graph(
let={
"_n": Const(13916),
"k": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Const(2)), Mul(Const(-240), Var("x")), Ref("_n")), Const(0)))),
"upper": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'... | NT | null | COUNT | sympy | COUNT_CARTESIAN | [
"VIETA_SUM",
"LIN_FORM"
] | f0d186 | diophantine_product_count_v1 | null | 6 | 0 | [
"COUNT_CARTESIAN",
"LIN_FORM",
"VIETA_SUM"
] | 3 | 0.077 | 2026-02-08T11:18:56.316032Z | {
"verified": true,
"answer": 16,
"timestamp": "2026-02-08T11:18:56.392684Z"
} | d80a64 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 205,
"completion_tokens": 3053
},
"timestamp": "2026-02-14T12:01:17.693Z",
"answer": 16
},
{
... | 1 | [
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
},
{
"le... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
f92b33_n | comb_count_permutations_fixed_v1_1218484723_4747 | A security system has $n$ distinct access cards that must be assigned to $n$ distinct employees so that no employee receives their own original card. The number of such assignments is $D_n$, the number of derangements of $n$ elements. A technician first computes a parameter $M$ as follows: consider all integers $a$ wit... | 315 | COMB | null | COUNT | sympy | POLY_ORBIT_LEGENDRE | [
"POLY_ORBIT_LEGENDRE/SUM_GEOM"
] | 82d294 | comb_count_permutations_fixed_v1 | null | 7 | null | [
"POLY_ORBIT_LEGENDRE",
"SUM_GEOM"
] | 2 | 0.003 | 2026-02-25T06:24:16.546177Z | null | 2d3400 | f92b33 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 435,
"completion_tokens": 32768
},
"timestamp": "2026-03-30T22:20:22.024Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "POLY_ORBIT_LEGENDRE",
"status": "ok"
},
{
"lemma": "SUM_... | {
"lo": 1.5,
"mid": 4.69,
"hi": 7.23
} | |
525f4a | nt_count_coprime_and_v1_124444284_3496 | Let $k_1 = 11$ and let $k_2$ be the largest prime number less than or equal to $14$. Determine the number of positive integers $n$ such that $1 \leq n \leq 32892$, $\gcd(n, k_1) = 1$, and $\gcd(n, k_2) = 1$. | 27,602 | graphs = [
Graph(
let={
"upper": Const(32892),
"k1": Const(11),
"k2": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(14)), IsPrime(Var("n"))))),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), conditi... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | nt_count_coprime_and_v1 | null | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 3.729 | 2026-02-08T05:25:51.292513Z | {
"verified": true,
"answer": 27602,
"timestamp": "2026-02-08T05:25:55.021390Z"
} | 3b11ad | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 123,
"completion_tokens": 1385
},
"timestamp": "2026-02-12T08:31:29.743Z",
"answer": 27602
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"st... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
a8cee1 | nt_count_phi_equals_v1_798873815_522 | Let
\[w = \sum_{d \mid 32} \mu(d),\]
where $\mu$ is the Möbius function.
Let $u$ be the value of the Liouville function $\lambda(213)$.
Let $P$ be the set of all positive integers $p$ for which there exists an integer $q$ such that
\[pq = 216,\quad \gcd(p,q)=1,\quad p<q.\]
Let $c$ be the number of elements of $P$.
L... | 0 | graphs = [
Graph(
let={
"_n": Const(389),
"n1": Const(32),
"w": SumOverDivisors(n=Ref(name='n1'), var='d', expr=MoebiusMu(n=Var(name='d'))),
"n": Const(213),
"u": LiouvilleLambda(n=Ref(name='n')),
"upper": Sum(MinOverSet(set=SolutionsSe... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/MIN_PRIME_FACTOR/MOBIUS_SUM",
"LIOUVILLE_ONE"
] | 050fa6 | nt_count_phi_equals_v1 | null | 8 | 2 | [
"COPRIME_PAIRS",
"LIOUVILLE_ONE",
"MIN_PRIME_FACTOR",
"MOBIUS_SUM"
] | 4 | 0.121 | 2026-02-08T02:40:27.703560Z | {
"verified": true,
"answer": 0,
"timestamp": "2026-02-08T02:40:27.824816Z"
} | c220bc | CC BY 4.0 | [
{
"id": 4,
"model": "NousResearch/Hermes-4-405B",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 280,
"completion_tokens": 799
},
"timestamp": "2026-02-09T01:14:30.100Z",
"answer": 0
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIOUVILLE_ONE",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "n... | {
"lo": -4.84,
"mid": -1.64,
"hi": 2.05
} | ||
516ff5 | algebra_quadratic_discriminant_v1_865884756_3043 | Let $n$ be a positive integer such that $1 \leq n \leq 35$. Define $b$ to be the number of such integers $n$ for which the sum of the digits of $n$ is odd. Let $a = -1$ and $c = -81$. Compute $b^2 - 4ac$. | 0 | graphs = [
Graph(
let={
"_n": Const(2),
"a": Const(-1),
"b": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(35)), Eq(Mod(value=DigitSum(Var("n")), modulus=Const(2)), Const(1))))),
"c": Const(-81),
... | NT | null | COMPUTE | sympy | BINOMIAL_ALTERNATING | [
"L3B"
] | cc148f | algebra_quadratic_discriminant_v1 | null | 3 | 0 | [
"BINOMIAL_ALTERNATING",
"L3B"
] | 2 | 0.012 | 2026-02-08T17:08:08.301875Z | {
"verified": true,
"answer": 0,
"timestamp": "2026-02-08T17:08:08.313634Z"
} | 0cc8c7 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 119,
"completion_tokens": 704
},
"timestamp": "2026-02-17T19:56:46.208Z",
"answer": 0
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3B",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
4b6a4c | antilemma_v1_legendre_124444284_223 | Let $m = 16263$ and let $n$ be the smallest divisor of $1356277$ that is at least $2$. Let $x$ be the largest integer $k$ such that $n^k$ divides $m!$. Compute the Bell number $B_y$, where $y$ is the absolute value of $x$ modulo $11$. | 1 | graphs = [
Graph(
let={
"_m": Const(16263),
"_n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(1356277))))),
"x": MaxKDivides(target=Factorial(Ref("_m")), base=Ref("_n")),
"Q": Bell(M... | NT | COMB | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/V1",
"V1"
] | 1d9641 | antilemma_v1_legendre | null | 6 | 0 | [
"MIN_PRIME_FACTOR",
"V1"
] | 2 | 0.001 | 2026-02-08T03:04:56.245168Z | {
"verified": true,
"answer": 1,
"timestamp": "2026-02-08T03:04:56.246073Z"
} | 61a3e7 | 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": 1267
},
"timestamp": "2026-02-09T14:53:12.569Z",
"answer": 1
},
{
"id":... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K5",
"status": "same_pattern_wrong"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR... | {
"lo": -6.51,
"mid": -0.31,
"hi": 5.43
} | ||
a115be | nt_min_crt_v1_1915831931_1773 | Let $m = 8$, $a = 7$, $b = 8$, and $u = 88$. Let $k$ be the largest prime number $n$ such that $2 \leq n \leq 11$. Compute the smallest positive integer $n_1$ such that $1 \leq n_1 \leq u$, $n_1 \equiv a \pmod{m}$, and $n_1 \equiv b \pmod{k}$. | 63 | graphs = [
Graph(
let={
"_n": Const(2),
"m": Const(8),
"k": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Const(11)), IsPrime(Var("n"))))),
"a": Const(7),
"b": Const(8),
"upper": Const(8... | NT | null | EXTREMUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | nt_min_crt_v1 | null | 5 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.008 | 2026-02-08T16:26:12.126288Z | {
"verified": true,
"answer": 63,
"timestamp": "2026-02-08T16:26:12.134129Z"
} | 7eb497 | 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": 750
},
"timestamp": "2026-02-17T03:39:29.198Z",
"answer": 63
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
de9270 | nt_count_coprime_and_v1_1520064083_8587 | Let $U$ be the number of positive integers $n \leq 587460$ such that the $n$-th Fibonacci number is divisible by $30$. Let $k_1 = 7$ and $k_2 = 11$. Define $R$ to be the number of positive integers $n \leq U$ such that $\gcd(n, k_1) = 1$ and $\gcd(n, k_2) = 1$. Determine the value of $R$. | 7,630 | graphs = [
Graph(
let={
"upper": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(587460)), Divides(divisor=Const(30), dividend=Fibonacci(arg=Var(name='n')))))),
"k1": Const(7),
"k2": Const(11),
"result": C... | NT | null | COUNT | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE"
] | 66de3c | nt_count_coprime_and_v1 | null | 7 | 0 | [
"COUNT_FIB_DIVISIBLE"
] | 1 | 1.769 | 2026-02-08T10:15:42.711743Z | {
"verified": true,
"answer": 7630,
"timestamp": "2026-02-08T10:15:44.480348Z"
} | dbf56c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 149,
"completion_tokens": 1288
},
"timestamp": "2026-02-14T06:54:35.335Z",
"answer": 7630
},
{... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
966b45 | lin_form_endings_v1_809748730_728 | Let $a = 48$ and $b = 36$. Define $g$ to be the greatest common divisor of $a$ and $b$. Let $a' = \left\lfloor \frac{a}{g} \right\rfloor$ and $b' = \left\lfloor \frac{b}{g} \right\rfloor$. Given $A = 11$ and $B = 22$, compute the quantity $$Q = a' A + b' B - a' b'.$$ Multiply $Q$ by $17373$ to obtain $Q'$. Let $x$ be t... | 16,146 | graphs = [
Graph(
let={
"a_coeff": Const(48),
"b_coeff": Const(36),
"A_val": Const(11),
"B_val": Const(22),
"g_step": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"ap_node": Floor(Div(Ref("a_coeff"), Ref("g_step"))),
"bp_node": ... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 2 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T11:42:37.644074Z | {
"verified": true,
"answer": 16146,
"timestamp": "2026-02-08T11:42:37.645030Z"
} | 37ffbe | 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": 709
},
"timestamp": "2026-02-14T17:33:41.115Z",
"answer": 16146
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
100a93 | nt_count_divisors_in_range_v1_865884756_5824 | Let $n = 10080$. Let $a$ be the number of ordered pairs $(i,j)$ of positive integers such that $i + j = 37$, $1 \leq i \leq 36$, and $1 \leq j \leq 37$. Let $b = 847$. Compute the number of positive divisors $d$ of $n$ such that $a \leq d \leq b$. | 40 | graphs = [
Graph(
let={
"_n": Const(37),
"n": Const(10080),
"a": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref("_n")), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(36)), right=Integ... | NT | null | COUNT | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | nt_count_divisors_in_range_v1 | null | 4 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.63 | 2026-02-08T18:48:00.024437Z | {
"verified": true,
"answer": 40,
"timestamp": "2026-02-08T18:48:00.653978Z"
} | 057c4a | 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": 2758
},
"timestamp": "2026-02-18T19:41:27.275Z",
"answer": 40
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
e409f9 | comb_count_surjections_v1_1116507919_415 | Let $k$ be the number of ordered pairs $(i, j)$ of integers with $1 \leq i \leq 6$, $1 \leq j \leq 6$, and $i + j = 8$. Compute $k! \cdot S(6, k)$, where $S(6, k)$ denotes the Stirling number of the second kind. | 1,800 | graphs = [
Graph(
let={
"n": Const(6),
"k": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(8)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(6)), right=IntegerRange(start=Const(1), end=Const(6... | COMB | null | COUNT | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | comb_count_surjections_v1 | null | 3 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.011 | 2026-02-08T02:34:05.320855Z | {
"verified": true,
"answer": 1800,
"timestamp": "2026-02-08T02:34:05.332177Z"
} | 288948 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 197,
"completion_tokens": 773
},
"timestamp": "2026-02-08T19:31:31.211Z",
"answer": 1800
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"stat... | {
"lo": -4.8,
"mid": -2.89,
"hi": -0.93
} | ||
9e5743 | antilemma_sum_equals_v1_1080341949_226 | Let $n$ be the number of ordered pairs $(i,j)$ of positive integers such that $i + j = 87$ and $1 \le i \le 87$, $1 \le j \le 87$. Compute $n$. | 86 | graphs = [
Graph(
let={
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(87)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(87)), right=IntegerRange(start=Const(1), end=Const(87))))),
},
... | COMB | GEOM | COMPUTE | sympy | COMB1 | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 2 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS"
] | 2 | 0.022 | 2026-02-08T13:19:29.206096Z | {
"verified": true,
"answer": 86,
"timestamp": "2026-02-08T13:19:29.228355Z"
} | de2885 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 162,
"completion_tokens": 266
},
"timestamp": "2026-02-24T18:06:28.377Z",
"answer": 86
},
{
"id":... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"stat... | {
"lo": -9.23,
"mid": -6.18,
"hi": -4.06
} | ||
abc6c4 | diophantine_fbi2_min_v1_579913215_155 | Let $S$ be the set of all integers $t$ such that $10 \leq t \leq 95$ and there exist positive integers $a$, $b$ with $1 \leq a \leq 20$, $1 \leq b \leq 5$, satisfying $$t = 3a + 7b.$$
Let $U$ be the number of elements in $S$. Find the smallest integer $d$ such that $5 \leq d \leq U$, $d$ divides $64$, and $\frac{64}{d... | 8 | graphs = [
Graph(
let={
"_n": Const(5),
"k": Const(64),
"upper": 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=... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | diophantine_fbi2_min_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.006 | 2026-02-08T12:55:33.639047Z | {
"verified": true,
"answer": 8,
"timestamp": "2026-02-08T12:55:33.644745Z"
} | ee44ee | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 168,
"completion_tokens": 2613
},
"timestamp": "2026-02-15T07:55:57.522Z",
"answer": 8
},
{
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -9.12,
"mid": -6.02,
"hi": -3.62
} | ||
d4e2aa | antilemma_sum_equals_v1_655260480_5556 | Let $n$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 60$. Let $x$ be the number of ordered pairs $(i, j)$ of integers with $1 \leq i \leq 29$ and $1 \leq j \leq 29$ such that $i + j = n$. Compute the remainder when $17207 \cdot x$ is divided by $76211$. | 41,737 | graphs = [
Graph(
let={
"_n": 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")), Const(60))))),
"x"... | COMB | GEOM | COMPUTE | sympy | COMB1 | [
"COMB1/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | 3e1adf | antilemma_sum_equals_v1 | null | 4 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS"
] | 2 | 0.024 | 2026-02-08T18:33:35.903005Z | {
"verified": true,
"answer": 41737,
"timestamp": "2026-02-08T18:33:35.927301Z"
} | 4ef6a8 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 150,
"completion_tokens": 1460
},
"timestamp": "2026-02-18T17:30:22.053Z",
"answer": 41737
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
... | {
"lo": -3.12,
"mid": 1.47,
"hi": 6.57
} | ||
cce608 | comb_count_permutations_fixed_v1_1439011603_227 | Let $A$ be the set of all ordered pairs of positive integers $(x, y)$ such that $xy = 9$. Let $n$ be the minimum value of $x + y$ as $(x, y)$ ranges over $A$. Let $B$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 24$, $\gcd(p, q) = 1$, and $p < q$. Let $k$ be the ... | 60,615 | graphs = [
Graph(
let={
"_m": Const(47153),
"_n": Const(70056),
"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(9)))), e... | NT | COMB | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS",
"B3"
] | 1999ea | comb_count_permutations_fixed_v1 | null | 5 | 0 | [
"B3",
"COPRIME_PAIRS"
] | 2 | 0.005 | 2026-02-08T15:22:11.541990Z | {
"verified": true,
"answer": 60615,
"timestamp": "2026-02-08T15:22:11.546873Z"
} | 155f43 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 225,
"completion_tokens": 2910
},
"timestamp": "2026-02-16T05:13:43.327Z",
"answer": 60615
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
654c7f | comb_factorial_compute_v1_1918700295_2529 | Let $n$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p < q$, $\gcd(p, q) = 1$, and $pq = 10290$. Compute $n!$. | 40,320 | 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=10290)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(value=1))... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_factorial_compute_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.002 | 2026-02-08T07:56:50.571897Z | {
"verified": true,
"answer": 40320,
"timestamp": "2026-02-08T07:56:50.574173Z"
} | 7e8972 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 100,
"completion_tokens": 2377
},
"timestamp": "2026-02-13T13:50:47.417Z",
"answer": 40320
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
03404f | comb_bell_compute_v1_677425708_692 | Define $u = \sum_{k=0}^{n_2} (-1)^k \binom{n_2}{k}$, where $n_2 = \sum_{k=0}^{3} (-1)^k \binom{3}{k}$. Define $w = \sum_{k=0}^{10} (-1)^k \binom{10}{k}$. Let $n = 9u + w$, where 9 is the number of ordered pairs $(i,j)$ with $1 \leq i \leq 3$ and $1 \leq j \leq 3$. Compute the Bell number $B_n$, which counts the number ... | 21,147 | graphs = [
Graph(
let={
"n2": Const(0),
"u": Summation(var="k", start=Summation(var="k", start=Const(0), end=Const(3), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Const(3), k=Var("k")))), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n2"), k=Var("k")))),
"... | COMB | null | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN/BINOMIAL_ALTERNATING"
] | d0de27 | comb_bell_compute_v1 | null | 4 | 2 | [
"BINOMIAL_ALTERNATING",
"COUNT_CARTESIAN"
] | 2 | 0.003 | 2026-02-08T03:41:23.389739Z | {
"verified": true,
"answer": 21147,
"timestamp": "2026-02-08T03:41:23.392974Z"
} | e060f5 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 270,
"completion_tokens": 489
},
"timestamp": "2026-02-08T20:56:35.751Z",
"answer": 21147
},
{
"i... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma":... | {
"lo": -4.92,
"mid": -2.9,
"hi": -0.7
} | ||
f99a41 | nt_min_with_divisor_count_v1_458359167_5095 | Find the smallest positive integer $n$ at most $87025$ that has exactly $10$ positive divisors. | 48 | graphs = [
Graph(
let={
"upper": Const(87025),
"div_count": Const(10),
"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("re... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/ONE_PHI_2"
] | 761f00 | nt_min_with_divisor_count_v1 | null | 4 | 0 | [
"COPRIME_PAIRS",
"ONE_PHI_2"
] | 2 | 8.207 | 2026-02-08T12:16:32.943718Z | {
"verified": true,
"answer": 48,
"timestamp": "2026-02-08T12:16:41.150830Z"
} | e1f56c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 70,
"completion_tokens": 1033
},
"timestamp": "2026-02-14T23:52:18.192Z",
"answer": 48
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "ONE_PHI_2",
"status": "ok_later"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status"... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
844ead | sequence_lucas_compute_v1_1978505735_2140 | Let $n = 23$. Define $L_n$ to be the $n$th Lucas number, where the Lucas sequence is defined by $L_1 = 1$, $L_2 = 3$, and $L_k = L_{k-1} + L_{k-2}$ for $k \geq 3$. Let $c$ be the number of positive integers $p$ for which there exists an integer $q$ such that $pq = 150$, $\gcd(p, q) = 1$, and $p < q$. Compute the remain... | 14,340 | graphs = [
Graph(
let={
"_n": Const(78415),
"n": Const(23),
"result": Lucas(arg=Ref(name='n')),
"_c": 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'), Va... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | c90628 | sequence_lucas_compute_v1 | negation_mod | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.002 | 2026-02-08T16:40:33.765839Z | {
"verified": true,
"answer": 14340,
"timestamp": "2026-02-08T16:40:33.767732Z"
} | 397a2d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 181,
"completion_tokens": 1645
},
"timestamp": "2026-02-17T11:08:56.601Z",
"answer": 14340
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
0b298e | sequence_fibonacci_compute_v1_898971024_1854 | Let $n = \sum_{k=1}^{6} \phi(k) \left\lfloor \frac{6}{k} \right\rfloor$, where $\phi(k)$ denotes Euler's totient function. Let $F_n$ be the $n$th Fibonacci number, where $F_1 = 1$, $F_2 = 1$, and $F_k = F_{k-1} + F_{k-2}$ for $k \geq 3$. Compute the remainder when $44121 \cdot F_n$ is divided by $96700$. | 28,666 | graphs = [
Graph(
let={
"_n": Const(96700),
"n": Summation(var="k", start=Const(1), end=Const(6), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(6), Var("k"))))),
"result": Fibonacci(arg=Ref(name='n')),
"Q": Mod(value=Mul(Const(44121), Ref("result")), modulus=... | NT | null | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | sequence_fibonacci_compute_v1 | null | 4 | 0 | [
"K2"
] | 1 | 0.001 | 2026-02-08T16:23:26.505927Z | {
"verified": true,
"answer": 28666,
"timestamp": "2026-02-08T16:23:26.506902Z"
} | 7b2b69 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 167,
"completion_tokens": 2338
},
"timestamp": "2026-02-17T02:46:46.325Z",
"answer": 28666
},
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
}
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
1cf86e | nt_sum_divisors_mod_v1_1742523217_961 | Let $n$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 6350400$. Let $\sigma(n)$ denote the sum of the positive divisors of $n$. Compute the remainder when $\sigma(n)$ is divided by 11071. | 8,273 | 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")), Const(6350400)))), expr=Sum(Var("x"), Var("y")))),
"M": Const(1107... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_divisors_mod_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.001 | 2026-02-08T03:22:17.510712Z | {
"verified": true,
"answer": 8273,
"timestamp": "2026-02-08T03:22:17.512006Z"
} | 1c7f59 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 178,
"completion_tokens": 1649
},
"timestamp": "2026-02-10T01:10:42.686Z",
"answer": 8273
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status":... | {
"lo": -5.15,
"mid": 0.01,
"hi": 5.44
} | ||
82e7b6_n | alg_poly4_min_v1_1218484723_3543 | A software algorithm computes a performance score based on two parameters $a$ and $b$, each between $1$ and $300$. The score is $S \cdot b^4 + 12288a^4 + 6144a^3b + 57600a^2b^2 + 14208ab^3$, where $S$ is the smallest possible sum of two positive numbers whose product is $16353936$. What is the lowest achievable score? | 98,328 | ALG | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | alg_poly4_min_v1 | null | 6 | null | [
"B3"
] | 1 | 0.859 | 2026-02-25T05:10:47.597230Z | null | 4ac130 | 82e7b6 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 209,
"completion_tokens": 8521
},
"timestamp": "2026-03-30T20:12:29.761Z",
"answer": 98328
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | |
f29ed4 | antilemma_k3_v1_784195855_7586 | Let $n = 77644$. Compute the sum of $\phi(d)$ over all positive divisors $d$ of $n$, where $\phi$ denotes Euler's totient function. | 77,644 | graphs = [
Graph(
let={
"_n": Const(77644),
"x": SumOverDivisors(n=Ref(name='_n'), 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 | 2026-02-08T09:24:16.168388Z | {
"verified": true,
"answer": 77644,
"timestamp": "2026-02-08T09:24:16.168801Z"
} | f1e692 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 100,
"completion_tokens": 262
},
"timestamp": "2026-02-15T20:40:23.853Z",
"answer": 1080
},
{
"id": 11,
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
ab3250 | antilemma_sum_equals_v1_124444284_1511 | Determine the number of ordered pairs $(i,j)$ of positive integers such that $i + j = 26$ and $1 \leq i \leq 25$, $1 \leq j \leq 25$. | 25 | graphs = [
Graph(
let={
"_n": Const(26),
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref("_n")), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(25)), right=IntegerRange(start=Const(1), end=Con... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 2 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.015 | 2026-02-08T03:57:41.211279Z | {
"verified": true,
"answer": 25,
"timestamp": "2026-02-08T03:57:41.225871Z"
} | 34887c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 158,
"completion_tokens": 259
},
"timestamp": "2026-02-10T16:17:29.060Z",
"answer": 25
},
{
"id":... | 2 | [
{
"lemma": "COUNT_COPRIME_GRID",
"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",
"stat... | {
"lo": -10,
"mid": -7.79,
"hi": -5.57
} | ||
bd400f | nt_sum_over_divisible_v1_168721529_1508 | Let $s$ be the minimum value of $x + y$ where $x$ and $y$ are positive integers such that $xy = 9025$. Let $T$ be the set of all positive integers $n \leq 6666$ such that $n$ is divisible by $s$. Let $S$ be the sum of all elements in $T$. Compute the Bell number of $|S| \bmod 11$. | 21,147 | graphs = [
Graph(
let={
"_n": Const(9025),
"upper": Const(6666),
"divisor": 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... | COMB | null | SUM | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_over_divisible_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.224 | 2026-02-08T13:44:34.875198Z | {
"verified": true,
"answer": 21147,
"timestamp": "2026-02-08T13:44:35.098841Z"
} | cbc061 | 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": 1305
},
"timestamp": "2026-02-09T18:16:14.630Z",
"answer": 21147
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": 1.15,
"mid": 4.18,
"hi": 6.61
} | ||
dc51b6 | nt_gcd_compute_v1_655260480_5294 | Let $a = 230616$ and $b = 435608$. Define $\text{result} = \gcd(a, b)$. Let $S$ be the set of all positive integers $n$ such that $1 \leq n \leq 244$, $n$ is even, and $\gcd(n, 21) = 1$. Let $\text{count}$ be the number of elements in $S$. Define
$$
\text{digit_sum} = \sum_{i=0}^{\text{NumDigits}(\text{result}) - 1} \t... | 266 | graphs = [
Graph(
let={
"_n": Const(2),
"a": Const(230616),
"b": Const(435608),
"result": GCD(a=Ref("a"), b=Ref("b")),
"Q": Sum(Summation(var="i", start=Const(0), end=Sub(NumDigits(x=Abs(arg=Ref(name='result')), base=None), Const(1)), expr=Mul(Digi... | NT | null | COMPUTE | sympy | C5 | [
"C5"
] | 4bcb45 | nt_gcd_compute_v1 | digits_weighted_mod | 4 | 0 | [
"C5"
] | 1 | 0.005 | 2026-02-08T18:24:07.004831Z | {
"verified": true,
"answer": 266,
"timestamp": "2026-02-08T18:24:07.009729Z"
} | b27c55 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 242,
"completion_tokens": 1623
},
"timestamp": "2026-02-18T16:49:32.815Z",
"answer": 266
},
{
... | 1 | [
{
"lemma": "C5",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
88dc65_n | comb_count_derangements_v1_1419126231_990 | A theater has $n$ performers, each assigned a unique costume. At the end of a show, costumes are returned randomly such that no one gets their own — a derangement. The number of performers $n$ is calculated by summing $2^k$ for $k = 1$ to $3$, multiplying the sum by 3, and dividing by 9. How many ways can the costumes ... | 1,854 | COMB | null | COUNT | sympy | SUM_INDEPENDENT | [
"SUM_INDEPENDENT",
"SUM_GEOM"
] | a4c575 | comb_count_derangements_v1 | null | 4 | null | [
"SUM_GEOM",
"SUM_INDEPENDENT"
] | 2 | 0.001 | 2026-02-25T10:30:19.717745Z | null | 6ec227 | 88dc65 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 204,
"completion_tokens": 6275
},
"timestamp": "2026-03-31T04:13:06.656Z",
"answer": 32071101049
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "SUM_GEOM",
"status": "ok"
},
{
"lemma": "SUM_INDEPENDENT",
"status": "ok"
},
{
"lemma": "V8",
"status": ... | {
"lo": 3.8,
"mid": 6.33,
"hi": 9.49
} | |
1603bf | diophantine_fbi2_count_v1_1978505735_1242 | Let $ s $ be the set of all ordered pairs $ (x, y) $ of positive integers such that $ xy = 32400 $. Let $ \text{sums} $ be the set of all values $ x + y $ for $ (x, y) \in s $. Define $ k $ to be the minimum element of $ \text{sums} $. Compute the number of integers $ d $ such that $ 2 \leq d \leq 81 $, $ d $ divides $... | 28,908 | graphs = [
Graph(
let={
"k": 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(32400)))), expr=Sum(Var("x"), Var("y")))),
"result": CountOv... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | diophantine_fbi2_count_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.008 | 2026-02-08T15:59:08.158837Z | {
"verified": true,
"answer": 28908,
"timestamp": "2026-02-08T15:59:08.166505Z"
} | f059ce | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 201,
"completion_tokens": 1529
},
"timestamp": "2026-02-16T18:05:33.063Z",
"answer": 28908
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
ca42fb | antilemma_sum_equals_v1_1978505735_7606 | Let $T$ be the set of all integers $t$ such that $12 \leq t \leq 91$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 8$, $1 \leq b \leq 7$, and $t = 7a + 5b$.
Let $N$ be the number of elements in $T$.
Let $S$ be the set of all ordered pairs $(i, j)$ of positive integers such that $1 \leq i \leq 55$,... | 87 | 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=8)), Geq(left=Var(name='b'), right=Const(value=... | COMB | GEOM | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | ada383 | antilemma_sum_equals_v1 | null | 5 | 0 | [
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 2 | 0.009 | 2026-02-08T20:21:46.991409Z | {
"verified": true,
"answer": 87,
"timestamp": "2026-02-08T20:21:47.000283Z"
} | 7907c9 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 235,
"completion_tokens": 2496
},
"timestamp": "2026-02-19T00:24:26.849Z",
"answer": 87
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
... | {
"lo": -3.12,
"mid": 1.47,
"hi": 6.57
} | ||
4892e0 | sequence_fibonacci_compute_v1_717093673_3333 | Let $S$ be the set of all nonnegative integers $j$ such that $0 \leq j \leq 4865$ and $\binom{4865}{j}$ is odd. Let $m$ be the number of elements in $S$. Define $n = m + 9$. Let $F_n$ denote the $n$th Fibonacci number, where $F_0 = 0$, $F_1 = 1$, and $F_k = F_{k-1} + F_{k-2}$ for $k \geq 2$. Find the remainder when $26... | 13,463 | graphs = [
Graph(
let={
"_n": Const(67312),
"n": Sum(CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(4865)), Eq(Mod(value=Binom(n=Const(4865), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')), Const(9))... | ALG | COMB | COMPUTE | sympy | V8 | [
"V8"
] | 86348e | sequence_fibonacci_compute_v1 | null | 6 | 0 | [
"V8"
] | 1 | 0.002 | 2026-02-08T17:30:02.122491Z | {
"verified": true,
"answer": 13463,
"timestamp": "2026-02-08T17:30:02.124252Z"
} | 0cb89a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 185,
"completion_tokens": 3122
},
"timestamp": "2026-02-18T03:54:21.298Z",
"answer": 13463
},
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||
972ea3 | nt_lcm_compute_v1_717093673_1956 | Let $a$ be the number of prime numbers $n$ such that $2 \leq n \leq 6947$. Let $b = 2862$. Compute the least common multiple of $a$ and $b$. | 94,446 | graphs = [
Graph(
let={
"a": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(6947)), IsPrime(Var("n"))))),
"b": Const(2862),
"result": LCM(a=Ref("a"), b=Ref("b")),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | L3C | [
"COUNT_PRIMES"
] | 07c874 | nt_lcm_compute_v1 | null | 4 | 0 | [
"COUNT_PRIMES",
"L3C"
] | 2 | 0.011 | 2026-02-08T16:24:53.303713Z | {
"verified": true,
"answer": 94446,
"timestamp": "2026-02-08T16:24:53.314535Z"
} | 75f8d2 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 94,
"completion_tokens": 3143
},
"timestamp": "2026-02-17T03:06:15.750Z",
"answer": 94446
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
08f509 | comb_count_surjections_v1_458359167_1298 | Let $n$ be the number of ordered pairs $(i,j)$ of integers with $1 \le i \le 6$ and $1 \le j \le 6$ such that $i + j = 6$. Let $k = 4$. Compute $k! \cdot S(n, k)$, where $S(n, k)$ denotes the Stirling number of the second kind. | 240 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(6)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(6)), right=IntegerRange(start=Const(1), end=Const(6))))),
"k": Con... | COMB | null | COUNT | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | comb_count_surjections_v1 | null | 4 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.015 | 2026-02-08T04:32:24.693431Z | {
"verified": true,
"answer": 240,
"timestamp": "2026-02-08T04:32:24.708543Z"
} | daa3ab | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 195,
"completion_tokens": 655
},
"timestamp": "2026-02-24T00:56:45.748Z",
"answer": 240
},
{
"id"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status":... | {
"lo": -7.18,
"mid": -4.99,
"hi": -3
} | ||
6aa513 | antilemma_v8_lucas_124444284_494 | Let $m = 49151$. A pair of positive integers $(p, q)$ is called reduced if $p < q$, $\gcd(p, q) = 1$, and $p \cdot q = 108$. Let $n$ be the number of such reduced pairs.
Let $x$ be the number of nonnegative integers $j$ such that $0 \leq j \leq 49151$ and
\[
\binom{49151}{j} \equiv \phi(1) \pmod{n},
\]
where $\phi$ de... | 32,768 | graphs = [
Graph(
let={
"_m": Const(49151),
"_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=108)), Eq(left=GCD(a=Var(name='p'), b=Var(na... | NT | COMB | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/V8",
"ONE_PHI_1",
"V8"
] | 5f4336 | antilemma_v8_lucas | null | 7 | 0 | [
"COPRIME_PAIRS",
"ONE_PHI_1",
"V8"
] | 3 | 0.004 | 2026-02-08T03:19:55.274571Z | {
"verified": true,
"answer": 32768,
"timestamp": "2026-02-08T03:19:55.278191Z"
} | 9ae542 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 247,
"completion_tokens": 2008
},
"timestamp": "2026-02-09T18:23:10.209Z",
"answer": 32768
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "ONE_PHI_1",
"status": "ok"
},... | {
"lo": -6.51,
"mid": -0.31,
"hi": 5.43
} | ||
a482e0 | modular_modexp_compute_v1_601307018_2267 | Let $N$ be the number of positive integers $t$ such that there exist integers $c, b$ with $1 \leq c \leq 2$, $1 \leq b \leq 9$, $t = 21c + 6b$, $27 \leq t \leq 96$. Let $M$ be the largest prime $n$ with $2 \leq n \leq N$. Let $e$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers with ... | 27,673 | 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=... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/MAX_PRIME_BELOW",
"B3"
] | 2a7052 | modular_modexp_compute_v1 | null | 6 | 0 | [
"B3",
"LIN_FORM",
"MAX_PRIME_BELOW"
] | 3 | 0.007 | 2026-03-10T02:56:09.962748Z | {
"verified": true,
"answer": 27673,
"timestamp": "2026-03-10T02:56:09.969556Z"
} | a68aab | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 263,
"completion_tokens": 6681
},
"timestamp": "2026-03-29T04:52:34.973Z",
"answer": 27673
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
... | {
"lo": -2.46,
"mid": 1.23,
"hi": 4.93
} | ||
e7cb19 | comb_count_permutations_fixed_v1_784195855_4634 | Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 54$, $\gcd(p, q) = 1$, and $p < q$. Let $L$ be the number of elements in $S$. Define $n$ to be the largest prime number satisfying $L \leq n \leq 11$. Let $k$ be the largest prime number not exceeding 10. Compu... | 2,970 | graphs = [
Graph(
let={
"_n": Const(11),
"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 | COMB | COUNT | sympy | MIN_PRIME_FACTOR | [
"COPRIME_PAIRS/MAX_PRIME_BELOW"
] | 2248fc | comb_count_permutations_fixed_v1 | null | 6 | 0 | [
"COPRIME_PAIRS",
"MAX_PRIME_BELOW",
"MIN_PRIME_FACTOR"
] | 3 | 0.015 | 2026-02-08T07:13:34.924900Z | {
"verified": true,
"answer": 2970,
"timestamp": "2026-02-08T07:13:34.939728Z"
} | 9fea1e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 175,
"completion_tokens": 1737
},
"timestamp": "2026-02-13T08:59:25.540Z",
"answer": 2970
},
{... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "POLY_PADIC_VAL_CONS... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
a71b69 | comb_count_partitions_v1_1915831931_3081 | Let $n = 38$ and let $\text{result} = p(n)$, the number of integer partitions of $n$. Let $\pi$ be the number of prime numbers $p$ such that $2 \leq p \leq 2143$. Let $Q$ be the remainder when $\pi - \text{result}$ is divided by $95890$. Compute $Q$. | 70,199 | graphs = [
Graph(
let={
"_n": Const(2),
"n": Const(38),
"result": Partition(arg=Ref(name='n')),
"Q": Mod(value=Sub(CountOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Ref("_n")), Leq(Var("n1"), Const(2143)), IsPrime(Var("n1"))))), Ref("re... | NT | COMB | COUNT | sympy | SUM_ARITHMETIC | [
"COUNT_PRIMES"
] | ad5c3c | comb_count_partitions_v1 | negation_mod | 6 | 0 | [
"COUNT_PRIMES",
"SUM_ARITHMETIC"
] | 2 | 0.027 | 2026-02-08T17:21:10.151508Z | {
"verified": true,
"answer": 70199,
"timestamp": "2026-02-08T17:21:10.178198Z"
} | 11f920 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 127,
"completion_tokens": 1196
},
"timestamp": "2026-02-18T01:08:23.153Z",
"answer": 70199
},
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
5848c9 | geo_visible_lattice_v1_1520064083_3995 | Let $n = 100$. Define $R$ to be the number of ordered pairs $(x, y)$ of positive integers such that $1 \leq x, y \leq n$ and $\gcd(x, y) = 1$. Compute the remainder when $34054 \cdot R$ is divided by $88707$. | 67,146 | graphs = [
Graph(
let={
"n": Const(100),
"result": VisibleLatticePoints(n=Ref(name='n')),
"Q": Mod(value=Mul(Const(34054), Ref("result")), modulus=Const(88707)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 6 | 0 | null | null | 0.216 | 2026-02-08T06:00:52.694947Z | {
"verified": true,
"answer": 67146,
"timestamp": "2026-02-08T06:00:52.910910Z"
} | 576056 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 182,
"completion_tokens": 3207
},
"timestamp": "2026-02-24T05:06:44.254Z",
"answer": 67146
},
{
"... | 1 | [] | {
"lo": 1.97,
"mid": 4.36,
"hi": 6.69
} | ||||
791c93 | nt_count_divisors_in_range_v1_1742523217_3031 | Let $n = 166320$. Define $S$ as the set of all positive integers $p$ such that there exists a positive integer $q$ satisfying $pq = 205800$, $\gcd(p, q) = 1$, and $p < q$. Let $a = |S|$. Compute the number of positive divisors $d$ of $n$ such that $a \leq d \leq 55442$. | 151 | graphs = [
Graph(
let={
"n": Const(166320),
"a": 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 | COUNT | sympy | MAX_PRIME_BELOW | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_count_divisors_in_range_v1 | null | 6 | 0 | [
"COPRIME_PAIRS",
"MAX_PRIME_BELOW"
] | 2 | 1.005 | 2026-02-08T05:30:20.403089Z | {
"verified": true,
"answer": 151,
"timestamp": "2026-02-08T05:30:21.407649Z"
} | 3d87ea | 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": 3276
},
"timestamp": "2026-02-12T11:43:39.777Z",
"answer": 151
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
}
] | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
27cfed | comb_count_permutations_fixed_v1_2051736721_5458 | Let $n = 9$ and let $k$ be the largest prime number satisfying $2 \leq k \leq 3$. Compute the value of
$$
\binom{n}{k} \cdot !(n - k),
$$
where $!m$ denotes the number of derangements of $m$ elements. | 22,260 | graphs = [
Graph(
let={
"_n": Const(2),
"n": Const(9),
"k": MaxOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Ref("_n")), Leq(Var("n1"), Const(3)), IsPrime(Var("n1"))))),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub(l... | NT | COMB | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | comb_count_permutations_fixed_v1 | null | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.002 | 2026-02-08T18:36:33.137761Z | {
"verified": true,
"answer": 22260,
"timestamp": "2026-02-08T18:36:33.139559Z"
} | 6efd67 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 113,
"completion_tokens": 778
},
"timestamp": "2026-02-18T18:19:34.824Z",
"answer": 22260
},
{... | 1 | [
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
fdfc1a | geo_count_lattice_triangle_v1_1520064083_7718 | Let $A$ be the area of the triangle with vertices at $(0, 0)$, $(180, 111)$, and $(300, 289)$, multiplied by 2. Compute $A$ as
\[
A = \left| 180 \cdot 289 - 111 \cdot \sum_{k=1}^{24} \varphi(k) \left\lfloor \frac{24}{k} \right\rfloor \right|.
\]
Let $B$ be the number of lattice points on the boundary of this triangle, ... | 60,192 | graphs = [
Graph(
let={
"_m": Const(180),
"_n": Const(111),
"area_2x": Abs(arg=Sum(Mul(Const(value=180), Const(value=289)), Mul(Summation(expr=Mul(EulerPhi(n=Var(name='k')), Floor(arg=Div(left=Const(value=24), right=Var(name='k')))), var='k', start=Const(value=1), end=Con... | NT | null | COUNT | sympy | B1 | [
"B1",
"K2"
] | 492c3e | geo_count_lattice_triangle_v1 | negation_mod | 6 | 0 | [
"B1",
"K2"
] | 2 | 0.011 | 2026-02-08T09:16:21.825806Z | {
"verified": true,
"answer": 60192,
"timestamp": "2026-02-08T09:16:21.836678Z"
} | 6c7b7d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 291,
"completion_tokens": 1239
},
"timestamp": "2026-02-14T02:12:34.938Z",
"answer": 60192
},
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
e91298 | nt_sum_divisors_mod_v1_677425708_1639 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 176400$. Let $T$ be the set of all positive integers $n$ such that $1 \le n \le \min\{x + y : (x, y) \in S\}$ and $n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{7}$. Let $n$ be the number of elements in $T$. Let $\sigma$ be th... | 360 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("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(Va... | NT | null | COMPUTE | sympy | B3 | [
"B3/L3C"
] | 345f3b | nt_sum_divisors_mod_v1 | null | 7 | 0 | [
"B3",
"L3C"
] | 2 | 0.008 | 2026-02-08T04:21:10.388316Z | {
"verified": true,
"answer": 360,
"timestamp": "2026-02-08T04:21:10.396386Z"
} | 149991 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 252,
"completion_tokens": 2597
},
"timestamp": "2026-02-09T22:44:00.551Z",
"answer": 360
},
{
"id... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok_later"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
767a38 | comb_sum_binomial_row_v1_1918700295_2997 | Let $n = 14$ and let $r = \left( \sum_{d \mid 2} \phi(d) \right)^n$, where $\phi$ denotes Euler's totient function. Compute the remainder when $62298 \cdot r$ is divided by $71165$. | 42,002 | graphs = [
Graph(
let={
"_n": Const(71165),
"n": Const(14),
"result": Pow(SumOverDivisors(n=Const(value=2), var='d', expr=EulerPhi(n=Var(name='d'))), Ref("n")),
"Q": Mod(value=Mul(Const(62298), Ref("result")), modulus=Ref("_n")),
},
goal=Ref("Q... | NT | null | SUM | sympy | K3 | [
"K3"
] | 54c41e | comb_sum_binomial_row_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T08:20:59.461819Z | {
"verified": true,
"answer": 42002,
"timestamp": "2026-02-08T08:20:59.462777Z"
} | 789fbb | 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": 1480
},
"timestamp": "2026-02-13T17:44:47.837Z",
"answer": 42002
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
b3ad73 | nt_count_coprime_v1_124444284_9491 | Let $k$ be the number of nonnegative integers $j$ with $0 \le j \le 16451$ such that $\binom{16451}{j}$ is odd. Determine the number of positive integers $n$ with $1 \le n \le 18225$ that are relatively prime to $k$. | 9,113 | graphs = [
Graph(
let={
"upper": Const(18225),
"k": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(16451)), Eq(Mod(value=Binom(n=Const(16451), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')),
... | NT | null | COUNT | sympy | V8 | [
"V8"
] | 86348e | nt_count_coprime_v1 | null | 7 | 0 | [
"V8"
] | 1 | 1.748 | 2026-02-08T12:32:03.471109Z | {
"verified": true,
"answer": 9113,
"timestamp": "2026-02-08T12:32:05.218896Z"
} | 37c156 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 115,
"completion_tokens": 1227
},
"timestamp": "2026-02-15T01:46:33.477Z",
"answer": 9113
},
{... | 1 | [
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
23ba97 | diophantine_fbi2_count_v1_1978505735_7486 | Let $ k $ be the number of positive integers $ t $ for which there exist positive integers $ a $ and $ b $ such that $ 1 \leq a \leq 48 $, $ 1 \leq b \leq 51 $, $ 10 \leq t \leq 501 $, and $ t = 3a + 7b $. Let $ r $ be the number of integers $ d $ such that $ 3 \leq d \leq 202 $, $ d $ divides $ k $, and $ 2 \leq \frac... | 18,729 | graphs = [
Graph(
let={
"_n": Const(202),
"k": 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... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | diophantine_fbi2_count_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.014 | 2026-02-08T20:17:25.930252Z | {
"verified": true,
"answer": 18729,
"timestamp": "2026-02-08T20:17:25.944407Z"
} | ac02bd | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 284,
"completion_tokens": 7828
},
"timestamp": "2026-02-19T00:17:41.877Z",
"answer": 18729
},
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
977a0c | comb_binomial_compute_v1_784195855_3851 | Let $m = 2$. Define $T$ as the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 64$. Let $s$ be the minimum value of $x + y$ as $(x, y)$ ranges over $T$. Let $n$ be the largest prime number $n$ such that $m \leq n \leq s$. Let $k = 6$, and define $r = \binom{n}{k}$. Define $U$ as the set of all or... | 41,802 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(97191),
"n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_m")), Leq(Var("n"), MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(a... | NT | null | COMPUTE | sympy | B3 | [
"B3/MAX_PRIME_BELOW",
"B3"
] | fd33c1 | comb_binomial_compute_v1 | affine_mod | 5 | 0 | [
"B3",
"MAX_PRIME_BELOW"
] | 2 | 0.003 | 2026-02-08T06:40:20.044448Z | {
"verified": true,
"answer": 41802,
"timestamp": "2026-02-08T06:40:20.047639Z"
} | f95af2 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 225,
"completion_tokens": 1311
},
"timestamp": "2026-02-13T03:05:25.947Z",
"answer": 41802
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MOD_SUB",
"status":... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
a6cf8e | nt_count_with_divisor_count_v1_784195855_2542 | Let $r$ be the number of positive integers $n \leq 6000$ that have exactly 3 positive divisors. Let $s$ be the number of positive integers $n \leq 96$ such that $8$ divides the $n$-th Fibonacci number. Compute the value of
$$
r + 2^{r \bmod s} \bmod 74039.$$
(Note: The Fibonacci sequence is defined by $F_1 = F_2 = 1$ a... | 53 | graphs = [
Graph(
let={
"_n": Const(8),
"upper": Const(6000),
"div_count": Const(3),
"result": CountOverSet(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"))))),
... | NT | null | COUNT | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE"
] | 5f885f | nt_count_with_divisor_count_v1 | mod_exp | 5 | 0 | [
"COUNT_FIB_DIVISIBLE"
] | 1 | 0.259 | 2026-02-08T05:50:49.739345Z | {
"verified": true,
"answer": 53,
"timestamp": "2026-02-08T05:50:49.998515Z"
} | 6eaad2 | 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": 1609
},
"timestamp": "2026-02-12T14:49:32.487Z",
"answer": 53
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
c22d7e | lin_form_endings_v1_1520064083_314 | Let $a = 16$ and $b = 40$. Let $A = 48$ and $B = 27$. Define $g = \gcd(a, b)$. Let $a' = \left\lfloor \frac{a}{g} \right\rfloor$ and $b' = \left\lfloor \frac{b}{g} \right\rfloor$. Define $T$ to be the quantity
$$
T = a' \cdot A + b' \cdot B - a' \cdot b'.
$$
Define $S$ to be the quantity
$$
S = a \cdot A + b \cdot B - ... | 1,572 | graphs = [
Graph(
let={
"a_coeff": Const(16),
"b_coeff": Const(40),
"A_val": Const(48),
"B_val": Const(27),
"g_step": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"ap_node": Floor(Div(Ref("a_coeff"), Ref("g_step"))),
"bp_node": ... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 6 | null | [
"LIN_FORM"
] | 1 | 0.003 | 2026-02-08T03:14:37.617379Z | {
"verified": true,
"answer": 1572,
"timestamp": "2026-02-08T03:14:37.620119Z"
} | 4a5834 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 272,
"completion_tokens": 434
},
"timestamp": "2026-02-10T13:37:10.191Z",
"answer": 1572
},
{
"id... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"st... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
e79cd3 | comb_binomial_compute_v1_601307018_3570 | Find the number of ordered pairs $(a, b)$ of positive integers with $1 \leq a \leq b \leq 25$ such that $2a^2 - 4ab + 2b^2 = 338$. Let $n$ be this number. Compute $\binom{n}{6}$. | 924 | graphs = [
Graph(
let={
"_n": Const(25),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Ref("_n")), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(25)), Leq(Var("a"), Var("b")), Eq(Sum(Mul(Const(-4), Var... | COMB | null | COMPUTE | sympy | QF_PSD_ORBIT | [
"QF_PSD_ORBIT"
] | 1d37f3 | comb_binomial_compute_v1 | null | 4 | 0 | [
"QF_PSD_ORBIT"
] | 1 | 0.003 | 2026-03-10T04:09:58.599116Z | {
"verified": true,
"answer": 924,
"timestamp": "2026-03-10T04:09:58.602173Z"
} | 9c38e6 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 180,
"completion_tokens": 512
},
"timestamp": "2026-03-29T09:07:13.753Z",
"answer": 924
},
{
"id"... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "QF_PSD_ORBIT",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no... | {
"lo": -10,
"mid": -6.41,
"hi": -2.82
} | ||
0798e8 | diophantine_fbi2_count_v1_784195855_6314 | Let $k = 180$ and $n = 4$. Consider the set of all positive integers $d$ such that $3 \leq d \leq 62$, $d$ divides $k$, and $\frac{k}{d}$ is an integer satisfying $4 \leq \frac{k}{d} \leq 63$. Determine the value of the number of elements in this set. | 13 | graphs = [
Graph(
let={
"_n": Const(4),
"k": Const(180),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(3)), Leq(Var("d"), Const(62)), Divides(divisor=Var("d"), dividend=Ref("k")), Geq(Div(Ref("k"), Var("d")), Ref("_n")), Leq(Div(R... | NT | null | COUNT | sympy | K13 | [
"COPRIME_PAIRS"
] | 2bb3aa | diophantine_fbi2_count_v1 | null | 3 | 0 | [
"COPRIME_PAIRS",
"K13"
] | 2 | 0.093 | 2026-02-08T08:34:42.246151Z | {
"verified": true,
"answer": 13,
"timestamp": "2026-02-08T08:34:42.339215Z"
} | da7e95 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 144,
"completion_tokens": 671
},
"timestamp": "2026-02-15T20:16:08.580Z",
"answer": 13
},
{
"id": 11,
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8",
"status": "... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
4e97f1 | nt_max_prime_below_v1_1526740231_128 | Let $S$ be the set of all positive integers $p$ such that there exists a positive integer $q$ satisfying $pq = 24$, $\gcd(p, q) = 1$, and $p < q$. Let $L$ be the number of elements in $S$. Determine the largest prime number $n$ such that $L \le n \le 65536$. | 65,521 | graphs = [
Graph(
let={
"upper": Const(65536),
"result": 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'), V... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_max_prime_below_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 1.823 | 2026-02-08T11:22:00.871304Z | {
"verified": true,
"answer": 65521,
"timestamp": "2026-02-08T11:22:02.694600Z"
} | 79babf | 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": 1252
},
"timestamp": "2026-02-14T12:45:01.076Z",
"answer": 65521
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
31a731 | alg_poly_preperiod_count_v1_1218484723_4438 | Define sequences modulo $29$: $N = (a^2 + a - 1) \bmod 29$, $M = (N^2 + N - 1) \bmod 29$, $R = (M^2 + M - 1) \bmod 29$, $S = (R^2 + R - 1) \bmod 29$, $T = (S^2 + S - 1) \bmod 29$. Find the number of non-negative integers $a$ with $0 \le a \le 811$ such that $T = M$, $R \ne M$, and $S \ne M$. | 196 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Pow(Var("a"), Const(2)), Var("a"), Const(-1)), modulus=Const(29)),
"p2": Mod(value=Sum(Pow(Ref("p1"), Const(2)), Ref("p1"), Const(-1)), modulus=Const(29)),
"p3": Mod(value=Sum(Pow(Ref("p2"), Const(2)), Ref("p2"), Const(-1)), mod... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_preperiod_count_v1 | null | 5 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.03 | 2026-02-25T06:04:43.713408Z | {
"verified": true,
"answer": 196,
"timestamp": "2026-02-25T06:04:43.743781Z"
} | fc75ab | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 252,
"completion_tokens": 16055
},
"timestamp": "2026-03-29T15:44:32.244Z",
"answer": 196
},
{
"i... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -2.45,
"mid": 1.37,
"hi": 5.29
} | ||
80263e | nt_count_divisible_v1_151522320_2286 | Let $T$ be the set of all integers $t$ such that $21 \leq t \leq 102$ and there exist positive integers $a \leq 6$, $b \leq 4$ for which $t = 9a + 12b$.
Let $d$ be the number of elements in $T$.
Compute the number of positive integers $n$ such that $1 \leq n \leq 72900$ and $n$ is divisible by $d$. | 3,313 | graphs = [
Graph(
let={
"upper": Const(72900),
"divisor": 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=6)), Ge... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_count_divisible_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 2.313 | 2026-02-08T04:43:19.112091Z | {
"verified": true,
"answer": 3313,
"timestamp": "2026-02-08T04:43:21.425558Z"
} | 94d3a9 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 220,
"completion_tokens": 1128
},
"timestamp": "2026-02-11T21:48:37.011Z",
"answer": 3313
},
{
"... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8_SUM",
"status": "no"
}... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
cdddba | comb_count_derangements_v1_2051736721_184 | Let $n$ be the number of nonnegative integers $j \leq 1092$ for which $\binom{1092}{j}$ is odd. Compute the remainder when $99083$ times the subfactorial of $n$ is divided by $96654$. | 74,069 | graphs = [
Graph(
let={
"_n": Const(1092),
"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(1092), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')),
"res... | COMB | null | COUNT | sympy | V8 | [
"V8"
] | 86348e | comb_count_derangements_v1 | null | 6 | 0 | [
"V8"
] | 1 | 0.003 | 2026-02-08T15:17:33.443618Z | {
"verified": true,
"answer": 74069,
"timestamp": "2026-02-08T15:17:33.447049Z"
} | 1dbbcf | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 168,
"completion_tokens": 3065
},
"timestamp": "2026-02-24T20:16:36.312Z",
"answer": 74069
},
{
"... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
}
] | {
"lo": -2.43,
"mid": 1.2,
"hi": 4.84
} | ||
17a96c | comb_count_permutations_fixed_v1_655260480_735 | Let $n = 7$ and $k = 2$. Define $\mathcal{S}$ as the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = 6$. Let $P$ be the maximum value of $xy$ as $(x, y)$ ranges over $\mathcal{S}$. Define $T$ as the set of all positive integers $n_1$ such that $1 \leq n_1 \leq 924$ and $P$ divides $F_{n_1}$, w... | 95,102 | graphs = [
Graph(
let={
"_n": Const(924),
"n": Const(7),
"k": Const(2),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub(left=Ref(name='n'), right=Ref(name='k')))),
"Q": Mod(value=Sub(CountOverSet(set=SolutionsSet(var=Var("n1"), co... | NT | COMB | COUNT | sympy | B1 | [
"B1/COUNT_FIB_DIVISIBLE"
] | bfd4a3 | comb_count_permutations_fixed_v1 | negation_mod | 6 | 0 | [
"B1",
"COUNT_FIB_DIVISIBLE"
] | 2 | 0.006 | 2026-02-08T15:33:11.998198Z | {
"verified": true,
"answer": 95102,
"timestamp": "2026-02-08T15:33:12.003886Z"
} | e63710 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 238,
"completion_tokens": 1801
},
"timestamp": "2026-02-16T08:36:23.190Z",
"answer": 95102
},
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok_later"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V3",
"status": ... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
e6d10f | comb_factorial_compute_v1_1218484723_1073 | Let $n$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 25$ such that $$
144a^2b + \left|\left\{ v : 25 \le v \le 4789,\ \exists\text{ integers }a,b\text{ with }1 \le a \le 11,\ 1 \le b \le 11\text{ such that }4b^2 - 16ab + 41a^2 = v \right\}\right| \cdot ab^2 + 27b^3 + 64a^3 = 571787.... | 5,040 | graphs = [
Graph(
let={
"_m": Const(27),
"_n": Const(3),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(25)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(25)), Eq(Sum(Mul(Const(144),... | COMB | null | COMPUTE | sympy | QF_PSD_DISTINCT | [
"QF_PSD_DISTINCT/POLY3_COUNT"
] | 5dc0d1 | comb_factorial_compute_v1 | null | 6 | 0 | [
"POLY3_COUNT",
"QF_PSD_DISTINCT"
] | 2 | 0.005 | 2026-02-25T02:46:47.262443Z | {
"verified": true,
"answer": 5040,
"timestamp": "2026-02-25T02:46:47.267026Z"
} | d628be | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 266,
"completion_tokens": 22838
},
"timestamp": "2026-03-10T05:16:12.587Z",
"answer": 1
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "POLY3_COUNT",
"status": "ok_later"
},
{
"lemma": "QF_PSD_DISTINCT",
"status": "ok"
},
{
"lemma": "V7",
... | {
"lo": 3.81,
"mid": 5.7,
"hi": 7.82
} | ||
17bed8_n | comb_count_partitions_v1_1419126231_761 | A composer writes a piece of music with $n$ measures, where $n$ is the sum of the integers from $1$ to $9$. Each measure can be partitioned into beats in various ways, and the total number of distinct rhythmic structures (regardless of order) is given by the partition function $p(n)$. Let $M = p(n)$. Compute the remain... | 170 | COMB | null | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | comb_count_partitions_v1 | null | 2 | null | [
"SUM_ARITHMETIC"
] | 1 | 0.002 | 2026-02-25T10:15:39.679332Z | null | 01f3e5 | 17bed8 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 205,
"completion_tokens": 3307
},
"timestamp": "2026-03-31T03:54:10.622Z",
"answer": 7008
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V7",
... | {
"lo": 1.5,
"mid": 4.69,
"hi": 7.23
} | |
d0249d | antilemma_k2_v1_1520064083_9284 | Let $n = 221$. Compute
$$
\sum_{k=1}^{\sum_{d \mid 221} \phi(d)} \phi(k) \left\lfloor \frac{221}{k} \right\rfloor.
$$ | 24,531 | graphs = [
Graph(
let={
"_n": Const(221),
"x": Summation(var="k", start=Const(1), end=SumOverDivisors(n=Const(value=221), var='d', expr=EulerPhi(n=Var(name='d'))), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Ref("_n"), Var("k"))))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3/K2",
"K2"
] | c7f244 | antilemma_k2_v1 | null | 4 | 0 | [
"K2",
"K3"
] | 2 | 0.001 | 2026-02-08T10:40:07.066089Z | {
"verified": true,
"answer": 24531,
"timestamp": "2026-02-08T10:40:07.067343Z"
} | 8c90af | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 96,
"completion_tokens": 926
},
"timestamp": "2026-02-14T08:01:23.625Z",
"answer": 24531
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
6f58b4 | antilemma_sum_equals_v1_1978505735_1439 | Let $c = 634$ and $m = 5003$. Let $n$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 164$. Let $x$ be the number of ordered pairs $(i, j)$ with $1 \leq i \leq 80$ and $1 \leq j \leq 81$ such that $i + j = n$. Let $s$ be the number of ordered pairs $(x_{11}, x_{21})$ of posit... | 26,130 | graphs = [
Graph(
let={
"_c": Const(634),
"_m": Const(5003),
"_n": 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')),... | COMB | GEOM | COMPUTE | sympy | COMB1 | [
"COMB1/COUNT_SUM_EQUALS",
"COMB1",
"COUNT_SUM_EQUALS"
] | 02c13a | antilemma_sum_equals_v1 | two_moduli | 5 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS"
] | 2 | 0.007 | 2026-02-08T16:09:04.152787Z | {
"verified": true,
"answer": 26130,
"timestamp": "2026-02-08T16:09:04.159547Z"
} | 36d36f | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 297,
"completion_tokens": 1886
},
"timestamp": "2026-02-24T20:03:28.672Z",
"answer": 26130
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
... | {
"lo": -4.1,
"mid": -1.76,
"hi": 1.3
} | ||
30019e | nt_count_intersection_v1_898971024_2006 | Let $N = 50000$. Consider the set of all positive integers $n$ such that $1 \le n \le N$, $7$ divides $n$, and $\gcd(n, 6) = 1$. Let $A$ be the number of elements in this set. Let $B$ be the maximum prime number less than or equal to $1010$. Compute the value of $(A \bmod 293) + B \cdot (A \bmod 337)$. | 22,235 | graphs = [
Graph(
let={
"_n": Const(2),
"N": Const(50000),
"a": Const(7),
"b": Const(6),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("N")), Divides(divisor=Ref("a"), dividend=Var("n... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | 08a653 | nt_count_intersection_v1 | two_moduli | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 5.392 | 2026-02-08T16:28:49.749682Z | {
"verified": true,
"answer": 22235,
"timestamp": "2026-02-08T16:28:55.141278Z"
} | 6d48af | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 150,
"completion_tokens": 1544
},
"timestamp": "2026-02-17T04:21:29.400Z",
"answer": 22235
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
c9e61e | nt_euler_phi_compute_v1_1353956133_590 | Let $n = 80089$. Define $\phi(n)$ to be the number of positive integers less than or equal to $n$ that are relatively prime to $n$. Compute the remainder when $$\phi(n)^2 + \phi(n) + \sum_{d\mid 20} \phi(d)$$ is divided by $86386$. | 10,454 | graphs = [
Graph(
let={
"n": Const(80089),
"result": EulerPhi(n=Ref("n")),
"Q": Mod(value=Sum(Pow(Ref("result"), Const(2)), Mul(Const(1), Ref("result")), SumOverDivisors(n=Const(value=20), var='d', expr=EulerPhi(n=Var(name='d')))), modulus=Const(86386)),
},
... | NT | null | COMPUTE | sympy | K3 | [
"K3"
] | 373090 | nt_euler_phi_compute_v1 | quadratic_mod | 4 | 0 | [
"K3"
] | 1 | 0.002 | 2026-02-08T11:33:41.278844Z | {
"verified": true,
"answer": 10454,
"timestamp": "2026-02-08T11:33:41.280613Z"
} | c74117 | 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": 1220
},
"timestamp": "2026-02-14T17:50:36.630Z",
"answer": 10454
},
... | 1 | [
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
2232ea | comb_count_partitions_v1_48377204_2042 | Let $n$ be the number of positive integers $k$ such that $1 \leq k \leq 572$ and $13$ divides $k$. Let $p(n)$ denote the number of integer partitions of $n$. Find the value of $p(n)$. | 75,175 | graphs = [
Graph(
let={
"_n": Const(13),
"n": CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(1)), Leq(Var("k"), Const(572)), Divides(divisor=Ref("_n"), dividend=Var("k"))), domain='positive_integers')),
"result": Partition(arg=Ref(name='n'))... | NT | COMB | COUNT | sympy | C2 | [
"C2"
] | 9685eb | comb_count_partitions_v1 | null | 4 | 0 | [
"C2"
] | 1 | 0.002 | 2026-02-08T16:34:05.766351Z | {
"verified": true,
"answer": 75175,
"timestamp": "2026-02-08T16:34:05.768436Z"
} | fb4979 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 103,
"completion_tokens": 839
},
"timestamp": "2026-02-17T06:29:35.852Z",
"answer": 75175
},
{... | 1 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
4723a7 | nt_euler_phi_compute_v1_1520064083_2079 | Let $m = 12$ and $n = 5$. Define $N = 68121$ and let $r = \phi(N)$, the number of positive integers at most $N$ that are relatively prime to $N$. Let $c$ be the number of positive integers $k$ such that $1 \le k \le n$ and $\gcd(k, m) = 1$. Let $d_{\text{max}}$ be the largest positive divisor of 238 that is at most 14.... | 43,849 | graphs = [
Graph(
let={
"_m": Const(12),
"_n": Const(5),
"n": Const(68121),
"result": EulerPhi(n=Ref("n")),
"Q": Sum(Ref("result"), Mod(value=Pow(CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("... | NT | null | COMPUTE | sympy | MAX_DIVISOR | [
"MAX_DIVISOR",
"C4"
] | 089193 | nt_euler_phi_compute_v1 | mod_exp | 5 | 0 | [
"C4",
"MAX_DIVISOR"
] | 2 | 0.002 | 2026-02-08T04:30:33.854331Z | {
"verified": true,
"answer": 43849,
"timestamp": "2026-02-08T04:30:33.856651Z"
} | 43e0fd | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 249,
"completion_tokens": 1277
},
"timestamp": "2026-02-10T16:56:05.892Z",
"answer": 43849
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
c14c91 | sequence_count_fib_divisible_v1_655260480_1344 | Let $N$ be the number of positive integers $n \leq 11349$ such that $9$ divides $n$ and $\gcd(n, 35) = 1$. Let $u$ be the largest positive divisor of $762065$ that is at most $N$. Determine the number of positive integers $n_1 \leq u$ such that $5$ divides the $n_1$-th Fibonacci number. Multiply this number by $80031$ ... | 46,539 | graphs = [
Graph(
let={
"upper": MaxOverSet(set=SolutionsSet(var=Var("d1"), condition=And(Geq(Var("d1"), Const(1)), Leq(Var("d1"), CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(11349)), Divides(divisor=Const(9), dividend=Var("n")), Eq(GCD(... | NT | null | COUNT | sympy | C5 | [
"C5/MAX_DIVISOR"
] | 454bdd | sequence_count_fib_divisible_v1 | null | 7 | 0 | [
"C5",
"MAX_DIVISOR"
] | 2 | 0.089 | 2026-02-08T16:04:14.814929Z | {
"verified": true,
"answer": 46539,
"timestamp": "2026-02-08T16:04:14.904228Z"
} | cccb08 | 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": 2366
},
"timestamp": "2026-02-16T20:31:49.331Z",
"answer": 46539
},
... | 1 | [
{
"lemma": "C5",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok_later"
},
{
"lemma": "MOD_ADD",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
24bc2e | comb_count_derangements_v1_397696148_498 | Let $u = \sum_{k=0}^{4} (-1)^k \binom{4}{k}$. Let $S$ be the set of all integers $t$ such that $5 \leq t \leq 12$ and there exist integers $a$ and $b$ with $1 \leq a \leq 2$, $1 \leq b \leq 3$, and $t = 3a + 2b$. Let $n_1$ be the sum of the number of elements in $S$ and $u$. Let $c = \sum_{k=0}^{n_1} (-1)^k \binom{n_1}... | 1,854 | graphs = [
Graph(
let={
"_n": Const(7),
"n2": Const(4),
"u": Summation(var="k", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n2"), k=Var("k")))),
"n1": Sum(CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(n... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/BINOMIAL_ALTERNATING"
] | bebeab | comb_count_derangements_v1 | null | 6 | 2 | [
"BINOMIAL_ALTERNATING",
"LIN_FORM"
] | 2 | 0.002 | 2026-02-08T11:30:53.470926Z | {
"verified": true,
"answer": 1854,
"timestamp": "2026-02-08T11:30:53.472801Z"
} | 5f9087 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 284,
"completion_tokens": 1305
},
"timestamp": "2026-02-24T14:05:51.516Z",
"answer": 1854
},
{
"i... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma"... | {
"lo": -7.18,
"mid": -5,
"hi": -3.01
} | ||
d8559e | sequence_fibonacci_compute_v1_48377204_1459 | Let $S$ be the set of all ordered pairs $(x_1, y_1)$ of positive integers such that $x_1 + y_1 = 22$. Define $P$ to be the maximum value of $x_1 y_1$ over all such pairs in $S$. Let $T$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = P$. Define $n$ to be the minimum value of $x + y$ over a... | 67,712 | graphs = [
Graph(
let={
"_n": Const(68071),
"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... | NT | null | COMPUTE | sympy | B1 | [
"B1/B3"
] | 80b49d | sequence_fibonacci_compute_v1 | null | 6 | 0 | [
"B1",
"B3"
] | 2 | 0.003 | 2026-02-08T16:05:57.426330Z | {
"verified": true,
"answer": 67712,
"timestamp": "2026-02-08T16:05:57.429010Z"
} | c5182d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 231,
"completion_tokens": 1909
},
"timestamp": "2026-02-16T21:10:41.169Z",
"answer": 67712
},
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
31bb8e | geo_count_lattice_rect_v1_1116507919_277 | Let $a = 435$ and $b = 142$. Define $\mathcal{R}$ to be the rectangle in the coordinate plane with vertices at $(0,0)$, $(a,0)$, $(0,b)$, and $(a,b)$. Compute the number of lattice points (points with integer coordinates) that lie inside or on the boundary of $\mathcal{R}$. | 62,348 | graphs = [
Graph(
let={
"a": Const(435),
"b": Const(142),
"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 | 0.001 | 2026-02-08T02:30:17.134932Z | {
"verified": true,
"answer": 62348,
"timestamp": "2026-02-08T02:30:17.135607Z"
} | 14b1f2 | 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": 450
},
"timestamp": "2026-02-08T19:21:01.390Z",
"answer": 62348
},
{
"i... | 1 | [] | {
"lo": -3.8,
"mid": -1.88,
"hi": 0.06
} | ||||
dfeb77 | comb_catalan_compute_v1_1520064083_5189 | Let $n$ be the number of ordered pairs $(i,j)$ of positive integers such that $i + j = 11$, $1 \le i \le 10$, and $1 \le j \le 11$. Compute the $n$-th Catalan number. | 16,796 | graphs = [
Graph(
let={
"_n": Const(11),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref("_n")), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(10)), right=IntegerRange(start=Const(1), end=Con... | COMB | null | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | comb_catalan_compute_v1 | null | 4 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.01 | 2026-02-08T06:40:52.503527Z | {
"verified": true,
"answer": 16796,
"timestamp": "2026-02-08T06:40:52.513602Z"
} | 5c6a97 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 169,
"completion_tokens": 1243
},
"timestamp": "2026-02-24T06:48:44.434Z",
"answer": 16796
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status"... | {
"lo": -4.93,
"mid": -2.91,
"hi": -0.71
} | ||
a46f4f_l | modular_product_range_v1_124444284_1508 | Let
\[
P=\prod_{i=2}^{402} i,
\]
and let $r$ be the remainder when $P$ is divided by $11003$, so that $0\le r<11003$ and $r\equiv P\pmod{11003}$.
Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $x+y=178$, and let $M$ be the maximum value of $xy$ as $(x,y)$ ranges over $S$.
Define
\[
Q=3... | 7,924 | ALG | NT | COMPUTE | sympy | B1 | [
"B1"
] | b09d85 | modular_product_range_v1 | two_stage_modexp | 8 | 0 | [
"B1"
] | 1 | 0.004 | 2026-02-08T03:57:40.971334Z | {
"verified": false,
"answer": 99868,
"timestamp": "2026-02-08T03:57:40.975006Z"
} | 5f4801 | a46f4f | legacy_text | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 216,
"completion_tokens": 6057
},
"timestamp": "2026-02-11T20:21:04.804Z",
"answer": 7924
},
... | 0 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 2.46,
"mid": 5.21,
"hi": 8.42
} | |
c03c88_l | antilemma_sum_equals_v1_1742523217_1191 | Let $n = 100$. Let $x$ be the number of ordered pairs $(i,j)$ of positive integers such that $1 \leq i \leq 98$, $1 \leq j \leq 98$, and $i + j = n$. Compute $x + \left(2^{x \bmod 14} \bmod 86553\right)$. | 99 | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 3 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.003 | 2026-02-08T03:31:01.342865Z | {
"verified": false,
"answer": 8289,
"timestamp": "2026-02-08T03:31:01.346015Z"
} | b0e832 | c03c88 | 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": 194,
"completion_tokens": 747
},
"timestamp": "2026-02-10T04:45:12.502Z",
"answer": 8289
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V8_SU... | {
"lo": -3.83,
"mid": -1.68,
"hi": 1.09
} | |
31e928 | comb_count_permutations_fixed_v1_153355830_869 | Let $n = \sum_{k=1}^{4} \phi(k) \left\lfloor \frac{4}{k} \right\rfloor$ and let $k$ be the largest prime number at most $9$. Compute $\binom{n}{k} \cdot !(n - k)$, where $!m$ denotes the number of derangements of $m$ elements. | 240 | graphs = [
Graph(
let={
"_n": Const(9),
"n": Summation(var="k", start=Const(1), end=Const(4), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(4), Var("k"))))),
"k": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), I... | NT | COMB | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW",
"K2"
] | e3ad1e | comb_count_permutations_fixed_v1 | null | 6 | 0 | [
"K2",
"MAX_PRIME_BELOW"
] | 2 | 0.003 | 2026-02-08T04:13:10.723038Z | {
"verified": true,
"answer": 240,
"timestamp": "2026-02-08T04:13:10.725877Z"
} | 308f21 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 195,
"completion_tokens": 750
},
"timestamp": "2026-02-10T16:06:32.859Z",
"answer": 240
},
{
"id... | 2 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma"... | {
"lo": -9.14,
"mid": -6.05,
"hi": -3.73
} | ||
d7e2b0 | sequence_fibonacci_compute_v1_1918700295_1373 | Let $N$ be the number of positive integers $n \leq 181$ such that $n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{7}$. Compute the $N$-th Fibonacci number. | 75,025 | graphs = [
Graph(
let={
"_n": Const(181),
"n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_n")), Congruent(a=Var(name='n'), b=Floor(arg=Div(left=Var(name='n'), right=Const(value=2))), modulus=Const(value=7))))),
"... | NT | null | COMPUTE | sympy | L3C | [
"L3C"
] | 73f8b0 | sequence_fibonacci_compute_v1 | null | 6 | 0 | [
"L3C"
] | 1 | 0.001 | 2026-02-08T05:48:31.126368Z | {
"verified": true,
"answer": 75025,
"timestamp": "2026-02-08T05:48:31.127057Z"
} | 64c687 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 99,
"completion_tokens": 3118
},
"timestamp": "2026-02-12T14:15:30.720Z",
"answer": 75025
},
{... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
080bb9 | geo_count_lattice_rect_v1_48377204_461 | Compute the number of lattice points in the rectangle $[0, 40] \times [0, 96]$, including the boundary. | 3,977 | graphs = [
Graph(
let={
"a": Const(40),
"b": Const(96),
"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 | 0.002 | 2026-02-08T15:30:07.068039Z | {
"verified": true,
"answer": 3977,
"timestamp": "2026-02-08T15:30:07.070531Z"
} | 8fb0d6 | 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": 138
},
"timestamp": "2026-02-24T21:06:14.340Z",
"answer": 3977
},
{
"id... | 1 | [] | {
"lo": -8.52,
"mid": -5.43,
"hi": -3.2
} | ||||
76aa91 | nt_sum_divisors_range_v1_458359167_2197 | Let $n = 57055$. Define $S$ as the set of all nonnegative integers $j$ such that $0 \le j \le n$ and $\binom{n}{j}$ is odd. Let $k$ be the number of elements in $S$. Compute the sum of the number of positive divisors of all positive integers from $1$ to $k$, inclusive. | 75,108 | graphs = [
Graph(
let={
"_n": Const(57055),
"upper": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Ref("_n")), Eq(Mod(value=Binom(n=Const(57055), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')),
... | NT | null | SUM | sympy | V8 | [
"V8"
] | 86348e | nt_sum_divisors_range_v1 | null | 6 | 0 | [
"V8"
] | 1 | 0.282 | 2026-02-08T05:10:32.629228Z | {
"verified": true,
"answer": 75108,
"timestamp": "2026-02-08T05:10:32.910837Z"
} | 6b0567 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 193,
"completion_tokens": 5147
},
"timestamp": "2026-02-11T23:01:25.565Z",
"answer": 75108
},
{
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
},
{
"lemma": "VAL_SUM_EQ",
"status"... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
4f381a | antilemma_k2_v1_717093673_3998 | Compute the value of
$$
\sum_{k=1}^{432} \phi(k) \left\lfloor \frac{432}{k} \right\rfloor,
$$
where $\phi(k)$ denotes Euler's totient function. Let $x$ be this sum. Find the remainder when $81948 \cdot x$ is divided by $64615$. | 59,704 | graphs = [
Graph(
let={
"_n": Const(432),
"x": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(432), Var("k"))))),
"Q": Mod(value=Mul(Const(81948), Ref("x")), modulus=Const(64615)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K13 | [
"K2"
] | 6897ab | antilemma_k2_v1 | null | 5 | 0 | [
"K13",
"K2"
] | 2 | 0.002 | 2026-02-08T17:59:19.090090Z | {
"verified": true,
"answer": 59704,
"timestamp": "2026-02-08T17:59:19.092448Z"
} | 8aec78 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 119,
"completion_tokens": 1377
},
"timestamp": "2026-02-18T11:00:27.200Z",
"answer": 59704
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
94a548 | sequence_count_fib_divisible_v1_865884756_2911 | Let $d$ be the number of integers $t$ such that $10 \leq t \leq 28$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 4$, $1 \leq b \leq 2$, and $t = 4a + 6b$. Determine the number of positive integers $n$ such that $1 \leq n \leq 851$ and $d$ divides the $n$th Fibonacci number. | 141 | graphs = [
Graph(
let={
"upper": Const(851),
"d": 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=V... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | sequence_count_fib_divisible_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.035 | 2026-02-08T17:00:51.381774Z | {
"verified": true,
"answer": 141,
"timestamp": "2026-02-08T17:00:51.417010Z"
} | fcb737 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 150,
"completion_tokens": 1224
},
"timestamp": "2026-02-17T17:24:35.858Z",
"answer": 141
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
a6ba1c | antilemma_k3_v1_124444284_8509 | Let $n$ be a positive integer. Define $\phi(n)$ to be the number of positive integers less than or equal to $n$ that are relatively prime to $n$. Compute the sum of $\phi(d)$ over all positive divisors $d$ of $31040$. | 31,040 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=31040), 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 | 2026-02-08T09:44:44.521422Z | {
"verified": true,
"answer": 31040,
"timestamp": "2026-02-08T09:44:44.521726Z"
} | e61baf | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 104,
"completion_tokens": 377
},
"timestamp": "2026-02-14T05:51:29.809Z",
"answer": 31040
},
{... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
e288ee | antilemma_k3_v1_898971024_3038 | Let $x$ be the sum of $\phi(d)$ over all positive divisors $d$ of $6654$. Compute the remainder when $44121 \cdot x$ is divided by $57818$. | 39,148 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=6654), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Mod(value=Mul(Const(44121), Ref("x")), modulus=Const(57818)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T17:08:12.807832Z | {
"verified": true,
"answer": 39148,
"timestamp": "2026-02-08T17:08:12.808471Z"
} | 196ba2 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 89,
"completion_tokens": 2172
},
"timestamp": "2026-02-17T19:21:44.534Z",
"answer": 39148
},
{... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
a76ac6 | nt_min_coprime_above_v1_1918700295_2973 | Let $S$ be the set of all prime numbers $n$ such that $2 \leq n \leq 325$. Define $m$ to be the largest element of $S$. Now, let $T$ be the set of all integers $n$ such that $55555 < n \leq 55882$ and $\gcd(n, m) = 1$. Determine the value of the smallest element of $T$. | 55,556 | graphs = [
Graph(
let={
"start": Const(55555),
"upper": Const(55882),
"modulus": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(325)), IsPrime(Var("n"))))),
"result": MinOverSet(set=SolutionsSet(var=Var("n"... | NT | null | EXTREMUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | nt_min_coprime_above_v1 | null | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.057 | 2026-02-08T08:20:32.008262Z | {
"verified": true,
"answer": 55556,
"timestamp": "2026-02-08T08:20:32.065431Z"
} | 19db67 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 136,
"completion_tokens": 1139
},
"timestamp": "2026-02-13T17:20:15.552Z",
"answer": 55556
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma... | {
"lo": -5.92,
"mid": -3.14,
"hi": 0.26
} | ||
4bd1e0 | nt_count_coprime_and_v1_124444284_1179 | Let $d_0$ be the minimum value of $d$ over all integers $d \geq 2$ that divide $1773593$. Let $g = \gcd(13, d_0)$. Let $S$ be the set of all integers $n$ such that $n \geq \sum_{d \mid g} \mu(d)$, $n \leq 52200$, $\gcd(n, 5) = 1$, and $\gcd(n, 9) = 1$. Compute the number of elements in $S$. | 27,840 | graphs = [
Graph(
let={
"upper": Const(52200),
"k1": Const(5),
"k2": Const(9),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), SumOverDivisors(n=GCD(a=Const(value=13), b=MinOverSet(set=SolutionsSet(var=Var(name='d'), condition... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/MOBIUS_COPRIME"
] | 60ba20 | nt_count_coprime_and_v1 | null | 6 | 0 | [
"MIN_PRIME_FACTOR",
"MOBIUS_COPRIME"
] | 2 | 6.77 | 2026-02-08T03:43:28.043978Z | {
"verified": true,
"answer": 27840,
"timestamp": "2026-02-08T03:43:34.813582Z"
} | ec6a6d | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 237,
"completion_tokens": 1562
},
"timestamp": "2026-02-09T10:41:18.843Z",
"answer": 27840
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok_later"
},
{
"lemma": "V7",
... | {
"lo": -6.49,
"mid": 0.51,
"hi": 7.52
} | ||
87f0f7 | diophantine_fbi2_min_v1_784195855_702 | Let $k$ be the sum of all prime numbers $n$ such that $2 \leq n \leq 19$. Let $S$ be the set of all integers $d$ with $4 \leq d \leq 87$ such that $d$ divides $k$ and $\frac{k}{d} \geq 2$. Determine the value of the smallest element in $S$. | 7 | graphs = [
Graph(
let={
"_n": Const(19),
"k": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))),
"upper": Const(87),
"result": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And... | NT | null | EXTREMUM | sympy | B3 | [
"SUM_PRIMES"
] | 83231d | diophantine_fbi2_min_v1 | null | 4 | 0 | [
"B3",
"SUM_PRIMES"
] | 2 | 0.06 | 2026-02-08T04:33:53.203703Z | {
"verified": true,
"answer": 7,
"timestamp": "2026-02-08T04:33:53.263209Z"
} | 310cf0 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 197,
"completion_tokens": 512
},
"timestamp": "2026-02-10T17:03:51.376Z",
"answer": 7
},
{
"id":... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "SUM_PRIMES",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
0317f0 | diophantine_sum_product_min_v1_898971024_2708 | Let $S = 12$ and $P = 36$. Let $N$ be the set of all prime numbers $n$ such that $2 \leq n \leq 11$, and let $m$ be the largest element of $N$. Determine the value of the smallest positive integer $x$ such that $1 \leq x \leq m$ and $x(S - x) = P$. | 6 | graphs = [
Graph(
let={
"S": Const(12),
"P": Const(36),
"result": MinOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), Const(1)), Leq(Var("x"), MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(11)), IsPr... | NT | null | EXTREMUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | diophantine_sum_product_min_v1 | null | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.014 | 2026-02-08T16:55:21.241989Z | {
"verified": true,
"answer": 6,
"timestamp": "2026-02-08T16:55:21.255781Z"
} | 7142b6 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 144,
"completion_tokens": 356
},
"timestamp": "2026-02-16T08:39:50.068Z",
"answer": 6
},
{
"id": 11,
"... | 2 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
... | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
bbc15d | comb_sum_binomial_mod_v1_1218484723_4850 | Let $S$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 30$ satisfying $26a^2 + 26b^2 - 52ab = 936$. Compute $$\sum_{k=8}^{S} \binom{51}{k} \bmod 11069,$$ and then find the remainder when $86399$ times this value is divided by $86702$. | 46,897 | graphs = [
Graph(
let={
"_n": Const(11069),
"sum": Summation(var="k", start=Const(8), end=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... | COMB | null | COMPUTE | sympy | QF_PSD_COUNT | [
"QF_PSD_COUNT"
] | 09ce67 | comb_sum_binomial_mod_v1 | null | 5 | 0 | [
"QF_PSD_COUNT"
] | 1 | 0.005 | 2026-02-25T06:29:03.830998Z | {
"verified": true,
"answer": 46897,
"timestamp": "2026-02-25T06:29:03.835933Z"
} | 20a1c8 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 208,
"completion_tokens": 7467
},
"timestamp": "2026-03-29T18:02:23.597Z",
"answer": 46897
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "... | {
"lo": -3.33,
"mid": 1.03,
"hi": 5.26
} | ||
ce0e6c | nt_sum_divisors_mod_v1_2051736721_2930 | Let $n = 20160$ and $M = 10259$. Let $\sigma$ be the sum of all positive divisors of $n$. Let $\text{result}$ be the remainder when $\sigma$ is divided by $M$. Let $c$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 6718464$. Find the remainder when $c - \text{result... | 84,325 | graphs = [
Graph(
let={
"_n": Const(86576),
"n": Const(20160),
"M": Const(10259),
"sigma": SumDivisors(n=Ref("n")),
"result": Mod(value=Ref("sigma"), modulus=Ref("M")),
"_c": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | fc629c | nt_sum_divisors_mod_v1 | negation_mod | 4 | 0 | [
"B3"
] | 1 | 0.004 | 2026-02-08T17:00:29.527886Z | {
"verified": true,
"answer": 84325,
"timestamp": "2026-02-08T17:00:29.532142Z"
} | e55609 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 152,
"completion_tokens": 2272
},
"timestamp": "2026-02-17T16:51:30.910Z",
"answer": 84325
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
7bae8f | sequence_lucas_compute_v1_971394319_1039 | Let $T$ be the set of all integers $t$ such that $12 \leq t \leq 37$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 2$, $1 \leq b \leq 10$, and $t = 7a + 2b + 3$. Let $n$ be the number of elements in $T$. Define $\text{result} = L_n$, the $n$-th Lucas number. Compute the smallest positive integer $k$... | 2,460 | 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=1... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | sequence_lucas_compute_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.003 | 2026-02-08T13:27:04.852355Z | {
"verified": true,
"answer": 2460,
"timestamp": "2026-02-08T13:27:04.855298Z"
} | d11364 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 181,
"completion_tokens": 2520
},
"timestamp": "2026-02-15T15:55:33.410Z",
"answer": 2460
},
{... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
e227b0 | comb_binomial_compute_v1_784195855_8482 | Let $ d $ be the smallest integer greater than or equal to $ 2 $ that divides $ 927979 $. Compute the value of $ \binom{d}{7} $. | 1,716 | 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(927979))))),
"k": Const(7),
"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 | 2 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.001 | 2026-02-08T16:06:45.479838Z | {
"verified": true,
"answer": 1716,
"timestamp": "2026-02-08T16:06:45.480972Z"
} | 1eaa16 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 83,
"completion_tokens": 2721
},
"timestamp": "2026-02-16T21:07:39.510Z",
"answer": 1716
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
934056 | diophantine_product_count_v1_1918700295_382 | Let $k = 480$. Let $U$ be the number of positive integers $j$ such that $1 \le j \le 427$ and $j^5 \le 14195130030907$. Define $S$ to be the set of all positive integers $x$ such that $1 \le x \le U$, $x$ divides $k$, and $\frac{k}{x} \le U$. Compute the number of elements in $S$. | 22 | graphs = [
Graph(
let={
"k": Const(480),
"upper": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(1)), Leq(Var("j"), Const(427)), Leq(Pow(Var("j"), Const(5)), Const(14195130030907))), domain='positive_integers')),
"result": CountOverSet(set=S... | NT | null | COUNT | sympy | VIETA_SUM | [
"C3"
] | 8a214c | diophantine_product_count_v1 | null | 5 | 0 | [
"C3",
"VIETA_SUM"
] | 2 | 0.045 | 2026-02-08T03:11:57.255230Z | {
"verified": true,
"answer": 22,
"timestamp": "2026-02-08T03:11:57.299888Z"
} | a66a79 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 209,
"completion_tokens": 2628
},
"timestamp": "2026-02-10T13:24:33.569Z",
"answer": 22
},
{
"id"... | 1 | [
{
"lemma": "C3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}... | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
99537e | sequence_count_fib_divisible_v1_1918700295_101 | Let $T$ be the set of all integers $t$ such that $15 \leq t \leq 428$ and there exist positive integers $a \leq 45$, $b \leq 22$ satisfying $t = 7a + 5b + 3$. Let $u = |T|$. Determine the number of positive integers $n$ with $1 \leq n \leq u$ such that the $n$th Fibonacci number is divisible by 10. | 26 | graphs = [
Graph(
let={
"upper": 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=45)), Geq(left=Var(name='b'), right=Const(va... | NT | null | COUNT | sympy | SUM_DIVISIBLE | [
"LIN_FORM"
] | 7b2633 | sequence_count_fib_divisible_v1 | null | 6 | 0 | [
"LIN_FORM",
"SUM_DIVISIBLE"
] | 2 | 0.271 | 2026-02-08T03:00:14.703270Z | {
"verified": true,
"answer": 26,
"timestamp": "2026-02-08T03:00:14.974355Z"
} | 9f9909 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 217,
"completion_tokens": 17168
},
"timestamp": "2026-02-23T20:52:13.582Z",
"answer": 26
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": 1.1,
"mid": 4.17,
"hi": 6.61
} | ||
c31227 | alg_poly_orbit_hensel_v1_1218484723_5378 | Let $N = (2a^3 + 3a) \bmod 29791$, $M = (2N^3 + 3N) \bmod 29791$, $R = (2M^3 + 3M) \bmod 29791$, and $S = (2R^3 + 3R) \bmod 29791$. Find the number of non-negative integers $a$ with $0 \leq a \leq 39711402$ such that $S = a$, but $N \neq a$, $M \neq a$, and $R \neq a$. | 5,332 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Mul(Const(2), Pow(Var("a"), Const(3))), Mul(Const(3), Var("a"))), modulus=Const(29791)),
"p2": Mod(value=Sum(Mul(Const(2), Pow(Ref("p1"), Const(3))), Mul(Const(3), Ref("p1"))), modulus=Const(29791)),
"p3": Mod(value=Sum(Mul(Cons... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_orbit_hensel_v1 | null | 6 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.145 | 2026-02-25T06:57:31.852057Z | {
"verified": true,
"answer": 5332,
"timestamp": "2026-02-25T06:57:31.996900Z"
} | 2d8b57 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 244,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T20:51:30.583Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 3.81,
"mid": 6.33,
"hi": 9.49
} | ||
9fc788 | comb_catalan_compute_v1_1218484723_1412 | Let $C_n$ denote the $n$-th Catalan number. Let $N = C_{10}$. Find the remainder when $44121N$ is divided by $75667$. | 49,385 | graphs = [
Graph(
let={
"n": Const(10),
"result": Catalan(Ref("n")),
"Q": Mod(value=Mul(Const(44121), Ref("result")), modulus=Const(75667)),
},
goal=Ref("Q"),
)
] | COMB | null | COMPUTE | sympy | STARS_BARS | [
"STARS_BARS",
"ONE_BINOM_0"
] | a839e8 | comb_catalan_compute_v1 | null | 2 | 0 | [
"ONE_BINOM_0",
"STARS_BARS"
] | 2 | 0.022 | 2026-02-25T03:08:19.594878Z | {
"verified": true,
"answer": 49385,
"timestamp": "2026-02-25T03:08:19.616557Z"
} | 2a0a21 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 151,
"completion_tokens": 1651
},
"timestamp": "2026-03-10T06:58:25.473Z",
"answer": 49385
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "ONE_BINOM_0",
"status": "ok"
},
{
"lemma": "STARS_BARS",
"status": "ok"
},
{
"lemma": "V7",
"status":... | {
"lo": -2.47,
"mid": 1.2,
"hi": 4.81
} | ||
49c261 | antilemma_k2_v1_677425708_621 | Let $ x = \sum_{k=1}^{247} \phi(k) \left\lfloor \frac{247}{k} \right\rfloor $, where $ \phi(k) $ denotes Euler's totient function. Let $ c = 128 $. Define $ Q $ to be the remainder when $ c - x $ is divided by $ 83177 $. Compute $ Q $. | 52,677 | graphs = [
Graph(
let={
"x": Summation(var="k", start=Const(1), end=Const(247), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(247), Var("k"))))),
"_c": Const(128),
"Q": Mod(value=Sub(Ref("_c"), Ref("x")), modulus=Const(83177)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | antilemma_k2_v1 | null | 7 | 0 | [
"K2"
] | 1 | 0 | 2026-02-08T03:37:39.713259Z | {
"verified": true,
"answer": 52677,
"timestamp": "2026-02-08T03:37:39.713625Z"
} | 3d8301 | 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": 726
},
"timestamp": "2026-02-08T20:50:43.871Z",
"answer": 52677
},
{
"i... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
}
] | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
5d16cd | nt_num_divisors_compute_v1_153355830_2586 | Let $n$ be the sum of all real solutions $x$ to the equation $x^2 - 7056x - 412612 = 0$. Let $r$ be the number of positive divisors of $n$. Compute the remainder when $92921 \cdot r$ is divided by $85360$. | 84,165 | graphs = [
Graph(
let={
"_n": Const(85360),
"n": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Const(2)), Mul(Const(-7056), Var("x")), Const(-412612)), Const(0)))),
"result": NumDivisors(n=Ref("n")),
"Q": Mod(value=Mul(Const(92921), ... | NT | null | COMPUTE | sympy | VIETA_SUM | [
"VIETA_SUM"
] | b33a7a | nt_num_divisors_compute_v1 | null | 4 | 0 | [
"VIETA_SUM"
] | 1 | 0.003 | 2026-02-08T07:14:11.759150Z | {
"verified": true,
"answer": 84165,
"timestamp": "2026-02-08T07:14:11.762255Z"
} | ad7800 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 113,
"completion_tokens": 1197
},
"timestamp": "2026-02-13T09:06:28.635Z",
"answer": 84165
},
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "VIETA_SUM",
"status": "ok"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} |
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