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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
a0f332 | algebra_quadratic_discriminant_v1_1918700295_2798 | Let $a = 3$ and $b = 5$. Define $c$ to be the number of ordered pairs $(i, j)$ of positive integers such that $1 \leq i \leq 3$, $1 \leq j \leq 5$, and $\gcd(i, j) = 1$. Let $r = b^2 - 4ac$. Compute $73441 - r$. | 73,560 | graphs = [
Graph(
let={
"a": Const(3),
"b": Const(5),
"c": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(GCD(a=Var("i"), b=Var("j")), Const(1)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(3)), right=IntegerRa... | NT | null | COMPUTE | sympy | COUNT_COPRIME_GRID | [
"COUNT_COPRIME_GRID"
] | 20ec03 | algebra_quadratic_discriminant_v1 | null | 3 | 0 | [
"COUNT_COPRIME_GRID"
] | 1 | 0.001 | 2026-02-08T08:13:03.836559Z | {
"verified": true,
"answer": 73560,
"timestamp": "2026-02-08T08:13:03.837916Z"
} | 9f024b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 132,
"completion_tokens": 639
},
"timestamp": "2026-02-13T16:36:52.596Z",
"answer": 73560
},
{... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
379f8f | modular_modexp_compute_v1_1125832087_1607 | Let $a$ be the largest prime number at most $29$. Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 14288400$. Define $e$ to be the minimum value of $x + y$ as $(x, y)$ ranges over $S$. Compute the remainder when $a^e$ is divided by $16384$. | 3,233 | graphs = [
Graph(
let={
"_n": Const(29),
"a": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))),
"e": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), conditi... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW",
"B3"
] | 78ed98 | modular_modexp_compute_v1 | null | 6 | 0 | [
"B3",
"MAX_PRIME_BELOW"
] | 2 | 0.003 | 2026-02-08T03:50:11.026586Z | {
"verified": true,
"answer": 3233,
"timestamp": "2026-02-08T03:50:11.029140Z"
} | 5cbed9 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 195,
"completion_tokens": 7233
},
"timestamp": "2026-02-10T14:35:55.117Z",
"answer": 4825
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
},
{
"lem... | {
"lo": 1.96,
"mid": 5.23,
"hi": 8.52
} | ||
778b61 | comb_sum_binomial_mod_v1_798873815_376 | Let $n = 10141$. Let $m$ be the largest prime number between 2 and 25. Compute the sum $$\sum_{k=m}^{173} \binom{218}{k},$$ and let $r$ be the remainder when this sum is divided by $n$. Determine the value of $$\sum_{j=1}^{|r|} \tau(j),$$ where $\tau(j)$ denotes the number of positive divisors of $j$. | 25,555 | graphs = [
Graph(
let={
"_n": Const(10141),
"sum": Summation(var="k", start=MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(25)), IsPrime(Var("n"))))), end=Const(173), expr=Binom(n=Const(218), k=Var("k"))),
"result": Mo... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | comb_sum_binomial_mod_v1 | null | 7 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.014 | 2026-02-08T02:37:07.980734Z | {
"verified": true,
"answer": 25555,
"timestamp": "2026-02-08T02:37:07.994531Z"
} | 89aaad | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 209,
"completion_tokens": 32768
},
"timestamp": "2026-02-23T15:20:59.796Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": 3.94,
"mid": 5.6,
"hi": 7.62
} | ||
fe17c1 | comb_count_surjections_v1_865884756_5725 | Let $m = 7$. Consider the set of all ordered pairs $(i,j)$ of positive integers such that $i + j = m$, where $1 \leq i \leq 5$ and $1 \leq j \leq 6$. Let $n$ be the number of such pairs. Now let $k$ be the number of ordered triples $(x_1, x_2, x_3)$ of positive odd integers such that $x_1 + x_2 + x_3 = n$. Compute the ... | 5,796 | graphs = [
Graph(
let={
"_m": Const(7),
"_n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref("_m")), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(5)), right=IntegerRange(start=Const(1), end=Cons... | COMB | null | COUNT | sympy | LIN_FORM | [
"COUNT_SUM_EQUALS/COMB1"
] | 5b2e59 | comb_count_surjections_v1 | null | 6 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 3 | 0.036 | 2026-02-08T18:45:52.712812Z | {
"verified": true,
"answer": 5796,
"timestamp": "2026-02-08T18:45:52.748636Z"
} | eb6544 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 188,
"completion_tokens": 1518
},
"timestamp": "2026-02-18T19:23:44.421Z",
"answer": 5796
},
{... | 1 | [
{
"lemma": "COMB1",
"status": "ok_later"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma... | {
"lo": -3.12,
"mid": 1.47,
"hi": 6.57
} | ||
24a489 | comb_count_surjections_v1_1218484723_4063 | Let $k = 3$ and $n = \sum_{i=0}^{2} 2^i$. Compute $k! \cdot S(n, k)$, where $S(n, k)$ denotes the Stirling number of the second kind. | 1,806 | graphs = [
Graph(
let={
"_n": Const(2),
"n": Summation(var="k1", start=Const(0), end=Ref("_n"), expr=Pow(Const(2), Var("k1"))),
"k": Const(3),
"result": Mul(Factorial(Ref("k")), Stirling2(n=Ref(name='n'), k=Ref(name='k'))),
},
goal=Ref("result"... | COMB | null | COUNT | sympy | SUM_GEOM | [
"SUM_GEOM"
] | 04214c | comb_count_surjections_v1 | null | 3 | 0 | [
"SUM_GEOM"
] | 1 | 0.002 | 2026-02-25T05:42:49.809452Z | {
"verified": true,
"answer": 1806,
"timestamp": "2026-02-25T05:42:49.811222Z"
} | e39ad1 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 165,
"completion_tokens": 606
},
"timestamp": "2026-03-29T13:35:28.176Z",
"answer": 1806
},
{
"id... | 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_GEOM",
"status": "ok"
},
{
"lemma": "V8",
"st... | {
"lo": -6.5,
"mid": -3.34,
"hi": -0.88
} | ||
caf186 | geo_visible_lattice_v1_1742523217_4968 | Let $n = 90$. Define $\text{result}$ to be the number of ordered pairs $(x, y)$ of positive integers such that $1 \leq x, y \leq n$ and $\gcd(x, y) = 1$. Let $Q = 47089 - \text{result}$. Compute $Q$. | 42,130 | graphs = [
Graph(
let={
"n": Const(90),
"result": VisibleLatticePoints(n=Ref(name='n')),
"Q": Sub(Const(47089), Ref("result")),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 5 | 0 | null | null | 1.984 | 2026-02-08T10:41:36.475784Z | {
"verified": true,
"answer": 42130,
"timestamp": "2026-02-08T10:41:38.459658Z"
} | 705e5b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 183,
"completion_tokens": 7419
},
"timestamp": "2026-02-24T12:14:36.149Z",
"answer": 42130
},
{
"... | 1 | [] | {
"lo": 1.15,
"mid": 4.18,
"hi": 6.61
} | ||||
934e5e | antilemma_k3_v1_1520064083_4806 | Compute the sum of $\phi(d)$ over all positive divisors $d$ of 74445, where $\phi$ denotes Euler's totient function. | 74,445 | graphs = [
Graph(
let={
"_n": Const(74445),
"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 | 2026-02-08T06:26:26.913923Z | {
"verified": true,
"answer": 74445,
"timestamp": "2026-02-08T06:26:26.914364Z"
} | 7b5c07 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 77,
"completion_tokens": 599
},
"timestamp": "2026-02-13T00:18:34.168Z",
"answer": 74445
},
{
... | 1 | [
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
}
] | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
4bc56a | sequence_count_fib_divisible_v1_677425708_1820 | Let $ n = 5 $ and $ u = 438 $. Define $ d $ to be the largest integer such that $ 41^d $ divides $ 41^5 $. Determine the number of positive integers $ m $ such that $ 1 \leq m \leq 438 $ and $ d $ divides $ F_m $, where $ F_m $ denotes the $ m $-th Fibonacci number. | 87 | graphs = [
Graph(
let={
"_n": Const(5),
"upper": Const(438),
"d": MaxKDivides(target=Pow(Const(41), Ref("_n")), base=Const(41)),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Divides(d... | NT | null | COUNT | sympy | K14 | [
"K14"
] | a49bcb | sequence_count_fib_divisible_v1 | null | 5 | 0 | [
"K14"
] | 1 | 0.02 | 2026-02-08T04:28:54.293842Z | {
"verified": true,
"answer": 87,
"timestamp": "2026-02-08T04:28:54.313836Z"
} | cfd637 | 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": 980
},
"timestamp": "2026-02-10T01:28:25.498Z",
"answer": 87
},
{
"id":... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -6.5,
"mid": -0.2,
"hi": 6.11
} | ||
1df4f9 | nt_num_divisors_compute_v1_865884756_3955 | Let $m$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that
$$pq=54,\qquad \gcd(p,q)=1,\qquad p<q.$$
Let $S$ be the set of all integers $n_1$ such that $n_1\ge m$, $n_1\le U$, and $n_1$ is prime, where $U$ is defined as follows.
First, let $T$ be the set of all integers $t$ ... | 88,242 | graphs = [
Graph(
let={
"_m": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=54)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(value=1)), ... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/COMB1/MAX_PRIME_BELOW",
"LIN_FORM/COMB1/MAX_PRIME_BELOW"
] | b98bc8 | nt_num_divisors_compute_v1 | null | 6 | 0 | [
"COMB1",
"COPRIME_PAIRS",
"LIN_FORM",
"MAX_PRIME_BELOW"
] | 4 | 0.019 | 2026-02-08T17:40:46.547492Z | {
"verified": true,
"answer": 88242,
"timestamp": "2026-02-08T17:40:46.566812Z"
} | a42c3e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 341,
"completion_tokens": 3114
},
"timestamp": "2026-02-18T06:36:37.492Z",
"answer": 88242
},
... | 1 | [
{
"lemma": "COMB1",
"status": "ok_later"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"statu... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
a1e775 | lin_form_endings_v1_677425708_783 | Let $a = 28$ and $b = 98$. Compute the least common multiple of $a$ and $b$, multiply it by $14621$, and then compute the remainder when this product is divided by $55440$. | 38,276 | graphs = [
Graph(
let={
"a_coeff": Const(28),
"b_coeff": Const(98),
"_inner_result": LCM(a=Ref("a_coeff"), b=Ref("b_coeff")),
"_scale_k": Const(14621),
"_scaled": Mul(Ref("_scale_k"), Ref("_inner_result")),
"_mod_M": Const(55440),
... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 2 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T03:43:49.585807Z | {
"verified": true,
"answer": 38276,
"timestamp": "2026-02-08T03:43:49.586431Z"
} | 3863fb | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 163,
"completion_tokens": 336
},
"timestamp": "2026-02-09T11:48:20.417Z",
"answer": 38276
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
1cc01e | geo_visible_lattice_v1_1520064083_6504 | 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 value of the Bell number $B_m$, where $m$ is the remainder when $r$ is divided by 11. | 15 | graphs = [
Graph(
let={
"n": Const(100),
"result": VisibleLatticePoints(n=Ref(name='n')),
"Q": Bell(Mod(value=Abs(arg=Ref(name='result')), modulus=Const(11))),
},
goal=Ref("Q"),
)
] | GEOM | COMB | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 6 | 0 | null | null | 0.435 | 2026-02-08T08:08:02.940417Z | {
"verified": true,
"answer": 15,
"timestamp": "2026-02-08T08:08:03.375129Z"
} | 652c03 | 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": 8636
},
"timestamp": "2026-02-24T08:56:20.676Z",
"answer": 15
},
{
"id"... | 1 | [] | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||||
1bfb51_l | comb_bell_compute_v1_124444284_6170 | Let $n$ be the number of nonnegative integers $j$ with $0\le j\le580$ such that
$$\binom{580}{j}\equiv1\pmod{2}.$$
Let $B_n$ denote the $n$th Bell number, and let
$$Q=47961-B_n.$$
Compute $Q$. | 0 | COMB | null | COMPUTE | sympy | V8 | [
"V8"
] | 86348e | comb_bell_compute_v1 | null | 8 | 0 | [
"V8"
] | 1 | 0.001 | 2026-02-08T08:10:47.200932Z | {
"verified": false,
"answer": 43821,
"timestamp": "2026-02-08T08:10:47.201879Z"
} | 379eec | 1bfb51 | 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": 187,
"completion_tokens": 1095
},
"timestamp": "2026-02-24T08:58:04.583Z",
"answer": 43821
},
{
"... | 1 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | |
d51f2c | antilemma_k3_v1_1520064083_6444 | Let $n = 35749$. Compute the sum of $\varphi(d)$ over all positive divisors $d$ of $n$, where $\varphi$ denotes Euler's totient function. | 35,749 | graphs = [
Graph(
let={
"_n": Const(35749),
"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 | 2 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T08:04:25.582713Z | {
"verified": true,
"answer": 35749,
"timestamp": "2026-02-08T08:04:25.583404Z"
} | 55d9e0 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 84,
"completion_tokens": 1183
},
"timestamp": "2026-02-13T15:03:39.309Z",
"answer": 35749
},
{... | 1 | [
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V3",
"status":... | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
4ba8d5 | antilemma_k3_v1_1440796553_652 | Let $n = 52736$. Define
$$
x = \sum_{d \mid n} \phi(d),
$$
where the sum is over all positive divisors $d$ of $n$, and $\phi(d)$ is the number of positive integers less than or equal to $d$ that are relatively prime to $d$.
Let $A$ be the set of all integers $x$ such that $x^2 - 1009x + 60480 = 0$. Let $B$ be the sum ... | 24,430 | graphs = [
Graph(
let={
"_n": Const(52736),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Mod(value=Sum(Mod(value=Ref("x"), modulus=Const(199)), Mul(SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Const(2)),... | NT | COMB | COMPUTE | sympy | VIETA_SUM | [
"VIETA_SUM",
"K3"
] | 4765cd | antilemma_k3_v1 | two_moduli | 6 | 0 | [
"K3",
"VIETA_SUM"
] | 2 | 0.001 | 2026-02-08T11:55:03.942409Z | {
"verified": true,
"answer": 24430,
"timestamp": "2026-02-08T11:55:03.943588Z"
} | 098736 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 199,
"completion_tokens": 1114
},
"timestamp": "2026-02-14T20:38:01.191Z",
"answer": 24430
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
e19c5d | lin_form_endings_v1_168721529_312 | Let $a = 24$, $b = 60$, $A = 47$, and $B = 18$. Let $g = \gcd(a, b)$, and define $s = \left\lfloor \frac{aA + bB - a - b}{g} \right\rfloor + 1$. Compute the remainder when $13866 \cdot s$ is divided by $57299$. | 4,291 | graphs = [
Graph(
let={
"a_coeff": Const(24),
"b_coeff": Const(60),
"A_val": Const(47),
"B_val": Const(18),
"g_step": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"numerator": Sub(Sum(Mul(Ref("a_coeff"), Ref("A_val")), Mul(Ref("b_coeff"), R... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 3 | null | [
"LIN_FORM"
] | 1 | 0.004 | 2026-02-08T12:59:23.499970Z | {
"verified": true,
"answer": 4291,
"timestamp": "2026-02-08T12:59:23.503553Z"
} | 08d462 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 205,
"completion_tokens": 681
},
"timestamp": "2026-02-09T03:33:38.185Z",
"answer": 4291
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no... | {
"lo": -2,
"mid": 1.85,
"hi": 5.2
} | ||
1d0678 | nt_count_with_divisor_count_v1_784195855_7242 | Let $t$ be an integer. Consider the set of all integers $t$ such that $5 \leq t \leq 15$ and there exist integers $a$ and $b$ with $1 \leq a \leq 3$, $1 \leq b \leq 3$, and $t = 3a + 2b$. Let $d$ be the number of elements in this set.
Let $S$ be the set of all positive integers $n \leq 55225$ such that the number of ... | 100 | graphs = [
Graph(
let={
"upper": Const(55225),
"div_count": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=3)), ... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_count_with_divisor_count_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 3.872 | 2026-02-08T09:09:48.535654Z | {
"verified": true,
"answer": 100,
"timestamp": "2026-02-08T09:09:52.407627Z"
} | d48329 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 262,
"completion_tokens": 2481
},
"timestamp": "2026-02-14T00:59:48.300Z",
"answer": 100
},
{
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
26a6a7 | antilemma_sum_factor_cartesian_v1_151522320_383 | Let $S$ be the set of all ordered pairs $(i,j)$ of integers with $1 \leq i \leq 8$ and $1 \leq j \leq 8$. Let $T$ be the set of all products $i \cdot j$ where $(i,j) \in S$. Compute the sum of all elements in $T$. | 1,296 | graphs = [
Graph(
let={
"x": SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=EulerPhi(n=Const(2)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(8)), right=IntegerRange(start=Const(1), end=Const(8)))), expr=Mul(Var("i"), Var("j... | NT | null | COMPUTE | sympy | SUM_FACTOR_CARTESIAN | [
"SUM_FACTOR_CARTESIAN",
"ONE_PHI_2"
] | 09bd3b | antilemma_sum_factor_cartesian_v1 | null | 2 | 0 | [
"ONE_PHI_2",
"SUM_FACTOR_CARTESIAN"
] | 2 | 0.001 | 2026-02-08T03:12:42.575718Z | {
"verified": true,
"answer": 1296,
"timestamp": "2026-02-08T03:12:42.576459Z"
} | 148b96 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 193,
"completion_tokens": 2200
},
"timestamp": "2026-02-09T02:06:35.735Z",
"answer": 680
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "ONE_PHI_2",
"status":... | {
"lo": -6.49,
"mid": 0.51,
"hi": 7.52
} | ||
39cb70 | alg_poly_preperiod_count_v1_1218484723_5399 | Let $S = R^3 + 3R \bmod 37$, where $R = M^3 + 3M \bmod 37$, $M = N^3 + 3N \bmod 37$, and $N = a^3 + 3a \bmod 37$. Find the number of non-negative integers $a$ with $0 \le a \le 14281$ such that $S = M$ and $R \neq M$. | 3,860 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Pow(Var("a"), Const(3)), Mul(Const(3), Var("a"))), modulus=Const(37)),
"p2": Mod(value=Sum(Pow(Ref("p1"), Const(3)), Mul(Const(3), Ref("p1"))), modulus=Const(37)),
"p3": Mod(value=Sum(Pow(Ref("p2"), Const(3)), Mul(Const(3), Ref(... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_preperiod_count_v1 | null | 6 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.016 | 2026-02-25T06:58:02.269592Z | {
"verified": true,
"answer": 3860,
"timestamp": "2026-02-25T06:58:02.285683Z"
} | f16502 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 213,
"completion_tokens": 6220
},
"timestamp": "2026-03-29T20:55:17.855Z",
"answer": 3860
},
{
"i... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -3.33,
"mid": 1.03,
"hi": 5.26
} | ||
75d16e | nt_count_divisible_v1_1978505735_1407 | Let $n = 73303$ and $U = 51529$. Let $d$ be the number of integers $j$ with $0 \leq j \leq 20740$ such that $\binom{20740}{j}$ is odd. Let $R$ be the number of positive integers $m$ with $1 \leq m \leq U$ such that $m$ is divisible by $d$. Let $c = 66389$, and define $Q$ as the remainder when $c \cdot R$ is divided by ... | 21,032 | graphs = [
Graph(
let={
"_n": Const(73303),
"upper": Const(51529),
"divisor": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(20740)), Eq(Mod(value=Binom(n=Const(20740), k=Var("j")), modulus=Const(2)), Const(1))), dom... | ALG | COMB | COUNT | sympy | V8 | [
"V8"
] | 86348e | nt_count_divisible_v1 | null | 5 | 0 | [
"V8"
] | 1 | 1.828 | 2026-02-08T16:08:08.203109Z | {
"verified": true,
"answer": 21032,
"timestamp": "2026-02-08T16:08:10.031590Z"
} | cd77a6 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 239,
"completion_tokens": 1120
},
"timestamp": "2026-02-24T20:02:06.793Z",
"answer": 21032
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
}
] | {
"lo": -2.4,
"mid": 1.57,
"hi": 5.75
} | ||
c59563 | nt_count_divisible_and_v1_151522320_1357 | Let $n$ be a positive integer. Determine the value of the number of positive integers $n$ such that $n \leq 35520$, $n$ is divisible by 6, and $n$ is divisible by 10. | 1,184 | graphs = [
Graph(
let={
"upper": Const(35520),
"d1": Const(6),
"d2": Const(10),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), EulerPhi(n=Const(1))), Leq(Var("n"), Ref("upper")), Eq(Mod(value=Var("n"), modulus=Ref("d1")), Con... | NT | null | COUNT | sympy | ONE_PHI_1 | [
"ONE_PHI_1"
] | f6b5a5 | nt_count_divisible_and_v1 | null | 3 | 0 | [
"ONE_PHI_1"
] | 1 | 1.248 | 2026-02-08T03:53:35.616860Z | {
"verified": true,
"answer": 1184,
"timestamp": "2026-02-08T03:53:36.864993Z"
} | acdf4f | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 149,
"completion_tokens": 337
},
"timestamp": "2026-02-18T07:18:36.179Z",
"answer": 1184
}
] | 2 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "ONE_PHI_1",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
4d07e7 | algebra_vieta_sum_v1_1742523217_3357 | Let $m=2$ and $N=99828$. For each positive integer $k$, let $\varphi(k)$ denote the number of positive integers not exceeding $k$ that are relatively prime to $k$.
Let $P$ be the set of all positive integers $p$ such that there exists a positive integer $q$ with
$$pq=216,\quad \gcd(p,q)=1,\quad p<q.$$Let $r$ be the nu... | 26,094 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(99828),
"result": ProductOverSet(set=SolutionsSet(var=Var(name='x'), condition=Eq(left=Sum(Mul(Ref(name='_m'), Pow(base=Var(name='x'), exp=Summation(expr=Mul(EulerPhi(n=Var(name='k')), Floor(arg=Div(left=CountOverSet(set... | NT | null | COMPUTE | sympy | LIN_FORM | [
"COUNT_CARTESIAN",
"COPRIME_PAIRS/K2"
] | 59e2bd | algebra_vieta_sum_v1 | affine_mod | 8 | 0 | [
"COPRIME_PAIRS",
"COUNT_CARTESIAN",
"K2",
"LIN_FORM"
] | 4 | 0.082 | 2026-02-08T05:48:53.695652Z | {
"verified": true,
"answer": 26094,
"timestamp": "2026-02-08T05:48:53.778097Z"
} | 6e5e02 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 301,
"completion_tokens": 2119
},
"timestamp": "2026-02-12T14:54:34.666Z",
"answer": 26094
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K2",
"status": "ok_later"
},
{
"lemma": "L3b",
"status": "no"... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
4b382c | comb_catalan_compute_v1_784195855_7471 | Let $n_2 = 8$ and define
$$
t = \sum_{k=0}^{n_2} (-1)^k \binom{n_2}{k}.
$$
Let $a = 3$ and $b = 2 + t$. Define $n_1 = a + b$ and
$$
f = \sum_{k=0}^{n_1} (-1)^k \binom{n_1}{k}.
$$
Let $n = 11 + f$. Compute the $n$-th Catalan number, and let $m = |n\text{-th Catalan number}| + 2$. Find the remainder when the Fibonacci se... | 840 | graphs = [
Graph(
let={
"n2": Const(8),
"t": Summation(var="k", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n2"), k=Var("k")))),
"a": Const(3),
"b": Sum(Const(2), Ref("t")),
"n1": Sum(Ref("a"), Ref("b")),
... | COMB | NT | COMPUTE | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING"
] | c21569 | comb_catalan_compute_v1 | null | 4 | 2 | [
"BINOMIAL_ALTERNATING"
] | 1 | 0.002 | 2026-02-08T09:20:18.787266Z | {
"verified": true,
"answer": 840,
"timestamp": "2026-02-08T09:20:18.788954Z"
} | 17245b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 292,
"completion_tokens": 32768
},
"timestamp": "2026-02-24T11:12:33.649Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8"... | {
"lo": 1.15,
"mid": 4.18,
"hi": 6.61
} | ||
9d9d4d | diophantine_fbi2_count_v1_784195855_579 | Let $k = 60$. Consider the set of all integers $d$ such that $3 \leq d \leq 52$, $d$ divides $k$, and $2 \leq \frac{k}{d} \leq 51$. Let $r$ be the number of such integers $d$. Compute the remainder when $80461 \cdot r$ is divided by $76914$. | 31,923 | graphs = [
Graph(
let={
"_n": Const(3),
"k": Const(60),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Leq(Var("d"), Const(52)), Divides(divisor=Var("d"), dividend=Ref("k")), Geq(Div(Ref("k"), Var("d")), Const(2)), Leq(Div(Re... | NT | null | COUNT | sympy | MAX_DIVISOR | [
"MAX_DIVISOR"
] | 51757e | diophantine_fbi2_count_v1 | null | 3 | 0 | [
"MAX_DIVISOR"
] | 1 | 0.006 | 2026-02-08T04:28:37.963742Z | {
"verified": true,
"answer": 31923,
"timestamp": "2026-02-08T04:28:37.970229Z"
} | ad10db | 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": 720
},
"timestamp": "2026-02-10T16:51:10.097Z",
"answer": 31923
},
{
"... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"sta... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
18e3b4 | antilemma_product_of_sums_v1_168721529_1187 | Let $S$ be the set of all ordered pairs $(i,j)$ of positive integers such that $1 \le i \le 7$ and $1 \le j \le 3$. Define $S_1$ to be the sum of $i \cdot j$ over all pairs $(i,j)$ in $S$.
Let $T$ be the set of all ordered pairs $(k,\ell)$ of positive integers such that $1 \le k \le 6$ and $1 \le \ell \le 8$. Define $... | 11,432 | graphs = [
Graph(
let={
"S1": SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Const(1), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(7)), right=IntegerRange(start=Const(1), end=Const(3)))), expr=Mul(Var("i"), Var("j")))),
... | NT | null | COMPUTE | sympy | PRODUCT_OF_SUMS | [
"PRODUCT_OF_SUMS"
] | f2b2b0 | antilemma_product_of_sums_v1 | null | 3 | 0 | [
"PRODUCT_OF_SUMS"
] | 1 | 0.001 | 2026-02-08T13:31:22.305082Z | {
"verified": true,
"answer": 11432,
"timestamp": "2026-02-08T13:31:22.305975Z"
} | 65a4d8 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 288,
"completion_tokens": 4157
},
"timestamp": "2026-02-09T14:26:35.802Z",
"answer": 11432
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "PRODUCT_OF_SUMS",
"status": "ok"
... | {
"lo": -1.99,
"mid": 2.14,
"hi": 6.33
} | ||
0a19cb | antilemma_cartesian_v1_898971024_2455 | Compute the number of ordered pairs $(i, j)$ such that $1 \leq i \leq 23$ and $1 \leq j \leq 28$. | 644 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(23)), right=IntegerRange(start=Const(1), end=Const(28)))),
"Q": Ref("x"),
},
goal=Ref("Q"),
)
] | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | antilemma_cartesian_v1 | null | 2 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.001 | 2026-02-08T16:46:19.813669Z | {
"verified": true,
"answer": 644,
"timestamp": "2026-02-08T16:46:19.814495Z"
} | 385888 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 81,
"completion_tokens": 354
},
"timestamp": "2026-02-24T21:48:59.133Z",
"answer": 644
},
{
... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.42,
"hi": -4.85
} | ||
aec6ad | nt_gcd_compute_v1_153355830_1954 | Let $n$ be a positive integer such that $1 \leq n \leq 57973$ and $$n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{7}.$$ Let $c$ be the number of such integers $n$. Compute the value of $$c - \gcd(557697, 1035723) \pmod{78011}.$$ | 6,621 | graphs = [
Graph(
let={
"_n": Const(57973),
"a": Const(557697),
"b": Const(1035723),
"result": GCD(a=Ref("a"), b=Ref("b")),
"_c": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_n")), Congruent... | NT | null | COMPUTE | sympy | L3C | [
"L3C"
] | fba717 | nt_gcd_compute_v1 | negation_mod | 6 | 0 | [
"L3C"
] | 1 | 0.002 | 2026-02-08T06:48:13.596997Z | {
"verified": true,
"answer": 6621,
"timestamp": "2026-02-08T06:48:13.598767Z"
} | f432e0 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 133,
"completion_tokens": 1544
},
"timestamp": "2026-02-13T05:11:49.311Z",
"answer": 6621
},
{... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
cc63d4 | nt_lcm_compute_v1_677425708_3797 | Let $a$ be the number of ordered pairs $(i,j)$ such that $1 \leq i \leq 31$ and $1 \leq j \leq 46$. Let $b = 1903$. Let $L$ be the least common multiple of $a$ and $b$. Compute the remainder when $64820 \times L$ is divided by $76969$. Find the value of this remainder. | 42,593 | graphs = [
Graph(
let={
"a": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(31)), right=IntegerRange(start=Const(1), end=Const(46)))),
"b": Const(1903),
"result": LCM(a=Ref("a"), b=Ref("b")),
"Q": Mod(value=Mul(Const(64820), Ref(... | NT | null | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | nt_lcm_compute_v1 | null | 3 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.001 | 2026-02-08T05:56:37.847511Z | {
"verified": true,
"answer": 42593,
"timestamp": "2026-02-08T05:56:37.848257Z"
} | b179fc | 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": 2278
},
"timestamp": "2026-02-12T16:53:52.253Z",
"answer": 42593
},
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
024f93 | diophantine_product_count_v1_124444284_8637 | Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 1982464$. Let $T$ be the set of all values $x + y$ where $(x,y) \in S$. Define $n_0$ to be the minimum element of $T$.
Let $U$ be the set of all integers $n$ such that $1 \leq n \leq n_0$ and $n \equiv \left\lfloor \frac{n}{2} \right... | 22 | 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(1982464)))), expr=Sum(Var("x"), Var("y")))),
"k": Const(420... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"B3/L3C"
] | 345f3b | diophantine_product_count_v1 | null | 7 | 0 | [
"B3",
"L3C",
"MAX_PRIME_BELOW"
] | 3 | 0.091 | 2026-02-08T11:51:15.862828Z | {
"verified": true,
"answer": 22,
"timestamp": "2026-02-08T11:51:15.953346Z"
} | 3ac402 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 228,
"completion_tokens": 2570
},
"timestamp": "2026-02-14T19:42:17.143Z",
"answer": 22
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok_later"
},
{
"lemma": "V7",
"status": "no"
},
... | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
b651ef | nt_count_primes_v1_151522320_87 | Let $p$ be the number of prime numbers $n$ such that $2 \leq n \leq 33856$.
Let $S$ be the set of all positive integers $t$ such that $32 \leq t \leq 10847$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 434$, $1 \leq b \leq 288$, and
$$
t = 21a + 6b + 5.
$$
Let $q$ be the number of elements in $S$.... | 80,706 | graphs = [
Graph(
let={
"_n": Const(80731),
"upper": Const(33856),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("upper")), IsPrime(Var("n"))))),
"Q": Mod(value=Sub(CountOverSet(set=SolutionsSet(... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 324ba4 | nt_count_primes_v1 | negation_mod | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.881 | 2026-02-08T02:58:05.754202Z | {
"verified": true,
"answer": 80706,
"timestamp": "2026-02-08T02:58:06.634772Z"
} | d68835 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 254,
"completion_tokens": 32768
},
"timestamp": "2026-02-23T20:10:45.182Z",
"answer": null
},
{
... | 0 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"... | {
"lo": 4.68,
"mid": 6.57,
"hi": 9.55
} | ||
994ccd | diophantine_fbi2_count_v1_168721529_29 | Let $k$ be the sum of all nonnegative integers $j$ with $0 \leq j \leq 60$ such that
$$
\binom{60}{j} \equiv 1 \pmod{2}.
$$
Let $r$ be the number of integers $d$ such that $5 \leq d \leq 204$, $d$ divides $k$, and
$$
2 \leq \frac{k}{d} \leq 201.
$$
Find the value of $r$. | 18 | graphs = [
Graph(
let={
"k": SumOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(60)), Eq(Mod(value=Binom(n=Const(60), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')),
"result": CountOverSet(set=SolutionsSet... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"V8"
] | 86348e | diophantine_fbi2_count_v1 | null | 5 | 0 | [
"MIN_PRIME_FACTOR",
"V8"
] | 2 | 0.115 | 2026-02-08T12:46:17.061564Z | {
"verified": true,
"answer": 18,
"timestamp": "2026-02-08T12:46:17.176414Z"
} | a20705 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 230,
"completion_tokens": 3581
},
"timestamp": "2026-02-08T20:57:40.331Z",
"answer": 18
},
{
"id"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -2,
"mid": 1.85,
"hi": 5.2
} | ||
9cc061 | nt_sum_gcd_range_mod_v1_397696148_185 | Let $N$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 1000000$. Let $k$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 57600$. Let $M = 10613$. Define $\text{sum} = \sum_{n=1}^{N} \gcd(n, k)$. Compute the remain... | 10,225 | 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(1000000)))), expr=Sum(Var("x"), Var("y")))),
"k": MinOverSet... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_gcd_range_mod_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.123 | 2026-02-08T11:21:20.569504Z | {
"verified": true,
"answer": 10225,
"timestamp": "2026-02-08T11:21:20.692953Z"
} | a658e1 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 163,
"completion_tokens": 3273
},
"timestamp": "2026-02-14T12:23:43.279Z",
"answer": 10225
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
dbf05b | comb_count_partitions_v1_1918700295_2794 | Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $p < q$, $pq = 24$, and $\gcd(p, q) = 1$. Let $m$ be the number of elements in $S$. Let $T$ be the set of all positive integers $t$ that can be expressed as $t = 5a + 4b$ for integers $a$ and $b$ with $1 \leq a \leq ... | 63,261 | graphs = [
Graph(
let={
"_n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=24)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(value=1)), ... | NT | COMB | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/MAX_PRIME_BELOW",
"LIN_FORM/MAX_PRIME_BELOW"
] | d6bd1c | comb_count_partitions_v1 | null | 6 | 0 | [
"COPRIME_PAIRS",
"LIN_FORM",
"MAX_PRIME_BELOW"
] | 3 | 0.006 | 2026-02-08T08:12:35.075374Z | {
"verified": true,
"answer": 63261,
"timestamp": "2026-02-08T08:12:35.081760Z"
} | 9b38fc | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 213,
"completion_tokens": 2241
},
"timestamp": "2026-02-13T16:39:23.154Z",
"answer": 63261
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "POLY_PADIC_VAL_CON... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
823fcb | modular_min_linear_v1_1470522791_1351 | Let $m$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 1157776$. Determine the smallest positive integer $x$ such that $1 \leq x \leq m$ and
$$
1665x \equiv 2115 \pmod{m}.
$$ | 1,339 | graphs = [
Graph(
let={
"a": Const(1665),
"b": Const(2115),
"m": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(1157776)))),... | NT | null | EXTREMUM | sympy | B3 | [
"B3"
] | 0cd20d | modular_min_linear_v1 | null | 4 | 0 | [
"B3"
] | 1 | 8.976 | 2026-02-08T13:35:37.589427Z | {
"verified": true,
"answer": 1339,
"timestamp": "2026-02-08T13:35:46.565063Z"
} | 30554b | 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": 2323
},
"timestamp": "2026-02-15T18:19:18.552Z",
"answer": 1339
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
ba8fdf | diophantine_product_count_v1_717093673_3206 | Let $S$ be the set of all ordered pairs of positive integers $(x, y)$ such that $xy = 900$. Let $T$ be the set of all values $x + y$ where $(x, y) \in S$. Let $k$ be the minimum element of $T$.
Let $N$ be the number of positive integers $x_1$ such that $1 \leq x_1 \leq 36$, $x_1$ divides $k$, and $\frac{k}{x_1} \leq 3... | 17,714 | graphs = [
Graph(
let={
"_n": Const(900),
"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")), Ref("_n")))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | diophantine_product_count_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.007 | 2026-02-08T17:25:34.821725Z | {
"verified": true,
"answer": 17714,
"timestamp": "2026-02-08T17:25:34.828333Z"
} | 086a1e | 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": 911
},
"timestamp": "2026-02-18T01:54:29.531Z",
"answer": 17714
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
2deb61 | nt_min_coprime_above_v1_1439011603_1716 | Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 8340544$. Define $\alpha$ to be the minimum value of $x + y$ over all such pairs. Let $\beta$ be the smallest integer $n$ such that $\alpha < n \leq 5823$ and $\gcd(n, 37) = 1$. Compute the remainder when $$\n\beta \bmod 293 + 3001 \cd... | 23,116 | graphs = [
Graph(
let={
"start": 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(8340544)))), expr=Sum(Var("x"), Var("y")))),
"upper": Co... | NT | null | EXTREMUM | sympy | B3 | [
"B3"
] | 0cd20d | nt_min_coprime_above_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.015 | 2026-02-08T16:14:05.828123Z | {
"verified": true,
"answer": 23116,
"timestamp": "2026-02-08T16:14:05.842805Z"
} | 532f34 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 164,
"completion_tokens": 1137
},
"timestamp": "2026-02-16T23:00:43.315Z",
"answer": 23116
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
01d89f | antilemma_sum_equals_v1_784195855_7212 | Compute the number of ordered pairs $(i,j)$ of positive integers such that $1 \leq i \leq 101$, $1 \leq j \leq 101$, and $i + j = 103$. | 100 | graphs = [
Graph(
let={
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(103)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(101)), right=IntegerRange(start=Const(1), end=Const(101))))),
},
... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 3 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.003 | 2026-02-08T09:08:49.528381Z | {
"verified": true,
"answer": 100,
"timestamp": "2026-02-08T09:08:49.531347Z"
} | e01e13 | 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": 243
},
"timestamp": "2026-02-24T10:34:47.605Z",
"answer": 100
},
{
"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": -5.97,
"mid": -3.97,
"hi": -1.93
} | ||
d3d71d | comb_factorial_compute_v1_784195855_1660 | 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 = 147000$. 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=147000)), 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 | 6 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.001 | 2026-02-08T05:12:11.698434Z | {
"verified": true,
"answer": 40320,
"timestamp": "2026-02-08T05:12:11.699328Z"
} | a2a36f | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 164,
"completion_tokens": 916
},
"timestamp": "2026-02-11T23:03:20.871Z",
"answer": 40320
},
{
"... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -3.49,
"mid": 1.84,
"hi": 7.55
} | ||
6dfc58 | diophantine_fbi2_count_v1_349078426_500 | Let $k$ be the number of prime numbers $n$ such that $2 \leq n \leq 1069$. Determine the number of positive integers $d$ with $4 \leq d \leq 103$ such that $d$ divides $k$, and $\frac{k}{d}$ is an integer between $6$ and $105$, inclusive. | 10 | graphs = [
Graph(
let={
"_n": Const(1069),
"k": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(4)), ... | NT | null | COUNT | sympy | COUNT_COPRIME_GRID | [
"COUNT_PRIMES"
] | 07c874 | diophantine_fbi2_count_v1 | null | 4 | 0 | [
"COUNT_COPRIME_GRID",
"COUNT_PRIMES"
] | 2 | 0.033 | 2026-02-08T13:06:11.550409Z | {
"verified": true,
"answer": 10,
"timestamp": "2026-02-08T13:06:11.583505Z"
} | a890d0 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 122,
"completion_tokens": 1202
},
"timestamp": "2026-02-15T09:26:47.310Z",
"answer": 10
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
1b53d8 | v1_endings_v1_601307018_433 | Let $L = 58260!$. Let $U$ be the largest integer $k$ such that $5^k$ divides $L$. Let $V = 2U$. Let $A_1$ be the largest integer $k$ such that $2^k$ divides $L$, and let $A_2 = 5A_1$. Let $A_3$ be the largest integer $k$ such that $3^k$ divides $L$, and let $A_4 = 2A_3$. Define $A_5 = V + A_2 + A_4 + 965$. Find the rem... | 79,595 | graphs = [
Graph(
let={
"n_val": Const(58260),
"p1_val": Const(5),
"p2_val": Const(2),
"p3_val": Const(3),
"n_fact": Factorial(Ref("n_val")),
"vp1": MaxKDivides(target=Ref("n_fact"), base=Ref("p1_val")),
"vp2": MaxKDivides(t... | NT | null | COMPUTE | sympy | V1 | [
"V1"
] | dae96f | v1_endings_v1 | null | 5 | null | [
"V1"
] | 1 | 0.001 | 2026-03-10T00:57:35.242296Z | {
"verified": true,
"answer": 79595,
"timestamp": "2026-03-10T00:57:35.243748Z"
} | 508489 | CC BY 4.0 | null | null | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K5",
"status": "same_pattern_wrong"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V1",
"status": "... | {
"lo": -10,
"mid": 0,
"hi": 10
} | ||
a7be96 | antilemma_sum_equals_v1_1742523217_474 | Let $m = 55246$. Let $n$ be the number of integers $t$ such that $30 \leq t \leq 315$ and there exist integers $a$ and $b$ with $1 \leq a \leq 7$, $1 \leq b \leq 12$, and $t = 9a + 21b$. Let $x$ be the number of ordered pairs $(i, j)$ of integers with $1 \leq i \leq 83$ and $1 \leq j \leq 83$ such that $i + j = n$. Let... | 33,413 | graphs = [
Graph(
let={
"_m": Const(55246),
"_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=7)), Geq(left=V... | 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 | 0.008 | 2026-02-08T03:04:36.469722Z | {
"verified": true,
"answer": 33413,
"timestamp": "2026-02-08T03:04:36.477997Z"
} | d1e91b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 273,
"completion_tokens": 4721
},
"timestamp": "2026-02-23T21:29:11.092Z",
"answer": 33413
},
{
"... | 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": -0.05,
"mid": 2.89,
"hi": 5.27
} | ||
b8e0ae | alg_poly3_min_v1_1218484723_3825 | Let $A = \left|\{ t : \exists\, a,b \in \mathbb{Z},\ 1 \leq a \leq 155,\ 1 \leq b \leq 600,\ t = 14a + 10b,\ 24 \leq t \leq 8170 \}\right|$ and $B = \left|\{ t_1 : \exists\, a,b \in \mathbb{Z},\ 1 \leq a \leq 1950,\ 1 \leq b \leq 32,\ t_1 = 2a + 5b + 13,\ 20 \leq t_1 \leq 4073 \}\right|$. Find the minimum value of $A a... | 15,552 | graphs = [
Graph(
let={
"_m": Const(6750),
"_n": Const(2),
"result": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(346)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(346))))... | ALG | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | alg_poly3_min_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.225 | 2026-02-25T05:28:30.956945Z | {
"verified": true,
"answer": 15552,
"timestamp": "2026-02-25T05:28:31.182353Z"
} | c30b82 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 325,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T12:31:57.114Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 3.81,
"mid": 6.33,
"hi": 9.49
} | ||
5aae0c | nt_sum_gcd_range_mod_v1_655260480_740 | Let $\mathcal{R}$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = 166$. Let $N$ be the maximum value of $xy$ as $(x, y)$ ranges over $\mathcal{R}$. Define $k = 84$. Let $s = \sum_{n=1}^{N} \gcd(n, k)$. Let $r$ be the remainder when $s$ is divided by 10853. Find the remainder when $44121... | 29,008 | graphs = [
Graph(
let={
"_n": Const(166),
"N": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Ref("_n")))), expr=Mul(Var("x"), Var("y")))),
... | NT | null | COMPUTE | sympy | B1 | [
"B1"
] | 5b950e | nt_sum_gcd_range_mod_v1 | null | 5 | 0 | [
"B1"
] | 1 | 0.326 | 2026-02-08T15:33:12.144514Z | {
"verified": true,
"answer": 29008,
"timestamp": "2026-02-08T15:33:12.470850Z"
} | f8e335 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 163,
"completion_tokens": 2389
},
"timestamp": "2026-02-16T08:38:07.207Z",
"answer": 29008
},
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
966cc3 | comb_sum_binomial_row_v1_601307018_9483 | Let $M$ be the minimum value of $-28ab + 41a^2 + 5b^2$ over all ordered pairs $(a, b)$ of positive integers with $1 \leq a, b \leq 11$. Let $n$ be the number of integers $t$ in the range $19 \leq t \leq 36$ that can be expressed as $t = 3a + 2b + 14$ for some positive integers $a, b$ with $1 \leq a \leq 4$, $1 \leq b \... | 65,536 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(11)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(11)))), expr=Sum(Mul(Const(-28), Var("a"), ... | COMB | null | SUM | sympy | QF_PSD_MIN | [
"QF_PSD_MIN/LIN_FORM"
] | 8ce6bc | comb_sum_binomial_row_v1 | null | 5 | 0 | [
"LIN_FORM",
"QF_PSD_MIN"
] | 2 | 0.005 | 2026-03-10T09:54:31.579229Z | {
"verified": true,
"answer": 65536,
"timestamp": "2026-03-10T09:54:31.584307Z"
} | 9bc7b5 | 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": 3175
},
"timestamp": "2026-04-19T11:25:55.499Z",
"answer": 65536
},
{
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok_later"
},
{
"lemma": "QF_PSD_MIN",
"status": "ok"
},
{
"lemma": "V... | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
f6633c | comb_binomial_compute_v1_601307018_9264 | Let $n = \sum_{k=1}^{5} \varphi(k) \cdot \left\lfloor \frac{5}{k} \right\rfloor$, and let $M = \binom{n}{7}$. Find the remainder when $40574M$ is divided by $52359$. | 31,716 | graphs = [
Graph(
let={
"_n": Const(5),
"n": Summation(var="k1", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k1")), Floor(Div(Const(5), Var("k1"))))),
"k": Const(7),
"result": Binom(n=Ref("n"), k=Ref("k")),
"Q": Mod(value=Mul(Const(4057... | COMB | NT | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | comb_binomial_compute_v1 | null | 4 | 0 | [
"K2"
] | 1 | 0.003 | 2026-03-10T09:39:27.521014Z | {
"verified": true,
"answer": 31716,
"timestamp": "2026-03-10T09:39:27.523772Z"
} | 6ba27d | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 179,
"completion_tokens": 1584
},
"timestamp": "2026-04-19T11:01:12.000Z",
"answer": 31716
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
234740 | nt_num_divisors_compute_v1_458359167_20 | Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 97558461000$, $\gcd(p, q) = 1$, and $p < q$.
Let $n = |S|$. Determine the value of $\tau(n)$, the number of positive divisors of $n$. | 7 | 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=97558461000)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(val... | NT | null | COMPUTE | sympy | L3C | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_num_divisors_compute_v1 | null | 5 | 0 | [
"COPRIME_PAIRS",
"L3C"
] | 2 | 0.012 | 2026-02-08T02:57:08.095257Z | {
"verified": true,
"answer": 7,
"timestamp": "2026-02-08T02:57:08.107593Z"
} | a04951 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 194,
"completion_tokens": 2832
},
"timestamp": "2026-02-23T20:27:42.426Z",
"answer": 6
},
{
"id... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
... | {
"lo": 1.1,
"mid": 4.17,
"hi": 6.61
} | ||
495238 | lin_form_endings_v1_458359167_3630 | Let $a = 48$, $b = 36$, $A = 42$, and $B = 52$. Let $g = \gcd(a, b)$, and define
$$
a' = \left\lfloor \frac{a}{g} \right\rfloor, \quad b' = \left\lfloor \frac{b}{g} \right\rfloor.
$$
Compute the value of
$$
(7407 \cdot (a' \cdot A + b' \cdot B - a' \cdot b')) \bmod 85019.
$$ | 15,471 | graphs = [
Graph(
let={
"a_coeff": Const(48),
"b_coeff": Const(36),
"A_val": Const(42),
"B_val": Const(52),
"g_step": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"ap_node": Floor(Div(Ref("a_coeff"), Ref("g_step"))),
"bp_node": ... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 3 | null | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T11:12:26.028195Z | {
"verified": true,
"answer": 15471,
"timestamp": "2026-02-08T11:12:26.029726Z"
} | bad609 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 164,
"completion_tokens": 650
},
"timestamp": "2026-02-14T11:12:39.401Z",
"answer": 15471
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
cd3ff4 | antilemma_k3_v1_124444284_6 | Let $n = 39840$. Define
$$
x = \sum_{d \mid n} \phi(d),
$$
where $\phi$ denotes Euler's totient function. Compute the value of
$$
\left( x \bmod 199 \right) + 2003 \cdot \left( x \bmod 499 \right),
$$
and then take the result modulo $59700$. Find the value of this final quantity. | 3,497 | graphs = [
Graph(
let={
"_n": Const(39840),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"_c": Const(2003),
"Q": Mod(value=Sum(Mod(value=Ref("x"), modulus=Const(199)), Mul(Ref("_c"), Mod(value=Ref("x"), modulus=Const(499))))... | NT | COMB | COMPUTE | sympy | K13 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 4 | 0 | [
"K13",
"K3"
] | 2 | 0.002 | 2026-02-08T02:52:53.825958Z | {
"verified": true,
"answer": 3497,
"timestamp": "2026-02-08T02:52:53.827613Z"
} | 14d217 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 211,
"completion_tokens": 561
},
"timestamp": "2026-02-08T19:57:37.569Z",
"answer": 4497
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": 1.96,
"mid": 3.41,
"hi": 4.8
} | ||
563517 | nt_count_divisible_v1_458359167_2147 | Let $A$ be the set of positive integers $n$ such that $n \leq 44850$ and $n$ is divisible by $8$. Let $r$ be the number of elements in $A$. Let $S$ be the Cartesian product of the sets $\{1, 2, 3, 4\}$ and $\{1, 2, \dots, 827\}$. Compute the remainder when the product of the number of elements in $S$ and $r$ is divided... | 46,093 | graphs = [
Graph(
let={
"upper": Const(44850),
"divisor": Const(8),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(value=Var("n"), modulus=Ref("divisor")), Const(0))))),
"Q": Mod... | NT | null | COUNT | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 27a9f8 | nt_count_divisible_v1 | affine_mod | 2 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 3.399 | 2026-02-08T05:09:25.483501Z | {
"verified": true,
"answer": 46093,
"timestamp": "2026-02-08T05:09:28.882619Z"
} | 3dd732 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 224,
"completion_tokens": 1180
},
"timestamp": "2026-02-11T23:00:07.858Z",
"answer": 46093
},
{
"... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
... | {
"lo": -3.45,
"mid": 1.15,
"hi": 6.18
} | ||
98155f | algebra_vieta_sum_v1_2051736721_5395 | Let $P(x) = x^4 - 5x^3 - 23x^2 + 45x + m$, where $m$ is the largest positive divisor of $16002$ that is at most $126$. Find the sum of all real roots of the equation $P(x) = 0$. | 5 | graphs = [
Graph(
let={
"_n": Const(16002),
"result": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Const(4)), Mul(Const(-5), Pow(Var("x"), Const(3))), Mul(Const(-23), Pow(Var("x"), Const(2))), Mul(Const(45), Var("x")), MaxOverSet(set=SolutionsSet(var=Var("... | NT | null | COMPUTE | sympy | B1 | [
"MAX_DIVISOR"
] | 51757e | algebra_vieta_sum_v1 | null | 4 | 0 | [
"B1",
"MAX_DIVISOR"
] | 2 | 0.085 | 2026-02-08T18:31:45.046466Z | {
"verified": true,
"answer": 5,
"timestamp": "2026-02-08T18:31:45.131439Z"
} | 9d0803 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 131,
"completion_tokens": 285
},
"timestamp": "2026-02-16T12:24:31.703Z",
"answer": 5
},
{
"id": 11,
"... | 2 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
5e51bb | comb_count_derangements_v1_124444284_2711 | Let $m = 4$ and $n_0 = 2$. Define $N$ to be the largest prime number $n$ such that $$ n \le \sum_{k=1}^{4} \phi(k) \left\lfloor \frac{m}{k} \right\rfloor. $$ Compute the subfactorial of $N$, denoted $!N$. | 1,854 | graphs = [
Graph(
let={
"_m": Const(4),
"_n": Const(2),
"n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Summation(var="k", start=Const(1), end=Const(4), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Ref("_m"), Var("k")))))),... | NT | COMB | COUNT | sympy | SUM_ARITHMETIC | [
"K2/MAX_PRIME_BELOW"
] | f058da | comb_count_derangements_v1 | null | 5 | 0 | [
"K2",
"MAX_PRIME_BELOW",
"SUM_ARITHMETIC"
] | 3 | 0.011 | 2026-02-08T04:53:57.640076Z | {
"verified": true,
"answer": 1854,
"timestamp": "2026-02-08T04:53:57.651225Z"
} | 20c897 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 192,
"completion_tokens": 1471
},
"timestamp": "2026-02-11T22:42:06.454Z",
"answer": 1854
},
{
"... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "V8",
"status": "no"
... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.33
} | ||
e82c4f | modular_sum_quadratic_residues_v1_397696148_1556 | Let $p$ be the largest prime number at most $433$. Let $r = \frac{p(p-1)}{4}$. Compute the remainder when $14147r$ is divided by $63349$. | 16,701 | graphs = [
Graph(
let={
"_n": Const(433),
"p": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), Const(4)),
"_c": Const(14147),... | NT | null | SUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | modular_sum_quadratic_residues_v1 | null | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.001 | 2026-02-08T12:38:50.671063Z | {
"verified": true,
"answer": 16701,
"timestamp": "2026-02-08T12:38:50.672189Z"
} | c23929 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 90,
"completion_tokens": 1336
},
"timestamp": "2026-02-15T03:05:31.996Z",
"answer": 16701
},
{... | 1 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
c80d25 | modular_mod_compute_v1_1742523217_5018 | Let $a = 180$. Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 1234321$. Define $m$ to be the minimum value of $x + y$ as $(x,y)$ ranges over $S$. Compute the remainder when $a$ is divided by $m$. | 180 | graphs = [
Graph(
let={
"a": Const(180),
"m": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(1234321)))), expr=Sum(Var("x"), Var("y"))))... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | modular_mod_compute_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.001 | 2026-02-08T10:45:29.671981Z | {
"verified": true,
"answer": 180,
"timestamp": "2026-02-08T10:45:29.672891Z"
} | 271b52 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 137,
"completion_tokens": 723
},
"timestamp": "2026-02-15T21:02:56.012Z",
"answer": 180
},
{
"id": 11,
... | 2 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
3f86a2 | algebra_quadratic_discriminant_v1_168721529_73 | Let $a = -2$, $b = -10$, and $n = 2$. Let $c$ be the sum of all real solutions $x$ to the equation $x^n - 72x - 3193 = 0$. Compute $b^2 - 4ac$. | 676 | graphs = [
Graph(
let={
"_n": Const(2),
"a": Const(-2),
"b": Const(-10),
"c": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Ref("_n")), Mul(Const(-72), Var("x")), Const(-3193)), Const(0)))),
"result": Sub(Pow(Ref("b"), Co... | NT | null | COMPUTE | sympy | VIETA_SUM | [
"VIETA_SUM"
] | b33a7a | algebra_quadratic_discriminant_v1 | null | 6 | 0 | [
"VIETA_SUM"
] | 1 | 0.002 | 2026-02-08T12:48:00.100682Z | {
"verified": true,
"answer": 676,
"timestamp": "2026-02-08T12:48:00.102479Z"
} | eb0536 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 177,
"completion_tokens": 532
},
"timestamp": "2026-02-08T20:59:38.982Z",
"answer": 676
},
{
"id"... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "VIETA_SUM",
"status": "ok"
}
] | {
"lo": -5.3,
"mid": -2.05,
"hi": 1.82
} | ||
7c98e8 | nt_lcm_compute_v1_971394319_1517 | Let $a = 1579$ and $b = 1533$. Define $L = \mathrm{lcm}(a, b)$. Let $s$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 1028196$. Compute the remainder when $s - L$ is divided by $92658$. | 83,187 | graphs = [
Graph(
let={
"a": Const(1579),
"b": Const(1533),
"result": LCM(a=Ref("a"), b=Ref("b")),
"Q": Mod(value=Sub(MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(a... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | fc629c | nt_lcm_compute_v1 | negation_mod | 4 | 0 | [
"B3"
] | 1 | 0.002 | 2026-02-08T13:43:11.150859Z | {
"verified": true,
"answer": 83187,
"timestamp": "2026-02-08T13:43:11.153205Z"
} | 7f6c9f | 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": 1488
},
"timestamp": "2026-02-15T20:17:19.371Z",
"answer": 83187
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
}... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
dddec4 | comb_bell_compute_v1_1125832087_587 | Let $S$ be the set of all positive integers $d$ such that $d \leq 8$ and $d$ divides $\sum_{d' \mid 88} \phi(d')$, where $\phi$ denotes Euler's totient function. Let $n$ be the maximum element of $S$. Define $B_n$ to be the $n$th Bell number, which counts the number of partitions of a set of $n$ elements. Let $Q = 4536... | 41,220 | graphs = [
Graph(
let={
"_n": Const(8),
"n": MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Leq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=SumOverDivisors(n=Const(value=88), var='d', expr=EulerPhi(n=Var(name='d'))))))),
"res... | NT | COMB | COMPUTE | sympy | K3 | [
"K3/MAX_DIVISOR"
] | 43ff77 | comb_bell_compute_v1 | null | 5 | 0 | [
"K3",
"MAX_DIVISOR"
] | 2 | 0.002 | 2026-02-08T03:09:36.695008Z | {
"verified": true,
"answer": 41220,
"timestamp": "2026-02-08T03:09:36.696953Z"
} | 39800a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 225,
"completion_tokens": 1538
},
"timestamp": "2026-02-10T13:14:54.883Z",
"answer": 41220
},
{
"... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": ... | {
"lo": -5.55,
"mid": -3.02,
"hi": 0.31
} | ||
5c514a | nt_min_phi_inverse_v1_809748730_468 | Let $S$ be the set of all positive integers $n$ such that $1 \leq n \leq 59$ and the sum of the decimal digits of $n$ leaves a remainder of 1 when divided by 2. Let $u = |S|$. Let $T$ be the set of all positive integers $n$ such that $1 \leq n \leq u$ and $\phi(n) = 10$. Compute the minimum value of $T$. | 11 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(59)), Eq(Mod(value=DigitSum(Var("n")), modulus=Ref("_n")), Const(1))))),
"k": Const(10),
"result": MinOverSe... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"L3B"
] | cc148f | nt_min_phi_inverse_v1 | null | 7 | 0 | [
"L3B",
"LIN_FORM"
] | 2 | 0.149 | 2026-02-08T11:32:25.024334Z | {
"verified": true,
"answer": 11,
"timestamp": "2026-02-08T11:32:25.173554Z"
} | 5261f9 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 146,
"completion_tokens": 2167
},
"timestamp": "2026-02-14T15:33:52.219Z",
"answer": 11
},
{
... | 1 | [
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3B",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
f9f2eb | nt_min_coprime_above_v1_2051736721_5599 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = 72$. Let $P$ be the maximum value of $xy$ over all such pairs. Let $n$ be the smallest integer greater than $P$ and at most $1328$ such that $\gcd(n, 22) = 1$. Compute $n$. | 1,297 | graphs = [
Graph(
let={
"start": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Const(72)))), expr=Mul(Var("x"), Var("y")))),
"upper": Const(1... | NT | null | EXTREMUM | sympy | B1 | [
"B1"
] | 5b950e | nt_min_coprime_above_v1 | null | 4 | 0 | [
"B1"
] | 1 | 0.01 | 2026-02-08T18:40:59.921417Z | {
"verified": true,
"answer": 1297,
"timestamp": "2026-02-08T18:40:59.931620Z"
} | a525df | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 130,
"completion_tokens": 814
},
"timestamp": "2026-02-18T18:36:39.676Z",
"answer": 1297
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
6d5e03 | comb_catalan_compute_v1_458359167_606 | Let $n$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 20$. Determine the value of the $n$-th Catalan number. | 16,796 | graphs = [
Graph(
let={
"_n": Const(20),
"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... | COMB | null | COMPUTE | sympy | COMB1 | [
"COMB1"
] | 567f58 | comb_catalan_compute_v1 | null | 4 | 0 | [
"COMB1"
] | 1 | 0.002 | 2026-02-08T03:26:18.534872Z | {
"verified": true,
"answer": 16796,
"timestamp": "2026-02-08T03:26:18.537269Z"
} | 2b19d8 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 161,
"completion_tokens": 606
},
"timestamp": "2026-02-10T14:22:07.020Z",
"answer": 16796
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -9.23,
"mid": -6.18,
"hi": -4.06
} | ||
b1fe68 | geo_count_lattice_rect_v1_865884756_6341 | Let $a = 64$ and $b = 101$. Define the set of lattice points in the rectangle $[0, a] \times [0, b]$ as the set of all ordered pairs $(x, y)$ of nonnegative integers such that $0 \le x \le a$ and $0 \le y \le b$. Compute the number of such lattice points. | 6,630 | graphs = [
Graph(
let={
"a": Const(64),
"b": Const(101),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 2 | 0 | null | null | 0 | 2026-02-08T19:09:49.657018Z | {
"verified": true,
"answer": 6630,
"timestamp": "2026-02-08T19:09:49.657509Z"
} | 439b62 | 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": 383
},
"timestamp": "2026-02-25T01:00:23.658Z",
"answer": 6630
},
{
... | 1 | [] | {
"lo": -8.48,
"mid": -5.37,
"hi": -3.03
} | ||||
80885b | modular_min_modexp_v1_1918700295_1833 | Let $a = 3$, $b = 3$, and let $m$ be the smallest divisor of $467821919$ that is at least $2$. Determine the smallest positive integer $x$ such that $1 \leq x \leq 48$ and $a^x \equiv b \pmod{m}$. Compute this value of $x$. | 1 | graphs = [
Graph(
let={
"a": Const(3),
"b": Const(3),
"m": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(467821919))))),
"upper": Const(48),
"result": MinOverSet(set=Soluti... | NT | null | EXTREMUM | sympy | C4 | [
"MIN_PRIME_FACTOR"
] | bc3776 | modular_min_modexp_v1 | null | 5 | 0 | [
"C4",
"MIN_PRIME_FACTOR"
] | 2 | 0.141 | 2026-02-08T06:04:32.072015Z | {
"verified": true,
"answer": 1,
"timestamp": "2026-02-08T06:04:32.212664Z"
} | 5aea88 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 140,
"completion_tokens": 505
},
"timestamp": "2026-02-15T17:06:46.990Z",
"answer": null
},
{
"id": 11,
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V8",
"status": "no... | {
"lo": -9.14,
"mid": -6.05,
"hi": -3.73
} | ||
e1544f | modular_sum_quadratic_residues_v1_601307018_645 | Let $p$ be the smallest positive divisor of $70325205721$ greater than $1$. Let $M = \frac{p(p - 1)}{4}$. Find the remainder when $44121M$ is divided by $83374$. | 56,011 | graphs = [
Graph(
let={
"_n": Const(2),
"p": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(70325205721))))),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), Const(4)),
"Q": Mod(... | NT | null | SUM | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | modular_sum_quadratic_residues_v1 | null | 3 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.004 | 2026-03-10T01:11:27.961078Z | {
"verified": true,
"answer": 56011,
"timestamp": "2026-03-10T01:11:27.965412Z"
} | 198dc3 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 164,
"completion_tokens": 32768
},
"timestamp": "2026-03-28T23:43:57.137Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": 4.01,
"mid": 6.11,
"hi": 9.15
} | ||
b50d2e | sequence_fibonacci_compute_v1_784195855_561 | Let $n$ be the number of integers $t$ such that $18 \leq t \leq 78$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 3$, $1 \leq b \leq 9$, and $t = 14a + 4b$. Compute the $n$-th Fibonacci number, where the Fibonacci sequence is defined by $F_1 = 1$, $F_2 = 1$, and $F_k = F_{k-1} + F_{k-2}$ for $k \geq... | 75,025 | 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=3)), Geq(left=Var(name='b'), right=Const(value=1... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | sequence_fibonacci_compute_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T04:27:30.226270Z | {
"verified": true,
"answer": 75025,
"timestamp": "2026-02-08T04:27:30.228420Z"
} | e66ec2 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 252,
"completion_tokens": 1199
},
"timestamp": "2026-02-10T16:50:45.869Z",
"answer": 75025
},
{
... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
7f2ff0 | sequence_fibonacci_compute_v1_1520064083_1427 | Let $n$ be the largest integer such that $2^n \leq 26863683$. 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$. Compute the remainder when $65938 \cdot F_n$ is divided by 87669. | 44,478 | graphs = [
Graph(
let={
"_n": Const(2),
"n": MaxOverSet(set=SolutionsSet(var=Var("k"), condition=Leq(Pow(Ref("_n"), Var("k")), Const(26863683)))),
"result": Fibonacci(arg=Ref(name='n')),
"Q": Mod(value=Mul(Const(65938), Ref("result")), modulus=Const(87669)),
... | NT | null | COMPUTE | sympy | MAX_VAL | [
"MAX_VAL"
] | 1da621 | sequence_fibonacci_compute_v1 | null | 4 | 0 | [
"MAX_VAL"
] | 1 | 0.002 | 2026-02-08T03:59:34.282037Z | {
"verified": true,
"answer": 44478,
"timestamp": "2026-02-08T03:59:34.284343Z"
} | e256ae | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 210,
"completion_tokens": 3339
},
"timestamp": "2026-02-10T16:31:40.334Z",
"answer": 44478
},
{
"... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "same_pattern_wrong"
},
{
"lemma": "MAX_VAL",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
... | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
0eee10 | nt_count_intersection_v1_1125832087_1066 | Let $a$ be the number of ordered pairs of positive odd integers $(x_1, x_2)$ such that $x_1 + x_2 = 10$. Let $N$ be the number of positive integers $n \leq 100000$ such that $a$ divides $n$ and $\gcd(n, 12) = 1$.
Compute $N$. | 6,667 | graphs = [
Graph(
let={
"N": Const(100000),
"a": 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")),... | NT | null | COUNT | sympy | COMB1 | [
"COMB1"
] | 567f58 | nt_count_intersection_v1 | null | 4 | 0 | [
"COMB1"
] | 1 | 9.469 | 2026-02-08T03:29:46.379745Z | {
"verified": true,
"answer": 6667,
"timestamp": "2026-02-08T03:29:55.848655Z"
} | ea2d5a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 193,
"completion_tokens": 1859
},
"timestamp": "2026-02-10T14:50:36.670Z",
"answer": 6667
},
{
"i... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
9c9a19 | geo_count_lattice_rect_v1_865884756_2703 | Compute the number of lattice points $(x, y)$ such that $0 \leq x \leq 233$ and $0 \leq y \leq 257$. | 60,372 | graphs = [
Graph(
let={
"a": Const(233),
"b": Const(257),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 2 | 0 | null | null | 0.002 | 2026-02-08T16:53:37.427036Z | {
"verified": true,
"answer": 60372,
"timestamp": "2026-02-08T16:53:37.429012Z"
} | 3f09d9 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 81,
"completion_tokens": 460
},
"timestamp": "2026-02-17T14:40:00.735Z",
"answer": 60372
},
{
... | 1 | [] | {
"lo": -5.64,
"mid": -3.17,
"hi": -0.81
} | ||||
07ed35 | antilemma_sum_equals_v1_971394319_631 | Let $m$ be the number of integers $t$ for which there exist integers $a$ and $b$ satisfying
\begin{itemize}
\item $1\le a\le 21$,
\item $1\le b\le 30$,
\item $7\le t\le 174$, and
\item $t=4a+3b$.
\end{itemize}
Let $n=43$.
Let $x$ be the number of ordered pairs $(i,j)$ of integers such that $1\le i\le 41$, $1\le j\le 4... | 41 | graphs = [
Graph(
let={
"_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=21)), Geq(left=Var(name='b'), right=Const(value... | COMB | GEOM | COMPUTE | sympy | COMB1 | [
"LIN_FORM/COMB1",
"COUNT_SUM_EQUALS"
] | b9178b | antilemma_sum_equals_v1 | negation_mod | 5 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 3 | 0.025 | 2026-02-08T13:13:46.355097Z | {
"verified": true,
"answer": 41,
"timestamp": "2026-02-08T13:13:46.379697Z"
} | c7f54c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 302,
"completion_tokens": 14485
},
"timestamp": "2026-02-24T17:29:22.769Z",
"answer": 41
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok_later"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"... | {
"lo": 1.15,
"mid": 4.18,
"hi": 6.61
} | ||
2078fb | algebra_poly_eval_v1_1125832087_1170 | Let $x = 27$. Define $y$ to be the smallest integer $d \geq 2$ such that $d$ divides the number of integers $t$ in the interval $[20, 1736]$ that can be expressed as $6a + 14b$ for some positive integers $a \leq 7$ and $b \leq 121$. Let $z = x^3 + y \cdot x^2 - 2x - 7$. Determine the value of the smallest positive inte... | 12,246 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(3),
"x": Const(27),
"result": Sum(Pow(Ref("x"), Ref("_n")), Mul(MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=CountOverSet(set=SolutionsSe... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/MIN_PRIME_FACTOR"
] | bb1a13 | algebra_poly_eval_v1 | null | 6 | 0 | [
"LIN_FORM",
"MIN_PRIME_FACTOR"
] | 2 | 0.008 | 2026-02-08T03:34:18.421389Z | {
"verified": true,
"answer": 12246,
"timestamp": "2026-02-08T03:34:18.429239Z"
} | deb4c8 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 248,
"completion_tokens": 9594
},
"timestamp": "2026-02-23T20:57:29.452Z",
"answer": 12246
},
{
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma":... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
86baff | diophantine_product_count_v1_1125832087_542 | Let $k$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 176400$. Let $u$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 14884$. Determine the number of positive integers $x$ such that $1 \leq x \leq u$, $x$ divides $k$, and $\fra... | 69,284 | 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(176400)))), expr=Sum(Var("x"), Var("y")))),
"upper": MinOver... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | diophantine_product_count_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.015 | 2026-02-08T03:09:01.507114Z | {
"verified": true,
"answer": 69284,
"timestamp": "2026-02-08T03:09:01.522266Z"
} | 5ecc49 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 246,
"completion_tokens": 4637
},
"timestamp": "2026-02-10T12:54:39.582Z",
"answer": 69284
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
44b050 | sequence_lucas_compute_v1_898971024_1203 | Let $n$ be the number of positive integers $k$ such that $1 \le k \le 296$, $8$ divides $k$, and $\gcd(k, 15) = 1$. Compute the $n$th Lucas number. Determine the value of this Lucas number. | 15,127 | graphs = [
Graph(
let={
"_n": Const(15),
"n": CountOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(1)), Leq(Var("n1"), Const(296)), Divides(divisor=Const(8), dividend=Var("n1")), Eq(GCD(a=Var("n1"), b=Ref("_n")), Const(1))))),
"result": Lucas(ar... | NT | null | COMPUTE | sympy | C5 | [
"C5"
] | 1d9668 | sequence_lucas_compute_v1 | null | 4 | 0 | [
"C5"
] | 1 | 0.002 | 2026-02-08T15:59:48.727706Z | {
"verified": true,
"answer": 15127,
"timestamp": "2026-02-08T15:59:48.729739Z"
} | 7eacd9 | 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": 1018
},
"timestamp": "2026-02-16T18:44:13.998Z",
"answer": 15127
},
... | 1 | [
{
"lemma": "C5",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
c68e12 | algebra_poly_eval_v1_1742523217_4972 | Let $z = 6$. Compute the value of $5z^4 - 10z^3 + z^2 + dz - 1$, where $d$ is the smallest divisor of 1225 that is at least 2. | 4,385 | graphs = [
Graph(
let={
"z": Const(6),
"result": Sum(Mul(Const(5), Pow(Ref("z"), Const(4))), Mul(Const(-10), Pow(Ref("z"), Const(3))), Pow(Ref("z"), Const(2)), Mul(MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Cons... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | algebra_poly_eval_v1 | null | 3 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.003 | 2026-02-08T10:41:39.010223Z | {
"verified": true,
"answer": 4385,
"timestamp": "2026-02-08T10:41:39.012815Z"
} | 7121ac | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 110,
"completion_tokens": 433
},
"timestamp": "2026-02-15T21:02:01.416Z",
"answer": 4355
},
{
"id": 11,... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_... | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
aee871 | antilemma_cartesian_v1_168721529_2086 | Let $x$ be the number of ordered pairs $(a,b)$ where $a$ is an integer from 1 to 27, inclusive, and $b$ is an integer from 1 to 29, inclusive. Define $S = \sum_{k=0}^{10} (-1)^k \binom{10}{k}$. Compute the sum of the number of positive divisors of $n$, as $n$ ranges from $|S|$ to $x$, inclusive. Find the value of this ... | 5,345 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(27)), right=IntegerRange(start=Const(1), end=Const(29)))),
"Q": Summation(var="n", start=Factorial(Summation(var="k", start=Const(0), end=Const(10), expr=Mul(Pow(Const(-1), Var(... | COMB | GEOM | COMPUTE | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING",
"COUNT_CARTESIAN",
"ONE_FACTORIAL_0"
] | 12185f | antilemma_cartesian_v1 | null | 5 | 0 | [
"BINOMIAL_ALTERNATING",
"COUNT_CARTESIAN",
"ONE_FACTORIAL_0"
] | 3 | 0.001 | 2026-02-08T14:07:00.584568Z | {
"verified": true,
"answer": 5345,
"timestamp": "2026-02-08T14:07:00.585989Z"
} | c94fa6 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 220,
"completion_tokens": 3716
},
"timestamp": "2026-02-10T01:52:43.115Z",
"answer": 5345
},
{
"i... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
... | {
"lo": -2.43,
"mid": 1.2,
"hi": 4.84
} | ||
e8238b | nt_sum_totient_over_divisors_v1_655260480_1140 | Let $n$ be the number of positive integers $n_1$ with $1 \le n_1 \le 59256$ such that $7$ divides the $n_1$-th Fibonacci number. Compute the remainder when $89363$ times the sum of $\phi(d)$ over all positive divisors $d$ of $n$ is divided by 58899. | 4,779 | graphs = [
Graph(
let={
"_n": Const(7),
"n": CountOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(1)), Leq(Var("n1"), Const(59256)), Divides(divisor=Ref("_n"), dividend=Fibonacci(arg=Var(name='n1')))))),
"result": SumOverDivisors(n=Ref(name='n')... | NT | null | COMPUTE | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE"
] | 66de3c | nt_sum_totient_over_divisors_v1 | null | 5 | 0 | [
"COUNT_FIB_DIVISIBLE"
] | 1 | 0.008 | 2026-02-08T15:55:40.621555Z | {
"verified": true,
"answer": 4779,
"timestamp": "2026-02-08T15:55:40.629560Z"
} | b737b1 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 126,
"completion_tokens": 2680
},
"timestamp": "2026-02-16T17:08:35.892Z",
"answer": 4779
},
{... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
12e7aa | comb_count_partitions_v1_151522320_567 | Let $m = 42$. Consider the set of all ordered pairs $(x,y)$ of positive integers such that $x + y = m$. Let $P$ be the set of all values of $xy$ over these pairs. Define $n$ to be the minimum value of $x + y$ over all ordered pairs $(x,y)$ of positive integers such that $xy$ equals the maximum element of $P$. Let $r$ b... | 1,224 | graphs = [
Graph(
let={
"_m": Const(42),
"_n": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Ref("_m")))), expr=Mul(Var("x"), Var("y")))),
... | NT | COMB | COUNT | sympy | B1 | [
"B1/B3"
] | 80b49d | comb_count_partitions_v1 | null | 7 | 0 | [
"B1",
"B3"
] | 2 | 0.002 | 2026-02-08T03:22:41.870415Z | {
"verified": true,
"answer": 1224,
"timestamp": "2026-02-08T03:22:41.872397Z"
} | 1ec7e0 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 238,
"completion_tokens": 4695
},
"timestamp": "2026-02-10T14:16:35.638Z",
"answer": 1224
},
{
"i... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "... | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
ec1470 | nt_sum_totient_over_divisors_v1_458359167_1940 | Let $n = 62059$. Define $R$ to be the sum of $\phi(d)$ over all positive divisors $d$ of $n$, where $\phi$ is Euler's totient function. Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 396900$. Define $T$ to be the minimum value of $x + y$ as $(x, y)$ ranges over $S$. Compute $R^2 +... | 1,775 | graphs = [
Graph(
let={
"n": Const(62059),
"result": SumOverDivisors(n=Ref(name='n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Mod(value=Sum(Pow(Ref("result"), Const(2)), Mul(Const(5), Ref("result")), MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Va... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | d720b5 | nt_sum_totient_over_divisors_v1 | quadratic_mod | 4 | 0 | [
"B3"
] | 1 | 0.001 | 2026-02-08T04:56:20.231403Z | {
"verified": true,
"answer": 1775,
"timestamp": "2026-02-08T04:56:20.232814Z"
} | 03ff10 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 234,
"completion_tokens": 1922
},
"timestamp": "2026-02-11T22:31:06.126Z",
"answer": 1775
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
17611f | nt_count_coprime_and_v1_168721529_1403 | Let $n$ be a positive integer. Define $k_1 = 3$ and let $k_2$ be the largest prime number satisfying $2 \leq n \leq 12$. Determine the number of positive integers $n$ with $1 \leq n \leq 47904$ such that $\gcd(n, k_1) = 1$ and $\gcd(n, k_2) = \phi(2)$. Compute this number. | 29,033 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": Const(47904),
"k1": Const(3),
"k2": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Const(12)), IsPrime(Var("n"))))),
"result": CountOverSet(set=Soluti... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW",
"ONE_PHI_2"
] | 256a94 | nt_count_coprime_and_v1 | null | 4 | 0 | [
"MAX_PRIME_BELOW",
"ONE_PHI_2"
] | 2 | 10.283 | 2026-02-08T13:40:54.573242Z | {
"verified": true,
"answer": 29033,
"timestamp": "2026-02-08T13:41:04.856570Z"
} | fe9c35 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 212,
"completion_tokens": 1127
},
"timestamp": "2026-02-09T16:32:47.862Z",
"answer": 29033
},
{
"... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},... | {
"lo": -1.99,
"mid": 2.14,
"hi": 6.33
} | ||
748a52 | modular_sum_quadratic_residues_v1_784195855_8743 | Let $p$ be the largest prime number $n$ such that $2 \leq n \leq 521$. Compute $\frac{p(p-1)}{4}$. | 67,730 | graphs = [
Graph(
let={
"_n": Const(2),
"p": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Const(521)), IsPrime(Var("n"))))),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), Const(4)),
},
goal=Ref("re... | NT | null | SUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | modular_sum_quadratic_residues_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.002 | 2026-02-08T16:17:58.738396Z | {
"verified": true,
"answer": 67730,
"timestamp": "2026-02-08T16:17:58.740046Z"
} | 8d187a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 81,
"completion_tokens": 787
},
"timestamp": "2026-02-17T01:07:24.089Z",
"answer": 67730
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
104caa | geo_count_lattice_triangle_v1_717093673_525 | Let $t$ be an integer. Determine the number of values of $t$ in the range $14 \le t \le 204$ for which there exist positive integers $a$ and $b$ with $1 \le a \le 6$, $1 \le b \le 21$, such that $t = 6a + 8b$. Let this number be $n$. Define $A = |100 \cdot 128 - 121n|$. Let $B$ be the sum of the greatest common divisor... | 954 | graphs = [
Graph(
let={
"_m": Const(121),
"_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=6)), Geq(left=Var... | ALG | NT | COUNT | sympy | LIN_FORM | [
"LIN_FORM/COMB1"
] | 268a62 | geo_count_lattice_triangle_v1 | null | 7 | 0 | [
"COMB1",
"LIN_FORM"
] | 2 | 0.018 | 2026-02-08T15:29:57.027246Z | {
"verified": true,
"answer": 954,
"timestamp": "2026-02-08T15:29:57.044991Z"
} | fc4968 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 245,
"completion_tokens": 5666
},
"timestamp": "2026-02-16T07:00:42.359Z",
"answer": 954
},
{
... | 1 | [
{
"lemma": "COMB1",
"status": "ok_later"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
91a6de | comb_count_derangements_v1_1918700295_222 | Let $n$ be the largest prime number satisfying $2 \leq n \leq \sum_{k=1}^4 k$. Compute the number of derangements of $n$ elements. | 1,854 | graphs = [
Graph(
let={
"_n": Const(2),
"n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Summation(var="k", start=Const(1), end=Const(4), expr=Var("k"))), IsPrime(Var("n"))))),
"result": Subfactorial(arg=Ref(name='n')),
... | NT | COMB | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC/MAX_PRIME_BELOW"
] | bde608 | comb_count_derangements_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW",
"SUM_ARITHMETIC"
] | 2 | 0.002 | 2026-02-08T03:06:18.990620Z | {
"verified": true,
"answer": 1854,
"timestamp": "2026-02-08T03:06:18.992665Z"
} | 131a51 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 152,
"completion_tokens": 986
},
"timestamp": "2026-02-10T13:09:22.721Z",
"answer": 1854
},
{
"id... | 1 | [
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status... | {
"lo": -5.55,
"mid": -3.02,
"hi": 0.31
} | ||
606933 | nt_count_divisors_in_range_v1_151522320_1870 | Let $n = 840$, $a = 4$, and $b = 169$. Define $r$ to be the number of positive divisors of $n$ that are at least $a$ and at most $b$. Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x \cdot y = 23059204$. Define $c$ to be the minimum value of $x + y$ over all such pairs in $S$. Compute ... | 9,579 | graphs = [
Graph(
let={
"n": Const(840),
"a": Const(4),
"b": Const(169),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Divides(divisor=Var("d"), dividend=Ref("n")), Geq(Var("d"), Ref("a")), Leq(Var("d"), Ref("b"))))),
"_c": Mi... | NT | null | COUNT | sympy | B3 | [
"B3"
] | fc629c | nt_count_divisors_in_range_v1 | negation_mod | 6 | 0 | [
"B3"
] | 1 | 0.012 | 2026-02-08T04:26:27.996289Z | {
"verified": true,
"answer": 9579,
"timestamp": "2026-02-08T04:26:28.007932Z"
} | 36bced | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 221,
"completion_tokens": 1794
},
"timestamp": "2026-02-10T16:35:08.550Z",
"answer": 9579
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
cdeb78 | alg_qf_psd_sum_v1_1218484723_3147 | Find the remainder when
$$
\sum_{\substack{a=1 \\ b=1}}^{p \leq 59} \left(2a^2 - 6ab + 9b^2\right)
$$
is divided by $55644$, where $p$ is the largest prime less than or equal to $59$. | 4,126 | graphs = [
Graph(
let={
"_n": Const(9),
"result": Mod(value=SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(V... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | alg_qf_psd_sum_v1 | null | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.016 | 2026-02-25T04:51:22.109336Z | {
"verified": true,
"answer": 4126,
"timestamp": "2026-02-25T04:51:22.125482Z"
} | 2d834b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 184,
"completion_tokens": 2523
},
"timestamp": "2026-03-29T08:40:14.753Z",
"answer": 4126
},
{
"i... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
... | {
"lo": -2.45,
"mid": 1.37,
"hi": 5.29
} | ||
685442 | alg_sum_powers_v1_1218484723_376 | Find the remainder when $\sum_{k=1}^{1090} k^3$ is divided by $\left|\left\{ (a, b) : 1 \le a \le 40,\ 1 \le b \le \left|\left\{ (a_1, b_1) : 1 \le a_1, b_1 \le 40,\ 16b_1^2 = 16 \right\}\right|,\ 2a^2 + 41b^2 - 2ab \le 31994 \right\}\right|.$ | 569 | graphs = [
Graph(
let={
"_m": Const(40),
"_n": Const(2),
"result": Mod(value=Summation(var="k", start=Const(1), end=Const(1090), expr=Pow(Var("k"), Const(3))), modulus=CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Cons... | ALG | null | COMPUTE | sympy | QF_PSD_COUNT | [
"QF_PSD_COUNT/QF_PSD_COUNT_LEQ"
] | 89ab91 | alg_sum_powers_v1 | null | 5 | 0 | [
"QF_PSD_COUNT",
"QF_PSD_COUNT_LEQ"
] | 2 | 0.135 | 2026-02-25T02:04:35.008227Z | {
"verified": true,
"answer": 569,
"timestamp": "2026-02-25T02:04:35.143334Z"
} | d6450a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 236,
"completion_tokens": 6246
},
"timestamp": "2026-03-28T22:25:40.018Z",
"answer": 569
},
{
"id... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT",
"status": "ok"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok_later"
}
] | {
"lo": 1.22,
"mid": 3.76,
"hi": 5.73
} | ||
1baa4c | comb_sum_binomial_row_v1_458359167_1064 | Let $n = \sum_{k=1}^{5} k$. Define $\text{result} = 2^n$. Find the value of $\text{result}$. | 32,768 | graphs = [
Graph(
let={
"_n": Const(5),
"n": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Var("k")),
"result": Pow(Const(2), Ref("n")),
},
goal=Ref("result"),
)
] | NT | null | SUM | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | comb_sum_binomial_row_v1 | null | 2 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.002 | 2026-02-08T04:15:41.039523Z | {
"verified": true,
"answer": 32768,
"timestamp": "2026-02-08T04:15:41.041185Z"
} | 160aaa | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 147,
"completion_tokens": 130
},
"timestamp": "2026-02-10T16:26:22.673Z",
"answer": 32768
},
{
"... | 2 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V3",
"statu... | {
"lo": -10,
"mid": -7.73,
"hi": -5.46
} | ||
75c5c8 | diophantine_fbi2_min_v1_48377204_333 | Let $T$ be the set of all integers $t$ such that $10 \le t \le 1070$ and $t = 4a + 6b$ for some integers $a, b$ with $1 \le a \le 197$ and $1 \le b \le 47$. Let $k = 36$. Define $u$ to be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy$ equals the number of elements in $T... | 11,054 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(2),
"k": Const(36),
"upper": 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"), V... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM/B3"
] | 05313e | diophantine_fbi2_min_v1 | null | 7 | 0 | [
"B3",
"LIN_FORM"
] | 2 | 0.007 | 2026-02-08T15:20:41.351125Z | {
"verified": true,
"answer": 11054,
"timestamp": "2026-02-08T15:20:41.357855Z"
} | d69e5b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 232,
"completion_tokens": 3785
},
"timestamp": "2026-02-16T05:46:42.031Z",
"answer": 11054
},
... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONS... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
5102d9 | algebra_poly_eval_v1_601307018_2397 | Let $a = 19$. Compute
$$
\left|\left\{ (a_1, b) : 1 \le a_1, b \le 25,\ 64a_1^3 + 27b^3 + 144a_1^2b + 108a_1b^2 = 456533 \right\}\right| \cdot a^3 - 3a - 10.
$$ | 41,087 | graphs = [
Graph(
let={
"a": Const(19),
"result": Sum(Mul(CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a1"), Var("b")]), condition=And(Geq(Var("a1"), Const(1)), Leq(Var("a1"), Const(25)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(25)), Eq(Sum(Mul(Const(64), Pow(Var("a1")... | ALG | null | COMPUTE | sympy | POLY3_COUNT | [
"POLY3_COUNT"
] | 355dbe | algebra_poly_eval_v1 | null | 3 | 0 | [
"POLY3_COUNT"
] | 1 | 0.003 | 2026-03-10T03:05:26.827641Z | {
"verified": true,
"answer": 41087,
"timestamp": "2026-03-10T03:05:26.830279Z"
} | 877bec | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 205,
"completion_tokens": 1480
},
"timestamp": "2026-03-29T05:15:57.395Z",
"answer": 41087
},
{
"... | 1 | [
{
"lemma": "POLY3_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -4.26,
"mid": -1.81,
"hi": 1.24
} | ||
f6d928 | modular_modexp_compute_v1_601307018_8573 | Let $M$ be the number of positive integers $t$ with $14 \le t \le 242$ that can be expressed as $t = 4c + 10b$ for some integers $c, b$ satisfying $1 \le c \le 38$, $1 \le b \le 9$. Let $R$ be the largest prime number $n$ such that $2 \le n \le 41$. Let $e$ be the number of positive integers $k$ with $1 \le k \le 55944... | 35,149 | graphs = [
Graph(
let={
"_m": Const(44121),
"_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=38)), Geq(left=... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/C2",
"MAX_PRIME_BELOW"
] | 7c9620 | modular_modexp_compute_v1 | null | 5 | 0 | [
"C2",
"LIN_FORM",
"MAX_PRIME_BELOW"
] | 3 | 0.007 | 2026-03-10T09:04:35.450955Z | {
"verified": true,
"answer": 35149,
"timestamp": "2026-03-10T09:04:35.458254Z"
} | 7e18f4 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 269,
"completion_tokens": 7698
},
"timestamp": "2026-04-19T09:16:49.587Z",
"answer": 35149
},
{
... | 1 | [
{
"lemma": "C2",
"status": "ok_later"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
... | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
5c4f91 | nt_sum_gcd_range_mod_v1_798873815_503 | Let $ N $ be the smallest integer $ d \geq 2 $ that divides $ 8287306393 $. Compute the sum $ \sum_{n=1}^{N} \gcd(n, 252) $, and let $ M = 11689 $. Find the remainder when this sum is divided by $ M $. | 5,784 | 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(8287306393))))),
"k": Const(252),
"M": Const(11689),
"sum": Summation(var="n", s... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | nt_sum_gcd_range_mod_v1 | null | 5 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.472 | 2026-02-08T02:40:21.813813Z | {
"verified": true,
"answer": 5784,
"timestamp": "2026-02-08T02:40:22.285933Z"
} | 15ebe1 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 178,
"completion_tokens": 32768
},
"timestamp": "2026-02-23T15:42:12.191Z",
"answer": null
},
{
... | 0 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": 4.67,
"mid": 6.56,
"hi": 9.55
} | ||
254dc9 | lte_diff_endings_v1_601307018_45 | Let $R = 31 - 3$, $T = 190187$, $K = T!$, and $L = 2$. Let $P$ be the largest integer $k$ such that $2^k$ divides $R$. Let $Q = T \cdot P$. Let $W$ be the largest integer $k$ such that $2^k$ divides $K$. Let $U = Q + W$. Find the remainder when $U$ is divided by $100000$. | 70,549 | graphs = [
Graph(
let={
"a_val": Const(31),
"b_val": Const(3),
"p_val": Const(2),
"n_val": Const(190187),
"ab_diff": Sub(Ref("a_val"), Ref("b_val")),
"vp_ab": MaxKDivides(target=Ref("ab_diff"), base=Ref("p_val")),
"n_times_C... | NT | null | COMPUTE | sympy | LTE_DIFF | [
"LTE_DIFF"
] | cf8260 | lte_diff_endings_v1 | null | 4 | null | [
"LTE_DIFF"
] | 1 | 0.001 | 2026-03-10T00:43:16.108402Z | {
"verified": true,
"answer": 70549,
"timestamp": "2026-03-10T00:43:16.109725Z"
} | e9627f | CC BY 4.0 | null | null | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V8",
"status": "no"... | {
"lo": -10,
"mid": 0,
"hi": 10
} | ||
e6e7f6 | geo_count_lattice_rect_v1_655260480_2467 | Let $a = 484$ and $b = 143$. Define a lattice point as a point in the plane with integer coordinates. Consider the rectangle with vertices at $(0,0)$, $(a,0)$, $(0,b)$, and $(a,b)$, including the boundary. Compute the number of lattice points contained in this rectangle. | 69,840 | graphs = [
Graph(
let={
"a": Const(484),
"b": Const(143),
"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 | 2026-02-08T16:45:14.094891Z | {
"verified": true,
"answer": 69840,
"timestamp": "2026-02-08T16:45:14.095999Z"
} | 82977a | 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": 556
},
"timestamp": "2026-02-17T11:23:04.865Z",
"answer": 69840
},
{... | 1 | [] | {
"lo": -5.64,
"mid": -3.17,
"hi": -0.81
} | ||||
718b2b | lin_form_endings_v1_784195855_1135 | Let $a = 21$ and $b = 14$. Define $d = \gcd(a, b)$. Let $r = \left\lfloor \frac{21}{d} \right\rfloor$. Multiply $r$ by $6182$, and let the result be $s$. Compute the remainder when $s$ is divided by $72978$. | 18,546 | graphs = [
Graph(
let={
"a_coeff": Const(21),
"b_coeff": Const(14),
"_inner_result": Floor(Div(Const(21), GCD(a=Ref("a_coeff"), b=Ref("b_coeff")))),
"_scale_k": Const(6182),
"_scaled": Mul(Ref("_scale_k"), Ref("_inner_result")),
"_mod_M... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 2 | null | [
"LIN_FORM"
] | 1 | 0 | 2026-02-08T04:52:29.955000Z | {
"verified": true,
"answer": 18546,
"timestamp": "2026-02-08T04:52:29.955452Z"
} | 8da0d0 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 144,
"completion_tokens": 265
},
"timestamp": "2026-02-11T21:59:11.739Z",
"answer": 18546
},
{
"id": 11,
... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -9.14,
"mid": -6.05,
"hi": -3.73
} | ||
342ece | comb_count_derangements_v1_1431428450_1349 | Let $n$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq = 5880$, $\gcd(p, q) = 1$, and $p < q$. Let $r$ be the number of derangements of $n$ elements. Compute the remainder when $30223r$ is divided by $73243$. | 50,599 | graphs = [
Graph(
let={
"_n": Const(73243),
"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=5880)), Eq(left=GCD(a=Var(name='p'), b=Var(na... | NT | COMB | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_count_derangements_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.002 | 2026-02-08T14:02:53.455091Z | {
"verified": true,
"answer": 50599,
"timestamp": "2026-02-08T14:02:53.457476Z"
} | f8919a | 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": 2510
},
"timestamp": "2026-02-15T23:31:37.685Z",
"answer": 50599
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
dc4c83 | comb_count_partitions_v1_865884756_3003 | Let $n = 1 + 2 + 3 + \cdots + 9$. Compute the number of integer partitions of $n$. Then find the remainder when $19321$ minus this number is divided by $64099$. | 58,385 | graphs = [
Graph(
let={
"_n": Const(9),
"n": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Var("k")),
"result": Partition(arg=Ref(name='n')),
"_c": Const(19321),
"Q": Mod(value=Sub(Ref("_c"), Ref("result")), modulus=Const(64099)),
... | COMB | null | COUNT | sympy | COPRIME_PAIRS | [
"SUM_ARITHMETIC"
] | eb34f0 | comb_count_partitions_v1 | null | 3 | 0 | [
"COPRIME_PAIRS",
"SUM_ARITHMETIC"
] | 2 | 0.021 | 2026-02-08T17:05:20.224634Z | {
"verified": true,
"answer": 58385,
"timestamp": "2026-02-08T17:05:20.245376Z"
} | ac2954 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 95,
"completion_tokens": 753
},
"timestamp": "2026-02-17T19:50:52.255Z",
"answer": 58385
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V7",
... | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||
e49337 | nt_count_divisors_in_range_v1_677425708_913 | Let $n = 840$. Compute the number of positive divisors $d$ of $n$ such that $3 \leq d \leq 125$. Let this number be $r$. Find the value of $$ r + 2^{r \bmod 16} \bmod 75125. $$ | 280 | graphs = [
Graph(
let={
"n": Const(840),
"a": Const(3),
"b": Const(125),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Divides(divisor=Var("d"), dividend=Ref("n")), Geq(Var("d"), Ref("a")), Leq(Var("d"), Ref("b"))))),
"Q": Sum... | NT | null | COUNT | sympy | MOBIUS_COPRIME | [
"COPRIME_PAIRS"
] | 64a51e | nt_count_divisors_in_range_v1 | mod_exp | 4 | 0 | [
"COPRIME_PAIRS",
"MOBIUS_COPRIME"
] | 2 | 0.158 | 2026-02-08T03:51:33.081032Z | {
"verified": true,
"answer": 280,
"timestamp": "2026-02-08T03:51:33.239158Z"
} | a8dcd3 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 181,
"completion_tokens": 2772
},
"timestamp": "2026-02-09T13:58:31.520Z",
"answer": 280
},
{
"id... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.02,
"hi": 0.31
} | ||
b6b32d | comb_sum_binomial_row_v1_601307018_4134 | Let $M = 0$, $R = \frac{2}{14} \sum_{(k_1, a),\ 1} k_1$, $S = 0$, $h = \sum_{k=0}^{S} (-1)^k \binom{S}{k}$, $n = 11h$, $u = \sum_{k_2=0}^{R} (-1)^{k_2} \binom{R}{k_2}$, and $w = \sum_{k_3=0}^{M} (-1)^{k_3} \binom{M}{k_3}$. Compute $(2 + u) \cdot w)^n$. | 2,048 | graphs = [
Graph(
let={
"_n": Const(2),
"n3": Const(0),
"h": Summation(var="k", start=Const(0), end=Ref("n3"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n3"), k=Var("k")))),
"n2": Div(Mul(Const(2), SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(ele... | COMB | null | SUM | sympy | SUM_INDEPENDENT | [
"SUM_INDEPENDENT/SUM_ARITHMETIC/BINOMIAL_ALTERNATING"
] | 610c6e | comb_sum_binomial_row_v1 | null | 2 | 3 | [
"BINOMIAL_ALTERNATING",
"SUM_ARITHMETIC",
"SUM_INDEPENDENT"
] | 3 | 0.005 | 2026-03-10T04:43:43.386100Z | {
"verified": true,
"answer": 2048,
"timestamp": "2026-03-10T04:43:43.390882Z"
} | 3973e9 | 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": 2139
},
"timestamp": "2026-03-29T11:09:27.541Z",
"answer": 2048
},
{
"i... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok_later"
},
{
"lemma... | {
"lo": -3.34,
"mid": 0.9,
"hi": 4.9
} | ||
6062a6 | algebra_vieta_sum_v1_1125832087_1121 | Let $S$ be the set of all real numbers $x$ such that
$$
-x^3 + 12x^2 - 27x - 40 = 0.
$$
Compute the sum of all elements of $S$. | 12 | graphs = [
Graph(
let={
"result": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Mul(Const(-1), Pow(Var("x"), Const(3))), Mul(Const(12), Pow(Var("x"), Const(2))), Mul(Const(-27), Var("x")), Const(-40)), Const(0)))),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | V8 | [
"V8/K3"
] | 0ba015 | algebra_vieta_sum_v1 | null | 3 | 0 | [
"K3",
"V8"
] | 2 | 0.033 | 2026-02-08T03:32:58.625639Z | {
"verified": true,
"answer": 12,
"timestamp": "2026-02-08T03:32:58.658661Z"
} | dc3256 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 161,
"completion_tokens": 903
},
"timestamp": "2026-02-10T14:53:13.015Z",
"answer": 12
},
{
"id":... | 2 | [
{
"lemma": "K3",
"status": "ok_later"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
},
... | {
"lo": -10,
"mid": -7.73,
"hi": -5.46
} | ||
68b455 | sequence_count_fib_divisible_v1_397696148_2577 | Let $x_1$ and $x_2$ be positive odd integers such that $x_1 + x_2 = 1586$. Let $u$ be the number of such ordered pairs $(x_1, x_2)$. Determine the number of positive integers $n$ with $1 \leq n \leq u$ such that the $n$-th Fibonacci number is divisible by 4. Find the value of this number. | 132 | graphs = [
Graph(
let={
"_n": Const(1586),
"upper": 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"... | NT | null | COUNT | sympy | LIN_FORM | [
"COMB1"
] | 567f58 | sequence_count_fib_divisible_v1 | null | 6 | 0 | [
"COMB1",
"LIN_FORM"
] | 2 | 0.314 | 2026-02-08T13:25:30.432613Z | {
"verified": true,
"answer": 132,
"timestamp": "2026-02-08T13:25:30.746839Z"
} | 030d5d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 139,
"completion_tokens": 860
},
"timestamp": "2026-02-15T15:22:49.969Z",
"answer": 132
},
{
... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
632b13 | nt_count_divisible_and_v1_1918700295_2828 | Let $d_1 = 10$. Let $S$ be the set of all ordered pairs $(i, j)$ of positive integers such that $1 \leq i \leq 15$, $1 \leq j \leq 16$, and $i + j = 17$. Let $d_2 = |S|$. Let $T$ be the set of all positive integers $t$ such that $7 \leq t \leq 20$ and there exist positive integers $a, b$ with $1 \leq a \leq 2$, $1 \leq... | 13,956 | graphs = [
Graph(
let={
"upper": Const(130110),
"d1": Const(10),
"d2": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(17)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(15)), right... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/BINOMIAL_ALTERNATING",
"COUNT_SUM_EQUALS"
] | d728f4 | nt_count_divisible_and_v1 | null | 7 | 0 | [
"BINOMIAL_ALTERNATING",
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 3 | 4.333 | 2026-02-08T08:14:33.407694Z | {
"verified": true,
"answer": 13956,
"timestamp": "2026-02-08T08:14:37.740446Z"
} | dd057a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 370,
"completion_tokens": 1946
},
"timestamp": "2026-02-24T09:11:08.497Z",
"answer": 13956
},
{
"... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
6278d2 | antilemma_product_of_sums_v1_798873815_68 | Let $S$ be the set of all integers $t$ such that $9 \leq t \leq 38$ and there exist integers $a$ and $b$ with $1 \leq a \leq 2$, $1 \leq b \leq 12$, and $t = 7a + 2b$. Let $S_1 = \sum_{k=1}^{|S|} k$.
Let $T$ be the set of all ordered pairs $(k, j)$ of positive integers such that $1 \leq k \leq 5$ and $1 \leq j \leq 7$... | 31,500 | graphs = [
Graph(
let={
"S1": Summation(var="k", start=Const(1), end=CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=2)), Geq... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/SUM_ARITHMETIC",
"PRODUCT_OF_SUMS",
"ONE_PHI_2"
] | 0630f6 | antilemma_product_of_sums_v1 | null | 5 | 0 | [
"LIN_FORM",
"ONE_PHI_2",
"PRODUCT_OF_SUMS",
"SUM_ARITHMETIC"
] | 4 | 0.003 | 2026-02-08T02:25:37.850182Z | {
"verified": true,
"answer": 31500,
"timestamp": "2026-02-08T02:25:37.852793Z"
} | 0c103b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 295,
"completion_tokens": 2824
},
"timestamp": "2026-02-08T18:57:44.931Z",
"answer": 31500
},
{
"... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "ONE_PHI_2",
"status": "ok"
},
{
"le... | {
"lo": -1.91,
"mid": 1.73,
"hi": 4.74
} | ||
76b7e1 | antilemma_cartesian_v1_1520064083_7676 | Let $x$ be the number of ordered pairs $(a, b)$ such that $1 \leq a \leq 42$ and $1 \leq b \leq 42$. Compute the value of
$$
3^{|x|} \bmod 99991 + 16110.
$$ | 94,701 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(42)), right=IntegerRange(start=Const(1), end=Const(42)))),
"Q": Sum(ModExp(base=Const(3), exp=Abs(arg=Ref(name='x')), mod=Const(99991)), Const(16110)),
},
goal=R... | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | antilemma_cartesian_v1 | null | 2 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.001 | 2026-02-08T09:14:26.843306Z | {
"verified": true,
"answer": 94701,
"timestamp": "2026-02-08T09:14:26.844029Z"
} | d1e21b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 177,
"completion_tokens": 32768
},
"timestamp": "2026-02-24T10:52:14.366Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"statu... | {
"lo": 3.25,
"mid": 5.68,
"hi": 8.81
} | ||
85fdab | alg_linear_system_2x2_v1_1218484723_5938 | Let $F_n$ denote the $n$-th Fibonacci number. Let $S$ be the number of positive integers $n$ with $1 \le n \le 58080$ such that $10 \mid F_n$.
Define
$$C = \left|\{(a_1, b_1) : 1 \le a_1 \le 40,\ 1 \le b_1 \le 40,\ 34a_1 b_1 + 17a_1^{2} + 17b_1^{2} = 40817\}\right|,$$
and
$$D = \left|\{v : C \le v \le S,\ \text{there ... | 95,325 | graphs = [
Graph(
let={
"_e": Const(40),
"_d": Const(5),
"_c": Const(2),
"_m": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(58080)), Divides(divisor=Const(10), dividend=Fibonacci(arg=Var(name='n')))))),... | NT | null | COMPUTE | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE/QF_PSD_DISTINCT/QF_PSD_MIN",
"QF_PSD_COUNT/QF_PSD_DISTINCT/QF_PSD_MIN",
"MAX_PRIME_BELOW/QF_PSD_MIN"
] | e86ed3 | alg_linear_system_2x2_v1 | null | 8 | 0 | [
"COUNT_FIB_DIVISIBLE",
"MAX_PRIME_BELOW",
"QF_PSD_COUNT",
"QF_PSD_DISTINCT",
"QF_PSD_MIN"
] | 5 | 0.221 | 2026-02-25T07:32:17.257932Z | {
"verified": true,
"answer": 95325,
"timestamp": "2026-02-25T07:32:17.478807Z"
} | bd4e45 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 552,
"completion_tokens": 4490
},
"timestamp": "2026-03-29T23:32:23.241Z",
"answer": 95325
},
{
"... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": ... | {
"lo": -3.33,
"mid": 1.03,
"hi": 5.26
} | ||
616514 | antilemma_k2_v1_151522320_1658 | Let $n = 314$ and let $$
x = \sum_{k=1}^{n} \phi(k) \left\lfloor \frac{n}{k} \right\rfloor,
$$ where $\phi(k)$ denotes Euler's totient function. Let $Q$ be the remainder when $64813 \cdot x$ is divided by $65227$. Compute $Q$. | 6,908 | graphs = [
Graph(
let={
"_n": Const(314),
"x": Summation(var="k", start=Const(1), end=Const(314), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Ref("_n"), Var("k"))))),
"_c": Const(64813),
"Q": Mod(value=Mul(Ref("_c"), Ref("x")), modulus=Const(65227)),
},
... | NT | COMB | COMPUTE | sympy | K13 | [
"K2"
] | 6897ab | antilemma_k2_v1 | null | 6 | 0 | [
"K13",
"K2"
] | 2 | 0.011 | 2026-02-08T04:10:19.075586Z | {
"verified": true,
"answer": 6908,
"timestamp": "2026-02-08T04:10:19.086532Z"
} | 55a36e | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 194,
"completion_tokens": 1768
},
"timestamp": "2026-02-10T15:38:17.165Z",
"answer": 6908
},
{
"... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -3.49,
"mid": 1.84,
"hi": 7.55
} |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.