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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
2c372f | algebra_quadratic_discriminant_v1_153355830_131 | Let $c$ be the number of positive integers $n$ not exceeding 419 such that $\gcd(n, 30) = 1$. Compute $2^2 - 4(-2)(c)$. | 900 | graphs = [
Graph(
let={
"_n": Const(2),
"a": Const(-2),
"b": Const(2),
"c": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(419)), Eq(GCD(a=Var("n"), b=Const(30)), Const(1))))),
"result": Sub(P... | NT | null | COMPUTE | sympy | B1 | [
"C4"
] | 08d162 | algebra_quadratic_discriminant_v1 | null | 4 | 0 | [
"B1",
"C4"
] | 2 | 0.01 | 2026-02-08T02:54:02.248118Z | {
"verified": true,
"answer": 900,
"timestamp": "2026-02-08T02:54:02.257745Z"
} | 430157 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 155,
"completion_tokens": 1086
},
"timestamp": "2026-02-10T11:49:22.583Z",
"answer": 900
},
{
"id... | 1 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.06,
"hi": -0.46
} | ||
36ee2a | antilemma_k3_v1_2051736721_6159 | Let $n = 87665$. Compute the remainder when $16386 \cdot \sum_{d \mid n} \phi(d)$ is divided by 65333. | 2,019 | graphs = [
Graph(
let={
"_n": Const(87665),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Mod(value=Mul(Const(16386), Ref("x")), modulus=Const(65333)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0 | 2026-02-08T18:58:27.676265Z | {
"verified": true,
"answer": 2019,
"timestamp": "2026-02-08T18:58:27.676640Z"
} | ada7dc | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 83,
"completion_tokens": 1941
},
"timestamp": "2026-02-18T21:02:04.097Z",
"answer": 2019
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
1c3abf | comb_count_permutations_fixed_v1_1520064083_7576 | Let $n$ be the largest prime number such that $2 \leq n \leq 12$. Let $k = 7$. Compute the value of $\binom{n}{k} \cdot !(n - k)$, where $!m$ denotes the number of derangements of $m$ elements. | 2,970 | graphs = [
Graph(
let={
"_n": Const(2),
"n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Const(12)), IsPrime(Var("n"))))),
"k": Const(7),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub(left... | NT | COMB | COUNT | sympy | B3 | [
"MAX_PRIME_BELOW"
] | dc3ad3 | comb_count_permutations_fixed_v1 | null | 3 | 0 | [
"B3",
"MAX_PRIME_BELOW"
] | 2 | 0.022 | 2026-02-08T09:10:22.644856Z | {
"verified": true,
"answer": 2970,
"timestamp": "2026-02-08T09:10:22.667292Z"
} | 698d08 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 121,
"completion_tokens": 532
},
"timestamp": "2026-02-15T20:34:59.870Z",
"answer": null
},
{
"id": 11,... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -9.14,
"mid": -6.05,
"hi": -3.73
} | ||
8b8b30 | antilemma_k3_v1_153355830_2031 | Compute the sum of $\phi(d)$ over all positive divisors $d$ of 64948, where $\phi$ denotes Euler's totient function. | 64,948 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=64948), 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 | 2026-02-08T06:52:27.647731Z | {
"verified": true,
"answer": 64948,
"timestamp": "2026-02-08T06:52:27.648156Z"
} | f95249 | 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": 5328
},
"timestamp": "2026-02-13T05:24:46.634Z",
"answer": 64948
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
... | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
8b944b | nt_sum_over_divisible_v1_1125832087_594 | Let $n = 196$. Define $\text{upper}$ as the maximum value of $x \cdot y$ over all pairs of positive integers $(x, y)$ such that $x + y = 196$. Let $\text{result}$ be the sum of all positive integers $n$ such that $1 \leq n \leq \text{upper}$ and $n$ is divisible by $158$. Compute the remainder when $\text{result}$ is d... | 62,829 | graphs = [
Graph(
let={
"_n": Const(196),
"upper": 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 | SUM | sympy | B1 | [
"B1"
] | 5b950e | nt_sum_over_divisible_v1 | null | 5 | 0 | [
"B1"
] | 1 | 0.315 | 2026-02-08T03:09:44.723891Z | {
"verified": true,
"answer": 62829,
"timestamp": "2026-02-08T03:09:45.039089Z"
} | 43e910 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 214,
"completion_tokens": 1116
},
"timestamp": "2026-02-10T13:15:18.241Z",
"answer": 62829
},
{
"... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
75f203 | modular_min_modexp_v1_784195855_6684 | Let $n = 313$. Let $a = 13$. Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 625$. Define $b$ to be the minimum value of $x + y$ as $(x,y)$ ranges over $S$. Let $m$ be the largest prime number less than or equal to $n$. Find the smallest positive integer $x$ such that $1 \le x \le 1... | 76 | graphs = [
Graph(
let={
"_n": Const(313),
"a": Const(13),
"b": 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(625)))), expr=... | NT | null | EXTREMUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW",
"B3"
] | 78ed98 | modular_min_modexp_v1 | null | 6 | 0 | [
"B3",
"MAX_PRIME_BELOW"
] | 2 | 0.011 | 2026-02-08T08:47:06.695012Z | {
"verified": true,
"answer": 76,
"timestamp": "2026-02-08T08:47:06.706433Z"
} | d0174e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 168,
"completion_tokens": 4524
},
"timestamp": "2026-02-13T21:55:27.390Z",
"answer": 76
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"... | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
c43c43 | geo_visible_lattice_v1_809748730_879 | Let $n = 79$. Define a visible lattice point as an ordered pair $(x, y)$ of positive integers with $1 \leq x, y \leq n$ such that $\gcd(x, y) = 1$. Let $v$ be the number of visible lattice points. Compute the Bell number $B_m$, where $m = |v| \bmod 11$. | 203 | graphs = [
Graph(
let={
"n": Const(79),
"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 | 4 | 0 | null | null | 0.212 | 2026-02-08T11:47:35.546011Z | {
"verified": true,
"answer": 203,
"timestamp": "2026-02-08T11:47:35.758128Z"
} | 380f0f | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 194,
"completion_tokens": 7093
},
"timestamp": "2026-02-24T14:47:25.462Z",
"answer": 203
},
{
"id... | 1 | [] | {
"lo": 1.15,
"mid": 4.18,
"hi": 6.61
} | ||||
10f044 | modular_inverse_v1_1520064083_9064 | Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 13380964$. Let $s = x + y$ for each pair in $S$. Define $N$ to be the minimum value of $s$ over all such pairs.
Let $T$ be the set of all positive integers $n$ such that $1 \le n \le N$, $4$ divides $n$, and $\gcd(n, 15) = 1$. Let $U$... | 271 | graphs = [
Graph(
let={
"_m": Const(4),
"_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(13380964)))), expr=Sum(Var("x"), Var("y")))... | NT | null | EXTREMUM | sympy | B3 | [
"B3/C5"
] | cde3b3 | modular_inverse_v1 | null | 6 | 0 | [
"B3",
"C5"
] | 2 | 0.104 | 2026-02-08T10:32:00.244723Z | {
"verified": true,
"answer": 271,
"timestamp": "2026-02-08T10:32:00.348307Z"
} | 267195 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 206,
"completion_tokens": 1671
},
"timestamp": "2026-02-14T07:38:11.918Z",
"answer": 271
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C5",
"status": "ok_later"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
4e2c09 | nt_count_divisible_and_v1_1125832087_186 | Let $T$ be the set of all positive integers $t$ such that $7 \leq t \leq 35$ and $t = 2a + 5b$ for some positive integers $a,b$ with $1 \leq a \leq 5$ and $1 \leq b \leq 5$. Let $c = |T|$, the number of elements in $T$.
Consider the set of all ordered pairs $(x,y)$ of positive integers such that $xy = c$. For each suc... | 2,601 | graphs = [
Graph(
let={
"upper": Const(78030),
"d1": 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")), CountOverSet(set=SolutionsSet(var=Var("t")... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/B3"
] | 05313e | nt_count_divisible_and_v1 | null | 5 | 0 | [
"B3",
"LIN_FORM"
] | 2 | 5.245 | 2026-02-08T02:55:26.525524Z | {
"verified": true,
"answer": 2601,
"timestamp": "2026-02-08T02:55:31.770061Z"
} | 3f3c8b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 329,
"completion_tokens": 1209
},
"timestamp": "2026-02-10T12:49:19.299Z",
"answer": 2601
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
... | {
"lo": -5.55,
"mid": -3.06,
"hi": -0.44
} | ||
0ad390 | nt_min_phi_inverse_v1_1125832087_859 | Let $n$ be an integer. Define $\alpha$ to be the number of prime numbers $n$ such that $2 \leq n \leq 173$. Let $k = 8$. Define $\beta$ to be the smallest positive integer $n$ such that $1 \leq n \leq \alpha$ and $\phi(n) = k$. Compute $\beta$. | 15 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Const(173)), IsPrime(Var("n"))))),
"k": Const(8),
"result": MinOverSet(set=SolutionsSet(var=Var("n"), condition=A... | NT | null | EXTREMUM | sympy | MOBIUS_COPRIME | [
"COUNT_PRIMES"
] | 07c874 | nt_min_phi_inverse_v1 | null | 6 | 0 | [
"COUNT_PRIMES",
"MOBIUS_COPRIME"
] | 2 | 0.059 | 2026-02-08T03:20:44.726789Z | {
"verified": true,
"answer": 15,
"timestamp": "2026-02-08T03:20:44.786229Z"
} | 632d4d | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 192,
"completion_tokens": 1307
},
"timestamp": "2026-02-10T14:00:49.333Z",
"answer": 15
},
{
"id"... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.02,
"hi": 0.31
} | ||
0a5647 | alg_poly_orbit_hensel_v1_601307018_4359 | Let $N = (2a^3 + 5a) \bmod 169$ and $M = (2N^3 + 5N) \bmod 169$. Find the number of non-negative integers $a$ with $0 \le a \le 328704$ such that $M = a$ and $N \ne a$. | 3,890 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Mul(Const(2), Pow(Var("a"), Const(3))), Mul(Const(5), Var("a"))), modulus=Const(169)),
"p2": Mod(value=Sum(Mul(Const(2), Pow(Ref("p1"), Const(3))), Mul(Const(5), Ref("p1"))), modulus=Const(169)),
"result": CountOverSet(set=Solut... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_orbit_hensel_v1 | null | 7 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.033 | 2026-03-10T04:55:12.090492Z | {
"verified": true,
"answer": 3890,
"timestamp": "2026-03-10T04:55:12.123251Z"
} | b6854e | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 186,
"completion_tokens": 4288
},
"timestamp": "2026-03-29T11:58:53.501Z",
"answer": 2
},
{
"i... | 0 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 3.34,
"mid": 5.77,
"hi": 8.89
} | ||
a09731 | antilemma_sum_equals_v1_2051736721_3855 | Let $x$ be the number of ordered pairs $(i, j)$ of integers such that $1 \leq i \leq 38$, $1 \leq j \leq 38$, and $i + j = 38$. Compute $\sum_{n=1}^{|x|} \phi(n)$. | 432 | graphs = [
Graph(
let={
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(38)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(38)), right=IntegerRange(start=Const(1), end=Const(38))))),
"Q": ... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 4 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.013 | 2026-02-08T17:36:19.536992Z | {
"verified": true,
"answer": 432,
"timestamp": "2026-02-08T17:36:19.549704Z"
} | 49ea4a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 110,
"completion_tokens": 1456
},
"timestamp": "2026-02-18T04:29:45.621Z",
"answer": 432
},
{
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SU... | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||
8e322e | modular_sum_quadratic_residues_v1_784195855_4490 | Let $p$ be the largest prime number less than or equal to 242. Compute the value of $$\frac{p(p-1)}{\text{the number of positive integers } p \text{ for which there exists a positive integer } q > p \text{ such that } pq = 900 \text{ and } \gcd(p, q) = 1}.$$ | 14,460 | graphs = [
Graph(
let={
"_n": Const(242),
"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))), CountOverSet(set=SolutionsSet(var=Var("p")... | NT | null | SUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW",
"COPRIME_PAIRS"
] | 05d703 | modular_sum_quadratic_residues_v1 | null | 5 | 0 | [
"COPRIME_PAIRS",
"MAX_PRIME_BELOW"
] | 2 | 0.002 | 2026-02-08T07:08:29.993109Z | {
"verified": true,
"answer": 14460,
"timestamp": "2026-02-08T07:08:29.995370Z"
} | f93c31 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 124,
"completion_tokens": 1416
},
"timestamp": "2026-02-13T08:14:13.760Z",
"answer": 14460
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
29a1f0 | nt_count_with_divisor_count_v1_1918700295_235 | Let $d$ be the smallest divisor of $3757$ that is at least $2$. Let $N$ be the number of positive integers $n$ such that $1 \leq n \leq 65536$ and the number of positive divisors of $n$ is equal to $d$. Compute $N$. | 1 | graphs = [
Graph(
let={
"upper": Const(65536),
"div_count": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(3757))))),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | nt_count_with_divisor_count_v1 | null | 4 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 2.843 | 2026-02-08T03:06:33.167510Z | {
"verified": true,
"answer": 1,
"timestamp": "2026-02-08T03:06:36.010381Z"
} | 04d245 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 179,
"completion_tokens": 767
},
"timestamp": "2026-02-10T13:10:18.246Z",
"answer": 1
},
{
"id": ... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
}
] | {
"lo": -5.5,
"mid": -0.08,
"hi": 5.44
} | ||
288665 | nt_lcm_compute_v1_1915831931_1595 | Let $n$ be the maximum value of $xy$ over all pairs of positive integers $(x, y)$ such that $x + y = 80$. Let $a = \sum_{d \mid n} \phi(d)$, where $\phi$ denotes Euler's totient function. Let $b = 2300$. Compute $\mathrm{LCM}(a, b)$. | 36,800 | graphs = [
Graph(
let={
"_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")), Const(80)))), expr=Mul(Var("x"), Var("y")))),
"a": SumOverDivisor... | NT | null | COMPUTE | sympy | B1 | [
"B1/K3"
] | 759f54 | nt_lcm_compute_v1 | null | 4 | 0 | [
"B1",
"K3"
] | 2 | 0.003 | 2026-02-08T16:17:52.621148Z | {
"verified": true,
"answer": 36800,
"timestamp": "2026-02-08T16:17:52.623882Z"
} | 812c95 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 124,
"completion_tokens": 507
},
"timestamp": "2026-02-17T00:32:10.409Z",
"answer": 36800
},
{... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K3",
"status": "ok_later"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
d1a44e | alg_qf_psd_orbit_v1_601307018_3702 | Find the number of ordered triples $(a, b, c)$ of positive integers such that $1 \leq a \leq b \leq c \leq 64$ and $$44a^2 - 36ab + 44b^2 - 36bc - 36ac + 44c^2 = 50396.$$ | 5 | graphs = [
Graph(
let={
"_n": Const(44),
"result": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b"), Var("c")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(64)), Geq(Var("b"), Const(1)), Leq(Var("b"), MaxOverSet(set=MapOverSet(set=SolutionsSet(var=... | ALG | null | COUNT | sympy | MAX_DIVISOR | [
"B1"
] | 5b950e | alg_qf_psd_orbit_v1 | null | 6 | 0 | [
"B1",
"MAX_DIVISOR"
] | 2 | 2.515 | 2026-03-10T04:18:12.124259Z | {
"verified": true,
"answer": 5,
"timestamp": "2026-03-10T04:18:14.639440Z"
} | be330a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 183,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T09:44:05.713Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 3.34,
"mid": 5.77,
"hi": 8.89
} | ||
c3a185 | diophantine_product_count_v1_124444284_6303 | Let $k$ be the number of integers $t$ such that $14 \le t \le 435$ and there exist integers $a$ and $b$ with $1 \le a \le 66$, $1 \le b \le 98$, and $t = 2a + 3b + 9$. Let $u$ be the number of integers $n$ such that $1 \le n \le 529$ and $n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{5}$. Let $r$ be the number ... | 18 | graphs = [
Graph(
let={
"_n": Const(529),
"k": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=66)), Geq(left=Var... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM",
"L3C"
] | ecf77f | diophantine_product_count_v1 | null | 7 | 0 | [
"L3C",
"LIN_FORM"
] | 2 | 0.015 | 2026-02-08T08:16:59.756485Z | {
"verified": true,
"answer": 18,
"timestamp": "2026-02-08T08:16:59.771301Z"
} | a364eb | 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": 3779
},
"timestamp": "2026-02-13T16:34:33.660Z",
"answer": 18
},
{
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
6def7b | modular_sum_quadratic_residues_v1_1978505735_5813 | Let $p$ be the largest prime number such that $2 \leq p \leq 403$. Define $$
result = \frac{p(p-1)}{4}.
$$ Let $Q$ be the remainder when $84511 \cdot result$ is divided by $72861$. Compute $Q$. | 53,129 | graphs = [
Graph(
let={
"_n": Const(84511),
"p": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(403)), IsPrime(Var("n"))))),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), Const(4)),
"Q": Mod(value=M... | NT | null | SUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | modular_sum_quadratic_residues_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.001 | 2026-02-08T19:14:46.156335Z | {
"verified": true,
"answer": 53129,
"timestamp": "2026-02-08T19:14:46.157426Z"
} | 9b9c79 | 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": 1326
},
"timestamp": "2026-02-18T21:43:21.393Z",
"answer": 53129
},
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
3fffac | comb_count_surjections_v1_124444284_330 | Let $n$ be the number of ordered pairs $(i, j)$ of integers such that $1 \leq i \leq 8$, $1 \leq j \leq 8$, and $i + j = 8$. Let $k$ be the number of ordered pairs $(a, b)$ such that $1 \leq a \leq 2$ and $1 \leq b \leq 3$. Compute $k! \cdot S(n, k)$, where $S(n, k)$ denotes the Stirling number of the second kind. | 15,120 | graphs = [
Graph(
let={
"_n": Const(8),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref("_n")), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(8)), right=IntegerRange(start=Const(1), end=Const... | COMB | null | COUNT | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS",
"COUNT_CARTESIAN"
] | e4fc6a | comb_count_surjections_v1 | null | 5 | 0 | [
"COUNT_CARTESIAN",
"COUNT_SUM_EQUALS"
] | 2 | 0.011 | 2026-02-08T03:13:11.119606Z | {
"verified": true,
"answer": 15120,
"timestamp": "2026-02-08T03:13:11.130406Z"
} | f2f8bd | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 234,
"completion_tokens": 718
},
"timestamp": "2026-02-09T16:16:13.099Z",
"answer": 15120
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no... | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
f782cf | comb_catalan_compute_v1_784195855_7540 | Let $A$ be the set of all integers $t$ for which there exist integers $a$ and $b$ satisfying $1\le a\le 2$, $1\le b\le 7$, $27\le t\le 84$, and
$$t = 21a + 6b.$$
Let $n_2 = \binom{|A|}{0} - 1$.
Define
$$t = \sum_{k=\binom{3}{3}-1}^{n_2} (-1)^k \binom{n_2}{k}.$$
Let $n_1=5$ and define
$$c = \sum_{k=0}^{n_1} (-1)^k \bi... | 58,786 | graphs = [
Graph(
let={
"n2": Sub(Binom(n=CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=2)), Geq(left=Var(name='b'), right=... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/ZERO_BINOM_0/BINOMIAL_ALTERNATING",
"LIN_FORM/BINOMIAL_ALTERNATING",
"ZERO_BINOM_N"
] | fde7c0 | comb_catalan_compute_v1 | null | 7 | 2 | [
"BINOMIAL_ALTERNATING",
"LIN_FORM",
"ZERO_BINOM_0",
"ZERO_BINOM_N"
] | 4 | 0.007 | 2026-02-08T09:23:18.442172Z | {
"verified": true,
"answer": 58786,
"timestamp": "2026-02-08T09:23:18.449357Z"
} | d0a65c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 391,
"completion_tokens": 3432
},
"timestamp": "2026-02-24T11:11:50.641Z",
"answer": 58786
},
{
"... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7... | {
"lo": -3.84,
"mid": -1.67,
"hi": 1.32
} | ||
1d79f2 | nt_sum_divisors_mod_v1_238844314_998 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 129600$. Define $n$ to be the minimum value of $x + y$ as $(x, y)$ ranges over $S$. Let $\sigma$ be the sum of all positive divisors of $n$. Compute the remainder when $\sigma$ is divided by $10337$. | 2,418 | 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(129600)))), expr=Sum(Var("x"), Var("y")))),
"M": Const(10337... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_divisors_mod_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.007 | 2026-02-08T13:50:55.992684Z | {
"verified": true,
"answer": 2418,
"timestamp": "2026-02-08T13:50:55.999679Z"
} | 22a190 | 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": 1454
},
"timestamp": "2026-02-15T21:20:02.204Z",
"answer": 2418
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
8503cf | antilemma_sum_equals_v1_1978505735_7747 | Compute the number of ordered pairs $(i, j)$ of positive integers such that $1 \leq i \leq 75$, $1 \leq j \leq 76$, and $i + j = 76$. | 75 | graphs = [
Graph(
let={
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(76)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(75)), right=IntegerRange(start=Const(1), end=Const(76))))),
},
... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 2 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.004 | 2026-02-08T20:24:36.267848Z | {
"verified": true,
"answer": 75,
"timestamp": "2026-02-08T20:24:36.271816Z"
} | 5fb391 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 92,
"completion_tokens": 747
},
"timestamp": "2026-02-25T01:55:35.752Z",
"answer": 75
},
{
... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"stat... | {
"lo": -10,
"mid": -7.4,
"hi": -4.8
} | ||
a1f509 | comb_count_partitions_v1_784195855_9745 | Let $n = 45$. Let $p(n)$ denote the number of integer partitions of $n$. Let $d$ be the smallest divisor of $2431$ that is at least 2. Compute $B_{|p(n)| \bmod d}$, where $B_k$ denotes the $k$th Bell number. | 1 | graphs = [
Graph(
let={
"_n": Const(2),
"n": Const(45),
"result": Partition(arg=Ref(name='n')),
"Q": Bell(Mod(value=Abs(arg=Ref(name='result')), modulus=MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"),... | NT | COMB | COUNT | sympy | LIN_FORM | [
"MIN_PRIME_FACTOR"
] | 58d7e9 | comb_count_partitions_v1 | bell_mod | 4 | 0 | [
"LIN_FORM",
"MIN_PRIME_FACTOR"
] | 2 | 0.057 | 2026-02-08T17:01:34.140741Z | {
"verified": true,
"answer": 1,
"timestamp": "2026-02-08T17:01:34.197870Z"
} | 925380 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 116,
"completion_tokens": 922
},
"timestamp": "2026-02-17T21:12:08.803Z",
"answer": 1
},
{
... | 1 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
606b79 | nt_count_gcd_equals_v1_865884756_121 | Let $n = 6765$. Let $S$ be the set of all positive integers $d_1$ such that $d_1 \leq n$ and $d_1$ divides $45873465$. Define $\text{upper}$ to be the maximum element of $S$. Let $k = 91$ and $d = 1$. Let $T$ be the set of all positive integers $n'$ such that $1 \leq n' \leq \text{upper}$ and $\gcd(n', k) = d$. Compute... | 5,353 | graphs = [
Graph(
let={
"_n": Const(6765),
"upper": MaxOverSet(set=SolutionsSet(var=Var("d1"), condition=And(Geq(Var("d1"), Const(1)), Leq(Var("d1"), Ref("_n")), Divides(divisor=Var("d1"), dividend=Const(45873465))))),
"k": Const(91),
"d": Const(1),
... | NT | null | COUNT | sympy | MAX_DIVISOR | [
"MAX_DIVISOR"
] | 51757e | nt_count_gcd_equals_v1 | null | 4 | 0 | [
"MAX_DIVISOR"
] | 1 | 5.11 | 2026-02-08T15:11:20.883894Z | {
"verified": true,
"answer": 5353,
"timestamp": "2026-02-08T15:11:25.993776Z"
} | 25cb5c | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 237,
"completion_tokens": 2329
},
"timestamp": "2026-02-11T11:04:50.248Z",
"answer": 5353
},
{
"... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V5",... | {
"lo": -7.08,
"mid": 0.22,
"hi": 7.52
} | ||
9838e7 | sequence_count_fib_divisible_v1_458359167_3621 | Compute the number of positive integers $n$ not exceeding 451 for which the $n$-th Fibonacci number is divisible by 3. | 112 | graphs = [
Graph(
let={
"upper": Const(451),
"d": Const(3),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Divides(divisor=Ref("d"), dividend=Fibonacci(arg=Var(name='n')))))),
},
go... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | sequence_count_fib_divisible_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.102 | 2026-02-08T08:28:06.122737Z | {
"verified": true,
"answer": 112,
"timestamp": "2026-02-08T08:28:06.224489Z"
} | a8ee9c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 75,
"completion_tokens": 1614
},
"timestamp": "2026-02-14T11:12:35.354Z",
"answer": 112
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
e3032d | nt_count_divisible_v1_1116507919_36 | Let $S$ be the set of all positive integers $n \leq 31873$ that are divisible by 27. Let $P$ be the set of all ordered pairs $(x,y)$ of positive integers such that $x + y = 56$, and let $M$ be the maximum value of $xy$ over all such pairs. Let $N = 65849$. Compute the remainder when $M - |S|$ is divided by $N$. | 65,453 | graphs = [
Graph(
let={
"_n": Const(65849),
"upper": Const(31873),
"divisor": Const(27),
"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")), C... | NT | null | COUNT | sympy | B1 | [
"B1"
] | d2b6e1 | nt_count_divisible_v1 | negation_mod | 3 | 0 | [
"B1"
] | 1 | 0.927 | 2026-02-08T02:23:59.588977Z | {
"verified": true,
"answer": 65453,
"timestamp": "2026-02-08T02:24:00.516403Z"
} | debe77 | 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": 632
},
"timestamp": "2026-02-08T18:31:52.831Z",
"answer": 65453
},
{
"i... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.53,
"mid": -3.77,
"hi": -1.89
} | ||
445131 | comb_binomial_compute_v1_601307018_6577 | Let $k$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \leq a \leq b \leq 35$ such that
$$
-4ab + 2a^2 + 2b^2 = \min\left\{ 600a_1 b_1^2 + 128a_1^3 + 480a_1^2 b_1 + 250b_1^3 \mid 1 \leq a_1, b_1 \leq 26 \right\}.
$$
Let $R = \binom{16}{k}$ and $Q = R$. Compute $Q$. | 12,870 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(2),
"n": Const(16),
"k": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(35)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(3... | COMB | null | COMPUTE | sympy | POLY3_MIN | [
"POLY3_MIN/QF_PSD_ORBIT"
] | 709050 | comb_binomial_compute_v1 | null | 6 | 0 | [
"POLY3_MIN",
"QF_PSD_ORBIT"
] | 2 | 0.011 | 2026-03-10T07:12:05.683475Z | {
"verified": true,
"answer": 12870,
"timestamp": "2026-03-10T07:12:05.694176Z"
} | 98dee2 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 256,
"completion_tokens": 1309
},
"timestamp": "2026-04-19T04:45:11.898Z",
"answer": 12870
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "POLY3_MIN",
"status": "ok"
},
{
"lemma": "QF_PSD_ORBIT",
"status": "ok_later"
},
{
"lemma": "V8",
"st... | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
9df64a | modular_count_residue_v1_717093673_503 | Let $m$ be the number of positive integers $n \leq 295$ that are divisible by $5$ and satisfy $\gcd(n, 6) = 1$. Let $r = \sum_{k=1}^3 k$. Determine the number of positive integers $n_1 \leq 53824$ such that $n_1 \equiv r \pmod{m}$. | 2,691 | graphs = [
Graph(
let={
"_n": Const(295),
"upper": Const(53824),
"m": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_n")), Divides(divisor=Const(5), dividend=Var("n")), Eq(GCD(a=Var("n"), b=Const(6)), Const(1))))),
... | NT | null | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC",
"C5"
] | 9d8cd4 | modular_count_residue_v1 | null | 4 | 0 | [
"C5",
"SUM_ARITHMETIC"
] | 2 | 2.268 | 2026-02-08T15:29:27.735757Z | {
"verified": true,
"answer": 2691,
"timestamp": "2026-02-08T15:29:30.004245Z"
} | 3c27d6 | 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": 964
},
"timestamp": "2026-02-16T06:57:36.120Z",
"answer": 2691
},
{
... | 1 | [
{
"lemma": "C5",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": ... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
263daa | algebra_poly_eval_v1_458359167_649 | Let $y = 21$. Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 6$, $\gcd(p,q) = 1$, and $p < q$. Let $k$ be the number of elements in $S$. Compute the value of $y^k - 6y + 10$. | 325 | graphs = [
Graph(
let={
"_n": Const(10),
"y": Const(21),
"result": Sum(Pow(Ref("y"), 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(val... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | algebra_poly_eval_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.002 | 2026-02-08T03:28:40.179568Z | {
"verified": true,
"answer": 325,
"timestamp": "2026-02-08T03:28:40.181332Z"
} | 83df04 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 194,
"completion_tokens": 552
},
"timestamp": "2026-02-10T14:39:52.926Z",
"answer": 325
},
{
"id"... | 2 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -9.14,
"mid": -6.05,
"hi": -3.74
} | ||
587b22 | sequence_fibonacci_compute_v1_655260480_635 | Let $n$ be the smallest divisor of $339082123$ that is at least $2$. Compute the $n$-th Fibonacci number, denoted $F_n$. Let $P$ be the maximum value of $xy$ over all ordered pairs $(x, y)$ of positive integers such that $x + y = 156$. Find the remainder when $F_n^2 + 23F_n + P$ is divided by $91255$. | 46,314 | graphs = [
Graph(
let={
"_n": Const(156),
"n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(339082123))))),
"result": Fibonacci(arg=Ref(name='n')),
"Q": Mod(value=Sum(Pow(Ref("result"... | NT | null | COMPUTE | sympy | B1 | [
"B1",
"MIN_PRIME_FACTOR"
] | 2cc618 | sequence_fibonacci_compute_v1 | quadratic_mod | 4 | 0 | [
"B1",
"MIN_PRIME_FACTOR"
] | 2 | 0.004 | 2026-02-08T15:30:16.815104Z | {
"verified": true,
"answer": 46314,
"timestamp": "2026-02-08T15:30:16.819414Z"
} | e8df2d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 140,
"completion_tokens": 1364
},
"timestamp": "2026-02-16T07:09:45.873Z",
"answer": 46314
},
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
81194f | diophantine_sum_product_min_v1_168721529_1108 | Let $N$ be the number of ordered pairs $(i, j)$ with $1 \leq i \leq 3$ and $1 \leq j \leq 30$ such that $\gcd(i, j) = 1$. Let $S = 22$ and $P = 40$. Let $M$ be the number of positive integers $n$ such that $1 \leq n \leq N$ and $n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{3}$. Determine the value of the small... | 2 | graphs = [
Graph(
let={
"_n": 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=IntegerRange(start=Const(1), end=Const(30))))),
"S... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"COUNT_COPRIME_GRID/L3C"
] | 565989 | diophantine_sum_product_min_v1 | null | 6 | 0 | [
"COUNT_COPRIME_GRID",
"L3C",
"LIN_FORM"
] | 3 | 0.128 | 2026-02-08T13:28:09.877727Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-02-08T13:28:10.005285Z"
} | 9f5a69 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 272,
"completion_tokens": 1334
},
"timestamp": "2026-02-09T13:47:21.207Z",
"answer": 2
},
{
"id":... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "L3C",
"status": "ok_later"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V3... | {
"lo": -8.27,
"mid": -5.03,
"hi": -1.92
} | ||
3d0d12 | comb_factorial_compute_v1_1520064083_9232 | Let $n$ be the number of integers $j$ with $0 \leq j \leq 32771$ such that $\binom{32771}{j}$ is odd. Define $r = n!$. Compute the remainder when $58629 \cdot r$ is divided by $74906$. | 37,732 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(32771)), Eq(Mod(value=Binom(n=Const(32771), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')),
"result": Factorial(Ref("n")),
... | ALG | COMB | COMPUTE | sympy | V8 | [
"V8"
] | 86348e | comb_factorial_compute_v1 | null | 5 | 0 | [
"V8"
] | 1 | 0.001 | 2026-02-08T10:38:00.710707Z | {
"verified": true,
"answer": 37732,
"timestamp": "2026-02-08T10:38:00.711798Z"
} | 3ca8b4 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 176,
"completion_tokens": 1826
},
"timestamp": "2026-02-24T12:09:31.503Z",
"answer": 37732
},
{
"... | 1 | [
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
}
] | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
7a6357 | comb_sum_binomial_row_v1_1520064083_3989 | Let $n = 15$. Consider the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 216$, $\gcd(p, q) = 1$, and $p < q$. Let $r$ be the number of elements in this set. Compute the remainder when $44121 \cdot r^n$ is divided by $62131$. | 30,689 | graphs = [
Graph(
let={
"_n": Const(44121),
"n": Const(15),
"result": Pow(CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=216)), E... | NT | null | SUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_sum_binomial_row_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.001 | 2026-02-08T06:00:23.851562Z | {
"verified": true,
"answer": 30689,
"timestamp": "2026-02-08T06:00:23.852564Z"
} | fbba43 | 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": 1878
},
"timestamp": "2026-02-12T18:04:25.824Z",
"answer": 30689
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
267f63 | alg_poly3_count_v1_1419126231_104 | Find the number of ordered triples $(a, b, c)$ of positive integers with $1 \le a, b, c \le 33$ such that $$
189b^3 - 28c^3 - 519ab^2 - 144b^2c - 88a^3 - 129a^2c - 69ac^2 + 483a^2b + 216abc + 108bc^2 = -970299.
$$ | 22 | graphs = [
Graph(
let={
"result": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b"), Var("c")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(33)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(33)), Geq(Var("c"), Const(1)), Leq(Var("c"), Const(33)), Eq(Sum(Mul(Co... | ALG | null | COUNT | sympy | LIN_FORM | [
"QF_PSD_COUNT_LEQ",
"QF_PSD_DISTINCT"
] | f25d80 | alg_poly3_count_v1 | null | 3 | null | [
"LIN_FORM",
"QF_PSD_COUNT_LEQ",
"QF_PSD_DISTINCT"
] | 3 | 14.044 | 2026-02-25T09:38:06.407598Z | {
"verified": true,
"answer": 22,
"timestamp": "2026-02-25T09:38:20.451753Z"
} | 02e595 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 210,
"completion_tokens": 32768
},
"timestamp": "2026-03-30T07:03:11.369Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
},
{
"lemma": "QF_PSD_DISTINCT",
"status": "ok"
}
] | {
"lo": 3.8,
"mid": 6.33,
"hi": 9.49
} | ||
b14179 | sequence_fibonacci_compute_v1_784195855_7728 | Let $ A $ be the set of all positive integers $ n $ such that $ 1 \leq n \leq 83 $ and $ \gcd(n, 12) = 1 $. Let $ k $ be the number of elements in $ A $. Let $ B $ be the set of all integers $ n $ such that $ 2 \leq n \leq k $ and $ n $ is prime. Let $ p $ be the maximum element of $ B $. Compute the $ p $-th Fibonacci... | 28,657 | graphs = [
Graph(
let={
"_n": Const(2),
"n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(83)), Eq(GCD(a=Var("n"), b=Const(12)), C... | NT | null | COMPUTE | sympy | C4 | [
"C4/MAX_PRIME_BELOW"
] | 757853 | sequence_fibonacci_compute_v1 | null | 5 | 0 | [
"C4",
"MAX_PRIME_BELOW"
] | 2 | 0.002 | 2026-02-08T09:28:19.919515Z | {
"verified": true,
"answer": 28657,
"timestamp": "2026-02-08T09:28:19.921126Z"
} | badae6 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 200,
"completion_tokens": 779
},
"timestamp": "2026-02-14T04:23:11.330Z",
"answer": 28657
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
... | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
48053c | nt_sum_gcd_range_mod_v1_1918700295_497 | Let $k$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 44100$. Let $S = \sum_{n=1}^{1087} \gcd(n, k)$. Find the remainder when $S$ is divided by $10111$. | 1,791 | graphs = [
Graph(
let={
"N": Const(1087),
"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(44100)))), expr=Sum(Var("x"), Var("y")))),... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_gcd_range_mod_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.117 | 2026-02-08T03:17:26.643166Z | {
"verified": true,
"answer": 1791,
"timestamp": "2026-02-08T03:17:26.760200Z"
} | f15e93 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 180,
"completion_tokens": 7648
},
"timestamp": "2026-02-10T13:45:19.764Z",
"answer": 1791
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
3e0cd0 | modular_count_residue_v1_1978505735_4425 | Let $m$ be the maximum value of $xy$ over all pairs of positive integers $(x, y)$ such that $x + y = 10$. Let $r = 1$. Let $N$ be the number of positive integers $n$ at most 70756 such that $n \equiv r \pmod{m}$. Compute the remainder when $31106 \cdot N$ is divided by 62083. | 27,392 | graphs = [
Graph(
let={
"_n": Const(62083),
"upper": Const(70756),
"m": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Const(10)))... | NT | null | COUNT | sympy | B1 | [
"B1"
] | 5b950e | modular_count_residue_v1 | null | 4 | 0 | [
"B1"
] | 1 | 4.029 | 2026-02-08T18:14:23.896364Z | {
"verified": true,
"answer": 27392,
"timestamp": "2026-02-08T18:14:27.925209Z"
} | 32f2ae | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 135,
"completion_tokens": 1508
},
"timestamp": "2026-02-18T15:35:06.192Z",
"answer": 27392
},
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
231003 | alg_qf_psd_orbit_v1_1218484723_5393 | Let $m = \min\{ x + y : x, y > 0,\ xy = 12321 \}$. Find the number of ordered pairs $(a, b)$ of positive integers with $1 \leq a \leq b \leq m$ such that $26a^2 - 20ab + 26b^2 = 1095200$. | 5 | graphs = [
Graph(
let={
"_n": Const(2),
"result": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(222)), Geq(Var("b"), Const(1)), Leq(Var("b"), MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elem... | ALG | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | alg_qf_psd_orbit_v1 | null | 5 | 0 | [
"B3"
] | 1 | 3.037 | 2026-02-25T06:57:44.515548Z | {
"verified": true,
"answer": 5,
"timestamp": "2026-02-25T06:57:47.552664Z"
} | f9029d | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 190,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T20:54:50.075Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 1.53,
"mid": 4.7,
"hi": 7.23
} | ||
db5673 | comb_factorial_compute_v1_458359167_4519 | Let $m = 321$. Define $D$ to be the set of all positive divisors of $321$. Compute $s = \sum_{d \in D} \phi(d)$, where $\phi$ denotes Euler's totient function. Now define $E$ to be the set of all positive divisors of $s$, and compute $t = \sum_{d \in E} \phi(d)$. Let $j$ be a nonnegative integer such that $0 \leq j \le... | 40,320 | graphs = [
Graph(
let={
"_m": Const(321),
"_n": Const(2),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Ref("_m")), Eq(Mod(value=Binom(n=SumOverDivisors(n=SumOverDivisors(n=Const(value=321), var='d', expr=EulerPhi(n=... | NT | null | COMPUTE | sympy | K3 | [
"K3/K3/V8"
] | 82cd0a | comb_factorial_compute_v1 | null | 6 | 0 | [
"K3",
"V8"
] | 2 | 0.003 | 2026-02-08T11:49:51.374401Z | {
"verified": true,
"answer": 40320,
"timestamp": "2026-02-08T11:49:51.377887Z"
} | 48789b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 192,
"completion_tokens": 1283
},
"timestamp": "2026-02-14T20:06:59.444Z",
"answer": 40320
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status":... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
87dd2d | modular_count_residue_v1_458359167_5425 | Let $T$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 4900$. Define $s$ to be the minimum value of $x + y$ as $(x, y)$ ranges over $T$. Let $A$ be the set of all positive integers $n$ such that $1 \leq n \leq s$ and $n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{7}$. Define $m$ t... | 2,977 | 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(4900)))), expr=Sum(Var("x"), Var("y")))),
"upper": Const(59... | NT | null | COUNT | sympy | B3 | [
"B3/L3C"
] | 345f3b | modular_count_residue_v1 | null | 7 | 0 | [
"B3",
"L3C"
] | 2 | 2.231 | 2026-02-08T12:28:47.940571Z | {
"verified": true,
"answer": 2977,
"timestamp": "2026-02-08T12:28:50.171314Z"
} | 327746 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 198,
"completion_tokens": 1288
},
"timestamp": "2026-02-15T01:57:33.966Z",
"answer": 2977
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok_later"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
6c6961 | sequence_lucas_compute_v1_1248542787_582 | Let $ S $ be the set of all positive integers $ n $ such that $ 1 \leq n \leq 20 $ and $ n $ is divisible by $ 20 $. Define $ N $ as the sum of all elements in $ S $. Let $ L_N $ denote the $ N $-th Lucas number, where the Lucas sequence is defined by $ L_1 = 1 $, $ L_2 = 3 $, and $ L_m = L_{m-1} + L_{m-2} $ for $ m \g... | 36,289 | graphs = [
Graph(
let={
"_n": Const(20),
"n": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_n")), Eq(Mod(value=Var("n"), modulus=Const(20)), Const(0))))),
"result": Lucas(arg=Ref(name='n')),
"_c": Const(43... | NT | null | COMPUTE | sympy | SUM_DIVISIBLE | [
"SUM_DIVISIBLE"
] | 02dbe3 | sequence_lucas_compute_v1 | null | 3 | 0 | [
"SUM_DIVISIBLE"
] | 1 | 0.001 | 2026-02-08T03:14:34.159160Z | {
"verified": true,
"answer": 36289,
"timestamp": "2026-02-08T03:14:34.160243Z"
} | 25d5dc | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 256,
"completion_tokens": 1980
},
"timestamp": "2026-02-09T05:47:21.990Z",
"answer": 36289
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "SUM_DIVISIBLE",
"status": "ok"
},
{
"lemma": "V5",
"status": "no... | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
c57e5a | geo_count_lattice_rect_v1_1915831931_3989 | Compute the number of lattice points $(x, y)$ such that $0 \leq x \leq 222$ and $0 \leq y \leq 230$. | 51,513 | graphs = [
Graph(
let={
"a": Const(222),
"b": Const(230),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 2 | 0 | null | null | 0.001 | 2026-02-08T18:02:23.608538Z | {
"verified": true,
"answer": 51513,
"timestamp": "2026-02-08T18:02:23.609913Z"
} | fb6196 | 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": 512
},
"timestamp": "2026-02-18T12:02:01.297Z",
"answer": 51513
},
{
... | 1 | [] | {
"lo": -5.64,
"mid": -3.17,
"hi": -0.81
} | ||||
76f83b | comb_bell_compute_v1_153355830_2207 | Let $n$ be the number of integers $t$ such that $6 \leq t \leq 16$ and there exist positive integers $a \in [1,3]$, $b \in [1,3]$ with $t = 3a + 2b + 1$. Compute the Bell number $B_n$, where $B_n$ denotes the number of partitions of a set of size $n$. | 21,147 | 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... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_bell_compute_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T06:59:07.715664Z | {
"verified": true,
"answer": 21147,
"timestamp": "2026-02-08T06:59:07.717100Z"
} | 98ca09 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 202,
"completion_tokens": 1051
},
"timestamp": "2026-02-24T07:24:35.706Z",
"answer": 21147
},
{
"... | 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": "no"
},
{
"lemma": "LIN_F... | {
"lo": -3.84,
"mid": -1.67,
"hi": 1.32
} | ||
b596e9 | diophantine_fbi2_count_v1_1520064083_2912 | Let $t$ be an integer satisfying $18 \le t \le 404$. Let $n$ be the number of such $t$ for which there exist positive integers $a \le 14$ and $b \le 33$ such that $t = 10a + 8b$. Let $k = 480$ and $m = 185$. Determine the number of positive integers $d$ such that $3 \le d \le n$, $d$ divides $k$, and $6 \le \frac{k}{d}... | 17 | graphs = [
Graph(
let={
"_m": Const(185),
"_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=14)), Geq(left=Va... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/COPRIME_PAIRS"
] | dfc39b | diophantine_fbi2_count_v1 | null | 6 | 0 | [
"COPRIME_PAIRS",
"LIN_FORM"
] | 2 | 0.011 | 2026-02-08T05:18:30.819901Z | {
"verified": true,
"answer": 17,
"timestamp": "2026-02-08T05:18:30.830707Z"
} | e5e866 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 167,
"completion_tokens": 4365
},
"timestamp": "2026-02-12T07:06:44.577Z",
"answer": 17
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok_later"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
9f6e40 | geo_count_lattice_rect_v1_458359167_4535 | Let $a = 233$ and $b = 197$. Let $R$ be the number of lattice points $(x, y)$ such that $0 \leq x \leq a$ and $0 \leq y \leq b$. Let $m = |R| + 2$. The Fibonacci sequence is defined by $F_1 = 1$, $F_2 = 1$, and $F_k = F_{k-1} + F_{k-2}$ for $k \geq 3$. Let $k$ be the smallest positive integer such that $F_k$ is divisib... | 69,504 | graphs = [
Graph(
let={
"a": Const(233),
"b": Const(197),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"Q": FibonacciEntryPoint(modulus=Sum(Abs(arg=Ref(name='result')), Const(value=2))),
},
goal=Ref("Q"),
)
] | GEOM | NT | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.003 | 2026-02-08T11:51:12.108769Z | {
"verified": true,
"answer": 69504,
"timestamp": "2026-02-08T11:51:12.111792Z"
} | c52963 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 252,
"completion_tokens": 32768
},
"timestamp": "2026-02-24T14:59:52.862Z",
"answer": null
},
{
... | 1 | [] | {
"lo": 3.25,
"mid": 5.68,
"hi": 8.81
} | ||||
51e562 | geo_count_lattice_triangle_v1_458359167_974 | Let the area of a triangle with vertices at $ (144, 128) $, $ (27, 0) $, and $ (0, 90) $ be denoted by $ A $. Let $ B $ be the number of lattice points on the boundary of this triangle. Given that $ 2A = |144 \cdot 128 + 27 \cdot (-90)| $ and $ B = \gcd(144, 90) + \gcd(|27 - 144|, |128 - 90|) + \gcd(|0 - 27|, |0 - 128|... | 16,475 | graphs = [
Graph(
let={
"area_2x": Abs(arg=Sum(Mul(Const(value=144), Const(value=128)), Mul(Const(value=27), Sub(left=Const(value=0), right=Const(value=90))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=144)), b=Abs(arg=Const(value=90))), GCD(a=Abs(arg=Sub(left=Const(value=27), right... | ALG | NT | COUNT | sympy | [] | geo_count_lattice_triangle_v1 | null | 6 | 0 | null | null | 0.004 | 2026-02-08T04:12:45.376561Z | {
"verified": true,
"answer": 16475,
"timestamp": "2026-02-08T04:12:45.380215Z"
} | 5ae873 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 293,
"completion_tokens": 1676
},
"timestamp": "2026-02-10T15:52:44.367Z",
"answer": 16475
},
{
... | 1 | [] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||||
8222a1 | modular_min_modexp_v1_349078426_969 | Let $a = 3$ and $b = 755$. Let $m$ be the largest prime number less than or equal to $969$.
Let $T$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 25921$. Define $s_{\min}$ to be the minimum value of $x + y$ over all such pairs.
Determine the smallest positive integer $x$ such that $1 ... | 309 | graphs = [
Graph(
let={
"a": Const(3),
"b": Const(755),
"m": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(969)), IsPrime(Var("n"))))),
"upper": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(element... | NT | null | EXTREMUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW",
"B3"
] | 78ed98 | modular_min_modexp_v1 | null | 7 | 0 | [
"B3",
"MAX_PRIME_BELOW"
] | 2 | 0.025 | 2026-02-08T13:21:16.476439Z | {
"verified": true,
"answer": 309,
"timestamp": "2026-02-08T13:21:16.501579Z"
} | 6ab6b4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 165,
"completion_tokens": 8091
},
"timestamp": "2026-02-15T13:31:48.593Z",
"answer": 309
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
e91b04 | geo_count_lattice_triangle_v1_1520064083_9329 | Let $A$ be twice the area of the triangle with vertices at $(121, 23)$, $(55, 128)$, and $(0, 0)$. Let $B$ be the sum of the greatest common divisors of the absolute differences in coordinates along each side of the triangle, specifically:
- $\gcd(|121|, |23|)$,
- $\gcd(|55 - 121|, |128 - 23|)$,
- $\gcd(|0 - 55|, |0 -... | 7,110 | graphs = [
Graph(
let={
"_n": Const(121),
"area_2x": Abs(arg=Sum(Mul(Const(value=121), MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var(name='x'), Var(name='y')]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(left=Mul(Var(name='x'),... | ALG | NT | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | geo_count_lattice_triangle_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.008 | 2026-02-08T10:40:57.388962Z | {
"verified": true,
"answer": 7110,
"timestamp": "2026-02-08T10:40:57.397116Z"
} | c22e17 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 203,
"completion_tokens": 449
},
"timestamp": "2026-02-15T21:01:55.416Z",
"answer": 3512
},
{
"id": 11,... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
de633a | nt_gcd_compute_v1_677425708_4142 | Let $N$ be the number of integers $n$ with $1\le n\le 436$ such that $2$ divides $n$ and $\gcd(n,35)=1$. Let $d$ be the smallest integer greater than or equal to $2$ that divides $N$.
Let $g=\gcd(543411,1026443)$.
Consider all ordered pairs $(x,y)$ of positive integers such that $xy=1587600$. Let $T$ be the minimum v... | 97,526 | graphs = [
Graph(
let={
"_c": Const(99255),
"_m": Const(10),
"_n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Va... | NT | null | COMPUTE | sympy | C5 | [
"C5/MIN_PRIME_FACTOR/B3"
] | a5f335 | nt_gcd_compute_v1 | quadratic_mod | 6 | 0 | [
"B3",
"C5",
"MIN_PRIME_FACTOR"
] | 3 | 0.003 | 2026-02-08T06:27:45.415789Z | {
"verified": true,
"answer": 97526,
"timestamp": "2026-02-08T06:27:45.419019Z"
} | ab20d6 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 204,
"completion_tokens": 2621
},
"timestamp": "2026-02-13T00:26:18.504Z",
"answer": 97526
},
... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "C5",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok_later"
},
{
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
26e133 | modular_sum_quadratic_residues_v1_124444284_8451 | Let $p$ be the number of integers $t$ such that $5 \leq t \leq 239$ and there exist integers $a$ and $b$ with $1 \leq a \leq 17$, $1 \leq b \leq 94$, and $t = 3a + 2b$. Define $\text{result} = \frac{p(p-1)}{4}$. Let $Q$ be the remainder when $95281 \cdot \text{result}$ is divided by $51869$. Compute $Q$. | 31,378 | graphs = [
Graph(
let={
"_n": Const(4),
"p": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=17)), Geq(left=Var(n... | NT | null | SUM | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | modular_sum_quadratic_residues_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T09:42:49.209136Z | {
"verified": true,
"answer": 31378,
"timestamp": "2026-02-08T09:42:49.210643Z"
} | 83c288 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 160,
"completion_tokens": 4838
},
"timestamp": "2026-02-14T05:47:54.824Z",
"answer": 31378
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
585ccf | nt_count_divisible_and_v1_153355830_1700 | Let $N$ be the number of positive integers $n$ such that $1 \leq n \leq 32808$, $n \equiv \sum_{k=0}^{7} (-1)^k \binom{7}{k} \pmod{6}$, and $n \equiv 0 \pmod{8}$. Compute the value of $N$. | 1,367 | graphs = [
Graph(
let={
"upper": Const(32808),
"d1": Const(6),
"d2": Const(8),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(value=Var("n"), modulus=Ref("d1")), Summation(var="k... | COMB | null | COUNT | sympy | L3C | [
"BINOMIAL_ALTERNATING"
] | c21569 | nt_count_divisible_and_v1 | null | 5 | 0 | [
"BINOMIAL_ALTERNATING",
"L3C"
] | 2 | 2.369 | 2026-02-08T06:33:56.369148Z | {
"verified": true,
"answer": 1367,
"timestamp": "2026-02-08T06:33:58.738183Z"
} | 392f50 | 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": 827
},
"timestamp": "2026-02-24T06:31:37.903Z",
"answer": 1367
},
{
"id... | 2 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -9.23,
"mid": -6.18,
"hi": -4.06
} | ||
4012c0 | diophantine_fbi2_min_v1_655260480_950 | Let $d$ be an integer such that $7 \leq d \leq 106$, $d$ divides $96$, and $\frac{96}{d} \geq 5$. Let $r$ be the smallest such $d$. Compute $r + \left(2^{r \bmod 16}\right) \bmod 70860$. | 264 | graphs = [
Graph(
let={
"_n": Const(7),
"k": Const(96),
"upper": Const(106),
"result": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Leq(Var("d"), Ref("upper")), Divides(divisor=Var("d"), dividend=Ref("k")), Geq(Div(Ref("k")... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | diophantine_fbi2_min_v1 | null | 3 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.012 | 2026-02-08T15:46:58.394347Z | {
"verified": true,
"answer": 264,
"timestamp": "2026-02-08T15:46:58.406539Z"
} | 132313 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 139,
"completion_tokens": 756
},
"timestamp": "2026-02-16T06:19:30.736Z",
"answer": 264
},
{
"id": 11,
... | 2 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
... | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
150c8d | antilemma_cartesian_v1_1125832087_130 | Let $N=5$. Let $K$ be the number of ordered triples $(x_1,x_2,x_3)$ of positive integers such that each of $x_1,x_2,x_3$ is odd and
$$x_1+x_2+x_3=N.$$
Let
$$L=\binom{K}{3}.$$
Let $X$ be the number of ordered pairs $(i,j)$ of integers with $1\le i\le35$ and $1\le j\le35$. Define
$$Q=\sum_{n=L}^{|X|} d(n),$$
where $d(n... | 8,915 | graphs = [
Graph(
let={
"_n": Const(5),
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(35)), right=IntegerRange(start=Const(1), end=Const(35)))),
"Q": Summation(var="n", start=Binom(n=CountOverSet(set=SolutionsSet(var=Tuple(elements=[Va... | COMB | GEOM | COMPUTE | sympy | COMB1 | [
"COMB1/ONE_BINOM_N",
"COUNT_CARTESIAN"
] | ea3b29 | antilemma_cartesian_v1 | sum_divisor_count | 6 | 0 | [
"COMB1",
"COUNT_CARTESIAN",
"ONE_BINOM_N"
] | 3 | 0.001 | 2026-02-08T02:52:42.132442Z | {
"verified": true,
"answer": 8915,
"timestamp": "2026-02-08T02:52:42.133786Z"
} | 7629f2 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 261,
"completion_tokens": 2726
},
"timestamp": "2026-02-10T11:47:02.341Z",
"answer": 8915
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "ONE_BINOM_N",
"... | {
"lo": -0.82,
"mid": 1.02,
"hi": 2.61
} | ||
2a4e16 | antilemma_sum_equals_v1_124444284_8174 | Let $x$ be the number of ordered pairs $(i, j)$ of positive integers such that $i + j = 82$, $1 \le i \le 81$, and $1 \le j \le 82$. Compute the sum $\sum_{n=1}^{|x|} \tau(n)$, where $\tau(n)$ denotes the number of positive divisors of $n$. | 373 | graphs = [
Graph(
let={
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(82)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(81)), right=IntegerRange(start=Const(1), end=Const(82))))),
"Q": ... | COMB | GEOM | COMPUTE | sympy | LIN_FORM | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 4 | 0 | [
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 2 | 0.023 | 2026-02-08T09:35:08.389427Z | {
"verified": true,
"answer": 373,
"timestamp": "2026-02-08T09:35:08.412882Z"
} | 6332f0 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 194,
"completion_tokens": 3377
},
"timestamp": "2026-02-24T11:29:37.683Z",
"answer": 373
},
{
"id... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status"... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
07b87e | sequence_lucas_compute_v1_717093673_3695 | Let $n = 23$. Determine the number of ordered pairs $(i, j)$ of integers such that $1 \leq i \leq 23$, $1 \leq j \leq 23$, and $i + j = n$. Let $m$ be this number. Compute the $m$-th Lucas number. | 39,603 | graphs = [
Graph(
let={
"_n": Const(23),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref("_n")), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(23)), right=IntegerRange(start=Const(1), end=Con... | NT | null | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | sequence_lucas_compute_v1 | null | 3 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.013 | 2026-02-08T17:45:57.925172Z | {
"verified": true,
"answer": 39603,
"timestamp": "2026-02-08T17:45:57.937924Z"
} | 5a96b4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 114,
"completion_tokens": 906
},
"timestamp": "2026-02-18T07:18:23.252Z",
"answer": 39603
},
{... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"statu... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
4a5f12 | diophantine_fbi2_count_v1_1520064083_91 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 44100$. Let $k$ be the minimum value of $x + y$ over all such pairs.
Now consider the set of all integers $d$ such that $6 \leq d \leq 65$, $d$ divides $k$, and $2 \leq \frac{k}{d} \leq 61$.
Compute the number of elements in this ... | 12 | graphs = [
Graph(
let={
"_n": Const(6),
"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(44100)))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | COUNT | sympy | EULER_TOTIENT_SUM | [
"B3"
] | 0cd20d | diophantine_fbi2_count_v1 | null | 6 | 0 | [
"B3",
"EULER_TOTIENT_SUM"
] | 2 | 0.042 | 2026-02-08T03:00:05.755142Z | {
"verified": true,
"answer": 12,
"timestamp": "2026-02-08T03:00:05.796947Z"
} | d10d79 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 217,
"completion_tokens": 1971
},
"timestamp": "2026-02-10T12:21:33.817Z",
"answer": 12
},
{
"id"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no... | {
"lo": -5.55,
"mid": -3.02,
"hi": 0.3
} | ||
89027e | comb_count_derangements_v1_2051736721_3299 | Let $a$ be the number of positive integers $n_2$ such that $1 \leq n_2 \leq 99953$, $7$ divides $n_2$, and $\gcd(n_2, 12) = 1$. Let $b$ be the number of positive integers $n_1$ such that $1 \leq n_1 \leq a$ and $15$ divides $F_{n_1}$, where $F_k$ denotes the $k$-th Fibonacci number. Let $n$ be the number of positive in... | 3,459 | graphs = [
Graph(
let={
"_n": Const(15),
"n": CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(1)), Leq(Var("k"), CountOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(1)), Leq(Var("n1"), CountOverSet(set=SolutionsSet(var=Var("n2... | NT | COMB | COUNT | sympy | C5 | [
"C5/COUNT_FIB_DIVISIBLE/C2"
] | b8f1ca | comb_count_derangements_v1 | null | 6 | 0 | [
"C2",
"C5",
"COUNT_FIB_DIVISIBLE"
] | 3 | 0.006 | 2026-02-08T17:14:29.579665Z | {
"verified": true,
"answer": 3459,
"timestamp": "2026-02-08T17:14:29.585473Z"
} | fc5031 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 235,
"completion_tokens": 2420
},
"timestamp": "2026-02-17T22:24:57.675Z",
"answer": 3459
},
{... | 1 | [
{
"lemma": "C2",
"status": "ok_later"
},
{
"lemma": "C5",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok_later"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K17",
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
7381c9 | alg_poly_orbit_count_v1_601307018_5920 | For a non-negative integer $a$, define a sequence by $N = a^2 + a + 5 \bmod 17$, $M = N^2 + N + 5 \bmod 17$, $R = M^2 + M + 5 \bmod 17$, $S = R^2 + R + 5 \bmod 17$, $T = S^2 + S + 5 \bmod 17$, and $K = T^2 + T + 5 \bmod 17$. Find the number of integers $a$ with $0 \le a \le 3467$ such that $K = a$ but $a$ is not equal ... | 1,224 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Pow(Var("a"), Const(2)), Var("a"), Const(5)), modulus=Const(17)),
"p2": Mod(value=Sum(Pow(Ref("p1"), Const(2)), Ref("p1"), Const(5)), modulus=Const(17)),
"p3": Mod(value=Sum(Pow(Ref("p2"), Const(2)), Ref("p2"), Const(5)), modulu... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_orbit_count_v1 | null | 6 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.053 | 2026-03-10T06:29:46.262070Z | {
"verified": true,
"answer": 1224,
"timestamp": "2026-03-10T06:29:46.314899Z"
} | 917a42 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 273,
"completion_tokens": 3395
},
"timestamp": "2026-04-19T03:10:04.678Z",
"answer": 1224
},
{
"... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 2.1,
"mid": 5.36,
"hi": 8.63
} | ||
83cbbe | antilemma_v1_legendre_458359167_164 | Let $ n = 17108 $. Let $ p $ be the largest prime number such that $ 2 \leq p \leq 16 $. Let $ k $ be the largest integer such that $ p^k $ divides $ n! $. Compute the multiplicative order of $ 2 $ modulo $ 2|k| + 3 $.
Find the value of this multiplicative order. | 2,850 | graphs = [
Graph(
let={
"_n": Const(17108),
"x": MaxKDivides(target=Factorial(Ref("_n")), base=MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(16)), IsPrime(Var("n")))))),
"Q": MultiplicativeOrder(base=Const(value=2), m... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW/V1",
"V1"
] | 8b2738 | antilemma_v1_legendre | null | 7 | 0 | [
"MAX_PRIME_BELOW",
"V1"
] | 2 | 0.002 | 2026-02-08T03:03:06.131965Z | {
"verified": true,
"answer": 2850,
"timestamp": "2026-02-08T03:03:06.133469Z"
} | c886f9 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 182,
"completion_tokens": 638
},
"timestamp": "2026-02-17T17:58:02.026Z",
"answer": 2850
}
] | 2 | [
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "same_pattern_wrong"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status... | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
5be1ee | comb_bell_compute_v1_458359167_183 | Let $n = 9$ and $N = 116$. Let $P$ be the set of all ordered pairs $(x,y)$ of positive integers such that $x + y = N$. Let $M$ be the maximum value of $xy$ over all pairs $(x,y) \in P$. Let $B$ be the Bell number $B_n$, the number of partitions of a set of $n$ elements. Find the remainder when $M - B$ is divided by $69... | 52,174 | graphs = [
Graph(
let={
"_n": Const(116),
"n": Const(9),
"result": Bell(Ref("n")),
"Q": Mod(value=Sub(MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')... | COMB | null | COMPUTE | sympy | B1 | [
"B1"
] | d2b6e1 | comb_bell_compute_v1 | negation_mod | 5 | 0 | [
"B1"
] | 1 | 0.002 | 2026-02-08T03:03:22.854780Z | {
"verified": true,
"answer": 52174,
"timestamp": "2026-02-08T03:03:22.856584Z"
} | 7c27f6 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 215,
"completion_tokens": 508
},
"timestamp": "2026-02-10T12:31:58.542Z",
"answer": 52174
},
{
"i... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -4.92,
"mid": -2.9,
"hi": -0.7
} | ||
198088 | algebra_poly_eval_v1_717093673_366 | Let $n$ be an integer satisfying $1 \leq n \leq 91$. Define $y$ to be the number of such integers $n$ that are divisible by 7 and satisfy $\gcd(n, 12) = 1$. Compute the value of $$10y^4 + 3y^3 - 8y^2 + 7y + 10.$$ | 6,470 | graphs = [
Graph(
let={
"_n": Const(10),
"y": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(91)), Divides(divisor=Const(7), dividend=Var("n")), Eq(GCD(a=Var("n"), b=Const(12)), Const(1))))),
"result": Sum(Mul(Ref("_... | NT | null | COMPUTE | sympy | C5 | [
"C5"
] | 1d9668 | algebra_poly_eval_v1 | null | 3 | 0 | [
"C5"
] | 1 | 0.003 | 2026-02-08T15:23:33.451345Z | {
"verified": true,
"answer": 6470,
"timestamp": "2026-02-08T15:23:33.454326Z"
} | 224ad7 | 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": 1351
},
"timestamp": "2026-02-16T06:12:24.401Z",
"answer": 6470
},
{... | 1 | [
{
"lemma": "C5",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
644096 | nt_count_coprime_v1_238844314_371 | Let $k$ be the largest prime number $n$ such that $2 \leq n \leq 12$. Compute the number of positive integers $n$ such that $1 \leq n \leq 70225$ and $\gcd(n, k) = 1$. | 63,841 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": Const(70225),
"k": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Const(12)), IsPrime(Var("n"))))),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), conditio... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | nt_count_coprime_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 11.428 | 2026-02-08T13:18:22.767034Z | {
"verified": true,
"answer": 63841,
"timestamp": "2026-02-08T13:18:34.194955Z"
} | ddc9e3 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 104,
"completion_tokens": 469
},
"timestamp": "2026-02-15T13:00:08.001Z",
"answer": 63841
},
{... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
e42b25 | alg_poly3_sum_v1_601307018_8315 | Find the remainder when $$\sum_{\substack{a=1 \\ b=1 \\ c=1}}^{56} \left( 34a^3 - 27c^3 - 78a c^2 + 231a b^2 - 465a^2b - 108a^2c - 84b^2c + 30b c^2 - 144b^3 + \left|\left\{ (a_1,b_1) : 1 \leq a_1,b_1 \leq 30,\ 10a_1^2 - 18a_1b_1 + 25b_1^2 \leq 4133 \right\}\right| a b c \right)$$ is divided by $65517$. | 52,821 | graphs = [
Graph(
let={
"_n": Const(2),
"result": Mod(value=SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b"), Var("c")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(56)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(56)), Geq(Var("c"),... | ALG | null | COMPUTE | sympy | QF_PSD_COUNT_LEQ | [
"QF_PSD_COUNT_LEQ"
] | 009d0f | alg_poly3_sum_v1 | null | 6 | 0 | [
"QF_PSD_COUNT_LEQ"
] | 1 | 1.585 | 2026-03-10T08:48:40.722646Z | {
"verified": true,
"answer": 52821,
"timestamp": "2026-03-10T08:48:42.308005Z"
} | 75d218 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 281,
"completion_tokens": 10084
},
"timestamp": "2026-04-19T08:49:06.959Z",
"answer": 52821
},
{
... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
}
] | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
164509 | comb_catalan_compute_v1_124444284_2384 | Let $T$ be the set of all integers $t$ such that $27 \leq t \leq 60$ and there exist positive integers $a$ and $b$ with $a \leq 2$, $b \leq 5$, and $t = 9a + 6b + 12$. Let $n = |T|$. Compute $20449 - C_n$, where $C_n$ denotes the $n$-th Catalan number. | 3,653 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=2)), Geq(left=Var(name='b'), right=Const(value=1... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_catalan_compute_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T04:38:12.410345Z | {
"verified": true,
"answer": 3653,
"timestamp": "2026-02-08T04:38:12.412449Z"
} | f4e29a | 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": 14110
},
"timestamp": "2026-02-24T01:25:55.926Z",
"answer": 3653
},
{
"... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"st... | {
"lo": -4.92,
"mid": -2.9,
"hi": -0.7
} | ||
e38794 | comb_sum_binomial_row_v1_784195855_10386 | Let $m = 1024$. Define $n_0$ to be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = m$. Then define $n$ to be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = n_0$. Compute $2^n$. | 65,536 | graphs = [
Graph(
let={
"_m": Const(1024),
"_n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_m")))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | SUM | sympy | B3 | [
"B3/B3"
] | 8ffef9 | comb_sum_binomial_row_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.002 | 2026-02-08T17:49:13.186230Z | {
"verified": true,
"answer": 65536,
"timestamp": "2026-02-08T17:49:13.188322Z"
} | 948314 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 146,
"completion_tokens": 289
},
"timestamp": "2026-02-16T12:06:32.260Z",
"answer": 65536
},
{
"id": 11,
... | 2 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status... | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
5e5151 | modular_min_modexp_v1_865884756_5594 | Let $ a = 13 $. Let $ b $ be the number of positive integers $ n $ less than or equal to 424 such that the sum of the decimal digits of $ n $ is even. Let $ m = 971 $ and let $ x $ be the smallest positive integer such that $ 1 \leq x \leq 97 $ and $ a^x \equiv b \pmod{m} $. Compute the remainder when $ 63599 \cdot x $... | 51,483 | graphs = [
Graph(
let={
"_n": Const(424),
"a": Const(13),
"b": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_n")), Eq(Mod(value=DigitSum(Var("n")), modulus=Const(2)), Const(0))))),
"m": Const(971),
... | NT | null | EXTREMUM | sympy | L3B | [
"L3B"
] | cc148f | modular_min_modexp_v1 | null | 7 | 0 | [
"L3B"
] | 1 | 0.008 | 2026-02-08T18:42:33.295643Z | {
"verified": true,
"answer": 51483,
"timestamp": "2026-02-08T18:42:33.303561Z"
} | ee9298 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 151,
"completion_tokens": 5436
},
"timestamp": "2026-02-18T18:54:19.269Z",
"answer": 51483
},
... | 1 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3B",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
8c0505 | comb_count_surjections_v1_677425708_2661 | Compute the number of integers $t$ with $15 \leq t \leq 42$ for which there exist positive integers $a$ and $b$, with $1 \leq a \leq 2$ and $1 \leq b \leq 4$, such that $t = 9a + 6b$. Denote this number by $n$. Compute the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = n$. Denote t... | 240 | graphs = [
Graph(
let={
"_n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=2)), Geq(left=Var(name='b'), right=Const(value=... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/COMB1"
] | 268a62 | comb_count_surjections_v1 | null | 5 | 0 | [
"COMB1",
"LIN_FORM"
] | 2 | 0.002 | 2026-02-08T05:10:50.380496Z | {
"verified": true,
"answer": 240,
"timestamp": "2026-02-08T05:10:50.382601Z"
} | 7c5265 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 268,
"completion_tokens": 7377
},
"timestamp": "2026-02-11T23:04:47.942Z",
"answer": 40824
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok_later"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM"... | {
"lo": 3.43,
"mid": 5.73,
"hi": 8.84
} | ||
f8db8c_n | comb_count_permutations_fixed_v1_1218484723_6816 | A game show has $n$ boxes labeled with numbers from $1$ to $n$, where $n = 2^0 + 2^1 + 2^2$. The host selects $k$ boxes, where $k = \binom{12}{0} - 1$, to open immediately. The remaining $n-k$ boxes are to be rearranged so that no box ends up in its original position. The number of ways to choose the $k$ boxes and dera... | 1,854 | COMB | null | COUNT | sympy | SUM_GEOM | [
"SUM_GEOM",
"ZERO_BINOM_0"
] | 71c45c | comb_count_permutations_fixed_v1 | null | 4 | null | [
"SUM_GEOM",
"ZERO_BINOM_0"
] | 2 | 0.001 | 2026-02-25T08:16:59.856587Z | null | 96d6c5 | f8db8c | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 237,
"completion_tokens": 1406
},
"timestamp": "2026-03-31T01:48:26.496Z",
"answer": 1854
},
{
"i... | 2 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "SUM_GEOM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"st... | {
"lo": -10,
"mid": -5.89,
"hi": -1.79
} | |
50abb2 | comb_binomial_compute_v1_1520064083_4909 | Let $ x $ and $ y $ be positive integers such that $ x + y = 154 $. Let $ P $ be the maximum value of $ xy $. Let $ d $ be the smallest divisor of $ P $ that is at least $ 2 $. Compute $ \binom{16}{d} $. | 11,440 | graphs = [
Graph(
let={
"_m": Const(2),
"_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")), Const(154)))), expr=Mul(Var("x"), Var("y")))),
... | NT | null | COMPUTE | sympy | B1 | [
"B1/MIN_PRIME_FACTOR"
] | 37b65c | comb_binomial_compute_v1 | null | 5 | 0 | [
"B1",
"MIN_PRIME_FACTOR"
] | 2 | 0.005 | 2026-02-08T06:30:51.453229Z | {
"verified": true,
"answer": 11440,
"timestamp": "2026-02-08T06:30:51.458285Z"
} | 28dfee | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 110,
"completion_tokens": 1364
},
"timestamp": "2026-02-13T00:57:19.431Z",
"answer": 11440
},
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": ... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
68a0ef | algebra_poly_eval_v1_865884756_1324 | Let $k = 22$ and define $r = 2k^3 - 5k^2 + 10k + 9$. Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 6002500$. Compute the value of
$$
(r^2 + 2r + \min_{(x,y) \in S} (x + y)) \bmod 84623.
$$ | 65,136 | graphs = [
Graph(
let={
"k": Const(22),
"result": Sum(Mul(Const(2), Pow(Ref("k"), Const(3))), Mul(Const(-5), Pow(Ref("k"), Const(2))), Mul(Const(10), Ref("k")), Const(9)),
"Q": Mod(value=Sum(Pow(Ref("result"), Const(2)), Mul(Const(2), Ref("result")), MinOverSet(set=MapOve... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | d720b5 | algebra_poly_eval_v1 | quadratic_mod | 4 | 0 | [
"B3"
] | 1 | 0.004 | 2026-02-08T15:57:12.494490Z | {
"verified": true,
"answer": 65136,
"timestamp": "2026-02-08T15:57:12.498107Z"
} | b1d484 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 144,
"completion_tokens": 1421
},
"timestamp": "2026-02-16T17:54:20.522Z",
"answer": 65136
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
13e995 | nt_sum_divisors_mod_v1_1520064083_10073 | Let $n$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 129600$. Let $\sigma(n)$ denote the sum of the positive divisors of $n$. Let $M = 10837$. Compute the remainder when $\sigma(n)$ is divided by $M$. | 2,418 | 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(129600)))), expr=Sum(Var("x"), Var("y")))),
"M": Const(10837... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_divisors_mod_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.002 | 2026-02-08T11:11:52.756253Z | {
"verified": true,
"answer": 2418,
"timestamp": "2026-02-08T11:11:52.758588Z"
} | d1690e | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 138,
"completion_tokens": 703
},
"timestamp": "2026-02-15T21:09:50.660Z",
"answer": 91
},
{
"id": 11,
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
89c94d | comb_factorial_compute_v1_1978505735_6766 | Let $m = 49049$. Let $P$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 216$, $\gcd(p, q) = 1$, and $p < q$. Let $n$ be the number of elements in $P$. Define $d_0$ to be the smallest divisor of $m$ that is at least $n$. Compute $d_0!$. | 5,040 | graphs = [
Graph(
let={
"_m": Const(49049),
"_n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=216)), Eq(left=GCD(a=Var(name='p'), b=Var(na... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/MIN_PRIME_FACTOR"
] | 52cee2 | comb_factorial_compute_v1 | null | 3 | 0 | [
"COPRIME_PAIRS",
"MIN_PRIME_FACTOR"
] | 2 | 0.001 | 2026-02-08T19:47:02.992465Z | {
"verified": true,
"answer": 5040,
"timestamp": "2026-02-08T19:47:02.993831Z"
} | b2cf4c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 145,
"completion_tokens": 2075
},
"timestamp": "2026-02-18T23:32:01.181Z",
"answer": 5040
},
{... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok_later"
},
{
"lemma": "MOD_ADD",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
91245f | modular_mod_compute_v1_601307018_3901 | For integers $a_1, b$ with $1 \le a_1, b \le 20$, define
$$
f(a_1, b) = 37b^{\sum_{k=1}^{2} \varphi(k) \cdot \lfloor 2/k \rfloor} + 27a_1^3 + \left|\left\{ v \in [25, 7225] : \exists\, a_1, b \in [1,17] \text{ such that } 8a_1b + 16b^2 + a_1^2 = v \right\}\right| \cdot a_1 b^2 - 81a_1^2 b.
$$
Let $a$ be the minimum val... | 51,721 | graphs = [
Graph(
let={
"_n": Const(20),
"a": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a1"), Var("b")]), condition=And(Geq(Var("a1"), Const(1)), Leq(Var("a1"), Const(20)), Geq(Var("b"), Const(1)), Leq(Var("b"), Ref("_n")))), expr=Sum(Mul(Const(37), Pow(Var(... | NT | null | COMPUTE | sympy | QF_PSD_DISTINCT | [
"QF_PSD_DISTINCT/POLY3_MIN",
"K2/POLY3_MIN"
] | 20e4d2 | modular_mod_compute_v1 | null | 7 | 0 | [
"K2",
"POLY3_MIN",
"QF_PSD_DISTINCT"
] | 3 | 0.025 | 2026-03-10T04:30:51.319329Z | {
"verified": true,
"answer": 51721,
"timestamp": "2026-03-10T04:30:51.344295Z"
} | 4e61c7 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 339,
"completion_tokens": 13593
},
"timestamp": "2026-03-29T10:18:57.481Z",
"answer": 51721
},
{
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY3_MIN",
"status": "ok_later"
},
{
"lemma"... | {
"lo": -3.34,
"mid": 0.9,
"hi": 4.9
} | ||
192b93 | comb_count_partitions_v1_124444284_2785 | Let $N$ be the number of positive integers $n$ at most 721 that are divisible by 7 and satisfy $\gcd(n, 10) = 1$. Determine the value of the number of integer partitions of $N$. | 53,174 | graphs = [
Graph(
let={
"_n": Const(7),
"n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(721)), Divides(divisor=Ref("_n"), dividend=Var("n")), Eq(GCD(a=Var("n"), b=Const(10)), Const(1))))),
"result": Partition(arg... | NT | COMB | COUNT | sympy | C5 | [
"C5"
] | 1d9668 | comb_count_partitions_v1 | null | 6 | 0 | [
"C5"
] | 1 | 0.001 | 2026-02-08T04:55:13.260865Z | {
"verified": true,
"answer": 53174,
"timestamp": "2026-02-08T04:55:13.261855Z"
} | 1e49cc | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 160,
"completion_tokens": 3675
},
"timestamp": "2026-02-11T22:44:46.364Z",
"answer": 53174
},
{
"... | 1 | [
{
"lemma": "C5",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.45,
"mid": 1.15,
"hi": 6.18
} | ||
00bdf4 | comb_count_surjections_v1_971394319_187 | Let $n_1$ be the number of elements in the Cartesian product of the sets $\{1, 2\}$ and $\{1, 2, \dots, 5\}$. Let $n$ be the number of integers $t$ with $10 \leq t \leq 24$ that can be expressed as $t = 4a + 6b$ for some integers $a$ and $b$ satisfying $1 \leq a \leq 3$ and $1 \leq b \leq 2$. Let $k$ be the number of o... | 1,800 | graphs = [
Graph(
let={
"_n": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(2)), right=IntegerRange(start=Const(1), end=Const(5)))),
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b')... | COMB | null | COUNT | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN/COMB1",
"LIN_FORM"
] | 5cdfce | comb_count_surjections_v1 | null | 5 | 0 | [
"COMB1",
"COUNT_CARTESIAN",
"LIN_FORM"
] | 3 | 0.003 | 2026-02-08T12:53:28.336556Z | {
"verified": true,
"answer": 1800,
"timestamp": "2026-02-08T12:53:28.340005Z"
} | 991cd5 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 309,
"completion_tokens": 1176
},
"timestamp": "2026-02-24T16:35:30.443Z",
"answer": 1800
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok_later"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
5e0637 | modular_count_residue_v1_898971024_1015 | Let $d$ be a positive integer such that $d \geq 2$ and $d$ divides 77077. Let $r$ be the smallest such $d$. Compute the number of positive integers $n$ such that $1 \leq n \leq 62001$ and $n \equiv r \pmod{11}$. | 5,636 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": Const(62001),
"m": Const(11),
"r": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(77077))))),
"result": CountOverSet(set=So... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | modular_count_residue_v1 | null | 3 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 2.356 | 2026-02-08T15:50:49.104071Z | {
"verified": true,
"answer": 5636,
"timestamp": "2026-02-08T15:50:51.460134Z"
} | 3e4a0c | 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": 1118
},
"timestamp": "2026-02-16T15:48:26.393Z",
"answer": 5636
},
{... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"s... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
292131 | lin_form_endings_v1_124444284_4956 | Let $a = 16$ and $b = 56$. Compute the least common multiple of $a$ and $b$, and denote it by $L$. Let $k = 1$ and define $S = k \cdot L + a + b$. Multiply $S$ by $5114$ to obtain a value $T$. Find the remainder when $T$ is divided by $55489$. | 53,152 | graphs = [
Graph(
let={
"a_coeff": Const(16),
"b_coeff": Const(56),
"k_val": Const(1),
"lcm_node": LCM(a=Ref("a_coeff"), b=Ref("b_coeff")),
"_inner_result": Sum(Mul(Ref("k_val"), Ref("lcm_node")), Ref("a_coeff"), Ref("b_coeff")),
"_scal... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 2 | null | [
"LIN_FORM"
] | 1 | 0 | 2026-02-08T06:19:10.106127Z | {
"verified": true,
"answer": 53152,
"timestamp": "2026-02-08T06:19:10.106535Z"
} | 1a54a9 | 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": 655
},
"timestamp": "2026-02-12T22:36:35.420Z",
"answer": 53152
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"st... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
9d8f61 | nt_max_prime_below_v1_1125832087_2301 | Let $t$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 54$, $\gcd(p, q) = 1$, and $p < q$. Let $S$ be the set of all prime numbers $n$ such that $t \leq n \leq 29241$. Compute the maximum element of $S$.\n\nFind the value of this maximum. | 29,231 | graphs = [
Graph(
let={
"upper": Const(29241),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), V... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_max_prime_below_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.944 | 2026-02-08T04:30:23.734954Z | {
"verified": true,
"answer": 29231,
"timestamp": "2026-02-08T04:30:24.679241Z"
} | 090884 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 209,
"completion_tokens": 3095
},
"timestamp": "2026-02-10T17:05:06.081Z",
"answer": 29231
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
aa0483 | nt_count_divisible_v1_898971024_2622 | Let $p$ and $q$ be positive integers such that $pq = 216$, $\gcd(p, q) = 1$, and $p < q$. Define $\_n$ to be the number of such integers $p$. Let $\text{result}$ be the number of positive integers $n$ at most $38416$ that are divisible by $13$. Compute $\text{result}^{\_n} + 8 \cdot \text{result} + c$, where $c$ is the... | 22,925 | 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=216)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(value=1)),... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/COUNT_FIB_DIVISIBLE"
] | 9cf65c | nt_count_divisible_v1 | quadratic_mod | 6 | 0 | [
"COPRIME_PAIRS",
"COUNT_FIB_DIVISIBLE"
] | 2 | 1.315 | 2026-02-08T16:53:01.334224Z | {
"verified": true,
"answer": 22925,
"timestamp": "2026-02-08T16:53:02.649296Z"
} | f5f42e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 197,
"completion_tokens": 2217
},
"timestamp": "2026-02-17T14:10:02.395Z",
"answer": 22925
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok_later"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"st... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
dee6cc | nt_min_crt_v1_1918700295_669 | Let $k$ be the number of positive integers $j$ such that $1 \leq j \leq 9$ and $j^4 \leq 6561$. Let $T$ be the set of all positive integers $t$ such that $24 \leq t \leq 234$ and there exist positive integers $a \leq 6$ and $b \leq 16$ for which $t = 15a + 9b$. Let $u$ be the number of elements in $T$. Find the smalles... | 17 | graphs = [
Graph(
let={
"_n": Const(4),
"m": Const(7),
"k": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(1)), Leq(Var("j"), Const(9)), Leq(Pow(Var("j"), Ref("_n")), Const(6561))), domain='positive_integers')),
"a": Const(3),
... | NT | null | EXTREMUM | sympy | COUNT_SUM_EQUALS | [
"LIN_FORM",
"C3"
] | ea43fe | nt_min_crt_v1 | null | 6 | 0 | [
"C3",
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 3 | 0.077 | 2026-02-08T03:22:10.045406Z | {
"verified": true,
"answer": 17,
"timestamp": "2026-02-08T03:22:10.122156Z"
} | da32dc | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 275,
"completion_tokens": 2842
},
"timestamp": "2026-02-10T14:10:23.007Z",
"answer": 17
},
{
"id"... | 1 | [
{
"lemma": "C3",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"le... | {
"lo": -5.92,
"mid": -3.15,
"hi": 0.25
} | ||
05cafa | sequence_fibonacci_compute_v1_971394319_1867 | Let $n = \sum_{k=1}^{6} \phi(k) \left\lfloor \frac{6}{k} \right\rfloor$, where $\phi$ denotes Euler's totient function. Let $F_n$ denote the $n$th Fibonacci number. Find the remainder when $39953 \cdot F_n$ is divided by $69503$. | 12,662 | graphs = [
Graph(
let={
"n": Summation(var="k", start=Const(1), end=Const(6), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(6), Var("k"))))),
"result": Fibonacci(arg=Ref(name='n')),
"_c": Const(39953),
"Q": Mod(value=Mul(Ref("_c"), Ref("result")), modulus=Con... | NT | null | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | sequence_fibonacci_compute_v1 | null | 4 | 0 | [
"K2"
] | 1 | 0.001 | 2026-02-08T13:58:19.894751Z | {
"verified": true,
"answer": 12662,
"timestamp": "2026-02-08T13:58:19.896058Z"
} | bfaeb8 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 123,
"completion_tokens": 1458
},
"timestamp": "2026-02-15T22:35:03.427Z",
"answer": 12662
},
... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
742593 | nt_count_intersection_v1_2051736721_1327 | Let $N = 20000$. Define $a$ to be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 22$. Define $b = 10$. Let $S$ be the set of all integers $n$ with $1 \leq n \leq N$ such that $a$ divides $n$ and $\gcd(n, b) = 1$. Compute the number of elements in $S$, and let $Q$ be the remaind... | 84,163 | graphs = [
Graph(
let={
"N": Const(20000),
"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 | MIN_PRIME_FACTOR | [
"COMB1"
] | 567f58 | nt_count_intersection_v1 | null | 4 | 0 | [
"COMB1",
"MIN_PRIME_FACTOR"
] | 2 | 3.224 | 2026-02-08T15:56:22.505608Z | {
"verified": true,
"answer": 84163,
"timestamp": "2026-02-08T15:56:25.729721Z"
} | 1b0ad0 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 182,
"completion_tokens": 1327
},
"timestamp": "2026-02-16T18:16:05.698Z",
"answer": 84163
},
... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
7c21bf | nt_count_coprime_v1_2051736721_4315 | Let $S$ be the set of all ordered pairs $(x_1, y_1)$ of positive integers such that $x_1 + y_1 = 50$. Define $P$ to be the maximum value of $x_1 y_1$ over all such pairs in $S$. Let $T$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = P$. Define $k$ to be the minimum value of $x + y$ over a... | 5,476 | graphs = [
Graph(
let={
"upper": Const(13689),
"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")), MaxOverSet(set=MapOverSet(set=SolutionsSet(... | NT | null | COUNT | sympy | B1 | [
"B1/B3"
] | 80b49d | nt_count_coprime_v1 | null | 5 | 0 | [
"B1",
"B3"
] | 2 | 1.04 | 2026-02-08T17:54:41.040844Z | {
"verified": true,
"answer": 5476,
"timestamp": "2026-02-08T17:54:42.080679Z"
} | da4930 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 197,
"completion_tokens": 1328
},
"timestamp": "2026-02-18T10:03:50.104Z",
"answer": 5476
},
{... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
17004f | diophantine_fbi2_count_v1_1978505735_8205 | Let $d$ be a positive integer. Define $m = 2$, $n = 4$, and $k = 180$. Let $S$ be the set of all integers $d$ satisfying the following conditions:
- $d \ge m$,
- $d \le \max\left\{ n' \in \mathbb{Z} \mid n' \ge 2,\ n' \le \sum_{k1=1}^{d} k1,\ \text{and}\ n'\ \text{is prime} \right\}$,
- $d$ divides $k$,
- $\frac{k}{d}... | 74,508 | graphs = [
Graph(
let={
"_d": Const(19),
"_m": Const(2),
"_n": Const(4),
"k": Const(180),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_m")), Leq(Var("d"), MaxOverSet(set=SolutionsSet(var=Var("n"), conditio... | NT | null | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC/MAX_PRIME_BELOW",
"LIN_FORM"
] | 21d638 | diophantine_fbi2_count_v1 | null | 7 | 0 | [
"LIN_FORM",
"MAX_PRIME_BELOW",
"SUM_ARITHMETIC"
] | 3 | 0.015 | 2026-02-08T20:43:17.808370Z | {
"verified": true,
"answer": 74508,
"timestamp": "2026-02-08T20:43:17.823749Z"
} | 015509 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 303,
"completion_tokens": 6024
},
"timestamp": "2026-02-19T01:00:29.439Z",
"answer": 74508
},
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"stat... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
0513f0 | nt_count_primes_v1_168721529_1832 | Let $A$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 54$, $\gcd(p, q) = 1$, and $p < q$. Let $L$ be the number of elements in $A$. Determine the number of prime numbers $n$ such that $L \leq n \leq 32768$. | 3,512 | graphs = [
Graph(
let={
"upper": Const(32768),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'),... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_count_primes_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.826 | 2026-02-08T13:56:55.873925Z | {
"verified": true,
"answer": 3512,
"timestamp": "2026-02-08T13:56:56.700421Z"
} | 4b171b | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 196,
"completion_tokens": 2054
},
"timestamp": "2026-02-11T08:05:27.243Z",
"answer": 3512
},
{
"... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -5.48,
"mid": 0.74,
"hi": 7.52
} | ||
91cba2 | alg_poly3_count_v1_1218484723_1025 | Let $C = \left|\left\{ (a_1, b_1) : 1 \le a_1, b_1 \le 35,\ 25 b_1^{2} + 10 a_1^{2} -18a_1 b_1 \le 4018 \right\}\right|$. Find the number of ordered pairs $(a, b)$ of positive integers with $1 \le a \le C$ and $1 \le b \le 322$ such that $$ 7a^3 + 21a b^2 -21a^2 b -7b^3 = -51109688. $$ | 128 | graphs = [
Graph(
let={
"_n": Const(25),
"result": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a1"), Var("b1")]), condition=And(Geq(Var("a1"), Const... | ALG | null | COUNT | sympy | QF_PSD_COUNT_LEQ | [
"QF_PSD_COUNT_LEQ"
] | 009d0f | alg_poly3_count_v1 | null | 6 | 0 | [
"QF_PSD_COUNT_LEQ"
] | 1 | 0.639 | 2026-02-25T02:45:02.366242Z | {
"verified": true,
"answer": 128,
"timestamp": "2026-02-25T02:45:03.004885Z"
} | 6e89cf | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 251,
"completion_tokens": 5109
},
"timestamp": "2026-03-10T04:47:39.379Z",
"answer": 128
},
{
"id... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
}
] | {
"lo": -2.78,
"mid": -0.24,
"hi": 2.7
} | ||
6163c5 | comb_binomial_compute_v1_655260480_4592 | Let $c = 9$. Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = c$. Define $m$ to be the minimum value of $x + y$ over all such pairs. Let $T$ be the set of all ordered pairs $(x_1, y_1)$ of positive integers such that $x_1 + y_1 = m$. Define $n'$ to be the maximum value of $x_1 y_1$ o... | 924 | graphs = [
Graph(
let={
"_c": Const(9),
"_m": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_c")))), expr=Sum(Var("x"), Var("y")))),
... | ALG | COMB | COMPUTE | sympy | B3 | [
"B3/B1/B3",
"LIN_FORM"
] | 3fc72c | comb_binomial_compute_v1 | null | 6 | 0 | [
"B1",
"B3",
"LIN_FORM"
] | 3 | 0.01 | 2026-02-08T18:00:27.891829Z | {
"verified": true,
"answer": 924,
"timestamp": "2026-02-08T18:00:27.901844Z"
} | 72aebc | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 315,
"completion_tokens": 1187
},
"timestamp": "2026-02-18T11:45:20.906Z",
"answer": 924
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.64,
"mid": -3.17,
"hi": -0.81
} | ||
f54a1f | nt_count_intersection_v1_1978505735_5393 | Let $N = 100000$, $a = 7$, and $b = 18$. Define $\text{result}$ to be the number of positive integers $n$ such that $1 \leq n \leq N$, $7$ divides $n$, and $\gcd(n, 18) = 1$. Let $m = |\text{result}| + 2$. Determine the value of $Q$, where $Q$ is the smallest positive integer $k$ such that the $k$-th Fibonacci number i... | 2,388 | graphs = [
Graph(
let={
"N": Const(100000),
"a": Const(7),
"b": Const(18),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("N")), Divides(divisor=Ref("a"), dividend=Var("n")), Eq(GCD(a=Var("n"), b=... | NT | null | COUNT | sympy | MOBIUS_COPRIME | [
"MOBIUS_COPRIME",
"B3"
] | 233389 | nt_count_intersection_v1 | null | 4 | 0 | [
"B3",
"MOBIUS_COPRIME"
] | 2 | 6.837 | 2026-02-08T18:58:06.180744Z | {
"verified": true,
"answer": 2388,
"timestamp": "2026-02-08T18:58:13.017307Z"
} | 1d2597 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 162,
"completion_tokens": 4107
},
"timestamp": "2026-02-18T20:51:52.646Z",
"answer": 2388
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
6c4df9 | algebra_poly_eval_v1_1353956133_42 | Let $m$ be the smallest divisor of $19343$ that is at least $2$. Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $x + y = 6$. Define $P$ to be the maximum value of $xy$ over all pairs $(x,y) \in S$. Compute $10m^2 + P \cdot m + 10$. | 5,507 | graphs = [
Graph(
let={
"_m": Const(6),
"_n": Const(2),
"m": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(19343))))),
"result": Sum(Mul(Const(10), Pow(Ref("m"), Ref("_n"))), Mul(MaxOv... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR",
"B1"
] | e7724f | algebra_poly_eval_v1 | null | 4 | 0 | [
"B1",
"MIN_PRIME_FACTOR"
] | 2 | 0.007 | 2026-02-08T11:16:46.728317Z | {
"verified": true,
"answer": 5507,
"timestamp": "2026-02-08T11:16:46.735083Z"
} | 771b60 | 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": 782
},
"timestamp": "2026-02-14T11:27:15.489Z",
"answer": 5507
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma":... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
276b6c | diophantine_product_count_v1_677425708_3651 | Let $ k = 720 $ and let $ m = 487 $. Determine the number of positive integers $ x $ such that $ 1 \leq x \leq m $, $ x $ divides $ k $, and $ \frac{k}{x} \leq m $. Compute this number. | 28 | graphs = [
Graph(
let={
"k": Const(720),
"upper": Const(487),
"result": CountOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), Const(1)), Leq(Var("x"), Ref("upper")), Divides(divisor=Var("x"), dividend=Ref("k")), Leq(Div(Ref("k"), Var("x")), Ref("upper"))... | NT | null | COUNT | sympy | K3 | [
"K3"
] | 54c41e | diophantine_product_count_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0.063 | 2026-02-08T05:52:45.323078Z | {
"verified": true,
"answer": 28,
"timestamp": "2026-02-08T05:52:45.386266Z"
} | d8d6e3 | 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": 3118
},
"timestamp": "2026-02-12T15:54:42.774Z",
"answer": 28
},
{
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
871369 | modular_modexp_compute_v1_1874849503_332 | Let $a$ be the smallest divisor of 18588623 that is at least 2. Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $x + y = 44$. Define $e$ to be the maximum value of $xy$ over all pairs $(x,y) \in S$. Compute the remainder when $a^e$ is divided by 69169. | 36,757 | graphs = [
Graph(
let={
"a": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(18588623))))),
"e": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR",
"B1"
] | e7724f | modular_modexp_compute_v1 | null | 6 | 0 | [
"B1",
"MIN_PRIME_FACTOR"
] | 2 | 0.002 | 2026-02-08T12:57:30.588812Z | {
"verified": true,
"answer": 36757,
"timestamp": "2026-02-08T12:57:30.590958Z"
} | 353d1b | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 198,
"completion_tokens": 7819
},
"timestamp": "2026-02-10T06:37:51.657Z",
"answer": 36757
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
... | {
"lo": -5.13,
"mid": 0.83,
"hi": 7.52
} | ||
2ff50f | antilemma_v7_kummer_1874849503_148 | Let $ x $ be the largest integer $ k $ such that $ 5^k $ divides $ \binom{130}{52} $. Compute $ x $. | 2 | graphs = [
Graph(
let={
"x": MaxKDivides(target=Binom(n=Const(130), k=Const(52)), base=Const(5)),
},
goal=Ref("x"),
)
] | NT | null | COMPUTE | sympy | V7 | [
"V7"
] | 0672d4 | antilemma_v7_kummer | null | 6 | null | [
"V7"
] | 1 | 0.001 | 2026-02-08T12:50:26.208200Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-02-08T12:50:26.208735Z"
} | 16ecac | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 148,
"completion_tokens": 693
},
"timestamp": "2026-02-09T14:10:09.140Z",
"answer": 2
},
{
"id": ... | 2 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V7",
"status": "ok"
}
] | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
e686d7_n | comb_catalan_compute_v1_601307018_4379 | A hiker walks along a trail with steps that can only go up or right, never crossing above a diagonal path. The number of such paths of length $2m$ is given by the $m$-th Catalan number. First, compute $n = \sum_{k=1}^{4} \varphi(k) \cdot \left\lfloor \frac{4}{k} \right\rfloor$, then let $M$ be the $n$-th Catalan number... | 49,987 | COMB | null | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | comb_catalan_compute_v1 | null | 4 | null | [
"K2"
] | 1 | 0.004 | 2026-03-10T04:55:48.449043Z | null | d94a68 | e686d7 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 247,
"completion_tokens": 956
},
"timestamp": "2026-03-29T18:37:28.489Z",
"answer": 49987
},
{
"i... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -10,
"mid": -5.89,
"hi": -1.79
} | |
294d60 | antilemma_k2_v1_898971024_2155 | Define
$$
x = \sum_{k=1}^{202} \phi(k) \left\lfloor \frac{202}{k} \right\rfloor,
$$
where $\phi(k)$ denotes Euler's totient function. Let $Q$ be the remainder when $81 - x$ is divided by $73991$. Compute $Q$. | 53,569 | graphs = [
Graph(
let={
"x": Summation(var="k", start=Const(1), end=Const(202), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(202), Var("k"))))),
"Q": Mod(value=Sub(Const(81), Ref("x")), modulus=Const(73991)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | antilemma_k2_v1 | null | 5 | 0 | [
"K2"
] | 1 | 0.001 | 2026-02-08T16:34:48.194504Z | {
"verified": true,
"answer": 53569,
"timestamp": "2026-02-08T16:34:48.195369Z"
} | 30cb03 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 117,
"completion_tokens": 728
},
"timestamp": "2026-02-17T07:46:03.844Z",
"answer": 53569
},
{... | 1 | [
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
8c5bc5 | antilemma_sum_equals_v1_1439011603_1922 | Let $n = 60$. Let $x$ be the number of ordered pairs $(i, j)$ of positive integers such that $i + j = n$ and $1 \leq i, j \leq 58$. Let $d_k$ denote the $k$-th digit of $|x|$ in base $10$, starting from the units digit as $k=0$. Compute $$\sum_{k=0}^{\text{number of digits of } |x| - 1} d_k (k+1)^2 + 64516.$$ | 64,543 | graphs = [
Graph(
let={
"_n": Const(60),
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref("_n")), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(58)), right=IntegerRange(start=Const(1), end=Con... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 5 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.008 | 2026-02-08T16:23:01.968249Z | {
"verified": true,
"answer": 64543,
"timestamp": "2026-02-08T16:23:01.975890Z"
} | 02736a | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 231,
"completion_tokens": 649
},
"timestamp": "2026-02-24T20:43:57.808Z",
"answer": 64543
},
{
"... | 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": -4.1,
"mid": -1.76,
"hi": 1.3
} | ||
250db3 | nt_max_prime_below_v1_971394319_307 | Let $p$ be a positive integer. Suppose there exist positive integers $q$ such that $p < q$, $pq = 24$, and $\gcd(p, q) = 1$. Let $L$ be the number of such integers $p$. Let $S$ be the set of all prime numbers $n$ such that $L \leq n \leq 65536$. Compute the largest element of $S$. | 65,521 | graphs = [
Graph(
let={
"upper": Const(65536),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), V... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_max_prime_below_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 2.104 | 2026-02-08T12:59:00.881012Z | {
"verified": true,
"answer": 65521,
"timestamp": "2026-02-08T12:59:02.985446Z"
} | b06e69 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 136,
"completion_tokens": 4005
},
"timestamp": "2026-02-15T08:12:00.343Z",
"answer": 65521
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"stat... | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
dedb38 | diophantine_fbi2_count_v1_809748730_961 | Compute the number of positive integers $d$ such that $3 \leq d \leq 111$, $d$ divides $360$, and $2 \leq \frac{360}{d} \leq 110$. | 18 | graphs = [
Graph(
let={
"k": Const(360),
"a": Const(2),
"b": Const(1),
"upper": Const(109),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(3)), Leq(Var("d"), Const(111)), Divides(divisor=Var("d"), dividend=R... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | diophantine_fbi2_count_v1 | null | 3 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.043 | 2026-02-08T11:51:00.657589Z | {
"verified": true,
"answer": 18,
"timestamp": "2026-02-08T11:51:00.701021Z"
} | 8776cb | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 92,
"completion_tokens": 1591
},
"timestamp": "2026-02-14T21:25:54.330Z",
"answer": 18
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
982d8f | nt_sum_gcd_range_mod_v1_1978505735_115 | Let $N$ be the maximum value of $xy$ where $x$ and $y$ are positive integers such that $x + y = 102$. Let $k = 252$ and $M = 11801$. Define $$
S = \sum_{n=1}^{N} \gcd(n, k).
$$ Let $r$ be the remainder when $S$ is divided by $M$. Finally, let $Q$ be the remainder when $13723 \cdot r$ is divided by $50756$. Compute $Q$. | 32,822 | graphs = [
Graph(
let={
"_n": Const(102),
"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 | 4 | 0 | [
"B1"
] | 1 | 0.122 | 2026-02-08T15:12:06.487497Z | {
"verified": true,
"answer": 32822,
"timestamp": "2026-02-08T15:12:06.609702Z"
} | 3ef97e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 160,
"completion_tokens": 2983
},
"timestamp": "2026-02-16T01:22:19.330Z",
"answer": 32822
},
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
ca1fd0 | comb_count_permutations_fixed_v1_655260480_5775 | Let $P$ be the set of all prime numbers $n_1$ such that $2 \leq n_1 \leq 3$. Define $n = \sum_{k=1}^{\max(P)} \phi(k) \left\lfloor \frac{3}{k} \right\rfloor$. Compute $\binom{n}{2} \cdot !(n-2)$, where $!m$ denotes the number of derangements of $m$ elements. | 135 | graphs = [
Graph(
let={
"_n": Const(3),
"n": Summation(var="k1", start=Const(1), end=MaxOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(2)), Leq(Var("n1"), Const(3)), IsPrime(Var("n1"))))), expr=Mul(EulerPhi(n=Var("k1")), Floor(Div(Ref("_n"), Var("k1"))))),... | NT | COMB | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW/K2"
] | 7eb1ee | comb_count_permutations_fixed_v1 | null | 3 | 0 | [
"K2",
"MAX_PRIME_BELOW"
] | 2 | 0.004 | 2026-02-08T18:39:36.781736Z | {
"verified": true,
"answer": 135,
"timestamp": "2026-02-08T18:39:36.785304Z"
} | 5f8720 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 143,
"completion_tokens": 1235
},
"timestamp": "2026-02-18T18:29:21.839Z",
"answer": 135
},
{
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K2",
"status": "ok_later"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
},
{
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
b1211d | comb_count_surjections_v1_1218484723_6534 | Let $k = 5$ and $n = \sum_{i=0}^{2} 2^i$. Let $N = k! \cdot S(n, k)$, where $S(n, k)$ denotes the Stirling number of the second kind. Find the remainder when $96842N$ is divided by $51653$. | 31,059 | graphs = [
Graph(
let={
"n": Summation(var="k1", start=Const(0), end=Const(2), expr=Pow(Const(2), Var("k1"))),
"k": Const(5),
"result": Mul(Factorial(Ref("k")), Stirling2(n=Ref(name='n'), k=Ref(name='k'))),
"Q": Mod(value=Mul(Const(96842), Ref("result")), modu... | COMB | null | COUNT | sympy | SUM_GEOM | [
"SUM_GEOM"
] | 04214c | comb_count_surjections_v1 | null | 3 | 0 | [
"SUM_GEOM"
] | 1 | 0.002 | 2026-02-25T08:05:38.705615Z | {
"verified": true,
"answer": 31059,
"timestamp": "2026-02-25T08:05:38.707122Z"
} | 7c6d62 | 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": 2227
},
"timestamp": "2026-03-30T02:04:49.324Z",
"answer": 31059
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "SUM_GEOM",
"status": "ok"
},
{
"lemma": "V7",
"status... | {
"lo": -3.33,
"mid": 1.03,
"hi": 5.26
} |
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