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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
2d683f | antilemma_v1_legendre_124444284_1082 | Let $m = 11$ and $n = 28997$. Let $S$ be the set of all positive integers $x, y$ such that $x \cdot y = 225$. Define $s$ to be the minimum value of $x + y$ over all such pairs $(x,y)$. Let $T$ be the set of all positive integers $k$ such that $1 \le k \le n$ and $\gcd(k, s) = 1$. Let $N$ be the number of elements in $T... | 771 | graphs = [
Graph(
let={
"_m": Const(11),
"_n": Const(28997),
"x": MaxKDivides(target=Factorial(CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_n")), Eq(GCD(a=Var("n"), b=MinOverSet(set=MapOverSet(set=SolutionsSet(var=... | NT | null | COMPUTE | sympy | B3 | [
"B3/C4/V1",
"V1"
] | c13241 | antilemma_v1_legendre | null | 6 | 0 | [
"B3",
"C4",
"V1"
] | 3 | 0.002 | 2026-02-08T03:40:55.998515Z | {
"verified": true,
"answer": 771,
"timestamp": "2026-02-08T03:40:56.000266Z"
} | 565a0a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 250,
"completion_tokens": 1855
},
"timestamp": "2026-02-10T02:26:30.103Z",
"answer": 771
},
{
"id... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C4",
"status": "ok_later"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K5",
"status": "same_pattern_wrong"
},
{
"lemma": "MOD_FACTORIAL",
"statu... | {
"lo": -6.51,
"mid": -0.31,
"hi": 5.43
} | ||
1624e8 | geo_count_lattice_triangle_v1_1520064083_7989 | Let $A$ be twice the area of the triangle with vertices at $(120, 5)$, $(253, 169)$, and $(0, 0)$, given by the absolute value of $120 \cdot 169 + 253 \cdot (-5)$. Let $b$ be the sum of the greatest common divisors of the absolute values of the differences in coordinates along each edge of the triangle, specifically:
... | 9,505 | graphs = [
Graph(
let={
"_n": Const(2),
"area_2x": Abs(arg=Sum(Mul(Const(value=120), Const(value=169)), Mul(Const(value=253), Sub(left=Const(value=0), right=Const(value=5))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=120)), b=Abs(arg=Const(value=5))), GCD(a=Abs(arg=Sub(... | ALG | NT | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | geo_count_lattice_triangle_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.008 | 2026-02-08T09:26:58.198715Z | {
"verified": true,
"answer": 9505,
"timestamp": "2026-02-08T09:26:58.206793Z"
} | 8c31c6 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 254,
"completion_tokens": 3995
},
"timestamp": "2026-02-14T05:58:14.239Z",
"answer": 9505
},
{... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
08f26c | nt_euler_phi_compute_v1_809748730_582 | Let $n = 75025$ and let $\phi(n)$ denote Euler's totient function. Let $A$ be the set of all ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 4$. Let $c$ be the number of elements in $A$. Consider the decimal digits of $|\phi(n)|$, indexed starting from 0 at the units place. Compute the sum
$$... | 65,175 | graphs = [
Graph(
let={
"_n": Const(4),
"n": Const(75025),
"result": EulerPhi(n=Ref("n")),
"Q": Sum(Summation(var="i", start=Const(0), end=Sub(NumDigits(x=Abs(arg=Ref(name='result')), base=None), Const(1)), expr=Mul(Digit(x=Abs(arg=Ref(name='result')), k=Var(n... | NT | null | COMPUTE | sympy | COMB1 | [
"COMB1"
] | 43779f | nt_euler_phi_compute_v1 | digits_weighted_mod | 6 | 0 | [
"COMB1"
] | 1 | 0.004 | 2026-02-08T11:36:14.193768Z | {
"verified": true,
"answer": 65175,
"timestamp": "2026-02-08T11:36:14.197952Z"
} | 03bec5 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 239,
"completion_tokens": 581
},
"timestamp": "2026-02-16T03:09:17.110Z",
"answer": 65054
},
{
"id": 11... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST... | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
851037 | antilemma_sum_equals_v1_1742523217_3782 | Let $n$ be the number of ordered pairs $(a, b)$ where $a$ and $b$ are integers with $1 \leq a \leq 3$ and $1 \leq b \leq 3$. Determine the number of ordered pairs $(i, j)$ of integers such that $1 \leq i \leq 8$, $1 \leq j \leq 9$, and $i + j = n$. | 8 | graphs = [
Graph(
let={
"_n": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(3)), right=IntegerRange(start=Const(1), end=Const(3)))),
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref(... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_CARTESIAN/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | 8bee9e | antilemma_sum_equals_v1 | null | 3 | 0 | [
"COUNT_CARTESIAN",
"COUNT_SUM_EQUALS"
] | 2 | 0.07 | 2026-02-08T06:05:19.322867Z | {
"verified": true,
"answer": 8,
"timestamp": "2026-02-08T06:05:19.392595Z"
} | 9278ea | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 208,
"completion_tokens": 591
},
"timestamp": "2026-02-24T05:19:20.245Z",
"answer": 8
},
{
"id": ... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
... | {
"lo": -9.23,
"mid": -6.18,
"hi": -4.06
} | ||
205956 | lin_form_endings_v1_677425708_2627 | Compute the remainder when $6227 \times \text{lcm}(42, 24)$ is divided by $71599$. | 43,750 | graphs = [
Graph(
let={
"a_coeff": Const(42),
"b_coeff": Const(24),
"_inner_result": LCM(a=Ref("a_coeff"), b=Ref("b_coeff")),
"_scale_k": Const(6227),
"_scaled": Mul(Ref("_scale_k"), Ref("_inner_result")),
"_mod_M": Const(71599),
... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 2 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T05:09:52.350672Z | {
"verified": true,
"answer": 43750,
"timestamp": "2026-02-08T05:09:52.351250Z"
} | c74690 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 137,
"completion_tokens": 555
},
"timestamp": "2026-02-11T22:59:04.029Z",
"answer": 43750
},
{
"i... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"statu... | {
"lo": -3.52,
"mid": 1.14,
"hi": 6.18
} | ||
0b8454 | geo_count_lattice_triangle_v1_601307018_2862 | Let $N = |196 \cdot 100 + 24 \cdot (0 - 128)|$ and $M = \gcd(196, 128) + \gcd(|24 - 196|, |100 - 128|) + \gcd(|0 - 24|, |0 - 100|)$. Compute $\frac{N + 2 - M}{2}$. | 8,259 | graphs = [
Graph(
let={
"area_2x": Abs(arg=Sum(Mul(Const(value=196), Const(value=100)), Mul(Const(value=24), Sub(left=Const(value=0), right=Const(value=128))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=196)), b=Abs(arg=Const(value=128))), GCD(a=Abs(arg=Sub(left=Const(value=24), rig... | GEOM | NT | COUNT | sympy | [] | geo_count_lattice_triangle_v1 | null | 4 | 0 | null | null | 0.005 | 2026-03-10T03:28:58.065181Z | {
"verified": true,
"answer": 8259,
"timestamp": "2026-03-10T03:28:58.070324Z"
} | f2ef12 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 198,
"completion_tokens": 633
},
"timestamp": "2026-03-29T06:43:32.568Z",
"answer": 8259
},
{
"id... | 1 | [] | {
"lo": -6.5,
"mid": -3.34,
"hi": -0.89
} | ||||
cdbe44 | comb_sum_binomial_row_v1_1520064083_8556 | Let $n$ be the number of prime numbers between 2 and 47, inclusive. Compute $2^n$. | 32,768 | graphs = [
Graph(
let={
"_n": Const(2),
"n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(47)), IsPrime(Var("n"))))),
"result": Pow(Ref("_n"), Ref("n")),
},
goal=Ref("result"),
)
] | NT | null | SUM | sympy | COUNT_PRIMES | [
"COUNT_PRIMES"
] | 07c874 | comb_sum_binomial_row_v1 | null | 3 | 0 | [
"COUNT_PRIMES"
] | 1 | 0.001 | 2026-02-08T10:15:06.502502Z | {
"verified": true,
"answer": 32768,
"timestamp": "2026-02-08T10:15:06.503416Z"
} | 22f70c | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 81,
"completion_tokens": 143
},
"timestamp": "2026-02-15T20:51:48.934Z",
"answer": 32768
},
{
"id": 11,
... | 2 | [
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -9.12,
"mid": -6.02,
"hi": -3.62
} | ||
16f5c3 | antilemma_k2_v1_717093673_4206 | Let $n = 69$. Compute the sum $$
\sum_{k=1}^{69} \phi(k) \left\lfloor \frac{69}{k} \right\rfloor,
$$
where $\phi(k)$ denotes Euler's totient function. Let $x$ be the value of this sum.
Now, let $d_i$ denote the $i$-th decimal digit of $|x|$ (with $i = 0$ being the units digit). Let $\ell$ be the number of digits in $|... | 14,961 | graphs = [
Graph(
let={
"_n": Const(69),
"x": Summation(var="k", start=Const(1), end=Const(69), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Ref("_n"), Var("k"))))),
"Q": Sum(Summation(var="i", start=Const(0), end=Sub(NumDigits(x=Abs(arg=Ref(name='x')), base=None), Const(1)),... | NT | COMB | COMPUTE | sympy | IDENTITY_POW_ZERO | [
"IDENTITY_POW_ZERO",
"K2"
] | fce51d | antilemma_k2_v1 | null | 6 | 0 | [
"IDENTITY_POW_ZERO",
"K2"
] | 2 | 0.003 | 2026-02-08T18:05:52.399477Z | {
"verified": true,
"answer": 14961,
"timestamp": "2026-02-08T18:05:52.402111Z"
} | 1d6e35 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 193,
"completion_tokens": 1557
},
"timestamp": "2026-02-18T13:32:00.776Z",
"answer": 14961
},
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "IDENTITY_POW_ZERO",
"status": "ok"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V7",
"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
819627 | sequence_lucas_compute_v1_1978505735_2892 | Let $ n $ be the number of integers $ t $ with $ 14 \leq t \leq 38 $ for which there exist positive integers $ a $ and $ b $, with $ 1 \leq a \leq 4 $ and $ 1 \leq b \leq 5 $, such that $ t = 4a + 3b + 7 $. Compute the $ n $-th Lucas number. | 9,349 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=4)), Geq(left=Var(name='b'), right=Const(value=1... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | sequence_lucas_compute_v1 | null | 3 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T17:14:28.899889Z | {
"verified": true,
"answer": 9349,
"timestamp": "2026-02-08T17:14:28.901498Z"
} | 0538c1 | 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": 2159
},
"timestamp": "2026-02-17T22:49:45.914Z",
"answer": 9349
},
{... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
b93fed | comb_count_permutations_fixed_v1_124444284_136 | Let $n = 7$. Let $k$ be the sum of $\mu(d)$ over all positive divisors $d$ of $46$, where $\mu$ is the M\"obius function. Compute $\binom{n}{k} \cdot !(n - k)$, where $!m$ denotes the number of derangements of $m$ elements. | 1,854 | graphs = [
Graph(
let={
"n": Const(7),
"k": SumOverDivisors(n=Const(value=46), var='d', expr=MoebiusMu(n=Var(name='d'))),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub(left=Ref(name='n'), right=Ref(name='k')))),
},
goal=Ref("result"),
... | NT | COMB | COUNT | sympy | LIN_FORM | [
"MOBIUS_SUM"
] | 518e32 | comb_count_permutations_fixed_v1 | null | 6 | 0 | [
"LIN_FORM",
"MOBIUS_SUM"
] | 2 | 0.03 | 2026-02-08T03:00:47.952730Z | {
"verified": true,
"answer": 1854,
"timestamp": "2026-02-08T03:00:47.982886Z"
} | fc8b95 | 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": 759
},
"timestamp": "2026-02-09T13:56:31.566Z",
"answer": 1854
},
{
"id... | 2 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MOBIUS_SUM",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
a82e6a | algebra_vieta_sum_v1_601307018_47 | Let $M$ be the sum of all positive integers $x$ such that $$x^4 - 30x^3 + 327x^2 - 1522x + \min\{ x_1 + y : x_1 > 0,\ y > 0,\ x_1 y = 1587600 \} = 0.$$ Find the remainder when $44121M$ is divided by $94678$. | 92,816 | graphs = [
Graph(
let={
"_n": Const(2),
"result": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Const(4)), Mul(Const(-30), Pow(Var("x"), Const(3))), Mul(Const(327), Pow(Var("x"), Ref("_n"))), Mul(Const(-1522), Var("x")), MinOverSet(set=MapOverSet(set=Soluti... | ALG | null | COMPUTE | sympy | POLY_ORBIT_COUNT | [
"B3"
] | 0cd20d | algebra_vieta_sum_v1 | null | 5 | 0 | [
"B3",
"POLY_ORBIT_COUNT"
] | 2 | 3.856 | 2026-03-10T00:43:46.125278Z | {
"verified": true,
"answer": 92816,
"timestamp": "2026-03-10T00:43:49.981313Z"
} | 017cdc | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 201,
"completion_tokens": 17359
},
"timestamp": "2026-03-28T22:20:36.103Z",
"answer": 92816
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -0.92,
"mid": 2.07,
"hi": 4.67
} | ||
ff26db | antilemma_k2_v1_1918700295_151 | Let $m = 2$ and let $S$ be the set of all real solutions $x$ to the equation $x^2 - 205x + 9514 = 0$. Let $N$ be the sum of all elements in $S$. Define $x = \sum_{k=1}^{205} \phi(k) \cdot \left\lfloor \frac{N}{k} \right\rfloor$, where $\phi$ is Euler's totient function. Find the remainder when $11111 - x$ is divided by... | 58,277 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Ref("_m")), Mul(Const(-205), Var("x")), Const(9514)), Const(0)))),
"x": Summation(var="k", start=Const(1), end=Const(205), expr=Mul(EulerPhi(n=Var("k")),... | NT | COMB | COMPUTE | sympy | VIETA_SUM | [
"VIETA_SUM/K2",
"K2"
] | 6be084 | antilemma_k2_v1 | null | 6 | 0 | [
"K2",
"VIETA_SUM"
] | 2 | 0.001 | 2026-02-08T03:01:27.332053Z | {
"verified": true,
"answer": 58277,
"timestamp": "2026-02-08T03:01:27.333171Z"
} | fe0cf1 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 231,
"completion_tokens": 1803
},
"timestamp": "2026-02-10T12:36:11.180Z",
"answer": 58277
},
{
"... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "VIETA_SUM"... | {
"lo": -3.55,
"mid": 0.8,
"hi": 4.81
} | ||
ea6e97 | antilemma_k3_v1_151522320_1275 | Let $n = 52118$. Define $x$ to be the sum of Euler's totient function $\phi(d)$ over all positive divisors $d$ of $n$. Compute $x$. | 52,118 | graphs = [
Graph(
let={
"_n": Const(52118),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 2 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T03:51:57.078430Z | {
"verified": true,
"answer": 52118,
"timestamp": "2026-02-08T03:51:57.078972Z"
} | 348ee3 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 152,
"completion_tokens": 561
},
"timestamp": "2026-02-10T15:55:16.733Z",
"answer": 52118
},
{
"i... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": ... | {
"lo": -5.55,
"mid": -3.02,
"hi": 0.31
} | ||
0a0c26 | comb_sum_binomial_row_v1_1742523217_207 | Let $n = \sum_{k=1}^{4} \phi(k) \left\lfloor \frac{4}{k} \right\rfloor$, where $\phi$ is Euler's totient function. Define $r = 2^n$. Compute the remainder when $21007 \cdot r$ is divided by 96589. Express your answer as an integer between 0 and 96588. | 68,410 | graphs = [
Graph(
let={
"_n": Const(4),
"n": Summation(var="k", start=Const(1), end=Const(4), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Ref("_n"), Var("k"))))),
"result": Pow(Const(2), Ref("n")),
"_c": Const(21007),
"Q": Mod(value=Mul(Ref("_c"), Ref... | NT | null | SUM | sympy | K2 | [
"K2"
] | 6897ab | comb_sum_binomial_row_v1 | null | 4 | 0 | [
"K2"
] | 1 | 0.001 | 2026-02-08T02:55:58.969949Z | {
"verified": true,
"answer": 68410,
"timestamp": "2026-02-08T02:55:58.970928Z"
} | 20b0a0 | 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": 1129
},
"timestamp": "2026-02-09T14:46:26.790Z",
"answer": 68410
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
}
] | {
"lo": -1,
"mid": 0.94,
"hi": 2.59
} | ||
61c6da | nt_min_phi_inverse_v1_458359167_2487 | Let $n = 4$, and let $u = \sum_{k=1}^{n} k$. Let $k = 2$. Consider the set of all integers $n$ such that $1 \leq n \leq u$ and $\phi(n) = k$. Determine the value of the smallest such $n$. | 3 | graphs = [
Graph(
let={
"_n": Const(4),
"upper": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Var("k")),
"k": Const(2),
"result": MinOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(EulerPh... | NT | null | EXTREMUM | sympy | COUNT_CARTESIAN | [
"SUM_ARITHMETIC"
] | eb34f0 | nt_min_phi_inverse_v1 | null | 4 | 0 | [
"COUNT_CARTESIAN",
"SUM_ARITHMETIC"
] | 2 | 0.038 | 2026-02-08T05:26:48.574644Z | {
"verified": true,
"answer": 3,
"timestamp": "2026-02-08T05:26:48.612656Z"
} | b1ee29 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 115,
"completion_tokens": 660
},
"timestamp": "2026-02-12T22:43:52.307Z",
"answer": 3
},
{
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
b3d188 | modular_modexp_compute_v1_1918700295_1709 | Let $a = 17$. 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 such pairs. Compute the remainder when $a^e$ is divided by $10404$. | 289 | graphs = [
Graph(
let={
"a": Const(17),
"e": 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(44)))), expr=Mul(Var("x"), Var("y")))),
... | NT | null | COMPUTE | sympy | B1 | [
"B1"
] | 5b950e | modular_modexp_compute_v1 | null | 4 | 0 | [
"B1"
] | 1 | 0.002 | 2026-02-08T05:58:26.816527Z | {
"verified": true,
"answer": 289,
"timestamp": "2026-02-08T05:58:26.818594Z"
} | 4e4106 | 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": 1815
},
"timestamp": "2026-02-12T17:49:40.754Z",
"answer": 289
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
2fe768 | algebra_poly_eval_v1_1520064083_5083 | Let $m = 17$. Let $s$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 47524$, and let $n$ be the minimum value of $x + y$ as $(x, y)$ ranges over $s$. Let $k$ be the number of integers $t$ such that $9 \leq t \leq 426$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 66$, ... | 50,209 | graphs = [
Graph(
let={
"_m": Const(10780),
"_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(47524)))), expr=Sum(Var("x"), Var("y"))... | NT | null | COMPUTE | sympy | B3 | [
"B3/LIN_FORM"
] | 9cebb8 | algebra_poly_eval_v1 | null | 7 | 0 | [
"B3",
"LIN_FORM"
] | 2 | 0.008 | 2026-02-08T06:37:23.223879Z | {
"verified": true,
"answer": 50209,
"timestamp": "2026-02-08T06:37:23.232285Z"
} | b41582 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 223,
"completion_tokens": 4149
},
"timestamp": "2026-02-13T02:49:59.854Z",
"answer": 50209
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok_later"
},
{
"lemma": "LTE_DIFF",
"status": ... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
3f3160 | modular_count_residue_v1_1978505735_3702 | Let $m$ be the number of integers $t$ with $17 \leq t \leq 45$ for which there exist integers $a$ and $b$ such that $1 \leq a \leq 8$, $1 \leq b \leq 3$, and $t = 2a + 7b + 8$. Let $r = 8$. Determine the number of positive integers $n$ such that $1 \leq n \leq 64516$ and $n \equiv r \pmod{m}$. | 2,805 | graphs = [
Graph(
let={
"upper": Const(64516),
"m": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=8)), Geq(left... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | modular_count_residue_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 2.084 | 2026-02-08T17:48:00.182597Z | {
"verified": true,
"answer": 2805,
"timestamp": "2026-02-08T17:48:02.266505Z"
} | 768236 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 159,
"completion_tokens": 2414
},
"timestamp": "2026-02-18T08:26:02.236Z",
"answer": 2805
},
{... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
848340 | comb_count_partitions_v1_1915831931_1930 | Let $S$ be the set of all integers $t$ such that $26 \leq t \leq 74$ and there exist integers $a$ and $b$ with $1 \leq a \leq 9$, $1 \leq b \leq 7$, and
$$
t = 3a + 4b + 19.
$$
Let $n$ be the number of elements in $S$. Let $p(n)$ denote the number of integer partitions of $n$. Compute
$$
89401 - p(n).
$$ | 26,140 | graphs = [
Graph(
let={
"_n": Const(89401),
"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=9)), Geq(left=Va... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_count_partitions_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T16:31:08.437910Z | {
"verified": true,
"answer": 26140,
"timestamp": "2026-02-08T16:31:08.440384Z"
} | 1acb06 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 159,
"completion_tokens": 2787
},
"timestamp": "2026-02-17T06:48:43.161Z",
"answer": 26140
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||
086021 | lin_form_endings_v1_1125832087_991 | Let $a = 56$ and $b = 42$. Let $k = 3$, and define $L = \mathrm{lcm}(a, b)$. Compute the value of $3L + a + b$, multiply the result by 6498, and then compute the remainder when this product is divided by 94685. | 29,711 | graphs = [
Graph(
let={
"a_coeff": Const(56),
"b_coeff": Const(42),
"k_val": Const(3),
"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 | 0.001 | 2026-02-08T03:24:44.306014Z | {
"verified": true,
"answer": 29711,
"timestamp": "2026-02-08T03:24:44.306644Z"
} | 35f2fb | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 182,
"completion_tokens": 652
},
"timestamp": "2026-02-10T14:28:34.674Z",
"answer": 29711
},
{
"i... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"st... | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
43a762 | nt_sum_totient_over_divisors_v1_349078426_478 | Let $n = 52889$. Define $\phi(d)$ to be Euler's totient function. Let $A$ be the sum of $\phi(d)$ over all positive divisors $d$ of $n$. Let $B$ be the maximum value of $xy$ over all pairs of positive integers $(x, y)$ such that $x + y = 122$. Let $S$ be the sum of the squares of the digit positions (counting from the ... | 3,991 | graphs = [
Graph(
let={
"_n": Const(122),
"n": Const(52889),
"result": SumOverDivisors(n=Ref(name='n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"_c": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositiv... | NT | null | COMPUTE | sympy | B1 | [
"B1"
] | 51a773 | nt_sum_totient_over_divisors_v1 | digits_weighted_mod | 5 | 0 | [
"B1"
] | 1 | 0.005 | 2026-02-08T13:05:48.350391Z | {
"verified": true,
"answer": 3991,
"timestamp": "2026-02-08T13:05:48.355501Z"
} | 18ffe4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 232,
"completion_tokens": 908
},
"timestamp": "2026-02-15T09:24:55.359Z",
"answer": 3991
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
a20c97 | comb_count_derangements_v1_1918700295_2214 | Let $n$ be the largest positive divisor of 91 that is at most 7. Compute the remainder when the subfactorial of $n$ is multiplied by 69025 and then divided by 87711. | 2,001 | graphs = [
Graph(
let={
"_n": Const(7),
"n": MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Leq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(91))))),
"result": Subfactorial(arg=Ref(name='n')),
"_c": Const(690... | NT | COMB | COUNT | sympy | MAX_DIVISOR | [
"MAX_DIVISOR"
] | 51757e | comb_count_derangements_v1 | null | 3 | 0 | [
"MAX_DIVISOR"
] | 1 | 0.001 | 2026-02-08T07:45:56.549660Z | {
"verified": true,
"answer": 2001,
"timestamp": "2026-02-08T07:45:56.551033Z"
} | 3333df | 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": 1165
},
"timestamp": "2026-02-13T12:04:14.793Z",
"answer": 2001
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
3eb0fd | comb_catalan_compute_v1_1915831931_2657 | Let $n$ be the number of integers $t$ with $10 \leq t \leq 32$ for which there exist integers $a$ and $b$ such that $1 \leq a \leq 2$, $1 \leq b \leq 5$, and $t = 6a + 4b$. Let $C_n$ denote the $n$-th Catalan number. Compute the remainder when $67937 \cdot C_n$ is divided by $61399$. | 30,836 | 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 | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.003 | 2026-02-08T17:02:40.927417Z | {
"verified": true,
"answer": 30836,
"timestamp": "2026-02-08T17:02:40.930835Z"
} | fc8d87 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 149,
"completion_tokens": 1518
},
"timestamp": "2026-02-17T18:19:52.943Z",
"answer": 30836
},
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"statu... | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||
d05e13 | antilemma_v8_lucas_1520064083_331 | Let $j$ be a nonnegative integer. Determine the number of integers $j$ with $0 \leq j \leq 65535$ such that $\binom{65535}{j}$ is odd. Compute this number. | 65,536 | graphs = [
Graph(
let={
"_n": Const(65535),
"x": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Ref("_n")), Eq(Mod(value=Binom(n=Const(65535), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')),
},
... | NT | COMB | COMPUTE | sympy | V8 | [
"V8"
] | 86348e | antilemma_v8_lucas | null | 6 | 0 | [
"V8"
] | 1 | 0.001 | 2026-02-08T03:15:39.786420Z | {
"verified": true,
"answer": 65536,
"timestamp": "2026-02-08T03:15:39.787422Z"
} | cbba3f | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 148,
"completion_tokens": 509
},
"timestamp": "2026-02-17T22:24:01.977Z",
"answer": 65536
}
] | 2 | [
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
ca8639 | lin_form_endings_v1_1125832087_362 | Let $a = 40$ and $b = 50$. Define $m = \left\lfloor \frac{50}{\gcd(40, 50)} \right\rfloor$. Let $k = 14053$, and define $s = k \cdot m$. Compute the remainder when $s$ is divided by $62621$. Determine the value of this remainder. | 7,644 | graphs = [
Graph(
let={
"a_coeff": Const(40),
"b_coeff": Const(50),
"_inner_result": Floor(Div(Const(50), GCD(a=Ref("a_coeff"), b=Ref("b_coeff")))),
"_scale_k": Const(14053),
"_scaled": Mul(Ref("_scale_k"), Ref("_inner_result")),
"_mod_... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 2 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T03:02:25.086582Z | {
"verified": true,
"answer": 7644,
"timestamp": "2026-02-08T03:02:25.087729Z"
} | 32a2b7 | 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": 323
},
"timestamp": "2026-02-10T12:33:34.251Z",
"answer": 7644
},
{
"id... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"statu... | {
"lo": -9.14,
"mid": -6.05,
"hi": -3.73
} | ||
8ccf00 | comb_factorial_compute_v1_1918700295_3746 | Let $n = 7$. Define $r = n!$. Let $q$ be the remainder when $|r|$ is divided by $11$. Compute the Bell number $B_q$. | 2 | graphs = [
Graph(
let={
"n": Const(7),
"result": Factorial(Ref("n")),
"Q": Bell(Mod(value=Abs(arg=Ref(name='result')), modulus=Const(11))),
},
goal=Ref("Q"),
)
] | COMB | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | 58d7e9 | comb_factorial_compute_v1 | bell_mod | 2 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.029 | 2026-02-08T08:51:18.333860Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-02-08T08:51:18.362518Z"
} | f4df2a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 151,
"completion_tokens": 367
},
"timestamp": "2026-02-24T10:12:08.518Z",
"answer": 2
},
{
"id": ... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",... | {
"lo": -7.18,
"mid": -5,
"hi": -3.01
} | ||
a9e351 | geo_count_lattice_rect_v1_124444284_6038 | Compute the number of lattice points in the rectangle $[0, 169] \times [0, 59]$, including the boundary. | 10,200 | graphs = [
Graph(
let={
"a": Const(169),
"b": Const(59),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0 | 2026-02-08T08:05:55.152308Z | {
"verified": true,
"answer": 10200,
"timestamp": "2026-02-08T08:05:55.152710Z"
} | f6aa9d | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 139,
"completion_tokens": 206
},
"timestamp": "2026-02-24T08:51:00.303Z",
"answer": 10200
},
{
"i... | 2 | [] | {
"lo": -9.23,
"mid": -6.18,
"hi": -4.06
} | ||||
9772aa | modular_count_residue_v1_1520064083_10101 | Let $P$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 169$. Let $m$ be the minimum value of $x + y$ over all such pairs. Let $R$ be the number of positive integers $n$ such that $1 \le n \le 51984$ and $n \equiv 19 \pmod{m}$. Compute the remainder when $32386 \cdot R$ is divided by $8476... | 65,445 | graphs = [
Graph(
let={
"upper": Const(51984),
"m": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(169)))), expr=Sum(Var("x"), Var("y"))... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | modular_count_residue_v1 | null | 3 | 0 | [
"B3"
] | 1 | 1.917 | 2026-02-08T11:12:16.571238Z | {
"verified": true,
"answer": 65445,
"timestamp": "2026-02-08T11:12:18.487866Z"
} | 334fdb | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 149,
"completion_tokens": 1358
},
"timestamp": "2026-02-14T10:49:52.489Z",
"answer": 65445
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
094e58_n | comb_factorial_compute_v1_1218484723_2647 | A digital counter starts at $1$ and doubles each second: $1$, $2$, $4$. After three seconds, it sums these values to get $n$. It then calculates the factorial of $n$. What value does it display? | 5,040 | COMB | null | COMPUTE | sympy | POLY_ORBIT_COUNT | [
"SUM_GEOM"
] | 04214c | comb_factorial_compute_v1 | null | 2 | null | [
"POLY_ORBIT_COUNT",
"SUM_GEOM"
] | 2 | 0.173 | 2026-02-25T04:23:55.001371Z | null | da1bc8 | 094e58 | narrative | 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": 695
},
"timestamp": "2026-03-30T18:46:55.838Z",
"answer": 5040
},
{
"id... | 1 | [
{
"lemma": "C2",
"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",
"status": "no"
}
... | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | |
2967f5 | diophantine_product_count_v1_153355830_632 | Let $k$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $x \cdot y = 32400$. Let $r$ be the number of positive integers $x$ such that $1 \leq x \leq 113$, $x$ divides $k$, and $\frac{k}{x} \leq 113$. Compute the smallest positive integer $m$ such that the $m$-th Fibonacci ... | 30 | graphs = [
Graph(
let={
"k": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(32400)))), expr=Sum(Var("x"), Var("y")))),
"upper": Const(11... | NT | null | COUNT | sympy | L3B | [
"B3"
] | 0cd20d | diophantine_product_count_v1 | null | 6 | 0 | [
"B3",
"L3B"
] | 2 | 0.332 | 2026-02-08T04:05:31.281360Z | {
"verified": true,
"answer": 30,
"timestamp": "2026-02-08T04:05:31.613393Z"
} | cf19c3 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 230,
"completion_tokens": 2384
},
"timestamp": "2026-02-10T15:15:52.460Z",
"answer": 30
},
{
"id... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
781523 | lin_form_endings_v1_677425708_2772 | Let $a = 63$ and $b = 36$. Define $r = \left\lfloor \frac{a}{\gcd(a,b)} \right\rfloor$. Let $k = 16469$ and $M = 90539$. Compute the remainder when $k \cdot r$ is divided by $M$. | 24,744 | graphs = [
Graph(
let={
"a_coeff": Const(63),
"b_coeff": Const(36),
"_inner_result": Floor(Div(Const(63), GCD(a=Ref("a_coeff"), b=Ref("b_coeff")))),
"_scale_k": Const(16469),
"_scaled": Mul(Ref("_scale_k"), Ref("_inner_result")),
"_mod_... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 3 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T05:15:39.150327Z | {
"verified": true,
"answer": 24744,
"timestamp": "2026-02-08T05:15:39.150844Z"
} | 1f67b6 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 136,
"completion_tokens": 232
},
"timestamp": "2026-02-11T22:26:56.050Z",
"answer": 24744
},
{
"id": 11,
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": ... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
f2c0eb | modular_modexp_compute_v1_1520064083_3729 | Let $a = 2$. Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $x + y = 114$. Define $e$ to be the maximum value of $xy$ over all pairs $(x,y) \in S$. Let $m = 36864$. Compute the remainder when $a^e$ is divided by $m$. | 32,768 | graphs = [
Graph(
let={
"a": Const(2),
"e": 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(114)))), expr=Mul(Var("x"), Var("y")))),
... | NT | null | COMPUTE | sympy | B1 | [
"B1"
] | 5b950e | modular_modexp_compute_v1 | null | 4 | 0 | [
"B1"
] | 1 | 0.001 | 2026-02-08T05:50:08.861571Z | {
"verified": true,
"answer": 32768,
"timestamp": "2026-02-08T05:50:08.862637Z"
} | 8d0ad6 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 129,
"completion_tokens": 1322
},
"timestamp": "2026-02-12T16:17:20.496Z",
"answer": 32768
},
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
cd5c7e | nt_count_coprime_and_v1_2051736721_517 | Let $k_1$ be the number of integers $j$ with $0 \leq j \leq 576$ such that $\binom{576}{j}$ is odd. Let $k_2 = 9$. Determine the number of positive integers $n$ with $1 \leq n \leq 89073$ such that $\gcd(n, k_1) = 1$ and $\gcd(n, k_2) = 1$. | 29,691 | graphs = [
Graph(
let={
"upper": Const(89073),
"k1": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(576)), Eq(Mod(value=Binom(n=Const(576), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')),
... | NT | null | COUNT | sympy | V8 | [
"V8"
] | 86348e | nt_count_coprime_and_v1 | null | 4 | 0 | [
"V8"
] | 1 | 19.258 | 2026-02-08T15:28:53.540915Z | {
"verified": true,
"answer": 29691,
"timestamp": "2026-02-08T15:29:12.798474Z"
} | 580831 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 141,
"completion_tokens": 1286
},
"timestamp": "2026-02-16T06:44:26.880Z",
"answer": 29691
},
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
},
{
"lemma": "V8_SUM",
"status... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
d89623 | comb_factorial_compute_v1_2051736721_4070 | Let $n_2 = 2$. Define
$$
t = \sum_{k=0}^{n_2} (-1)^k \binom{n_2}{k}.
$$
Let $n_1 = t$. Define
$$
e = \sum_{k_1=0}^{n_1} (-1)^{k_1} \binom{n_1}{k_1}.
$$
Let $n = 7e$. Compute $n!$. | 5,040 | graphs = [
Graph(
let={
"n2": Const(2),
"t": Summation(var="k", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n2"), k=Var("k")))),
"n1": Ref("t"),
"e": Summation(var="k1", start=Const(0), end=Ref("n1"), expr=Mul(Pow(Const(-1), ... | COMB | null | COMPUTE | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING"
] | c21569 | comb_factorial_compute_v1 | null | 3 | 2 | [
"BINOMIAL_ALTERNATING"
] | 1 | 0.002 | 2026-02-08T17:42:38.070800Z | {
"verified": true,
"answer": 5040,
"timestamp": "2026-02-08T17:42:38.072510Z"
} | 5cd67c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 142,
"completion_tokens": 463
},
"timestamp": "2026-02-24T22:50:01.920Z",
"answer": 5040
},
{
... | 2 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",... | {
"lo": -10,
"mid": -7.42,
"hi": -4.85
} | ||
307b84_l | geo_visible_lattice_v1_1918700295_239 | Let $n = 77$. Define $L$ to be the number of ordered pairs $(x, y)$ of positive integers such that $1 \leq x, y \leq n$ and $\gcd(x, y) = 1$. Compute the Bell number of $|L| \bmod 11$. | 5 | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 6 | 0 | null | null | 0.125 | 2026-02-08T03:06:38.470795Z | {
"verified": false,
"answer": 1,
"timestamp": "2026-02-08T03:06:38.595978Z"
} | 9703f3 | 307b84 | legacy_text | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 178,
"completion_tokens": 32768
},
"timestamp": "2026-02-23T21:45:32.592Z",
"answer": null
},
{
... | 0 | [] | {
"lo": 3.43,
"mid": 5.73,
"hi": 8.84
} | |||
cb8b92 | nt_max_prime_below_v1_1520064083_6647 | Let $P$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 72$, $\gcd(p, q) = 1$, and $p < q$. Let $m$ be the number of elements in $P$. Let $S$ be the set of all prime numbers $n$ such that $m \le n \le 22201$. Determine the value of the largest element in $S$. | 22,193 | graphs = [
Graph(
let={
"upper": Const(22201),
"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 | 0.528 | 2026-02-08T08:15:25.142098Z | {
"verified": true,
"answer": 22193,
"timestamp": "2026-02-08T08:15:25.669738Z"
} | a1aa09 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 149,
"completion_tokens": 5672
},
"timestamp": "2026-02-13T16:51:24.655Z",
"answer": 22193
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "V5",
"... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
2fb379 | nt_count_coprime_and_v1_865884756_39 | Let $k_1$ be the largest prime number $n$ such that $2 \leq n \leq 9$, and let $k_2 = 9$. Let $S$ be the set of all integers $n_1$ such that $1 \leq n_1 \leq 20224$, $\gcd(n_1, k_1) = 1$, and $\gcd(n_1, k_2) = 1$.
Let $N = |S|$. Compute the remainder when $26394 \cdot N$ is divided by $50557$. | 25,077 | graphs = [
Graph(
let={
"upper": Const(20224),
"k1": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(9)), IsPrime(Var("n"))))),
"k2": Const(9),
"result": CountOverSet(set=SolutionsSet(var=Var("n1"), conditio... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | nt_count_coprime_and_v1 | null | 5 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 2.355 | 2026-02-08T15:07:53.718489Z | {
"verified": true,
"answer": 25077,
"timestamp": "2026-02-08T15:07:56.073269Z"
} | 636972 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 239,
"completion_tokens": 2087
},
"timestamp": "2026-02-10T03:03:26.319Z",
"answer": 25077
},
{
"... | 1 | [
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.09,
"mid": -0.49,
"hi": 6.1
} | ||
899768 | comb_sum_binomial_row_v1_1915831931_1815 | Let $a$ be the number of positive integers $p$ for which there exists a positive integer $q > p$ such that $pq = 36$ and $\gcd(p, q) = 1$. Let $b$ be the number of positive integers $p_1$ for which there exists a positive integer $q > p_1$ such that $p_1 q = 1245090$ and $\gcd(p_1, q) = 1$. Compute $a^b$. | 65,536 | 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=36)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(value=1)), ... | NT | null | SUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/COPRIME_PAIRS"
] | 3bbd71 | comb_sum_binomial_row_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.004 | 2026-02-08T16:27:53.573472Z | {
"verified": true,
"answer": 65536,
"timestamp": "2026-02-08T16:27:53.577728Z"
} | 4a3fbf | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 152,
"completion_tokens": 2102
},
"timestamp": "2026-02-17T03:44:57.183Z",
"answer": 65536
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
a335e7 | algebra_vieta_sum_v1_1915831931_2586 | Let $k$ be the number of positive integers $n$ at most $307$ such that $\gcd(n, 14) = 1$. Let $S$ be the set of all real numbers $x$ satisfying
$$
x^4 - x^3 - 140x^2 + kx + 4320 = 0.
$$
Compute the absolute value of the sum of all elements of $S$. | 1 | graphs = [
Graph(
let={
"_n": Const(4),
"result": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Ref("_n")), Mul(Const(-1), Pow(Var("x"), Const(3))), Mul(Const(-140), Pow(Var("x"), Const(2))), Mul(CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"C4"
] | 08d162 | algebra_vieta_sum_v1 | null | 6 | 0 | [
"C4",
"MIN_PRIME_FACTOR"
] | 2 | 0.045 | 2026-02-08T16:57:52.330706Z | {
"verified": true,
"answer": 1,
"timestamp": "2026-02-08T16:57:52.375267Z"
} | 484532 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 154,
"completion_tokens": 749
},
"timestamp": "2026-02-16T08:54:14.161Z",
"answer": 3
},
{
"id": 11,
... | 1 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
34fbb3 | lte_diff_endings_v1_1116507919_506 | Let $a = 22$, $b = 1$, $p = 3$, $n = 729$, and $m = 486$. Define $d_n = a^n - b^n$ and $d_m = a^m - b^m$. Let $v_1$ be the largest integer $k$ such that $p^k$ divides $d_n$, and let $v_2$ be the largest integer $k$ such that $p^k$ divides $d_m$. Compute the remainder when $17882(v_1 - v_2)$ is divided by 56781. | 17,882 | graphs = [
Graph(
let={
"a_val": Const(22),
"b_val": Const(1),
"p_val": Const(3),
"n_val": Const(729),
"m_val": Const(486),
"a_pow_n": Pow(Ref("a_val"), Ref("n_val")),
"b_pow_n": Pow(Ref("b_val"), Ref("n_val")),
... | NT | null | COMPUTE | sympy | LTE_DIFF | [
"LTE_DIFF"
] | cf8260 | lte_diff_endings_v1 | null | 7 | null | [
"LTE_DIFF"
] | 1 | 0.001 | 2026-02-08T02:37:38.309549Z | {
"verified": true,
"answer": 17882,
"timestamp": "2026-02-08T02:37:38.310390Z"
} | 1d5281 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 245,
"completion_tokens": 825
},
"timestamp": "2026-02-08T19:38:35.721Z",
"answer": 17882
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -7.44,
"mid": -4.14,
"hi": -0.84
} | ||
a817a7 | alg_poly4_sum_v1_601307018_10679 | Let $A$ be the number of ordered pairs $(a1, b1)$ of positive integers with $1 \leq a1, b1 \leq 20$ such that $10a1^2 - 18a1b1 + 25b1^2 \leq 6185$. Let $m = \min\{|x - y| : x, y > 0,\, xy = 256685\}$. Compute the remainder when
$$
\sum_{\substack{a=1 \\ b=1}}^{A,\, m} \left(17a^4 - 4a^3b + 6a^2b^2 - 4ab^3 + b^4\right)... | 42,522 | graphs = [
Graph(
let={
"_m": Const(59702),
"_n": Const(2),
"result": Mod(value=SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var(... | ALG | null | COMPUTE | sympy | QF_PSD_COUNT_LEQ | [
"QF_PSD_COUNT_LEQ",
"B3_DIFF"
] | 0d9616 | alg_poly4_sum_v1 | null | 7 | 0 | [
"B3_DIFF",
"QF_PSD_COUNT_LEQ"
] | 2 | 1.462 | 2026-03-10T11:09:09.314684Z | {
"verified": true,
"answer": 42522,
"timestamp": "2026-03-10T11:09:10.776885Z"
} | 19faba | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 277,
"completion_tokens": 12918
},
"timestamp": "2026-04-19T14:30:28.445Z",
"answer": 42522
},
{
... | 1 | [
{
"lemma": "B3_DIFF",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
}
] | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
28d0a1 | antilemma_k3_v1_1526740231_11 | Let $n = 13873$. Define $x$ to be the sum of $\phi(d)$ over all positive divisors $d$ of $n$, where $\phi$ denotes Euler's totient function. Let $Q$ be the remainder when the difference between the sum of $\phi(d)$ over all positive divisors $d$ of $900$ and $x$ is divided by $79302$. Compute $Q$. | 66,329 | graphs = [
Graph(
let={
"_n": Const(13873),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Mod(value=Sub(SumOverDivisors(n=Const(value=900), var='d', expr=EulerPhi(n=Var(name='d'))), Ref("x")), modulus=Const(79302)),
},
... | NT | COMB | COMPUTE | sympy | K3 | [
"K3",
"K3"
] | afd97d | antilemma_k3_v1 | negation_mod | 3 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T11:18:28.452511Z | {
"verified": true,
"answer": 66329,
"timestamp": "2026-02-08T11:18:28.453458Z"
} | 248c95 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 133,
"completion_tokens": 386
},
"timestamp": "2026-02-14T11:51:00.338Z",
"answer": 66329
},
{... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
1dde66 | diophantine_fbi2_min_v1_1915831931_2356 | Let $a$ be the maximum value of $xy$ where $x$ and $y$ are positive integers such that $x + y = 130$. Let $s$ be the minimum value of $x + y$ where $x$ and $y$ are positive integers such that $xy = a$. Determine the value of the smallest integer $d$ such that $d \geq 2$, $d \leq s$, $d$ divides $120$, and $\frac{120}{d... | 2 | graphs = [
Graph(
let={
"_n": Const(2),
"k": Const(120),
"upper": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), MaxOverSet(set=Ma... | NT | null | EXTREMUM | sympy | B1 | [
"B1/B3"
] | 80b49d | diophantine_fbi2_min_v1 | null | 6 | 0 | [
"B1",
"B3"
] | 2 | 0.011 | 2026-02-08T16:44:47.531607Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-02-08T16:44:47.542420Z"
} | 8e8994 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 157,
"completion_tokens": 1006
},
"timestamp": "2026-02-17T12:13:57.405Z",
"answer": 2
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemm... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
a370b6 | diophantine_fbi2_min_v1_1918700295_1590 | Let $k = 24$. Determine the value of the smallest integer $d$ such that $7 \leq d \leq 34$, $d$ divides $k$, and $\frac{k}{d} \geq 3$. | 8 | graphs = [
Graph(
let={
"k": Const(24),
"a": Const(6),
"b": Const(2),
"upper": Const(34),
"result": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(7)), Leq(Var("d"), Ref("upper")), Divides(divisor=Var("d"), dividend=Ref... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | diophantine_fbi2_min_v1 | null | 3 | 0 | [
"LIN_FORM"
] | 1 | 0.041 | 2026-02-08T05:54:16.260118Z | {
"verified": true,
"answer": 8,
"timestamp": "2026-02-08T05:54:16.300761Z"
} | ff88a7 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 107,
"completion_tokens": 350
},
"timestamp": "2026-02-11T23:15:08.162Z",
"answer": 8
},
{
"id": 11,
"... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.73,
"hi": -5.46
} | ||
ea1e15 | modular_sum_quadratic_residues_v1_1520064083_9472 | Let $p$ be the largest prime number less than or equal to $282$. Compute $\frac{p(p-1)}{4}$. | 19,670 | graphs = [
Graph(
let={
"_n": Const(282),
"p": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), Const(4)),
},
goal=Ref("re... | NT | null | SUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | modular_sum_quadratic_residues_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.002 | 2026-02-08T10:47:04.433916Z | {
"verified": true,
"answer": 19670,
"timestamp": "2026-02-08T10:47:04.435715Z"
} | 435a8d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 74,
"completion_tokens": 480
},
"timestamp": "2026-02-14T08:50:11.135Z",
"answer": 19670
},
{
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
619757 | antilemma_v7_kummer_124444284_711 | Let $a$ be the largest integer such that $3^a$ divides $\binom{b}{c}$, where $b$ is the largest integer such that $5^b$ divides $9765625^{31}$, and $c$ is the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 3844$. Compute the value of $a$. | 3 | graphs = [
Graph(
let={
"_n": Const(31),
"x": MaxKDivides(target=Binom(n=MaxKDivides(target=Pow(Const(9765625), Ref("_n")), base=Const(5)), k=MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(a... | NT | null | COMPUTE | sympy | K14 | [
"K14/V7",
"B3/V7",
"V7"
] | cf107e | antilemma_v7_kummer | null | 6 | null | [
"B3",
"K14",
"V7"
] | 3 | 0.003 | 2026-02-08T03:27:55.945132Z | {
"verified": true,
"answer": 3,
"timestamp": "2026-02-08T03:27:55.947892Z"
} | dd0a05 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 201,
"completion_tokens": 2857
},
"timestamp": "2026-02-09T20:54:08.508Z",
"answer": 3
},
{
"id":... | 2 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "K14",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
... | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
e5a882 | antilemma_product_of_sums_v1_124444284_403 | Let $S_1$ be the sum of $i \cdot j$ over all ordered pairs $(i, j)$ where $1 \leq i \leq 5$ and $1 \leq j \leq 3$. Let $S_2$ be the sum of $k$ over all ordered pairs $(k, \ell)$ where $1 \leq k \leq 11$ and $1 \leq \ell \leq 5$. Compute the value of $S_1 \cdot S_2$. | 29,700 | graphs = [
Graph(
let={
"S1": SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Const(1), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(5)), right=IntegerRange(start=Const(1), end=Const(3)))), expr=Mul(Var("i"), Var("j")))),
... | NT | null | COMPUTE | sympy | PRODUCT_OF_SUMS | [
"PRODUCT_OF_SUMS",
"ONE_PHI_2"
] | 5bd3e5 | antilemma_product_of_sums_v1 | null | 2 | 0 | [
"ONE_PHI_2",
"PRODUCT_OF_SUMS"
] | 2 | 0.001 | 2026-02-08T03:15:38.832715Z | {
"verified": true,
"answer": 29700,
"timestamp": "2026-02-08T03:15:38.833923Z"
} | 99d09e | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 227,
"completion_tokens": 481
},
"timestamp": "2026-02-09T17:10:45.605Z",
"answer": 29700
},
{
"i... | 2 | [
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "ONE_PHI_2",
"status": "ok"
},
{
... | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
83ddf8 | comb_count_derangements_v1_601307018_2634 | Let $D_n$ denote the number of derangements of $n$ elements. For each non-negative integer $a$, define $R_a = (3a^4 + a^2 - 4a + 1) \bmod 4489$ and $S_a = (3R_a^4 + R_a^2 - 4R_a + 1) \bmod 4489$. Let $T$ be the set of integers $t$ such that $t = 3a + 5b$ for some integers $a, b$ with $1 \le a \le 501$, $1 \le b \le 600... | 14,833 | graphs = [
Graph(
let={
"_m": Const(4489),
"_n": Const(4),
"n": CountOverSet(set=SolutionsSet(var=Var("a"), condition=And(Geq(Var("a"), Const(0)), Leq(Var("a"), CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/POLY_ORBIT_HENSEL"
] | 007af8 | comb_count_derangements_v1 | null | 7 | 0 | [
"LIN_FORM",
"POLY_ORBIT_HENSEL"
] | 2 | 0.006 | 2026-03-10T03:18:18.172106Z | {
"verified": true,
"answer": 14833,
"timestamp": "2026-03-10T03:18:18.177821Z"
} | 04f05d | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 309,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T05:59:23.218Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_ORBIT_HENSEL",
"status": "ok_later"
},
{
"lemma": "V7",
... | {
"lo": 3.34,
"mid": 5.77,
"hi": 8.89
} | ||
42308b | comb_count_partitions_v1_2051736721_1032 | Let $n$ be the minimum value of $x + y$ where $x$ and $y$ are positive integers such that $xy = 441$. Let $c$ be the number of integers $t$ with $15 \leq t \leq 7821$ for which there exist positive integers $a \leq 211$ and $b \leq 987$ such that $t = 9a + 6b$. Compute the remainder when $c - p(n)$ is divided by $78328... | 27,755 | graphs = [
Graph(
let={
"_n": Const(78328),
"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(441)))), expr=Sum(Var("x"), Var("y")))),... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM",
"B3"
] | ad075d | comb_count_partitions_v1 | negation_mod | 6 | 0 | [
"B3",
"LIN_FORM"
] | 2 | 0.004 | 2026-02-08T15:48:30.981493Z | {
"verified": true,
"answer": 27755,
"timestamp": "2026-02-08T15:48:30.985502Z"
} | 87c38d | 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": 4750
},
"timestamp": "2026-02-24T18:40:27.755Z",
"answer": 27755
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"sta... | {
"lo": -2.4,
"mid": 1.57,
"hi": 5.75
} | ||
e7e3c0 | comb_binomial_compute_v1_1918700295_2458 | Let $n = 16$ and $k = 8$. Let $r = \binom{n}{k}$. Let $s$ be the number of ordered pairs $(i, j)$ with $1 \le i \le 63$ and $1 \le j \le 143$ such that $\gcd(i, j) = 1$. Let $Q$ be the remainder when $s - r$ is divided by $81506$. Find the value of $Q$. | 74,191 | graphs = [
Graph(
let={
"_n": Const(81506),
"n": Const(16),
"k": Const(8),
"result": Binom(n=Ref("n"), k=Ref("k")),
"Q": Mod(value=Sub(CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(GCD(a=Var("i"), b=Var("j")),... | NT | null | COMPUTE | sympy | COUNT_COPRIME_GRID | [
"COUNT_COPRIME_GRID"
] | b363a0 | comb_binomial_compute_v1 | negation_mod | 5 | 0 | [
"COUNT_COPRIME_GRID"
] | 1 | 0.001 | 2026-02-08T07:54:06.017651Z | {
"verified": true,
"answer": 74191,
"timestamp": "2026-02-08T07:54:06.018941Z"
} | c15cd1 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 147,
"completion_tokens": 4441
},
"timestamp": "2026-02-13T13:14:38.060Z",
"answer": 74191
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
067bae | geo_count_lattice_triangle_v1_1915831931_4069 | Let $n = 88$. The area of a triangle with vertices at $(0,0)$, $(144,169)$, and $(n,225)$ is to be computed using the shoelace formula. Let $A$ be twice the area of this triangle, so
$$
A = \left|144 \cdot 225 + 88 \cdot (-169)\right|.
$$
Let $B$ be the number of lattice points on the boundary of the triangle, computed... | 8,736 | graphs = [
Graph(
let={
"_n": Const(88),
"area_2x": Abs(arg=Sum(Mul(Const(value=144), Const(value=225)), Mul(Const(value=88), Sub(left=Const(value=0), right=Const(value=169))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=144)), b=Abs(arg=Const(value=169))), GCD(a=Abs(arg=... | NT | null | COUNT | sympy | B1 | [
"B1"
] | 5b950e | geo_count_lattice_triangle_v1 | null | 5 | 0 | [
"B1"
] | 1 | 0.009 | 2026-02-08T18:06:01.697040Z | {
"verified": true,
"answer": 8736,
"timestamp": "2026-02-08T18:06:01.705685Z"
} | 1a6b4a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 231,
"completion_tokens": 1207
},
"timestamp": "2026-02-18T13:11:22.965Z",
"answer": 8736
},
{... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
c30582_n | comb_count_permutations_fixed_v1_601307018_962 | A game show awards points in increments of $3a + 2b$, where a contestant chooses integers $a$ and $b$ each from $1$ to $3$. Only scores between $5$ and $15$ inclusive are valid. Let $n$ be the number of distinct valid scores. The host then selects $6$ of these scores to feature in a bonus round, and the remaining $n-6$... | 168 | COMB | null | COUNT | sympy | POLY_ORBIT_LEGENDRE | [
"LIN_FORM"
] | 7b2633 | comb_count_permutations_fixed_v1 | null | 3 | null | [
"LIN_FORM",
"POLY_ORBIT_LEGENDRE"
] | 2 | 0.008 | 2026-03-10T01:33:13.749407Z | null | c8329c | c30582 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 245,
"completion_tokens": 3550
},
"timestamp": "2026-03-29T14:44:13.736Z",
"answer": 168
},
{
"id... | 2 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -10,
"mid": -5.89,
"hi": -1.79
} | |
5bbada | comb_factorial_compute_v1_1742523217_3286 | Let $ n $ be the largest integer such that $ 3^n $ divides $ 9 \times 729 $. Compute $ n! $. | 40,320 | graphs = [
Graph(
let={
"_n": Const(729),
"n": MaxKDivides(target=Mul(Const(9), Ref("_n")), base=Const(3)),
"result": Factorial(Ref("n")),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | K13 | [
"K13"
] | 8d970a | comb_factorial_compute_v1 | null | 3 | 0 | [
"K13"
] | 1 | 0.001 | 2026-02-08T05:45:48.601509Z | {
"verified": true,
"answer": 40320,
"timestamp": "2026-02-08T05:45:48.602029Z"
} | 496070 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 125,
"completion_tokens": 239
},
"timestamp": "2026-02-18T19:28:25.324Z",
"answer": 40320
}
] | 2 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status... | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
af9eb0 | modular_count_residue_v1_1742523217_2560 | Let $n = 67535$ and $u = 83160$. Let $m$ be the number of nonnegative integers $j$ such that $0 \leq j \leq 32840$ and $\binom{32840}{j}$ is odd, increased by 4. Let $r = 1$. Define $S$ as the set of all integers $n$ such that $1 \leq n \leq u$ and $n \equiv r \pmod{m}$. Let $Q = 50639 \cdot |S| \bmod n$. Compute $Q$. | 16,410 | graphs = [
Graph(
let={
"_n": Const(67535),
"upper": Const(83160),
"m": Sum(CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(32840)), Eq(Mod(value=Binom(n=Const(32840), k=Var("j")), modulus=Const(2)), Const(1))), domai... | ALG | COMB | COUNT | sympy | V8 | [
"V8"
] | 86348e | modular_count_residue_v1 | null | 6 | 0 | [
"V8"
] | 1 | 5.591 | 2026-02-08T04:50:13.200562Z | {
"verified": true,
"answer": 16410,
"timestamp": "2026-02-08T04:50:18.791311Z"
} | 42dd40 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 242,
"completion_tokens": 14918
},
"timestamp": "2026-02-24T02:10:44.833Z",
"answer": 16410
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
}
] | {
"lo": -0.05,
"mid": 2.89,
"hi": 5.27
} | ||
d6264c_n | alg_qf_psd_count_leq_v1_1218484723_6312 | An engineer designs a rectangular tank whose base dimensions are positive integers $(x, y)$ and must satisfy $xy = 20151121$. Among all such designs, she chooses those with minimal possible sum $x + y$ and calls this minimum $M$. She then studies pressure values given by
$$v = -16ab + 2b^{2} + 32a^{2},$$
where $a$ and ... | 11,127 | ALG | null | COUNT | sympy | QF_PSD_DISTINCT | [
"QF_PSD_DISTINCT/QF_PSD_DISTINCT",
"B3/QF_PSD_DISTINCT"
] | fa89e7 | alg_qf_psd_count_leq_v1 | null | 7 | null | [
"B3",
"QF_PSD_DISTINCT"
] | 2 | 0.784 | 2026-02-25T07:52:54.640265Z | null | dfa560 | d6264c | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 424,
"completion_tokens": 22518
},
"timestamp": "2026-03-31T01:08:05.833Z",
"answer": 2921
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_DISTINCT",
"status": "ok"
}
] | {
"lo": 3.8,
"mid": 6.33,
"hi": 9.49
} | |
d5afd4 | diophantine_product_count_v1_1431428450_202 | Let $k = \sum_{k=1}^{15} k$. Let $\mathcal{S}$ be the set of all positive integers $x$ such that $1 \le x \le 79$, $x$ divides $k$, and $\frac{k}{x} \le 79$. Compute the number of elements in $\mathcal{S}$. Let $Q = 70756$ minus this number. Find the value of $Q$. | 70,742 | graphs = [
Graph(
let={
"k": Summation(var="k", start=Const(1), end=Const(15), expr=Var("k")),
"upper": Const(79),
"result": CountOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), Const(1)), Leq(Var("x"), Ref("upper")), Divides(divisor=Var("x"), dividend=... | NT | null | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | diophantine_product_count_v1 | null | 4 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.006 | 2026-02-08T13:17:42.306258Z | {
"verified": true,
"answer": 70742,
"timestamp": "2026-02-08T13:17:42.312073Z"
} | 71a6a0 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 137,
"completion_tokens": 1434
},
"timestamp": "2026-02-15T12:05:14.503Z",
"answer": 70742
},
... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
d12afe | comb_bell_compute_v1_1742523217_3258 | Let $d$ be the largest positive divisor of $78$ that is at most $6$. Let $n$ be the maximum value of $xy$ over all ordered pairs $(x, y)$ of positive integers such that $x + y = d$. Compute the Bell number $B_n$. | 21,147 | graphs = [
Graph(
let={
"_m": Const(6),
"_n": MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Leq(Var("d"), Ref("_m")), Divides(divisor=Var("d"), dividend=Const(78))))),
"n": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[V... | NT | COMB | COMPUTE | sympy | MAX_DIVISOR | [
"MAX_DIVISOR/B1"
] | 137cb2 | comb_bell_compute_v1 | null | 6 | 0 | [
"B1",
"MAX_DIVISOR"
] | 2 | 0.002 | 2026-02-08T05:45:11.148389Z | {
"verified": true,
"answer": 21147,
"timestamp": "2026-02-08T05:45:11.150160Z"
} | a7f00f | 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": 1103
},
"timestamp": "2026-02-12T13:36:04.483Z",
"answer": 21147
},
... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
84fdf8 | nt_num_divisors_compute_v1_1520064083_2951 | Let $n$ be the largest prime number less than or equal to 233. Let $c = 56109$. Compute the remainder when $c$ multiplied by the number of positive divisors of $n$ is divided by 98422. | 13,796 | graphs = [
Graph(
let={
"_n": Const(2),
"n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Const(233)), IsPrime(Var("n"))))),
"result": NumDivisors(n=Ref("n")),
"_c": Const(56109),
"Q": Mod(value=Mu... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | nt_num_divisors_compute_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.002 | 2026-02-08T05:21:20.808150Z | {
"verified": true,
"answer": 13796,
"timestamp": "2026-02-08T05:21:20.809719Z"
} | 29f28f | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 115,
"completion_tokens": 281
},
"timestamp": "2026-02-11T22:30:35.220Z",
"answer": 13796
},
{
"id": 11,
... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.73,
"hi": -5.46
} | ||
7dcb86 | comb_count_derangements_v1_48377204_2100 | Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 18$, $\gcd(p, q) = 1$, and $p < q$. Let $m$ be the number of elements in $S$. Let $n$ be the largest prime number less than or equal to 8 that is greater than or equal to $m$. Compute the subfactorial of $n$, t... | 8,070 | graphs = [
Graph(
let={
"_m": Const(95788),
"_n": Const(64793),
"n": MaxOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq... | NT | COMB | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/MAX_PRIME_BELOW"
] | 2248fc | comb_count_derangements_v1 | null | 6 | 0 | [
"COPRIME_PAIRS",
"MAX_PRIME_BELOW"
] | 2 | 0.002 | 2026-02-08T16:35:59.341868Z | {
"verified": true,
"answer": 8070,
"timestamp": "2026-02-08T16:35:59.343915Z"
} | 19575f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 173,
"completion_tokens": 2078
},
"timestamp": "2026-02-17T07:24:16.726Z",
"answer": 8070
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"statu... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
5d1470 | antilemma_k3_v1_151522320_245 | Let $n$ be a positive integer. Define $\phi(n)$ to be the number of positive integers less than or equal to $n$ that are relatively prime to $n$. Let $x$ be the sum of $\phi(d)$ over all positive divisors $d$ of $44002$. Compute the remainder when $44121 \cdot x$ is divided by $96161$. | 17,813 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=44002), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Mod(value=Mul(Const(44121), Ref("x")), modulus=Const(96161)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 4 | 0 | [
"K3"
] | 1 | 0 | 2026-02-08T03:06:06.724997Z | {
"verified": true,
"answer": 17813,
"timestamp": "2026-02-08T03:06:06.725349Z"
} | 301f9a | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 195,
"completion_tokens": 1268
},
"timestamp": "2026-02-09T00:42:51.978Z",
"answer": 17813
},
{
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -3.45,
"mid": 1.18,
"hi": 5.72
} | ||
474b5c_n | modular_modexp_compute_v1_601307018_432 | A fundraiser collects donations in increments equal to multiples of 181 between 1 and 1086, summing them into a total amount $S$. A raffle gives entries to every integer amount from 1 to $S$ that shares no common factor with 20. If each raffle entry doubles the prize pool, starting from 1, and the final prize is taken ... | 488 | NT | null | COMPUTE | sympy | SUM_DIVISIBLE | [
"SUM_DIVISIBLE/C4"
] | 12e9ba | modular_modexp_compute_v1 | null | 6 | null | [
"C4",
"SUM_DIVISIBLE"
] | 2 | 0.003 | 2026-03-10T00:57:35.228005Z | null | c88137 | 474b5c | narrative | CC BY 4.0 | [
{
"id": 1,
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"relaxed": false
},
"usage": {
"prompt_tokens": 194,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T14:09:12.648Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "C4",
"status": "ok_later"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
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},
{
"lemma": "SUM_DIVISIBLE",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"lem... | {
"lo": 1.7,
"mid": 5.03,
"hi": 8.38
} | |
a9e47f | modular_count_residue_v1_168721529_1054 | Let $m = 100$. Consider the set of all ordered pairs $(x,y)$ of positive integers such that $xy = m$. Let $S$ be the set of all values of $x + y$ as $(x,y)$ ranges over these pairs. Let $n$ be the minimum value in $S$.
Let $P$ be the set of all prime numbers $p$ such that $2 \leq p \leq n$. Let $m'$ be the largest ele... | 2,736 | graphs = [
Graph(
let={
"_m": Const(100),
"_n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_m")))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | COUNT | sympy | B3 | [
"B3/MAX_PRIME_BELOW"
] | f253c0 | modular_count_residue_v1 | null | 5 | 0 | [
"B3",
"MAX_PRIME_BELOW"
] | 2 | 1.687 | 2026-02-08T13:26:27.148089Z | {
"verified": true,
"answer": 2736,
"timestamp": "2026-02-08T13:26:28.835153Z"
} | 16d035 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 260,
"completion_tokens": 3955
},
"timestamp": "2026-02-09T13:30:48.642Z",
"answer": 2736
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MOD_FACTORIAL",
"st... | {
"lo": -8.27,
"mid": -5.03,
"hi": -1.92
} | ||
78edd7 | geo_count_lattice_rect_v1_124444284_4695 | Let $a = 55$ and $b = 167$. Define $\text{result}$ to be the number of lattice points in the rectangle $[0, a] \times [0, b]$, including the boundary. Let $c = 78713$ and define $Q$ to be the remainder when $c \cdot \text{result}$ is divided by $56092$. Compute $Q$. | 5,320 | graphs = [
Graph(
let={
"a": Const(55),
"b": Const(167),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"_c": Const(78713),
"Q": Mod(value=Mul(Ref("_c"), Ref("result")), modulus=Const(56092)),
},
goal=Ref("Q"),
)... | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 2 | 0 | null | null | 0.001 | 2026-02-08T06:11:38.559256Z | {
"verified": true,
"answer": 5320,
"timestamp": "2026-02-08T06:11:38.559905Z"
} | 0a6282 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 197,
"completion_tokens": 1823
},
"timestamp": "2026-02-24T05:36:08.617Z",
"answer": 5320
},
{
"i... | 1 | [] | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||||
c4a7fa | comb_factorial_compute_v1_2051736721_327 | Let $n$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p < q$, $\gcd(p, q) = 1$, and $pq = 12600$. Compute the remainder when $44121 \cdot n!$ is divided by $96302$. | 68,176 | graphs = [
Graph(
let={
"_n": Const(96302),
"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=12600)), Eq(left=GCD(a=Var(name='p'), b=Var(n... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_factorial_compute_v1 | null | 6 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.002 | 2026-02-08T15:22:05.439532Z | {
"verified": true,
"answer": 68176,
"timestamp": "2026-02-08T15:22:05.441961Z"
} | 76446b | 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": 3495
},
"timestamp": "2026-02-16T04:49:45.510Z",
"answer": 68176
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
bb101e_l | comb_factorial_compute_v1_717093673_2818 | Let $n$ be the number of integers $j$ with $0 \leq j \leq 16898$ such that $\binom{16898}{j} \equiv 1 \pmod{2}$. Compute the remainder when $11449 - n!$ is divided by $69553$. | 11,449 | ALG | COMB | COMPUTE | sympy | V8 | [
"V8"
] | 86348e | comb_factorial_compute_v1 | null | 6 | 0 | [
"V8"
] | 1 | 0.001 | 2026-02-08T17:13:01.915070Z | {
"verified": false,
"answer": 40682,
"timestamp": "2026-02-08T17:13:01.916479Z"
} | a5d6c0 | bb101e | legacy_text | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 109,
"completion_tokens": 2786
},
"timestamp": "2026-02-17T21:54:09.576Z",
"answer": 40682
},
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
}
] | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | |
425f15 | geo_visible_lattice_v1_1742523217_1469 | Let $n = 71$. Define $P$ to be the number of ordered pairs $(x, y)$ of positive integers such that $1 \le x, y \le n$ and $\gcd(x, y) = 1$. Compute the remainder when $23537 \cdot P$ is divided by $66168$. | 21,383 | graphs = [
Graph(
let={
"n": Const(71),
"result": VisibleLatticePoints(n=Ref(name='n')),
"Q": Mod(value=Mul(Const(23537), Ref("result")), modulus=Const(66168)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 5 | 0 | null | null | 0.279 | 2026-02-08T04:00:33.792256Z | {
"verified": true,
"answer": 21383,
"timestamp": "2026-02-08T04:00:34.071633Z"
} | 22a571 | 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": 7769
},
"timestamp": "2026-02-10T16:29:40.318Z",
"answer": 21383
},
{
"... | 1 | [] | {
"lo": -0.05,
"mid": 2.89,
"hi": 5.27
} | ||||
92b642 | comb_binomial_compute_v1_153355830_1935 | Let $n$ be the maximum value of $xy$ over all pairs of positive integers $(x, y)$ such that $x + y = 8$. Let $r = \binom{n}{7}$. Compute the sum of $d_i \cdot (i+1)^2$ over all digits $d_i$ of $r$, where $d_i$ is the $i$th digit from the right (starting at $i=0$), and add $44944$ to this sum. | 45,037 | graphs = [
Graph(
let={
"_n": Const(8),
"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")))),
... | ALG | COMB | COMPUTE | sympy | B1 | [
"B1"
] | 5b950e | comb_binomial_compute_v1 | null | 4 | 0 | [
"B1"
] | 1 | 0.002 | 2026-02-08T06:47:56.743141Z | {
"verified": true,
"answer": 45037,
"timestamp": "2026-02-08T06:47:56.745222Z"
} | 5d17bb | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 218,
"completion_tokens": 1276
},
"timestamp": "2026-02-24T07:07:20.674Z",
"answer": 45037
},
{
"... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -4.93,
"mid": -2.91,
"hi": -0.71
} | ||
3158cc | antilemma_sum_equals_v1_458359167_2600 | Let $n = 30$. Let $x$ be the number of ordered pairs $(i, j)$ of positive integers such that $i + j = n$, $1 \leq i \leq 28$, and $1 \leq j \leq 29$. Compute the Bell number $B_r$, where $r$ is the remainder when $|x|$ is divided by 11. | 203 | graphs = [
Graph(
let={
"_n": Const(30),
"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(28)), right=IntegerRange(start=Const(1), end=Con... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 2 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.022 | 2026-02-08T06:22:12.952392Z | {
"verified": true,
"answer": 203,
"timestamp": "2026-02-08T06:22:12.974423Z"
} | e95630 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 196,
"completion_tokens": 903
},
"timestamp": "2026-02-24T06:48:24.609Z",
"answer": 203
},
{
"id"... | 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": "V8",
"status": "no"
},
{
"lemma": "V8_SU... | {
"lo": -5.98,
"mid": -3.97,
"hi": -1.94
} | ||
8fff2d | comb_count_derangements_v1_48377204_2619 | Let $ m = 64 $. Let $ a $ be the minimum value of $ x + y $ over all pairs of positive integers $ (x, y) $ such that $ x \cdot y = m $. Let $ b $ be the minimum value of $ x_1 + y_1 $ over all pairs of positive integers $ (x_1, y_1) $ such that $ x_1 \cdot y_1 = a $. Compute the number of derangements of $ b $ elements... | 14,833 | graphs = [
Graph(
let={
"_m": Const(64),
"_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")))),
... | COMB | null | COUNT | sympy | B3 | [
"B3/B3"
] | 8ffef9 | comb_count_derangements_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.003 | 2026-02-08T16:50:45.848744Z | {
"verified": true,
"answer": 14833,
"timestamp": "2026-02-08T16:50:45.851520Z"
} | b05026 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 152,
"completion_tokens": 922
},
"timestamp": "2026-02-17T14:30:49.863Z",
"answer": 14833
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V8",
"status": ... | {
"lo": -8,
"mid": -4.75,
"hi": -2.28
} | ||
36c15c | nt_sum_divisors_mod_v1_124444284_2826 | Let $m = 2$, and let $n_0$ be the largest prime number $n$ such that $2 \leq n \leq 5$. Let $S$ be the set of all positive integers $j$ such that $$ j \leq \left| \left\{ t \in \mathbb{Z}^+ \mid 9 \leq t \leq 734,\ \exists a,b \in \mathbb{Z}^+ \text{ with } 1 \leq a \leq 17,\ 1 \leq b \leq 100,\ t = 2a + 7b \right\} \r... | 23,764 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_m")), Leq(Var("n"), Const(5)), IsPrime(Var("n"))))),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(1)), Leq(Var("... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW/C3",
"LIN_FORM/C3"
] | 7ba2c0 | nt_sum_divisors_mod_v1 | null | 7 | 0 | [
"C3",
"LIN_FORM",
"MAX_PRIME_BELOW"
] | 3 | 0.013 | 2026-02-08T05:02:22.724136Z | {
"verified": true,
"answer": 23764,
"timestamp": "2026-02-08T05:02:22.736782Z"
} | 8919c3 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 328,
"completion_tokens": 5490
},
"timestamp": "2026-02-11T22:47:12.406Z",
"answer": 23764
},
{
... | 1 | [
{
"lemma": "C3",
"status": "ok_later"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
03fa04 | diophantine_fbi2_count_v1_1439011603_97 | Let $k = 180$. Consider the set of integers $d$ such that $5 \le d \le 85$, $d$ divides $k$, and $5 \le \frac{k}{d} \le 85$. Let $r$ be the number of such integers $d$. Compute the remainder when the Bell number $B_{|r| \mod 11}$ is divided by $54317$. | 7,341 | graphs = [
Graph(
let={
"k": Const(180),
"a": Const(4),
"b": Const(4),
"upper": Const(81),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(5)), Leq(Var("d"), Const(85)), Divides(divisor=Var("d"), dividend=Ref... | NT | COMB | COUNT | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | diophantine_fbi2_count_v1 | null | 3 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.055 | 2026-02-08T15:12:57.915628Z | {
"verified": true,
"answer": 7341,
"timestamp": "2026-02-08T15:12:57.970999Z"
} | 628abd | 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": 1226
},
"timestamp": "2026-02-16T01:20:51.224Z",
"answer": 7341
},
{... | 1 | [
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
34d5d0 | diophantine_fbi2_count_v1_1520064083_10381 | Let $d$ be a positive integer. Determine the number of values of $d$ such that $4 \leq d \leq 147$, $d$ divides 840, and the quotient $\frac{840}{d}$ is an integer between 5 and 148, inclusive. | 22 | graphs = [
Graph(
let={
"k": Const(840),
"a": Const(3),
"b": Const(4),
"upper": Const(144),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(4)), Leq(Var("d"), Const(147)), Divides(divisor=Var("d"), dividend=R... | NT | null | COUNT | sympy | SUM_DIVISIBLE | [
"B3/B3",
"K13"
] | 7865dd | diophantine_fbi2_count_v1 | null | 3 | 0 | [
"B3",
"K13",
"SUM_DIVISIBLE"
] | 3 | 0.163 | 2026-02-08T11:22:34.034536Z | {
"verified": true,
"answer": 22,
"timestamp": "2026-02-08T11:22:34.197985Z"
} | e68390 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 106,
"completion_tokens": 1763
},
"timestamp": "2026-02-14T13:24:12.610Z",
"answer": 22
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
9604ec | comb_binomial_compute_v1_1978505735_5845 | Let $n$ be the largest prime number such that $2 \leq n \leq 14$. Let $k = 5$. Define $\text{result} = \binom{n}{k}$ and let $Q$ be the Bell number corresponding to the remainder when $|\text{result}|$ is divided by 11.
Find the value of $Q$. | 1 | graphs = [
Graph(
let={
"_n": Const(11),
"n": MaxOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(2)), Leq(Var("n1"), Const(14)), IsPrime(Var("n1"))))),
"k": Const(5),
"result": Binom(n=Ref("n"), k=Ref("k")),
"Q": Bell(Mod... | NT | COMB | COMPUTE | sympy | K2 | [
"MAX_PRIME_BELOW"
] | dc3ad3 | comb_binomial_compute_v1 | null | 4 | 0 | [
"K2",
"MAX_PRIME_BELOW"
] | 2 | 0.057 | 2026-02-08T19:15:10.556641Z | {
"verified": true,
"answer": 1,
"timestamp": "2026-02-08T19:15:10.613440Z"
} | dac656 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 122,
"completion_tokens": 633
},
"timestamp": "2026-02-18T21:45:11.634Z",
"answer": 1
},
{
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
27f7aa | alg_poly4_sum_v1_601307018_1535 | Find the remainder when $$\sum_{a=1}^{390} \sum_{b=1}^{d} \left( 82a^4 + 97b^4 + 332a^3b + 510a^2b^2 + 356ab^3 \right)$$ is divided by $97117$, where $d = \min\left\{ |x - y| : x, y > 0,\ xy = 312439 \right\}$. | 81,920 | graphs = [
Graph(
let={
"_n": Const(356),
"result": Mod(value=SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(390)), Geq(Var("b"), Const(1)), Leq(Var("b"), MinOverSet(set=MapOverSet(set=So... | ALG | null | COMPUTE | sympy | B3_DIFF | [
"B3_DIFF"
] | b47ea7 | alg_poly4_sum_v1 | null | 6 | 0 | [
"B3_DIFF"
] | 1 | 0.4 | 2026-03-10T02:16:37.935851Z | {
"verified": true,
"answer": 81920,
"timestamp": "2026-03-10T02:16:38.335899Z"
} | 10988f | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 213,
"completion_tokens": 14070
},
"timestamp": "2026-03-29T02:35:50.560Z",
"answer": 4778
},
{
... | 1 | [
{
"lemma": "B3_DIFF",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 3.99,
"mid": 6.11,
"hi": 9.15
} | ||
7003e4 | diophantine_fbi2_count_v1_124444284_8582 | Let $k = 720$. Let $D$ be the set of all integers $d$ such that $5 \leq d \leq 103$, $d$ divides $k$, and $4 \leq \frac{k}{d} \leq 102$. Let $r$ be the number of elements in $D$. Let $Q$ be the set of all positive integers $p$ for which there exists a positive integer $q > p$ such that $pq = 262571535772741429332880210... | 4,438 | graphs = [
Graph(
let={
"k": Const(720),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(5)), Leq(Var("d"), Const(103)), Divides(divisor=Var("d"), dividend=Ref("k")), Geq(Div(Ref("k"), Var("d")), Const(4)), Leq(Div(Ref("k"), Var("d")), Const(10... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 14fbb8 | diophantine_fbi2_count_v1 | quadratic_mod | 6 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.014 | 2026-02-08T09:47:52.917133Z | {
"verified": true,
"answer": 4438,
"timestamp": "2026-02-08T09:47:52.931590Z"
} | 48a878 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 193,
"completion_tokens": 4014
},
"timestamp": "2026-02-14T19:40:51.661Z",
"answer": 4438
},
{... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
6b61cf | comb_count_surjections_v1_2051736721_5359 | Let $n = 6$. Let $k$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 6$. Define $R = k! \cdot S(n, k)$, where $S(n, k)$ denotes the Stirling number of the second kind. Compute the remainder when $44121 \cdot R$ is divided by $54965$. | 25,495 | graphs = [
Graph(
let={
"_n": Const(44121),
"n": Const(6),
"k": 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... | COMB | null | COUNT | sympy | COMB1 | [
"COMB1"
] | 567f58 | comb_count_surjections_v1 | null | 5 | 0 | [
"COMB1"
] | 1 | 0.001 | 2026-02-08T18:31:23.157984Z | {
"verified": true,
"answer": 25495,
"timestamp": "2026-02-08T18:31:23.159337Z"
} | 4efad5 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 138,
"completion_tokens": 2027
},
"timestamp": "2026-02-18T17:34:07.859Z",
"answer": 25495
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.12,
"mid": 1.47,
"hi": 6.57
} | ||
dca7b2 | modular_modexp_compute_v1_784195855_5197 | Let $a = 13$. Define $e$ to be the number of integers $t$ with $20 \le t \le 2354$ for which there exist positive integers $a$ and $b$ with $1 \le a \le 88$, $1 \le b \le 187$, and
$$
t = 14a + 6b.
$$
Let $m = 70756$. Compute the remainder when $a^e$ is divided by $m$. | 17,921 | graphs = [
Graph(
let={
"a": Const(13),
"e": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=88)), Geq(left=Var(n... | NT | null | COMPUTE | sympy | C3 | [
"LIN_FORM"
] | 7b2633 | modular_modexp_compute_v1 | null | 4 | 0 | [
"C3",
"LIN_FORM"
] | 2 | 0.02 | 2026-02-08T07:44:07.617107Z | {
"verified": true,
"answer": 17921,
"timestamp": "2026-02-08T07:44:07.637362Z"
} | efc821 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 150,
"completion_tokens": 7431
},
"timestamp": "2026-02-13T12:29:57.426Z",
"answer": 17921
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
b1706f | alg_qf_psd_orbit_v1_1218484723_2324 | Find the number of ordered pairs $(a, b)$ of positive integers with $1 \leq a \leq b \leq 441$ such that $$\left|\left\{ (a_1, b_1) : 1 \leq a_1, b_1 \leq 35,\ 17b_1^4 + 17a_1^4 + 102a_1^2b_1^2 + 68a_1^3b_1 + 68a_1b_1^3 = 76116752 \right\}\right| \cdot b^2 + 25a^2 = 1600625.$$ | 6 | graphs = [
Graph(
let={
"_n": Const(441),
"result": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Ref("_n")), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(441)), Leq(Var("a"), Var("b")), Eq(Sum(Mul(CountOv... | ALG | null | COUNT | sympy | MOBIUS_COPRIME | [
"POLY4_COUNT"
] | 861d91 | alg_qf_psd_orbit_v1 | null | 5 | 0 | [
"MOBIUS_COPRIME",
"POLY4_COUNT"
] | 2 | 0.728 | 2026-02-25T04:09:34.078179Z | {
"verified": true,
"answer": 6,
"timestamp": "2026-02-25T04:09:34.805687Z"
} | c044df | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 257,
"completion_tokens": 10715
},
"timestamp": "2026-03-29T04:11:51.340Z",
"answer": 6
},
{
"id"... | 1 | [
{
"lemma": "POLY4_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 1.55,
"mid": 4.7,
"hi": 7.23
} | ||
cf2779 | nt_count_coprime_v1_397696148_2452 | Let $k$ be the number of ordered pairs $(i, j)$ of integers with $1 \le i \le 8$ and $1 \le j \le 9$ such that $\gcd(i, j) = 1$. Let $R$ be the number of positive integers $n$ with $1 \le n \le 36100$ such that $\gcd(n, k) = 1$. Compute the value of
$$
R + 2^{R \bmod 16} \bmod 77174.
$$ | 63,711 | graphs = [
Graph(
let={
"_n": Const(16),
"upper": Const(36100),
"k": 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(8)), right... | NT | null | COUNT | sympy | COUNT_COPRIME_GRID | [
"COUNT_COPRIME_GRID"
] | 20ec03 | nt_count_coprime_v1 | null | 6 | 0 | [
"COUNT_COPRIME_GRID"
] | 1 | 3.173 | 2026-02-08T13:20:10.333563Z | {
"verified": true,
"answer": 63711,
"timestamp": "2026-02-08T13:20:13.506806Z"
} | 03f255 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 161,
"completion_tokens": 889
},
"timestamp": "2026-02-15T14:33:42.950Z",
"answer": 63711
},
{... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
caf72d | nt_count_coprime_v1_1978505735_4201 | Let $ n = 169 $. Let $ k $ be the minimum value of $ x + y $ over all ordered pairs of positive integers $ (x, y) $ such that $ xy = 169 $. Let the upper bound be $ 69169 $. Determine the value of the number of positive integers $ n $ such that $ 1 \leq n \leq 69169 $ and $ \gcd(n, k) = 1 $. | 31,925 | graphs = [
Graph(
let={
"_n": Const(169),
"upper": Const(69169),
"k": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_n")))),... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | nt_count_coprime_v1 | null | 4 | 0 | [
"B3"
] | 1 | 5.24 | 2026-02-08T18:04:50.616612Z | {
"verified": true,
"answer": 31925,
"timestamp": "2026-02-08T18:04:55.856320Z"
} | a76fc6 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 138,
"completion_tokens": 1634
},
"timestamp": "2026-02-18T13:44:21.228Z",
"answer": 31925
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
043ff5 | modular_modexp_compute_v1_677425708_848 | Let $a = 11$. Let $e$ be the maximum value of $xy$ over all pairs of positive integers $(x, y)$ such that $x + y = 186$. Compute $a^e \mod 71824$. Determine the value of this result. | 29,739 | graphs = [
Graph(
let={
"a": Const(11),
"e": 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(186)))), expr=Mul(Var("x"), Var("y")))),
... | NT | null | COMPUTE | sympy | B1 | [
"B1"
] | 5b950e | modular_modexp_compute_v1 | null | 5 | 0 | [
"B1"
] | 1 | 0.002 | 2026-02-08T03:49:29.585224Z | {
"verified": true,
"answer": 29739,
"timestamp": "2026-02-08T03:49:29.586951Z"
} | 7d03ab | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 168,
"completion_tokens": 4949
},
"timestamp": "2026-02-10T14:27:34.389Z",
"answer": 29739
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
a44253 | comb_bell_compute_v1_1978505735_3440 | Let $n$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 16$. Let $r$ be the Bell number $B_n$. Let $Q = (34881 \cdot r) \bmod 94844$. Compute $Q$. | 54,772 | graphs = [
Graph(
let={
"_n": Const(94844),
"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(16)))), expr=Sum(Var("x"), Var("y")))),
... | COMB | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | comb_bell_compute_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.002 | 2026-02-08T17:38:39.916709Z | {
"verified": true,
"answer": 54772,
"timestamp": "2026-02-08T17:38:39.918716Z"
} | fe8bd8 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 115,
"completion_tokens": 1000
},
"timestamp": "2026-02-18T06:03:49.865Z",
"answer": 54772
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
... | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||
1aff99 | diophantine_sum_product_min_v1_1918700295_46 | Let $S = 62$ and $P = 432$. Define $r$ to be the smallest positive integer $x$ such that $1 \leq x \leq 61$ and $x(S - x) = P$. Let $c$ be the smallest positive integer $n$ such that the largest power of $11$ dividing $n!$ is at least the number of positive integers $m \leq 664$ for which the sum of the digits of $m$ i... | 3,325 | graphs = [
Graph(
let={
"_m": Const(664),
"_n": Const(11),
"S": Const(62),
"P": Const(432),
"result": MinOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), Const(1)), Leq(Var("x"), Const(61)), Eq(Mul(Var("x"), Sub(Ref("S"), Var("x")... | NT | null | EXTREMUM | sympy | L3B | [
"L3B/V5"
] | f21c51 | diophantine_sum_product_min_v1 | negation_mod | 7 | 0 | [
"L3B",
"V5"
] | 2 | 0.007 | 2026-02-08T02:57:40.409101Z | {
"verified": true,
"answer": 3325,
"timestamp": "2026-02-08T02:57:40.416208Z"
} | 66b797 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 227,
"completion_tokens": 3797
},
"timestamp": "2026-02-08T22:15:28.274Z",
"answer": 3325
},
{
"... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3B",
"status": "ok"
},
{
"lemma": "V5",
"status": "ok_later"... | {
"lo": -6.49,
"mid": 0.51,
"hi": 7.52
} | ||
b31aed | geo_visible_lattice_v1_151522320_2243 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $1 \leq x, y \leq 90$ and $\gcd(x, y) = 1$. Let $N$ be the number of elements in $S$. Compute the remainder when $625 - N$ is divided by $53366$. | 49,032 | graphs = [
Graph(
let={
"n": Const(90),
"result": VisibleLatticePoints(n=Ref(name='n')),
"_c": Const(625),
"Q": Mod(value=Sub(Ref("_c"), Ref("result")), modulus=Const(53366)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 4 | 0 | null | null | 0.169 | 2026-02-08T04:42:32.930183Z | {
"verified": true,
"answer": 49032,
"timestamp": "2026-02-08T04:42:33.098986Z"
} | 970802 | 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": 23839
},
"timestamp": "2026-02-24T01:34:49.739Z",
"answer": 49000
},
{
... | 1 | [] | {
"lo": 3.43,
"mid": 5.73,
"hi": 8.84
} | ||||
497b44 | diophantine_fbi2_count_v1_1978505735_5521 | Let $k = 60$. Determine the number of positive integers $d$ such that $5 \leq d \leq 54$, $d$ divides $k$, and the quotient $k/d$ is between 4 and 53, inclusive. Compute $51076$ minus this number. | 51,071 | graphs = [
Graph(
let={
"_n": Const(51076),
"k": Const(60),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(5)), Leq(Var("d"), Const(54)), Divides(divisor=Var("d"), dividend=Ref("k")), Geq(Div(Ref("k"), Var("d")), Const(4)), Leq(Div... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | diophantine_fbi2_count_v1 | null | 3 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.01 | 2026-02-08T19:02:40.164835Z | {
"verified": true,
"answer": 51071,
"timestamp": "2026-02-08T19:02:40.174419Z"
} | 5fae9e | 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": 1070
},
"timestamp": "2026-02-18T21:11:45.353Z",
"answer": 51071
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V7",
"statu... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
fd3083 | lin_form_endings_v1_397696148_40 | Let $a = 63$ and $b = 27$. Compute the least common multiple of $a$ and $b$, and denote it by $L$. Let $s = 1 \cdot L + a + b$. Multiply $s$ by $19580$ to obtain a value $v$. Let $M = 57456$. Find the remainder when $v$ is divided by $M$. | 4,500 | graphs = [
Graph(
let={
"a_coeff": Const(63),
"b_coeff": Const(27),
"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 | 0.001 | 2026-02-08T11:16:26.144566Z | {
"verified": true,
"answer": 4500,
"timestamp": "2026-02-08T11:16:26.145982Z"
} | 47953f | 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": 2318
},
"timestamp": "2026-02-14T10:59:03.088Z",
"answer": 4500
},
{... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
27857c | comb_bell_compute_v1_1439011603_2253 | Let $m = 2$. Define $N$ to be the number of nonnegative integers $j$ such that $0 \leq j \leq 20740$ and $\binom{20740}{j}$ is odd. Let $n$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = N$. Compute the $n$-th Bell number, which counts the number of partitions of a set of $... | 4,140 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(20740)), Eq(Mod(value=Binom(n=Const(20740), k=Var("j")), modulus=Ref("_m")), Const(1))), domain='nonnegative_integers')),
"... | COMB | null | COMPUTE | sympy | V8 | [
"V8/B3"
] | b4fc86 | comb_bell_compute_v1 | null | 7 | 0 | [
"B3",
"V8"
] | 2 | 0.002 | 2026-02-08T16:39:03.829536Z | {
"verified": true,
"answer": 4140,
"timestamp": "2026-02-08T16:39:03.831908Z"
} | dbcfcc | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 150,
"completion_tokens": 1572
},
"timestamp": "2026-02-17T08:11:20.101Z",
"answer": 4140
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
},
{
"... | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||
f5f54e | alg_sum_powers_v1_1419126231_602 | Find the remainder when $\sum_{k=1}^{1954} k^3$ is divided by the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 1194649$. | 33 | graphs = [
Graph(
let={
"_n": Const(3),
"result": Mod(value=Summation(var="k", start=Const(1), end=Const(1954), expr=Pow(Var("k"), Ref("_n"))), modulus=MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), Is... | ALG | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | alg_sum_powers_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.084 | 2026-02-25T10:04:49.628998Z | {
"verified": true,
"answer": 33,
"timestamp": "2026-02-25T10:04:49.712517Z"
} | 1b7f07 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 161,
"completion_tokens": 2588
},
"timestamp": "2026-03-30T09:07:48.883Z",
"answer": 33
},
{
"id"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | ||
7c6937 | alg_sym_quad_system_v1_601307018_3393 | Let $m = \min\{ |x - y| : x>0,\, y>0,\, xy = 12708361 \}$. Find the remainder when $$\sum_{\substack{a,b,c \geq 1 \\ a^2 + b^2 + c^2 = ab + bc + ca \\ 6a + 4b + 5c = m}} (a^4 + b^4 + c^4)$$ is divided by $5211$. | 2,295 | graphs = [
Graph(
let={
"_n": Const(6),
"result": Mod(value=SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b"), Var("c")]), condition=And(Eq(Sum(Pow(Var("a"), Const(2)), Pow(Var("b"), Const(2)), Pow(Var("c"), Const(2))), Sum(Mul(Var("a"), Var("b")), Mul... | ALG | null | COMPUTE | sympy | B3_DIFF | [
"B3_DIFF"
] | b47ea7 | alg_sym_quad_system_v1 | null | 7 | 0 | [
"B3_DIFF"
] | 1 | 1.137 | 2026-03-10T03:59:30.325419Z | {
"verified": true,
"answer": 2295,
"timestamp": "2026-03-10T03:59:31.462082Z"
} | 59a233 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 216,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T08:33:29.798Z",
"answer": null
},
{
... | 0 | [
{
"lemma": "B3_DIFF",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 3.34,
"mid": 5.77,
"hi": 8.89
} | ||
875d00 | nt_min_coprime_above_v1_1918700295_4140 | Let $a = 7921$, $b = 8145$, and $m = 214$. Consider the set of all integers $n$ such that $a < n \leq b$ and $\gcd(n, m) = 1$. Let $r$ be the smallest element of this set. Compute $r$. | 7,923 | graphs = [
Graph(
let={
"start": Const(7921),
"upper": Const(8145),
"modulus": Const(214),
"result": MinOverSet(set=SolutionsSet(var=Var("n"), condition=And(Gt(Var("n"), Ref("start")), Leq(Var("n"), Ref("upper")), Eq(GCD(a=Var("n"), b=Ref("modulus")), Const(1)... | NT | null | EXTREMUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW/LIOUVILLE_ONE",
"C3/LIOUVILLE_ONE",
"MOBIUS_SQUAREFREE"
] | 456970 | nt_min_coprime_above_v1 | null | 2 | 0 | [
"C3",
"LIOUVILLE_ONE",
"MAX_PRIME_BELOW",
"MOBIUS_SQUAREFREE"
] | 4 | 0.126 | 2026-02-08T09:09:57.717811Z | {
"verified": true,
"answer": 7923,
"timestamp": "2026-02-08T09:09:57.843655Z"
} | 353ab3 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 115,
"completion_tokens": 625
},
"timestamp": "2026-02-14T01:43:26.859Z",
"answer": 7923
},
{
... | 1 | [
{
"lemma": "C3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "LIOUVILLE_ONE",
"status": "ok_later"
},
{
"lemma":... | {
"lo": -9.12,
"mid": -6.02,
"hi": -3.62
} | ||
07c870 | comb_count_surjections_v1_655260480_1705 | Let $n$ be the number of integers $t$ with $24 \le t \le 31$ for which there exist positive integers $a \in \{1,2,3\}$ and $b \in \{1,2\}$ such that $t = 2a + 3b + 19$. Compute $3! \cdot S(n, 3)$, where $S(n, 3)$ denotes the number of ways to partition a set of $n$ elements into $3$ nonempty subsets. | 540 | 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 | COUNT | sympy | COUNT_SUM_EQUALS | [
"LIN_FORM"
] | 7b2633 | comb_count_surjections_v1 | null | 4 | 0 | [
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 2 | 0.059 | 2026-02-08T16:18:20.232962Z | {
"verified": true,
"answer": 540,
"timestamp": "2026-02-08T16:18:20.291685Z"
} | 844140 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 224,
"completion_tokens": 975
},
"timestamp": "2026-02-24T20:37:19.823Z",
"answer": 540
},
{
"id... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": ... | {
"lo": -5.65,
"mid": -3.17,
"hi": -0.81
} | ||
2a5a88 | nt_sum_gcd_range_mod_v1_458359167_3997 | Let $k$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 44100$. Let $S = \sum_{n=1}^{4000} \gcd(n, k)$. Let $M = 11657$. Compute the remainder when $44121 \cdot (S \bmod M)$ is divided by $53864$. | 50,427 | graphs = [
Graph(
let={
"_n": Const(53864),
"N": Const(4000),
"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)))),... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_gcd_range_mod_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.806 | 2026-02-08T11:28:15.036681Z | {
"verified": true,
"answer": 50427,
"timestamp": "2026-02-08T11:28:15.843034Z"
} | 1b6bb0 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 133,
"completion_tokens": 3730
},
"timestamp": "2026-02-14T14:28:10.925Z",
"answer": 50427
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
d02450 | comb_sum_binomial_row_v1_124444284_9333 | Let $n$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 36$. Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 72$, $\gcd(p, q) = 1$, and $p < q$. Compute the value of $|S|^n$. | 4,096 | graphs = [
Graph(
let={
"_n": Const(36),
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_n")))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | SUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS",
"B3"
] | 1999ea | comb_sum_binomial_row_v1 | null | 5 | 0 | [
"B3",
"COPRIME_PAIRS"
] | 2 | 0.002 | 2026-02-08T12:25:00.231941Z | {
"verified": true,
"answer": 4096,
"timestamp": "2026-02-08T12:25:00.233892Z"
} | b28ed4 | 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": 1641
},
"timestamp": "2026-02-15T00:46:44.646Z",
"answer": 4096
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma":... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
a41509 | nt_min_phi_inverse_v1_1915831931_2778 | Let $m=2$. Let $T$ be the number of integers $j$ with $0\le j\le 640$ such that
$$\binom{640}{j}\equiv 1\pmod{m}.$$
Let $L$ be the number of ordered pairs $(x_1,x_2)$ of positive odd integers such that
$$x_1+x_2=T.$$
Let $n$ be the least integer $d$ such that $d\ge L$ and $d$ divides $273829$.
Let $U$ be the number o... | 66,082 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(na... | NT | null | EXTREMUM | sympy | V8 | [
"V8/COMB1/MIN_PRIME_FACTOR/COUNT_SUM_EQUALS",
"COPRIME_PAIRS"
] | eb1e81 | nt_min_phi_inverse_v1 | two_stage_modexp | 8 | 0 | [
"COMB1",
"COPRIME_PAIRS",
"COUNT_SUM_EQUALS",
"MIN_PRIME_FACTOR",
"V8"
] | 5 | 0.571 | 2026-02-08T17:08:21.224385Z | {
"verified": true,
"answer": 66082,
"timestamp": "2026-02-08T17:08:21.794954Z"
} | 6b090f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 331,
"completion_tokens": 2971
},
"timestamp": "2026-02-17T20:19:33.887Z",
"answer": 66082
},
... | 1 | [
{
"lemma": "COMB1",
"status": "ok_later"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok_later"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
c8c6aa | modular_mod_compute_v1_151522320_1009 | Let $m = 4235$. Consider the set of all positive integers $j$ such that $1 \leq j \leq 2222$ and
$$
j^d \leq 54165190265169632,
$$
where $d$ is the smallest divisor of $m$ that is at least $2$. Let $a$ be the number of such integers $j$.
Compute the remainder when $44121 \cdot (a \bmod 10201)$ is divided by $63152$. | 24,958 | graphs = [
Graph(
let={
"_m": Const(4235),
"_n": Const(63152),
"a": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(1)), Leq(Var("j"), Const(2222)), Leq(Pow(Var("j"), MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/C3"
] | 92256e | modular_mod_compute_v1 | null | 5 | 0 | [
"C3",
"MIN_PRIME_FACTOR"
] | 2 | 0.005 | 2026-02-08T03:42:26.463447Z | {
"verified": true,
"answer": 24958,
"timestamp": "2026-02-08T03:42:26.468391Z"
} | 0b12d1 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 222,
"completion_tokens": 3676
},
"timestamp": "2026-02-10T15:32:29.418Z",
"answer": 24958
},
{
"... | 1 | [
{
"lemma": "C3",
"status": "ok_later"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V7",
"... | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
62656a | nt_count_gcd_equals_v1_124444284_8177 | Let $k$ be the number of integers $t$ such that $7 \leq t \leq 135$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 40$, $1 \leq b \leq 11$, and $t = 2a + 5b$. Let $d = 1$ and let $\text{upper} = 22201$. Compute the number of positive integers $n$ such that $1 \leq n \leq \text{upper}$ and $\gcd(n, k)... | 17,761 | graphs = [
Graph(
let={
"upper": Const(22201),
"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=40)), Geq(lef... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_count_gcd_equals_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 8.95 | 2026-02-08T09:35:09.132185Z | {
"verified": true,
"answer": 17761,
"timestamp": "2026-02-08T09:35:18.082433Z"
} | 310c77 | 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": 2926
},
"timestamp": "2026-02-14T05:05:49.710Z",
"answer": 17761
},
... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
05e7a0 | modular_product_range_v1_124444284_283 | Let $m = 58$. Consider the set of all ordered pairs $(x,y)$ of positive integers such that $x + y = m$. Let $n$ be the maximum value of $xy$ over all such pairs. Now consider the set of all ordered pairs $(x,y)$ of positive integers such that $xy = n$. Let $s$ be the minimum value of $x + y$ over all such pairs. Comput... | 1,141 | graphs = [
Graph(
let={
"_m": Const(58),
"_n": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Ref("_m")))), expr=Mul(Var("x"), Var("y")))),
... | NT | null | COMPUTE | sympy | B1 | [
"B1/B3"
] | 80b49d | modular_product_range_v1 | null | 6 | 0 | [
"B1",
"B3"
] | 2 | 0.004 | 2026-02-08T03:08:43.806839Z | {
"verified": true,
"answer": 1141,
"timestamp": "2026-02-08T03:08:43.810652Z"
} | 8afd9a | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 221,
"completion_tokens": 5562
},
"timestamp": "2026-02-23T17:07:20.863Z",
"answer": 1141
},
{
"... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
... | {
"lo": -3.49,
"mid": 1.84,
"hi": 7.55
} | ||
2e661c | geo_count_lattice_triangle_v1_655260480_1427 | Let $A$ be twice the area of a triangle with vertices at $(0,0)$, $(193,121)$, and $(55,128)$. Compute
$$
\frac{A + 2 - B}{2},
$$
where $B$ is the number of lattice points on the boundary of the triangle. Find the remainder when this value is multiplied by $22859$ and then divided by $53268$. | 25,920 | graphs = [
Graph(
let={
"area_2x": Abs(arg=Sum(Mul(Const(value=193), Const(value=128)), Mul(Const(value=55), Sub(left=Const(value=0), right=Const(value=121))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=193)), b=Abs(arg=Const(value=121))), GCD(a=Abs(arg=Sub(left=Const(value=55), rig... | ALG | NT | COUNT | sympy | [] | geo_count_lattice_triangle_v1 | null | 5 | 0 | null | null | 0.009 | 2026-02-08T16:07:55.667413Z | {
"verified": true,
"answer": 25920,
"timestamp": "2026-02-08T16:07:55.676357Z"
} | c641a8 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 129,
"completion_tokens": 1945
},
"timestamp": "2026-02-16T21:33:42.239Z",
"answer": 25920
},
... | 1 | [] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||||
24705f | nt_count_phi_equals_v1_1520064083_1822 | Let $n$ be a positive integer. Define $k = 540$ and $U = 1523$. Let $S$ be the set of all positive integers $n$ such that $1 \leq n \leq U$ and $\phi(n) = k$, where $\phi$ denotes Euler's totient function. Let $R$ be the number of elements in $S$. Let $P$ be the set of all prime numbers $n$ such that $2 \leq n \leq 12$... | 4,140 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": Const(1523),
"k": Const(540),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(EulerPhi(n=Var("n")), Ref("k"))))),
"Q": Bel... | NT | COMB | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | 88ea9c | nt_count_phi_equals_v1 | bell_mod | 7 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.099 | 2026-02-08T04:19:07.342352Z | {
"verified": true,
"answer": 4140,
"timestamp": "2026-02-08T04:19:07.441139Z"
} | 23bea6 | 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": 6425
},
"timestamp": "2026-02-11T23:21:59.052Z",
"answer": 4140
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
846d0c | comb_count_derangements_v1_153355830_1206 | Let $n$ be the number of positive integers $p$ such that there exists a positive integer $q > p$ with $pq = 220500$ and $\gcd(p, q) = 1$. Compute the number of derangements of $n$ elements. | 14,833 | 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=220500)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(value=1)... | NT | COMB | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_count_derangements_v1 | null | 6 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.001 | 2026-02-08T06:11:37.862589Z | {
"verified": true,
"answer": 14833,
"timestamp": "2026-02-08T06:11:37.863286Z"
} | 80c7a7 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 103,
"completion_tokens": 3180
},
"timestamp": "2026-02-12T21:43:47.413Z",
"answer": 14833
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_FACTORI... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} |
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