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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
8c7ac0 | comb_catalan_compute_v1_1218484723_901 | Let $C_n$ denote the $n$-th Catalan number. Let $n$ be the number of integers $t$ with $5 \leq t \leq 17$ that can be expressed as $t = 2a + 3b$ for some integers $a, b$ with $1 \leq a \leq 4$, $1 \leq b \leq 3$. Let $M = C_n$. Find the remainder when $51496M$ is divided by $52035$. | 3,661 | graphs = [
Graph(
let={
"_n": Const(52035),
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=4)), Geq(left=Va... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_catalan_compute_v1 | null | 3 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-25T02:37:18.225122Z | {
"verified": true,
"answer": 3661,
"timestamp": "2026-02-25T02:37:18.226974Z"
} | 48fd27 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 223,
"completion_tokens": 4454
},
"timestamp": "2026-03-10T02:42:36.047Z",
"answer": 3661
},
{
"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": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"st... | {
"lo": -0.93,
"mid": 2.04,
"hi": 4.6
} | ||
ae3b3a | algebra_quadratic_discriminant_v1_238844314_685 | Let $a = -2$, $b = -24$, and $c = -54$. Compute the value of $b^2 - ac$, where $a$, $b$, and $c$ are used as given, and $a$ is multiplied by the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq = 300$, $\gcd(p,q) = 1$, and $p < q$. | 144 | graphs = [
Graph(
let={
"_n": Const(2),
"a": Const(-2),
"b": Const(-24),
"c": Const(-54),
"result": Sub(Pow(Ref("b"), Ref("_n")), Mul(CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'),... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | algebra_quadratic_discriminant_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.004 | 2026-02-08T13:31:05.867332Z | {
"verified": true,
"answer": 144,
"timestamp": "2026-02-08T13:31:05.870929Z"
} | 2f8270 | 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": 1558
},
"timestamp": "2026-02-15T17:31:22.785Z",
"answer": 144
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST"... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
d2e346 | antilemma_sum_factor_cartesian_v1_677425708_626 | Compute the remainder when $72755$ times the sum of $ij$ over all ordered pairs $(i,j)$ of positive integers with $1 \leq i \leq 25$ and $1 \leq j \leq 22$ is divided by $73261$. | 6,398 | graphs = [
Graph(
let={
"x": SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Const(1), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(25)), right=IntegerRange(start=Const(1), end=Const(22)))), expr=Mul(Var("i"), Var("j")))),
... | NT | null | COMPUTE | sympy | SUM_FACTOR_CARTESIAN | [
"SUM_FACTOR_CARTESIAN"
] | d9e436 | antilemma_sum_factor_cartesian_v1 | null | 4 | 0 | [
"SUM_FACTOR_CARTESIAN"
] | 1 | 0 | 2026-02-08T03:37:53.792894Z | {
"verified": true,
"answer": 6398,
"timestamp": "2026-02-08T03:37:53.793330Z"
} | 0137e5 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 173,
"completion_tokens": 2559
},
"timestamp": "2026-02-08T20:51:54.848Z",
"answer": 6398
},
{
"i... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "SUM_FACTOR_CARTESIAN",
"status": "ok"... | {
"lo": -6.51,
"mid": -0.31,
"hi": 5.43
} | ||
497ba2 | geo_count_lattice_triangle_v1_1742523217_5659 | Let $A$ be the area of a triangle with vertices at $(0,0)$, $(180,77)$, and $(19,111)$, multiplied by 2. Let $B$ be the number of lattice points on the boundary of this triangle. Define $R = \frac{A + 2 - B}{2}$. Compute the remainder when $3249 - R$ is divided by $55411$. | 49,402 | graphs = [
Graph(
let={
"area_2x": Abs(arg=Sum(Mul(Const(value=180), Const(value=111)), Mul(Const(value=19), Sub(left=Const(value=0), right=Const(value=77))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=180)), b=Abs(arg=Const(value=77))), GCD(a=Abs(arg=Sub(left=Const(value=19), right... | ALG | NT | COUNT | sympy | [] | geo_count_lattice_triangle_v1 | null | 4 | 0 | null | null | 0.002 | 2026-02-08T11:09:09.368163Z | {
"verified": true,
"answer": 49402,
"timestamp": "2026-02-08T11:09:09.370551Z"
} | 97ef45 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 130,
"completion_tokens": 1293
},
"timestamp": "2026-02-14T10:39:48.789Z",
"answer": 49402
},
... | 1 | [] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||||
0fd9d7 | nt_count_divisors_in_range_v1_1978505735_5895 | Let $n = 50400$ and let $a = 4$. Define $b$ to be the value of the sum
$$
\sum_{k=1}^{63} \varphi(k) \left\lfloor \frac{63}{k} \right\rfloor.
$$
Consider the set of all positive integers $d$ that divide $n$, satisfy $a \leq d \leq b$, and are at least $a$ and at most $b$. Compute the number of elements in this set. Fin... | 87 | graphs = [
Graph(
let={
"_n": Const(63),
"n": Const(50400),
"a": Const(4),
"b": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(63), Var("k"))))),
"result": CountOverSet(set=SolutionsSet(var=Var("d")... | NT | null | COUNT | sympy | B3 | [
"K2"
] | 6897ab | nt_count_divisors_in_range_v1 | null | 3 | 0 | [
"B3",
"K2"
] | 2 | 0.078 | 2026-02-08T19:18:00.776618Z | {
"verified": true,
"answer": 87,
"timestamp": "2026-02-08T19:18:00.854567Z"
} | beb2c3 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 169,
"completion_tokens": 2776
},
"timestamp": "2026-02-18T21:53:31.499Z",
"answer": 87
},
{
... | 1 | [
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
bb7a54 | sequence_lucas_compute_v1_458359167_397 | Let $n = \sum_{k=1}^{6} k$. Let $L_n$ denote the $n$-th Lucas number, where $L_1 = 1$, $L_2 = 3$, and $L_m = L_{m-1} + L_{m-2}$ for $m \geq 3$. Let $Q$ be the remainder when $44121 \times L_n$ is divided by $74441$. Compute $Q$. | 64,450 | graphs = [
Graph(
let={
"_n": Const(44121),
"n": Summation(var="k", start=Const(1), end=Const(6), expr=Var("k")),
"result": Lucas(arg=Ref(name='n')),
"Q": Mod(value=Mul(Ref("_n"), Ref("result")), modulus=Const(74441)),
},
goal=Ref("Q"),
)
] | NT | null | COMPUTE | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | sequence_lucas_compute_v1 | null | 3 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.001 | 2026-02-08T03:15:36.921672Z | {
"verified": true,
"answer": 64450,
"timestamp": "2026-02-08T03:15:36.922996Z"
} | 899f06 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 211,
"completion_tokens": 1848
},
"timestamp": "2026-02-10T13:41:20.913Z",
"answer": 64450
},
{
"... | 1 | [
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
35fff5 | diophantine_fbi2_count_v1_458359167_1674 | Let $k = 180$. Define $S$ to be the set of all integers $d$ such that $3 \leq d \leq 79$, $d$ divides $k$, and $5 \leq \frac{k}{d} \leq 81$. Let $r$ be the number of elements in $S$. Let $T$ be the set of all integers $t$ such that $18 \leq t \leq 124$ and there exist positive integers $a \leq 4$ and $b \leq 17$ satisf... | 841 | graphs = [
Graph(
let={
"_n": Const(81),
"k": Const(180),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(3)), Leq(Var("d"), Const(79)), Divides(divisor=Var("d"), dividend=Ref("k")), Geq(Div(Ref("k"), Var("d")), Const(5)), Leq(Div(R... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 2ba0ea | diophantine_fbi2_count_v1 | quadratic_mod | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.014 | 2026-02-08T04:48:05.241171Z | {
"verified": true,
"answer": 841,
"timestamp": "2026-02-08T04:48:05.254962Z"
} | af3ec7 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 268,
"completion_tokens": 4555
},
"timestamp": "2026-02-11T21:58:33.582Z",
"answer": 841
},
{
"i... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
065dd5 | comb_binomial_compute_v1_601307018_6830 | Let $N$ be the minimum value of $|x - y|$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 131584$. Let $n$ be the largest positive integer $d$ such that $d^2 \leq N$ and $d \mid N$. Compute $\binom{n}{6}$. | 5,005 | graphs = [
Graph(
let={
"_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(131584)))), expr=Abs(arg=Sub(left=Var(name='x'), right=Var(name='y'))))... | COMB | NT | COMPUTE | sympy | B3_DIFF | [
"B3_DIFF/B3_DIFF/B3_CLOSEST"
] | 4abe3f | comb_binomial_compute_v1 | null | 6 | 0 | [
"B3_CLOSEST",
"B3_DIFF"
] | 2 | 0.008 | 2026-03-10T07:28:25.604532Z | {
"verified": true,
"answer": 5005,
"timestamp": "2026-03-10T07:28:25.612733Z"
} | 54d42c | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 187,
"completion_tokens": 2230
},
"timestamp": "2026-04-19T05:23:08.170Z",
"answer": 5005
},
{
"... | 1 | [
{
"lemma": "B3_CLOSEST",
"status": "ok_later"
},
{
"lemma": "B3_DIFF",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "... | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
4c3c71 | nt_count_coprime_and_v1_1470522791_1417 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x \cdot y = 19945156$. Let $m$ be the minimum value of $x + y$ as $(x, y)$ ranges over $S$. Determine the number of positive integers $n$ such that $1 \leq n \leq m$, $\gcd(n, 5) = 1$, and $\gcd(n, 7) = 1$. | 6,125 | graphs = [
Graph(
let={
"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")), Const(19945156)))), expr=Sum(Var("x"), Var("y")))),
"k1": Cons... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | nt_count_coprime_and_v1 | null | 4 | 0 | [
"B3"
] | 1 | 1.214 | 2026-02-08T13:36:54.370699Z | {
"verified": true,
"answer": 6125,
"timestamp": "2026-02-08T13:36:55.585148Z"
} | 831616 | 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": 1119
},
"timestamp": "2026-02-15T19:16:58.444Z",
"answer": 6125
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
907506 | antilemma_sum_equals_v1_677425708_2036 | Let $n = 38$. Consider the set of all ordered pairs $(i,j)$ of positive integers such that $i + j = n$, where $1 \leq i \leq 37$ and $1 \leq j \leq 37$. Let $x$ be the number of such pairs. Compute the remainder when $44041x$ is divided by $67169$. | 17,461 | graphs = [
Graph(
let={
"_n": Const(38),
"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(37)), right=IntegerRange(start=Const(1), end=Con... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 3 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.008 | 2026-02-08T04:43:19.301388Z | {
"verified": true,
"answer": 17461,
"timestamp": "2026-02-08T04:43:19.309062Z"
} | b9364d | 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": 1528
},
"timestamp": "2026-02-10T04:51:58.058Z",
"answer": 17461
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.83,
"mid": -1.68,
"hi": 1.09
} | ||
edf846 | comb_count_surjections_v1_153355830_13 | Let $n = 6$. Let $k$ be the number of ordered pairs $(i, j)$ of positive integers such that $i + j = 6$, $1 \leq i \leq 4$, and $1 \leq j \leq 5$. Compute $k! \cdot S(6, k)$, where $S(6, k)$ denotes the Stirling number of the second kind. | 1,560 | graphs = [
Graph(
let={
"n": Const(6),
"k": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(6)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(4)), right=IntegerRange(start=Const(1), end=Const(5... | COMB | null | COUNT | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | comb_count_surjections_v1 | null | 4 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.011 | 2026-02-08T02:51:05.030811Z | {
"verified": true,
"answer": 1560,
"timestamp": "2026-02-08T02:51:05.042201Z"
} | 6e70cc | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 206,
"completion_tokens": 1012
},
"timestamp": "2026-02-08T19:59:16.302Z",
"answer": 1560
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "n... | {
"lo": -3.89,
"mid": -1.91,
"hi": 0.05
} | ||
909272 | comb_count_permutations_fixed_v1_784195855_10387 | Let $ a = 2 $ and $ b = 4 $. Define $ n_2 = a + b $. Let
$$
c = \sum_{k=0}^{n_2} (-1)^k \binom{n_2}{k}.
$$
Define $ n_1 = c $, and let
$$
m = \sum_{k=0}^{n_1} (-1)^k \binom{n_1}{k}.
$$
Let $ n = 7 $ and $ k = 0 $. Compute $ \binom{n}{k} \cdot !\!(n - k) $, where $ !\!r $ denotes the number of derangements of $ r $ el... | 1,854 | graphs = [
Graph(
let={
"a": Const(2),
"b": Const(4),
"n2": Sum(Ref("a"), Ref("b")),
"c": 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("c"),
"m": Summat... | COMB | null | COUNT | sympy | B3 | [
"BINOMIAL_ALTERNATING"
] | c21569 | comb_count_permutations_fixed_v1 | null | 3 | 2 | [
"B3",
"BINOMIAL_ALTERNATING"
] | 2 | 0.044 | 2026-02-08T17:49:13.196480Z | {
"verified": true,
"answer": 1854,
"timestamp": "2026-02-08T17:49:13.240912Z"
} | 4264ff | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 190,
"completion_tokens": 901
},
"timestamp": "2026-02-18T13:35:23.437Z",
"answer": 1854
},
{
... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
... | {
"lo": -4.1,
"mid": -1.76,
"hi": 1.32
} | ||
5bae4d | nt_count_coprime_v1_124444284_4676 | Let $k$ be the largest prime number $p$ such that $2 \le p \le 13$. Let $S$ be the set of all positive integers $n$ such that $1 \le n \le 48400$ and $\gcd(n, k) = 1$. Determine the number of elements in $S$. | 44,677 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": Const(48400),
"k": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Const(13)), IsPrime(Var("n"))))),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), conditio... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | nt_count_coprime_v1 | null | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 3.891 | 2026-02-08T06:11:29.487335Z | {
"verified": true,
"answer": 44677,
"timestamp": "2026-02-08T06:11:33.378726Z"
} | 7bbe8b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 118,
"completion_tokens": 466
},
"timestamp": "2026-02-12T21:02:10.890Z",
"answer": 44677
},
{... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
cf6fb4 | alg_poly_preperiod_count_v1_1218484723_7408 | Define a function $f(x) = 3x^4 - 3x^3 - 4x^2 + 3x - 3 \bmod 47$. For non-negative integers $a$, let $N = f(a)$, $M = f(N)$, $R = f(M)$, $S = f(R)$, $T = f(S)$. Find the number of integers $a$ with $0 \leq a \leq 62039$ such that $T = M$, $R \neq M$, and $S \neq M$. | 36,960 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Mul(Const(3), Pow(Var("a"), Const(4))), Mul(Const(-3), Pow(Var("a"), Const(3))), Mul(Const(-4), Pow(Var("a"), Const(2))), Mul(Const(3), Var("a")), Const(-3)), modulus=Const(47)),
"p2": Mod(value=Sum(Mul(Const(3), Pow(Ref("p1"), Const(4))), ... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_preperiod_count_v1 | null | 6 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.174 | 2026-02-25T08:50:08.671853Z | {
"verified": true,
"answer": 36960,
"timestamp": "2026-02-25T08:50:08.846257Z"
} | be61b6 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 233,
"completion_tokens": 20159
},
"timestamp": "2026-03-30T04:25:27.725Z",
"answer": 36960
},
{
... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 1.53,
"mid": 4.7,
"hi": 7.23
} | ||
47066b | lin_form_endings_v1_784195855_7935 | Let $T$ be the set of all positive integers $t$ such that $109 \le t \le 2369$ and there exist positive integers $a$ and $b$ with $1 \le a \le 21$, $1 \le b \le 44$, and $t = 70a + 20b + 19$. Let $r$ be the number of elements in $T$. Let $s = 10185 \cdot r$. Compute the remainder when $s$ is divided by $99157$. | 69,431 | graphs = [
Graph(
let={
"_inner_result": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=21)), Geq(left=Var(name='b'), right=... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 3 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T09:37:31.201091Z | {
"verified": true,
"answer": 69431,
"timestamp": "2026-02-08T09:37:31.202403Z"
} | b4fb19 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 224,
"completion_tokens": 9454
},
"timestamp": "2026-02-24T11:36:28.456Z",
"answer": 69431
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
3ca85d | diophantine_fbi2_count_v1_168721529_2102 | Let $m = 3$ and $n = 4$. Define $k$ to be the smallest positive integer such that $m^88$ divides $k!$.
Let $S$ be the set of all positive integers $d$ satisfying the following conditions:
- $d \geq 4$,
- $d \leq \max\{ p \mid p \text{ is prime and } 2 \leq p \leq 55 \}$,
- $d$ divides $k$,
- $\frac{k}{d} \geq 4$,
- $\... | 21,964 | graphs = [
Graph(
let={
"_m": Const(3),
"_n": Const(4),
"k": MinOverSet(set=SolutionsSet(var=Var("n"), condition=Geq(MaxKDivides(target=Factorial(Var("n")), base=Ref("_m")), Const(88)), domain='Z_{>0}')),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), c... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW",
"V5"
] | 7b8c99 | diophantine_fbi2_count_v1 | null | 6 | 0 | [
"MAX_PRIME_BELOW",
"V5"
] | 2 | 0.03 | 2026-02-08T14:07:12.291185Z | {
"verified": true,
"answer": 21964,
"timestamp": "2026-02-08T14:07:12.321167Z"
} | f6a42e | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 282,
"completion_tokens": 1228
},
"timestamp": "2026-02-10T02:08:33.322Z",
"answer": 21964
}
] | 2 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
... | {
"lo": -10,
"mid": -1.96,
"hi": 6.09
} | ||
337303 | nt_count_digit_sum_v1_1439011603_221 | Let $s = 1 + 2 + 3 + 4 + 5 + 6$. Compute the number of positive integers $n$ from $1$ to $300304$ inclusive such that the sum of the decimal digits of $n$ equals $s$. | 16,792 | graphs = [
Graph(
let={
"_n": Const(6),
"upper": Const(300304),
"target_sum": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Var("k")),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("uppe... | NT | null | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | nt_count_digit_sum_v1 | null | 4 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 24.194 | 2026-02-08T15:21:14.281640Z | {
"verified": true,
"answer": 16792,
"timestamp": "2026-02-08T15:21:38.475887Z"
} | 982628 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 104,
"completion_tokens": 3516
},
"timestamp": "2026-02-16T05:13:30.016Z",
"answer": 16792
},
... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
40f377 | alg_telescope_v1_1419126231_1220 | Let $T$ be the set of integers $t$ for which there exist integers $a, b$ with $1 \le a \le 1325$, $1 \le b \le 206$, $t = 4a + 7b$, and $11 \le t \le 6742$. Let $M = \sum_{k=0}^{1874} (3k^2 + 3k + 1) \bmod |T|$. Find the remainder when $44121M$ is divided by $69931$. | 41,574 | graphs = [
Graph(
let={
"_n": Const(2),
"result": Mod(value=Summation(var="k", start=Const(0), end=Const(1874), expr=Sum(Mul(Const(3), Pow(Var("k"), Ref("_n"))), Mul(Const(3), Var("k")), Const(1))), modulus=CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'... | ALG | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | alg_telescope_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.124 | 2026-02-25T10:41:07.968756Z | {
"verified": true,
"answer": 41574,
"timestamp": "2026-02-25T10:41:08.092285Z"
} | 4dfd55 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 227,
"completion_tokens": 32768
},
"timestamp": "2026-03-30T11:53:50.643Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 3.8,
"mid": 6.33,
"hi": 9.49
} | ||
3959fc | diophantine_fbi2_min_v1_784195855_1834 | Let $p_1, p_2, \ldots, p_k$ be the prime numbers satisfying $2 \leq p_i \leq 9$. Let $S$ be the set of all positive divisors $d$ of 14 such that $d \geq \max(p_1, p_2, \ldots, p_k)$ and $\frac{14}{d} \geq 2$, with $d \leq 24$. Let $m$ be the smallest element of $S$. Compute the remainder when $44121 \cdot m$ is divided... | 8,055 | graphs = [
Graph(
let={
"_n": Const(2),
"k": Const(14),
"upper": Const(24),
"result": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Const(9)... | NT | null | EXTREMUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | diophantine_fbi2_min_v1 | null | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.004 | 2026-02-08T05:21:04.084288Z | {
"verified": true,
"answer": 8055,
"timestamp": "2026-02-08T05:21:04.088652Z"
} | 31509a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 169,
"completion_tokens": 615
},
"timestamp": "2026-02-12T06:51:40.840Z",
"answer": 8055
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"st... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
a94d6a | sequence_fibonacci_compute_v1_2051736721_416 | Let $F_n$ denote the $n$th Fibonacci number, defined by $F_1 = F_2 = 1$ and $F_n = F_{n-1} + F_{n-2}$ for $n \geq 3$. Let $c$ be the minimum value of $x + y$ over all ordered pairs of positive integers $(x, y)$ such that $xy = 1048576$. Let $Q$ be the sum of $c$ and the sum
$$
\sum_{i=0}^{k-1} d_i (i+1)^2,
$$
where $d_... | 2,176 | graphs = [
Graph(
let={
"n": Const(21),
"result": Fibonacci(arg=Ref(name='n')),
"_c": 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")... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 8e300c | sequence_fibonacci_compute_v1 | digits_weighted_mod | 4 | 0 | [
"B3"
] | 1 | 0.004 | 2026-02-08T15:24:02.967900Z | {
"verified": true,
"answer": 2176,
"timestamp": "2026-02-08T15:24:02.972143Z"
} | 9412cb | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 226,
"completion_tokens": 1035
},
"timestamp": "2026-02-16T04:58:10.553Z",
"answer": 2176
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
f4dc25 | nt_count_divisible_v1_1125832087_136 | Let $n = 3$ and let $d = \sum_{k=1}^{n} k$. Determine the number of positive integers $n$ such that $1 \leq n \leq 60000$ and $n$ is divisible by $d$. Compute the remainder when $44121$ times this count is divided by $70666$. | 42,162 | graphs = [
Graph(
let={
"_n": Const(3),
"upper": Const(60000),
"divisor": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Var("k")),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper"))... | NT | null | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | nt_count_divisible_v1 | null | 3 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 4.559 | 2026-02-08T02:52:43.813109Z | {
"verified": true,
"answer": 42162,
"timestamp": "2026-02-08T02:52:48.371992Z"
} | 7acf56 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 185,
"completion_tokens": 1996
},
"timestamp": "2026-02-10T11:47:08.936Z",
"answer": 42162
},
{
"... | 1 | [
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": 1.44,
"mid": 3,
"hi": 4.55
} | ||
9bf3ca | alg_qf_psd_min_v1_601307018_3521 | Find the minimum value of $43750c^2 - 43750ab + 61250ac - 35000bc + 35875a^2 + 26250b^2$ over all ordered triples $(a, b, c)$ of positive integers such that $1 \le a \le 47$, $1 \le c \le 47$, and $1 \le b \le \min \{ d : d \geq 2, d \mid 132023 \}$. | 88,375 | graphs = [
Graph(
let={
"_n": Const(2),
"result": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b"), Var("c")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(47)), Geq(Var("b"), Const(1)), Leq(Var("b"), MinOverSet(set=SolutionsSet(var=Var... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | alg_qf_psd_min_v1 | null | 5 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.355 | 2026-03-10T04:07:22.798154Z | {
"verified": true,
"answer": 88375,
"timestamp": "2026-03-10T04:07:23.152907Z"
} | 54e423 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 217,
"completion_tokens": 12159
},
"timestamp": "2026-03-29T09:00:59.889Z",
"answer": 88375
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -2.46,
"mid": 1.23,
"hi": 4.93
} | ||
db5334 | antilemma_sum_equals_v1_1520064083_8610 | Let $m = 94$. Define $A$ as the set of all ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = m$. Let $n = |A|$. Define $B$ as the set of all ordered pairs $(i, j)$ with $1 \le i \le 47$ and $1 \le j \le 47$ such that $i + j = n$. Let $x = |B|$. Compute the smallest positive integer $k$ such tha... | 12 | graphs = [
Graph(
let={
"_m": Const(94),
"_n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2")), R... | COMB | GEOM | COMPUTE | sympy | LIN_FORM | [
"COMB1/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | 3e1adf | antilemma_sum_equals_v1 | null | 6 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 3 | 0.082 | 2026-02-08T10:16:04.868806Z | {
"verified": true,
"answer": 12,
"timestamp": "2026-02-08T10:16:04.950511Z"
} | 912442 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 246,
"completion_tokens": 1944
},
"timestamp": "2026-02-24T11:54:55.135Z",
"answer": 12
},
{
"id"... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": ... | {
"lo": -4.92,
"mid": -2.91,
"hi": -0.68
} | ||
fbbed8 | modular_modexp_compute_v1_2051736721_3958 | Let $ a $ be the smallest divisor of $ 352843 $ that is at least $ 2 $. Let $ S $ be the set of all ordered pairs of positive integers $ (x, y) $ such that $ x + y = 180 $. Define $ e $ to be the maximum value of $ xy $ over all such pairs. Let $ m = 17424 $ and define $ r $ to be the remainder when $ a^e $ is divided ... | 47,359 | graphs = [
Graph(
let={
"a": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(352843))))),
"e": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=V... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR",
"B1"
] | e7724f | modular_modexp_compute_v1 | null | 4 | 0 | [
"B1",
"MIN_PRIME_FACTOR"
] | 2 | 0.002 | 2026-02-08T17:38:31.622766Z | {
"verified": true,
"answer": 47359,
"timestamp": "2026-02-08T17:38:31.624933Z"
} | 4df783 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 183,
"completion_tokens": 2913
},
"timestamp": "2026-02-18T05:06:36.612Z",
"answer": 47359
},
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
58cdbf | comb_count_derangements_v1_2051736721_3859 | Let $n$ be the number of positive integers $n_1$ such that $1 \leq n_1 \leq 17$ and the sum of the decimal digits of $n_1$ is even. Compute the subfactorial of $n$. | 14,833 | graphs = [
Graph(
let={
"_n": Const(17),
"n": CountOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(1)), Leq(Var("n1"), Ref("_n")), Eq(Mod(value=DigitSum(Var("n1")), modulus=Const(2)), Const(0))))),
"result": Subfactorial(arg=Ref(name='n')),
... | COMB | null | COUNT | sympy | L3B | [
"L3B"
] | cc148f | comb_count_derangements_v1 | null | 4 | 0 | [
"L3B"
] | 1 | 0.002 | 2026-02-08T17:36:29.076539Z | {
"verified": true,
"answer": 14833,
"timestamp": "2026-02-08T17:36:29.078190Z"
} | c9911f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 101,
"completion_tokens": 890
},
"timestamp": "2026-02-18T04:29:53.684Z",
"answer": 14833
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "L3B",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -4.1,
"mid": -1.76,
"hi": 1.32
} | ||
8497de | comb_binomial_compute_v1_865884756_5872 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = 14$. Define $M$ to be the maximum value of $xy$ over all pairs in $S$.
Let $T$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = M$. Define $n$ to be the minimum value of $x + y$ over all pairs in $T$.
... | 3,003 | graphs = [
Graph(
let={
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var(... | ALG | COMB | COMPUTE | sympy | SUM_ARITHMETIC | [
"B1/B3"
] | 80b49d | comb_binomial_compute_v1 | null | 4 | 0 | [
"B1",
"B3",
"SUM_ARITHMETIC"
] | 3 | 0.009 | 2026-02-08T18:50:34.751057Z | {
"verified": true,
"answer": 3003,
"timestamp": "2026-02-08T18:50:34.760389Z"
} | 681689 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 151,
"completion_tokens": 1125
},
"timestamp": "2026-02-25T00:38:36.528Z",
"answer": 3003
},
{... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -8.48,
"mid": -5.37,
"hi": -3.03
} | ||
344320 | modular_sum_quadratic_residues_v1_458359167_4132 | Let $p$ be the smallest divisor of $3902092937$ that is greater than or equal to $2$. Compute $\frac{p(p-1)}{4}$.
Find the value of this expression. | 14,460 | graphs = [
Graph(
let={
"_n": Const(2),
"p": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(3902092937))))),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), Const(4)),
},
goa... | NT | null | SUM | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | modular_sum_quadratic_residues_v1 | null | 3 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.001 | 2026-02-08T11:33:19.058081Z | {
"verified": true,
"answer": 14460,
"timestamp": "2026-02-08T11:33:19.059536Z"
} | 9dd6b1 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 90,
"completion_tokens": 1977
},
"timestamp": "2026-02-14T15:29:13.296Z",
"answer": 14460
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
c9b4fe | nt_num_divisors_compute_v1_971394319_192 | Let $S$ be the set of all positive integers $n$ such that $1 \leq n \leq 1740$ and $24$ divides the $n$th Fibonacci number. Let $k$ be the number of elements in $S$. Now consider the set of all ordered pairs $(i, j)$ of positive integers such that $1 \leq i \leq 144$, $1 \leq j \leq 144$, and $i + j = k$. Let $n$ be th... | 63,719 | graphs = [
Graph(
let={
"_m": Const(74762),
"_n": Const(44121),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n... | NT | null | COMPUTE | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE/COUNT_SUM_EQUALS"
] | 55c073 | nt_num_divisors_compute_v1 | null | 5 | 0 | [
"COUNT_FIB_DIVISIBLE",
"COUNT_SUM_EQUALS"
] | 2 | 0.004 | 2026-02-08T12:53:46.446638Z | {
"verified": true,
"answer": 63719,
"timestamp": "2026-02-08T12:53:46.450388Z"
} | a0af2c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 197,
"completion_tokens": 1963
},
"timestamp": "2026-02-15T07:00:07.987Z",
"answer": 63719
},
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok_later"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V1",
"sta... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
e543e2 | comb_count_permutations_fixed_v1_124444284_4092 | Let $n$ be the largest prime number satisfying $2 \leq n \leq 7$. Compute $\binom{n}{2} \cdot !(n-2)$, where $!k$ denotes the number of derangements of $k$ elements. Then find the remainder when $73299$ times this value is divided by $77920$. | 15,796 | graphs = [
Graph(
let={
"_n": Const(73299),
"n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(7)), IsPrime(Var("n"))))),
"k": Const(2),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub(le... | NT | COMB | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | comb_count_permutations_fixed_v1 | null | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.002 | 2026-02-08T05:46:06.110885Z | {
"verified": true,
"answer": 15796,
"timestamp": "2026-02-08T05:46:06.112998Z"
} | f3d35b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 118,
"completion_tokens": 1877
},
"timestamp": "2026-02-12T14:23:45.599Z",
"answer": 15796
},
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
3e5fe3 | nt_min_crt_v1_1978505735_1805 | Let $m = 7$ and $k$ be the number of ordered pairs $(i, j)$ with $i \in \{1, 2\}$ and $j \in \{1, 2, 3, 4, 5, 6\}$ such that $\gcd(i, j) = 1$. Let $a = 6$ and $b = 7$. Let $U$ be the number of positive integers $n$ such that $1 \leq n \leq 233$ and $\gcd(n, 30) = 1$. Determine the value of the smallest positive integer... | 34 | graphs = [
Graph(
let={
"_m": Const(233),
"_n": Const(30),
"m": Const(7),
"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)... | NT | null | EXTREMUM | sympy | COUNT_COPRIME_GRID | [
"COUNT_COPRIME_GRID",
"C4"
] | 040171 | nt_min_crt_v1 | null | 5 | 0 | [
"C4",
"COUNT_COPRIME_GRID"
] | 2 | 0.019 | 2026-02-08T16:24:13.203054Z | {
"verified": true,
"answer": 34,
"timestamp": "2026-02-08T16:24:13.222065Z"
} | 70fbd2 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 219,
"completion_tokens": 1705
},
"timestamp": "2026-02-17T02:28:13.386Z",
"answer": 34
},
{
... | 1 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
9031fe | comb_count_permutations_fixed_v1_2051736721_4424 | Let $n = 8$. Define
$$
k = \sum_{k_1=0}^{3} (-1)^{k_1} \binom{3}{k_1}.
$$
Compute $\binom{n}{k} \cdot !{(n - k)}$, where $!m$ denotes the number of derangements of $m$ elements. | 14,833 | graphs = [
Graph(
let={
"n": Const(8),
"k": Summation(var="k1", start=Const(0), end=Const(3), expr=Mul(Pow(Const(-1), Var("k1")), Binom(n=Const(3), k=Var("k1")))),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub(left=Ref(name='n'), right=Ref(name='k'))))... | COMB | null | COUNT | sympy | LTE_SUM | [
"BINOMIAL_ALTERNATING"
] | c21569 | comb_count_permutations_fixed_v1 | null | 3 | 0 | [
"BINOMIAL_ALTERNATING",
"LTE_SUM"
] | 2 | 0.009 | 2026-02-08T17:57:49.963644Z | {
"verified": true,
"answer": 14833,
"timestamp": "2026-02-08T17:57:49.972669Z"
} | df1bfe | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 120,
"completion_tokens": 1344
},
"timestamp": "2026-02-18T11:29:53.635Z",
"answer": 14833
},
... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
... | {
"lo": -4.1,
"mid": -1.76,
"hi": 1.32
} | ||
3c2142 | nt_sum_divisors_mod_v1_1742523217_489 | Let $n$ be the number of integers $t$ such that $7 \leq t \leq 7570$ and $t = 2a + 5b$ for some positive integers $a \leq 3770$ and $b \leq 6$. Let $\sigma(n)$ denote the sum of all positive divisors of $n$. Compute the remainder when $\sigma(n)$ is divided by 11783. | 5,234 | 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=3770)), Geq(left=Var(name='b'), right=Const(valu... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_sum_divisors_mod_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.006 | 2026-02-08T03:04:51.298568Z | {
"verified": true,
"answer": 5234,
"timestamp": "2026-02-08T03:04:51.304330Z"
} | 09fc1d | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 207,
"completion_tokens": 3460
},
"timestamp": "2026-02-09T03:40:19.640Z",
"answer": 5234
},
{
"... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
... | {
"lo": 1.96,
"mid": 5.23,
"hi": 8.52
} | ||
f69f15 | antilemma_k2_v1_677425708_2064 | Let $x = \sum_{k=1}^{151} \phi(k) \left\lfloor \frac{151}{k} \right\rfloor$, where $\phi$ denotes Euler's totient function. Find the value of $x$. | 11,476 | graphs = [
Graph(
let={
"x": Summation(var="k", start=Const(1), end=Const(151), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(151), Var("k"))))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K13 | [
"K2"
] | 6897ab | antilemma_k2_v1 | null | 5 | 0 | [
"K13",
"K2"
] | 2 | 0.002 | 2026-02-08T04:44:15.161019Z | {
"verified": true,
"answer": 11476,
"timestamp": "2026-02-08T04:44:15.163188Z"
} | 08d3d6 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 163,
"completion_tokens": 4224
},
"timestamp": "2026-02-10T05:25:29.189Z",
"answer": 11476
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -3.45,
"mid": 1.15,
"hi": 6.18
} | ||
a72d1e | diophantine_product_count_v1_865884756_4464 | Let $k = 120$ and let $u = 82$. Consider the set of all positive integers $x$ such that $1 \le x \le u$, $x$ divides $k$, and $\frac{k}{x} \le u$. Let $r$ be the number of elements in this set.
Now, let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 6$, $\gcd(... | 16,398 | graphs = [
Graph(
let={
"k": Const(120),
"upper": Const(82),
"result": CountOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), Const(1)), Leq(Var("x"), Ref("upper")), Divides(divisor=Var("x"), dividend=Ref("k")), Leq(Div(Ref("k"), Var("x")), Ref("upper")))... | NT | null | COUNT | sympy | C5 | [
"COPRIME_PAIRS"
] | 64a51e | diophantine_product_count_v1 | mod_exp | 6 | 0 | [
"C5",
"COPRIME_PAIRS"
] | 2 | 0.087 | 2026-02-08T17:56:12.345028Z | {
"verified": true,
"answer": 16398,
"timestamp": "2026-02-08T17:56:12.432034Z"
} | 3b0e2a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 215,
"completion_tokens": 1456
},
"timestamp": "2026-02-18T10:28:04.430Z",
"answer": 16398
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V7",
"status": "no... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
8ef769 | nt_count_primes_v1_1978505735_826 | Let $n$ be a positive integer. Define $\mathcal{P}$ as the set of all prime numbers $n$ such that $2 \le n \le 51529$. Let $A$ be the number of elements in $\mathcal{P}$.
Let $S$ be the set of all integers $t$ such that there exist integers $a$ and $b$ with $1 \le a \le 8$, $1 \le b \le 7$, and $t = 8a + 10b$, where $... | 50,586 | graphs = [
Graph(
let={
"_n": Const(6),
"upper": Const(51529),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("upper")), IsPrime(Var("n"))))),
"Q": Mod(value=Sum(Pow(Ref("result"), Const(2)), Mul(... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 2ba0ea | nt_count_primes_v1 | quadratic_mod | 4 | 0 | [
"LIN_FORM"
] | 1 | 1.169 | 2026-02-08T15:37:58.963024Z | {
"verified": true,
"answer": 50586,
"timestamp": "2026-02-08T15:38:00.132448Z"
} | acb617 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 205,
"completion_tokens": 4102
},
"timestamp": "2026-02-16T09:51:57.136Z",
"answer": 50586
},
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
0faa06 | algebra_vieta_sum_v1_784195855_2425 | Compute the sum of all real solutions $x$ to the equation $x^2 - 3x - 4 = 0$. | 3 | graphs = [
Graph(
let={
"result": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Const(2)), Mul(Const(-3), Var("x")), Const(-4)), Const(0)))),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"MAX_PRIME_BELOW"
] | dc3ad3 | algebra_vieta_sum_v1 | null | 2 | 0 | [
"COPRIME_PAIRS",
"MAX_PRIME_BELOW"
] | 2 | 0.036 | 2026-02-08T05:44:37.303467Z | {
"verified": true,
"answer": 3,
"timestamp": "2026-02-08T05:44:37.339153Z"
} | 16ac4d | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 83,
"completion_tokens": 186
},
"timestamp": "2026-02-11T23:01:43.360Z",
"answer": 3
},
{
"id": 11,
"m... | 2 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"statu... | {
"lo": -10,
"mid": -7.73,
"hi": -5.46
} | ||
55432e | nt_min_with_divisor_count_v1_168721529_1998 | Let $r$ be the smallest positive integer $n \leq 32400$ that has exactly 4 positive divisors. Let $c$ be the number of integers $t$ such that $7 \leq t \leq 6156$ and there exist positive integers $a \leq 218$ and $b \leq 1144$ satisfying $t = 2a + 5b$. Compute $c \cdot r$. | 36,876 | graphs = [
Graph(
let={
"upper": Const(32400),
"div_count": Const(4),
"result": MinOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(NumDivisors(n=Var("n")), Ref("div_count"))))),
"Q": Mul(CountOverSe... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM"
] | 3d6396 | nt_min_with_divisor_count_v1 | affine_mod | 4 | 0 | [
"LIN_FORM"
] | 1 | 5.016 | 2026-02-08T14:02:55.816314Z | {
"verified": true,
"answer": 36876,
"timestamp": "2026-02-08T14:03:00.832408Z"
} | 76e026 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 207,
"completion_tokens": 6280
},
"timestamp": "2026-02-11T08:09:36.274Z",
"answer": 36876
},
{
... | 1 | [
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -5.48,
"mid": 0.74,
"hi": 7.52
} | ||
6b1fa0_n | alg_sym_quad_system_v1_601307018_4866 | Three positive integers $a$, $b$, and $c$ represent the side lengths of a triangle that is both equilateral (in a transformed space where $a^2 + b^2 + c^2 = ab + bc + ca$) and satisfy a linear constraint $4a + 2b + c = 1624$ modeling a resource budget. For each such valid triple, the cube of each side contributes to a ... | 1,926 | ALG | null | COMPUTE | sympy | B3_CLOSEST | [
"B3_CLOSEST"
] | 25e610 | alg_sym_quad_system_v1 | null | 7 | null | [
"B3_CLOSEST"
] | 1 | 0.025 | 2026-03-10T05:34:12.454582Z | null | fbb90f | 6b1fa0 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 261,
"completion_tokens": 8597
},
"timestamp": "2026-03-29T19:19:45.420Z",
"answer": 1926
},
{
"i... | 1 | [
{
"lemma": "B3_CLOSEST",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 1.7,
"mid": 5.03,
"hi": 8.38
} | |
f0d3cc | nt_max_prime_below_v1_1918700295_2306 | Let $p$ and $q$ be positive integers such that $pq = 216$, $\gcd(p, q) = 1$, and $p < q$. Let $S$ be the set of all such integers $p$. Let $N$ be the number of elements in $S$. Determine the value of the largest prime number $n$ such that $N \leq n \leq 54289$. Let $Q$ be the remainder when $12551$ times this prime is ... | 40,297 | graphs = [
Graph(
let={
"_n": Const(88713),
"upper": Const(54289),
"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=... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_max_prime_below_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 2.633 | 2026-02-08T07:50:18.536113Z | {
"verified": true,
"answer": 40297,
"timestamp": "2026-02-08T07:50:21.168852Z"
} | 18c0db | 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": 3348
},
"timestamp": "2026-02-13T12:46:29.041Z",
"answer": 40297
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
80bda7 | geo_count_lattice_rect_v1_2051736721_4418 | Let $R$ be the rectangle with vertices at $(0,0)$, $(361,0)$, $(0,197)$, and $(361,197)$. Compute the number of lattice points contained in $R$, including its boundary. Let $Q$ be the remainder when $66564$ minus this number is divided by 76788. Find the value of $Q$. | 71,676 | graphs = [
Graph(
let={
"a": Const(361),
"b": Const(197),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"_c": Const(66564),
"Q": Mod(value=Sub(Ref("_c"), Ref("result")), modulus=Const(76788)),
},
goal=Ref("Q"),
... | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 2 | 0 | null | null | 0.003 | 2026-02-08T17:57:49.681090Z | {
"verified": true,
"answer": 71676,
"timestamp": "2026-02-08T17:57:49.684057Z"
} | ea1a1b | 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": 504
},
"timestamp": "2026-02-18T11:29:42.482Z",
"answer": 71676
},
{... | 1 | [] | {
"lo": -5.64,
"mid": -3.17,
"hi": -0.81
} | ||||
d5283d | comb_count_surjections_v1_1915831931_3190 | Let $n = 6$ and $k = 6$. Define $r = k! \cdot S(n, k)$, where $S(n, k)$ denotes the Stirling number of the second kind. Let $m = |r| + 2$. The Fibonacci entry point modulo $m$ is the smallest positive integer $Q$ such that the $Q$-th Fibonacci number is divisible by $m$. Compute $Q$. | 342 | graphs = [
Graph(
let={
"n": Const(6),
"k": Const(6),
"result": Mul(Factorial(Ref("k")), Stirling2(n=Ref(name='n'), k=Ref(name='k'))),
"Q": FibonacciEntryPoint(modulus=Sum(Abs(arg=Ref(name='result')), Const(value=2))),
},
goal=Ref("Q"),
)
] | COMB | NT | COUNT | sympy | COUNT_CARTESIAN | [
"COUNT_SUM_EQUALS"
] | 75ab0f | comb_count_surjections_v1 | null | 3 | 0 | [
"COUNT_CARTESIAN",
"COUNT_SUM_EQUALS"
] | 2 | 0.046 | 2026-02-08T17:24:43.234442Z | {
"verified": true,
"answer": 342,
"timestamp": "2026-02-08T17:24:43.279956Z"
} | a301c9 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 136,
"completion_tokens": 1704
},
"timestamp": "2026-02-18T02:52:51.533Z",
"answer": 342
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V8_SU... | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||
ec0cc1 | comb_count_partitions_v1_1978505735_1170 | Let $n = 41$. Determine the value of $p(n)$, the number of integer partitions of $n$. | 44,583 | graphs = [
Graph(
let={
"n": Const(41),
"result": Partition(arg=Ref(name='n')),
},
goal=Ref("result"),
)
] | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/V5"
] | e79893 | comb_count_partitions_v1 | null | 3 | 0 | [
"LIN_FORM",
"V5"
] | 2 | 0.014 | 2026-02-08T15:52:33.293204Z | {
"verified": true,
"answer": 44583,
"timestamp": "2026-02-08T15:52:33.307378Z"
} | 325497 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 135,
"completion_tokens": 8987
},
"timestamp": "2026-02-24T18:50:14.670Z",
"answer": 44583
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V5",
"statu... | {
"lo": -2.4,
"mid": 1.57,
"hi": 5.75
} | ||
a851c6 | modular_inverse_v1_151522320_223 | Let $a$ be the number of prime numbers $n$ such that $2 \leq n \leq 461$. Let $m = 1171$ and let $u = 1170$. Let $x$ be the smallest positive integer such that $1 \leq x \leq u$ and $a \cdot x \equiv 1 \pmod{m}$. Compute the remainder when $44121 \cdot x$ is divided by $67085$. | 28,310 | graphs = [
Graph(
let={
"_n": Const(44121),
"a": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(461)), IsPrime(Var("n"))))),
"m": Const(1171),
"upper": Const(1170),
"result": MinOverSet(set=So... | NT | null | EXTREMUM | sympy | COUNT_PRIMES | [
"COUNT_PRIMES"
] | 07c874 | modular_inverse_v1 | null | 5 | 0 | [
"COUNT_PRIMES"
] | 1 | 0.047 | 2026-02-08T03:04:59.774034Z | {
"verified": true,
"answer": 28310,
"timestamp": "2026-02-08T03:04:59.820752Z"
} | ec1e75 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 214,
"completion_tokens": 5105
},
"timestamp": "2026-02-10T13:05:09.285Z",
"answer": 28310
},
{
"... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -3.47,
"mid": 0.81,
"hi": 4.81
} | ||
87659e | nt_min_coprime_above_v1_1915831931_2711 | Let $a$ and $b$ be positive integers such that $ab = 30276$. Define $s$ to be the minimum possible value of $a + b$ over all such pairs. Let $n$ be the smallest integer greater than $26244$ and at most $26602$ such that $\gcd(n, s) = 1$. Compute $n$. | 26,249 | graphs = [
Graph(
let={
"start": Const(26244),
"upper": Const(26602),
"modulus": 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")), Co... | NT | null | EXTREMUM | sympy | B3 | [
"B3"
] | 0cd20d | nt_min_coprime_above_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.056 | 2026-02-08T17:04:12.687746Z | {
"verified": true,
"answer": 26249,
"timestamp": "2026-02-08T17:04:12.743920Z"
} | 2c73ac | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 125,
"completion_tokens": 1354
},
"timestamp": "2026-02-17T18:24:21.318Z",
"answer": 26249
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
1cd116 | modular_sum_quadratic_residues_v1_151522320_261 | Let $m = 21$ and $n = 65025$. Let $S$ be the set of all positive integers $k$ such that $1 \leq k \leq 689$ and $\gcd(k, m) = 1$. Let $p$ be the largest prime number at most $|S|$. Define $\text{result} = \frac{p(p-1)}{4}$ and $Q = n - \text{result}$. Find the value of $Q$. | 27,292 | graphs = [
Graph(
let={
"_m": Const(21),
"_n": Const(65025),
"p": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(689)), E... | NT | null | SUM | sympy | C4 | [
"C4/MAX_PRIME_BELOW"
] | 757853 | modular_sum_quadratic_residues_v1 | null | 6 | 0 | [
"C4",
"MAX_PRIME_BELOW"
] | 2 | 0.004 | 2026-02-08T03:07:01.717536Z | {
"verified": true,
"answer": 27292,
"timestamp": "2026-02-08T03:07:01.721056Z"
} | 2ed7b7 | 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": 1825
},
"timestamp": "2026-02-10T13:06:06.533Z",
"answer": 27292
},
{
"... | 1 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
... | {
"lo": -3.47,
"mid": 0.81,
"hi": 4.81
} | ||
045a27 | nt_count_coprime_and_v1_1978505735_3640 | Let $A$ be the set of all prime numbers $n$ such that $2 \leq n \leq 9$. Let $k_1$ be the largest prime in $A$. Let $\text{result}$ be the number of positive integers $n_2$ such that $1 \leq n_2 \leq 18795$, $\gcd(n_2, k_1) = 1$, and $\gcd(n_2, 9) = 1$.
Let $m = |\text{result}| + 2$. Compute the smallest positive inte... | 780 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": Const(18795),
"k1": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), MaxOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(2)), Leq(Var("n1"), Const(9))... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW/MAX_PRIME_BELOW"
] | 15be89 | nt_count_coprime_and_v1 | null | 5 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 4.533 | 2026-02-08T17:45:45.325572Z | {
"verified": true,
"answer": 780,
"timestamp": "2026-02-08T17:45:49.858788Z"
} | f38961 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 184,
"completion_tokens": 2345
},
"timestamp": "2026-02-18T07:33:57.662Z",
"answer": 780
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8_SUM",
"st... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
89b0a1 | alg_qf_psd_orbit_v1_1218484723_3866 | Let $Q$ be the number of ordered pairs $(a,b)$ of positive integers with $1 \le a \le b$ and $1 \le b \le 388$ such that
\[a^2 + b^2 = 138580.\]
Find $Q$. | 6 | graphs = [
Graph(
let={
"_n": Const(388),
"result": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a1"), Var("b1")]), condition=And(Geq(Var("a1"), Cons... | NT | null | COUNT | sympy | LIN_FORM | [
"MAX_PRIME_BELOW/QF_PSD_COUNT_LEQ"
] | 27f428 | alg_qf_psd_orbit_v1 | null | 7 | 0 | [
"LIN_FORM",
"MAX_PRIME_BELOW",
"QF_PSD_COUNT_LEQ"
] | 3 | 0.265 | 2026-02-25T05:30:26.356668Z | {
"verified": true,
"answer": 6,
"timestamp": "2026-02-25T05:30:26.621845Z"
} | ab36cc | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 169,
"completion_tokens": 16631
},
"timestamp": "2026-03-29T12:40:00.523Z",
"answer": 6
},
{
"id"... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUN... | {
"lo": 1.55,
"mid": 4.7,
"hi": 7.23
} | ||
57a8bb | nt_count_coprime_and_v1_865884756_4736 | Compute the number of ordered triples $ (x_1, x_2, x_3) $ of positive odd integers such that $ x_1 + x_2 + x_3 = 11 $. Let $ k $ be this number. Determine the number of positive integers $ n \leq 43691 $ such that $ \gcd(n, 8) = 1 $ and $ \gcd(n, k) = 1 $. Find the remainder when $ 69956 $ times this count is divided b... | 52,433 | graphs = [
Graph(
let={
"upper": Const(43691),
"k1": Const(8),
"k2": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2"), Var("x3")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsPositive(arg=Var(name='x3')), IsOdd(ar... | NT | null | COUNT | sympy | COMB1 | [
"COMB1"
] | 567f58 | nt_count_coprime_and_v1 | null | 4 | 0 | [
"COMB1"
] | 1 | 8.885 | 2026-02-08T18:05:00.305909Z | {
"verified": true,
"answer": 52433,
"timestamp": "2026-02-08T18:05:09.190598Z"
} | 27ea4c | 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": 1976
},
"timestamp": "2026-02-18T12:57:22.342Z",
"answer": 52433
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
6db345 | nt_count_divisible_and_v1_655260480_996 | Let $d_1 = \sum_{k=1}^{3} k$. Let $d_2$ be the minimum value of $x + y$ over all ordered pairs of positive integers $(x, y)$ such that $xy = 16$. Compute the number of positive integers $n \leq 73704$ that are divisible by both $d_1$ and $d_2$. Find the value of this count. | 3,071 | graphs = [
Graph(
let={
"_n": Const(16),
"upper": Const(73704),
"d1": Summation(var="k", start=Const(1), end=Const(3), expr=Var("k")),
"d2": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(n... | NT | null | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC",
"B3"
] | dee757 | nt_count_divisible_and_v1 | null | 6 | 0 | [
"B3",
"SUM_ARITHMETIC"
] | 2 | 3.032 | 2026-02-08T15:51:33.608367Z | {
"verified": true,
"answer": 3071,
"timestamp": "2026-02-08T15:51:36.640049Z"
} | 008a20 | 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": 636
},
"timestamp": "2026-02-16T15:04:19.308Z",
"answer": 3071
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
977709 | comb_factorial_compute_v1_124444284_917 | Let $n$ be the number of positive integers from $1$ to $13$ inclusive for which the sum of the digits is odd. Compute $n!$. | 5,040 | graphs = [
Graph(
let={
"_n": Const(2),
"n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(13)), Eq(Mod(value=DigitSum(Var("n")), modulus=Ref("_n")), Const(1))))),
"result": Factorial(Ref("n")),
},
g... | ALG | COMB | COMPUTE | sympy | L3B | [
"L3B"
] | cc148f | comb_factorial_compute_v1 | null | 3 | 0 | [
"L3B"
] | 1 | 0.001 | 2026-02-08T03:36:01.437626Z | {
"verified": true,
"answer": 5040,
"timestamp": "2026-02-08T03:36:01.438401Z"
} | aa8716 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 144,
"completion_tokens": 281
},
"timestamp": "2026-02-09T23:52:25.602Z",
"answer": 5040
},
{
"id... | 1 | [
{
"lemma": "L3B",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.97,
"mid": -3.96,
"hi": -1.93
} | ||
cbb4ae | geo_count_lattice_triangle_v1_1915831931_302 | Let $A$ be the area of the triangle with vertices at $(0,0)$, $(333,222)$, and $(169,128)$, multiplied by $2$. Let $B$ be the sum of the greatest common divisors of the absolute differences of the $x$- and $y$-coordinates along each side of the triangle. Specifically,
$$
B = \gcd(333, 222) + \gcd(|169 - 333|, |128 - 2... | 1,391 | graphs = [
Graph(
let={
"_n": Const(128),
"area_2x": Abs(arg=Sum(Mul(Const(value=333), Const(value=128)), Mul(Const(value=169), Sub(left=Const(value=0), right=Const(value=222))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=333)), b=Abs(arg=Const(value=222))), GCD(a=Abs(ar... | ALG | NT | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | geo_count_lattice_triangle_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.012 | 2026-02-08T15:20:44.433889Z | {
"verified": true,
"answer": 1391,
"timestamp": "2026-02-08T15:20:44.445573Z"
} | eef52f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 188,
"completion_tokens": 1309
},
"timestamp": "2026-02-16T04:11:09.600Z",
"answer": 1391
},
{... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
6c130d | geo_count_lattice_rect_v1_1431428450_105 | Let $a = 128$ and $b = 87$. Define the rectangle in the coordinate plane with vertices at $(0,0)$, $(a,0)$, $(0,b)$, and $(a,b)$. Compute the number of lattice points contained in this rectangle, including all boundary points. | 11,352 | graphs = [
Graph(
let={
"a": Const(128),
"b": Const(87),
"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 | 0.003 | 2026-02-08T13:15:19.625594Z | {
"verified": true,
"answer": 11352,
"timestamp": "2026-02-08T13:15:19.629089Z"
} | 69fb1c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 173,
"completion_tokens": 252
},
"timestamp": "2026-02-24T17:32:17.680Z",
"answer": 11352
},
{
"i... | 1 | [] | {
"lo": -4.92,
"mid": -2.91,
"hi": -0.68
} | ||||
84e6e7 | algebra_poly_eval_v1_601307018_8386 | Let $R \equiv a^3 + 5a \pmod{19}$, $S \equiv R^3 + 5R \pmod{19}$, $T \equiv S^3 + 5S \pmod{19}$, and $K \equiv T^3 + 5T \pmod{19}$. Let $y = 6$. Compute $$ 4 \cdot y^{\left|\{ a : 0 \le a \le 18,\ K = a,\ R \ne a,\ S \ne a,\ T \ne a \}\right|} + 2 \cdot y^{\left|\{ (a_1, b) : 1 \le a_1, b \le 10,\ 8a_1^3 + 24a_1 b^2 - ... | 5,647 | graphs = [
Graph(
let={
"_m": Const(8),
"_n": Const(2),
"y": Const(6),
"result": Sum(Mul(Const(4), Pow(Ref("y"), CountOverSet(set=SolutionsSet(var=Var("a"), condition=And(Geq(Var("a"), Const(0)), Leq(Var("a"), Const(18)), Eq(Ref("_po_p4"), Var("a")), Neq(Ref("... | ALG | null | COMPUTE | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT",
"POLY3_COUNT"
] | d5346d | algebra_poly_eval_v1 | null | 6 | 0 | [
"POLY3_COUNT",
"POLY_ORBIT_COUNT"
] | 2 | 0.016 | 2026-03-10T08:53:33.341288Z | {
"verified": true,
"answer": 5647,
"timestamp": "2026-03-10T08:53:33.357477Z"
} | f5b0ab | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 323,
"completion_tokens": 4124
},
"timestamp": "2026-04-19T08:56:06.375Z",
"answer": 5647
},
{
"... | 1 | [
{
"lemma": "POLY3_COUNT",
"status": "ok"
},
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
22a21b | lin_form_endings_v1_1125832087_2459 | Let $a = 25$ and $b = 15$. Let $k = 33$ and let $g = \gcd(a, b)$. Define $m = \left\lfloor \frac{k}{\gcd(k, g)} \right\rfloor$. Compute the remainder when $13182 \cdot m$ is divided by $69515$. | 17,916 | graphs = [
Graph(
let={
"a_coeff": Const(25),
"b_coeff": Const(15),
"k_val": Const(33),
"step": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"_inner_result": Floor(Div(Ref("k_val"), GCD(a=Ref("k_val"), b=Ref("step")))),
"_scale_k": Const(13... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 5 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T04:38:28.730160Z | {
"verified": true,
"answer": 17916,
"timestamp": "2026-02-08T04:38:28.730881Z"
} | e1e714 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 189,
"completion_tokens": 493
},
"timestamp": "2026-02-10T17:23:21.602Z",
"answer": 17916
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
f903c7 | modular_mod_compute_v1_1439011603_2686 | Let $a$ be the number of positive integers $n$ such that $1 \leq n \leq 25000$ and $5$ divides the $n$th Fibonacci number. Let $r$ be the remainder when $a$ is divided by $12544$. Compute the remainder when $32249 \cdot r$ is divided by $69500$. | 5,000 | graphs = [
Graph(
let={
"_n": Const(5),
"a": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(25000)), Divides(divisor=Ref("_n"), dividend=Fibonacci(arg=Var(name='n')))))),
"m": Const(12544),
"result": Mod(... | NT | null | COMPUTE | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE"
] | 66de3c | modular_mod_compute_v1 | null | 6 | 0 | [
"COUNT_FIB_DIVISIBLE"
] | 1 | 0.003 | 2026-02-08T16:54:41.316971Z | {
"verified": true,
"answer": 5000,
"timestamp": "2026-02-08T16:54:41.319960Z"
} | 32da10 | 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": 1073
},
"timestamp": "2026-02-17T16:18:06.506Z",
"answer": 5000
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
87d859 | nt_min_coprime_above_v1_898971024_744 | Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $x + y = 128$. Define $P$ to be the maximum value of $xy$ over all such pairs.
Let $T$ be the set of all ordered pairs $(x_1, y_1)$ of positive integers such that $x_1 y_1 = 4575321$. Define $Q$ to be the minimum value of $x_1 + y_1$ over a... | 4,097 | graphs = [
Graph(
let={
"start": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Const(128)))), expr=Mul(Var("x"), Var("y")))),
"upper": MinOve... | NT | null | EXTREMUM | sympy | B1 | [
"B1",
"B3"
] | 655d51 | nt_min_coprime_above_v1 | null | 5 | 0 | [
"B1",
"B3"
] | 2 | 0.034 | 2026-02-08T15:37:41.192231Z | {
"verified": true,
"answer": 4097,
"timestamp": "2026-02-08T15:37:41.226714Z"
} | 4d7292 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 191,
"completion_tokens": 1381
},
"timestamp": "2026-02-16T09:20:58.239Z",
"answer": 4097
},
{... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
f774b4 | nt_sum_divisors_mod_v1_1520064083_738 | Let $n$ be the minimum value of $x + y$ where $x$ and $y$ are positive integers such that $xy = 8100$. Let $\sigma$ be the sum of the positive divisors of $n$. Compute the remainder when $\sigma$ is divided by $10223$. | 546 | graphs = [
Graph(
let={
"_n": Const(8100),
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_n")))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_divisors_mod_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.002 | 2026-02-08T03:34:35.734904Z | {
"verified": true,
"answer": 546,
"timestamp": "2026-02-08T03:34:35.737377Z"
} | 2fadf6 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 174,
"completion_tokens": 1004
},
"timestamp": "2026-02-10T14:59:25.448Z",
"answer": 546
},
{
"id... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
... | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
74d7a0 | diophantine_fbi2_min_v1_655260480_3752 | Let $n = 5$ and $k = 81$. Define $S$ as the set of all positive integers $d$ such that $4 \leq d \leq \sum_{i=1}^{13} i$, $d$ divides $k$, and $\frac{k}{d} \geq n$. Compute the smallest element of $S$. | 9 | graphs = [
Graph(
let={
"_n": Const(5),
"k": Const(81),
"upper": Summation(var="k1", start=Const(1), end=Const(13), expr=Var("k1")),
"result": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(4)), Leq(Var("d"), Ref("upper")), Divides... | NT | null | EXTREMUM | sympy | K2 | [
"SUM_ARITHMETIC",
"K2"
] | 2a0f86 | diophantine_fbi2_min_v1 | null | 3 | 0 | [
"K2",
"SUM_ARITHMETIC"
] | 2 | 0.02 | 2026-02-08T17:31:54.017149Z | {
"verified": true,
"answer": 9,
"timestamp": "2026-02-08T17:31:54.036728Z"
} | 1d2530 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 134,
"completion_tokens": 523
},
"timestamp": "2026-02-16T10:48:17.743Z",
"answer": 9
},
{
"id": 11,
"... | 2 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
... | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
19806f | sequence_fibonacci_compute_v1_548369836_121 | Let $n$ be the largest prime number such that $2 \le n \le 26$. Compute the $n$th Fibonacci number, where the Fibonacci sequence is defined by $F_1 = 1$, $F_2 = 1$, and $F_m = F_{m-1} + F_{m-2}$ for all $m \ge 3$. | 28,657 | graphs = [
Graph(
let={
"_n": Const(2),
"n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Const(26)), IsPrime(Var("n"))))),
"result": Fibonacci(arg=Ref(name='n')),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | sequence_fibonacci_compute_v1 | null | 2 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.001 | 2026-02-08T02:46:39.974279Z | {
"verified": true,
"answer": 28657,
"timestamp": "2026-02-08T02:46:39.975155Z"
} | 9bc80a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 194,
"completion_tokens": 436
},
"timestamp": "2026-02-08T19:54:07.563Z",
"answer": 28657
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "n... | {
"lo": -6.62,
"mid": -4.76,
"hi": -2.89
} | ||
29e29c | comb_bell_compute_v1_458359167_3811 | Let $n$ be the number of ordered pairs $(i,j)$ of integers with $1 \leq i \leq 10$ and $1 \leq j \leq 10$ such that $i + j = 12$. Let $m = \sum_{k=0}^{0} (-1)^k \binom{0}{k}$. Define $N = n \cdot m$. Compute the Bell number $B_N$, which counts the number of partitions of a set of $N$ elements. Find the value of $B_N$. | 21,147 | graphs = [
Graph(
let={
"_n": Const(12),
"n2": Const(0),
"u": Summation(var="k", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n2"), k=Var("k")))),
"n1": Const(0),
"m": Summation(var="k", start=Const(0), end=Ref("n1... | COMB | null | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS/BINOMIAL_ALTERNATING"
] | ab0fe8 | comb_bell_compute_v1 | null | 4 | 2 | [
"BINOMIAL_ALTERNATING",
"COUNT_SUM_EQUALS"
] | 2 | 0.011 | 2026-02-08T11:22:36.792224Z | {
"verified": true,
"answer": 21147,
"timestamp": "2026-02-08T11:22:36.803256Z"
} | 48f8ee | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 229,
"completion_tokens": 834
},
"timestamp": "2026-02-24T13:34:34.333Z",
"answer": 21147
},
{
"i... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemm... | {
"lo": -3.84,
"mid": -1.67,
"hi": 1.32
} | ||
dfcfdc | lin_form_endings_v1_1520064083_2447 | Let $a = 24$ and $b = 60$. Let $g$ be the greatest common divisor of $a$ and $b$. Define $a' = \left\lfloor \frac{a}{g} \right\rfloor$ and $b' = \left\lfloor \frac{b}{g} \right\rfloor$. Let $A = 15$ and $B = 50$. Compute the value of
$$
\left( 8301 \cdot \left( a' \cdot A + b' \cdot B - a' \cdot b' \right) \right) \mod... | 17,034 | graphs = [
Graph(
let={
"a_coeff": Const(24),
"b_coeff": Const(60),
"A_val": Const(15),
"B_val": Const(50),
"g_step": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"ap_node": Floor(Div(Ref("a_coeff"), Ref("g_step"))),
"bp_node": ... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 3 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T04:44:45.283985Z | {
"verified": true,
"answer": 17034,
"timestamp": "2026-02-08T04:44:45.284932Z"
} | 3b59fa | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 254,
"completion_tokens": 971
},
"timestamp": "2026-02-11T21:51:09.024Z",
"answer": 17034
},
{
"i... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"st... | {
"lo": -3.45,
"mid": 1.15,
"hi": 6.18
} | ||
dc353b | alg_qf_psd_sum_v1_601307018_259 | Let $D$ be the largest positive divisor $d$ of $175142$ such that $d^2 \le 175142$. Find the remainder when $$\sum_{a=1}^{418} \sum_{b=1}^{D} (10a^2 - 8ab + 2b^2)$$ is divided by $79971$. | 15,751 | graphs = [
Graph(
let={
"_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"), Const(418)), Geq(Var("b"), Const(1)), Leq(Var("b"), MaxOverSet(set=SolutionsSet(var=Va... | NT | NT | COMPUTE | sympy | B3_CLOSEST | [
"B3_CLOSEST",
"ONE_PHI_2"
] | 5bfd45 | alg_qf_psd_sum_v1 | null | 4 | 0 | [
"B3_CLOSEST",
"ONE_PHI_2"
] | 2 | 0.322 | 2026-03-10T00:49:30.313633Z | {
"verified": true,
"answer": 15751,
"timestamp": "2026-03-10T00:49:30.635770Z"
} | f53549 | CC BY 4.0 | null | null | [
{
"lemma": "B3_CLOSEST",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "ONE_PHI_2",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{... | {
"lo": -10,
"mid": 0,
"hi": 10
} | ||
b92272 | sequence_fibonacci_compute_v1_798873815_363 | Consider all ordered pairs $(a,b)$ of positive integers such that $1 \le a \le 6$, $1 \le b \le 4$, and $t = 4a + 3b \ge 7$. Let $T$ be the set of all such integers $t$ satisfying $7 \le t \le 36$.
Let $n$ be the number of distinct values in $T$. Let $F_n$ denote the $n$-th Fibonacci number, where $F_1 = 1$, $F_2 = 1$... | 30,903 | graphs = [
Graph(
let={
"_n": Const(96385),
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=6)), Geq(left=Va... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | sequence_fibonacci_compute_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.003 | 2026-02-08T02:37:02.731811Z | {
"verified": true,
"answer": 30903,
"timestamp": "2026-02-08T02:37:02.734320Z"
} | 546a08 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 278,
"completion_tokens": 3854
},
"timestamp": "2026-02-23T15:12:09.670Z",
"answer": 30903
},
{
"... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": 1.13,
"mid": 2.83,
"hi": 4.45
} | ||
2e4efc | nt_sum_over_divisible_v1_168721529_2079 | Let $ m = 2 $ and $ n = 2 $. Let $ D $ be the set of all integers $ d \geq m $ that divide 3599. Let $ d_{\min} $ be the smallest element of $ D $. Define $ p_{\max} $ to be the largest prime number $ p $ such that $ n \geq 2 $, $ n \leq d_{\min} $, and $ p = n $. Let $ S $ be the set of all positive integers $ n \leq ... | 32,553 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(2),
"upper": Const(22801),
"divisor": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref(... | NT | null | SUM | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/MAX_PRIME_BELOW"
] | e4e16c | nt_sum_over_divisible_v1 | null | 4 | 0 | [
"MAX_PRIME_BELOW",
"MIN_PRIME_FACTOR"
] | 2 | 0.902 | 2026-02-08T14:05:16.097582Z | {
"verified": true,
"answer": 32553,
"timestamp": "2026-02-08T14:05:16.999888Z"
} | 5453c7 | 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": 5037
},
"timestamp": "2026-02-10T01:50:26.592Z",
"answer": 32553
},
{
"... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V... | {
"lo": -7.09,
"mid": -0.49,
"hi": 6.1
} | ||
23ca41 | sequence_fibonacci_compute_v1_48377204_1764 | Let $n$ be the number of positive integers $n_1 \leq 328$ that are divisible by $8$ and relatively prime to $15$. Compute the $n$-th Fibonacci number, where $F_1 = 1$, $F_2 = 1$, and $F_k = F_{k-1} + F_{k-2}$ for $k \geq 3$. Determine the value of this Fibonacci number. | 17,711 | graphs = [
Graph(
let={
"_n": Const(328),
"n": CountOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(1)), Leq(Var("n1"), Ref("_n")), Divides(divisor=Const(8), dividend=Var("n1")), Eq(GCD(a=Var("n1"), b=Const(15)), Const(1))))),
"result": Fibonacc... | NT | null | COMPUTE | sympy | C5 | [
"C5"
] | 1d9668 | sequence_fibonacci_compute_v1 | null | 4 | 0 | [
"C5"
] | 1 | 0.002 | 2026-02-08T16:23:25.605590Z | {
"verified": true,
"answer": 17711,
"timestamp": "2026-02-08T16:23:25.607185Z"
} | 77f358 | 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": 961
},
"timestamp": "2026-02-17T02:52:22.282Z",
"answer": 17711
},
{... | 1 | [
{
"lemma": "C5",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
1c4bc3 | nt_sum_divisors_mod_v1_809748730_1559 | Let $s = \sum_{k=1}^{5} \phi(k) \left\lfloor \frac{5}{k} \right\rfloor$, and let $n = \sum_{k=1}^{s} k$, where $\phi$ denotes Euler's totient function. Let $\sigma(n)$ be the sum of all positive divisors of $n$. Compute the remainder when $\sigma(n)$ is divided by 10789. | 360 | graphs = [
Graph(
let={
"n": Summation(var="k", start=Const(1), end=Summation(var="k", start=Const(1), end=Const(5), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(5), Var("k"))))), expr=Var("k")),
"M": Const(10789),
"sigma": SumDivisors(n=Ref("n")),
"result":... | NT | null | COMPUTE | sympy | K2 | [
"K2/SUM_ARITHMETIC"
] | 5a4674 | nt_sum_divisors_mod_v1 | null | 6 | 0 | [
"K2",
"SUM_ARITHMETIC"
] | 2 | 0.002 | 2026-02-08T12:32:52.999165Z | {
"verified": true,
"answer": 360,
"timestamp": "2026-02-08T12:32:53.001662Z"
} | 188207 | 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": 791
},
"timestamp": "2026-02-15T02:16:05.533Z",
"answer": 360
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no... | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
3f1158 | nt_count_divisors_in_range_v1_1125832087_1342 | Let $ n = 332640 $, $ a = 6 $, and $ b = 22182 $. Compute the number of positive divisors $ d $ of $ n $ such that $ a \leq d \leq b $. | 174 | graphs = [
Graph(
let={
"n": Const(332640),
"a": Const(6),
"b": Const(22182),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Divides(divisor=Var("d"), dividend=Ref("n")), Geq(Var("d"), Ref("a")), Leq(Var("d"), Ref("b"))))),
},
... | NT | null | COUNT | sympy | COUNT_COPRIME_GRID | [
"COUNT_COPRIME_GRID",
"LIN_FORM"
] | 66e6c4 | nt_count_divisors_in_range_v1 | null | 4 | 0 | [
"COUNT_COPRIME_GRID",
"LIN_FORM"
] | 2 | 0.211 | 2026-02-08T03:41:31.910536Z | {
"verified": true,
"answer": 174,
"timestamp": "2026-02-08T03:41:32.121281Z"
} | abb606 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 159,
"completion_tokens": 3417
},
"timestamp": "2026-02-10T15:24:53.865Z",
"answer": 174
},
{
"id... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
... | {
"lo": -3.53,
"mid": 1.02,
"hi": 5.49
} | ||
d560f2 | comb_bell_compute_v1_717093673_648 | Let $d$ be a positive integer. Define $S$ to be the set of all positive integers $d$ such that $1 \leq d \leq 9$ and $d$ divides $99$. Let $n$ be the largest element of $S$. Let $B_n$ denote the $n$th Bell number, which is the number of partitions of a set of $n$ elements. Compute the remainder when $84187 \cdot B_n$ i... | 18,185 | graphs = [
Graph(
let={
"n": MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Leq(Var("d"), Const(9)), Divides(divisor=Var("d"), dividend=Const(99))))),
"result": Bell(Ref("n")),
"_c": Const(84187),
"Q": Mod(value=Mul(Ref("_c"),... | NT | COMB | COMPUTE | sympy | MAX_DIVISOR | [
"MAX_DIVISOR"
] | 51757e | comb_bell_compute_v1 | null | 3 | 0 | [
"MAX_DIVISOR"
] | 1 | 0.001 | 2026-02-08T15:35:01.239416Z | {
"verified": true,
"answer": 18185,
"timestamp": "2026-02-08T15:35:01.240816Z"
} | e3a8ef | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 151,
"completion_tokens": 1324
},
"timestamp": "2026-02-16T10:30:56.234Z",
"answer": 18185
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
ef2b4c | geo_count_lattice_rect_v1_865884756_5980 | Compute the number of lattice points $(x, y)$ such that $0 \le x \le 31$ and $0 \le y \le 104$. Let $Q$ be the remainder when $1089$ minus this number is divided by $79400$. Find the value of $Q$. | 77,129 | graphs = [
Graph(
let={
"a": Const(31),
"b": Const(104),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"Q": Mod(value=Sub(Const(1089), Ref("result")), modulus=Const(79400)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.001 | 2026-02-08T18:54:37.494456Z | {
"verified": true,
"answer": 77129,
"timestamp": "2026-02-08T18:54:37.495359Z"
} | d245a1 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 110,
"completion_tokens": 484
},
"timestamp": "2026-02-18T20:12:12.482Z",
"answer": 77129
},
{... | 1 | [] | {
"lo": -7.92,
"mid": -4.6,
"hi": -1.84
} | ||||
26c0c2 | nt_sum_divisors_compute_v1_655260480_2758 | Let $n = 85849$. Compute the sum of all positive divisors of $n$.
Find the value of this sum. | 86,143 | graphs = [
Graph(
let={
"n": Const(85849),
"result": SumDivisors(n=Ref("n")),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | MOBIUS_COPRIME | [
"MOBIUS_COPRIME",
"OMEGA_ZERO"
] | 1e95d3 | nt_sum_divisors_compute_v1 | null | 3 | 0 | [
"MOBIUS_COPRIME",
"OMEGA_ZERO"
] | 2 | 0.007 | 2026-02-08T16:59:49.260023Z | {
"verified": true,
"answer": 86143,
"timestamp": "2026-02-08T16:59:49.266977Z"
} | c0aca8 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 73,
"completion_tokens": 800
},
"timestamp": "2026-02-17T16:52:09.617Z",
"answer": 86143
},
{
... | 1 | [
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "OMEGA_ZERO",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
},
{
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
0b6b8d | nt_count_divisible_v1_2051736721_4861 | Let $d$ be the number of ordered pairs $(i, j)$ of positive integers such that $1 \leq i \leq 4$, $1 \leq j \leq 7$, and $\gcd(i, j) = 1$. Let $N$ be the number of positive integers $n$ such that $1 \leq n \leq 60000$ and $n$ is divisible by $d$.
Compute the remainder when $16541 \cdot N$ is divided by $51602$. | 33,478 | graphs = [
Graph(
let={
"_n": Const(51602),
"upper": Const(60000),
"divisor": 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(4... | NT | null | COUNT | sympy | COUNT_COPRIME_GRID | [
"COUNT_COPRIME_GRID"
] | 20ec03 | nt_count_divisible_v1 | null | 3 | 0 | [
"COUNT_COPRIME_GRID"
] | 1 | 1.788 | 2026-02-08T18:13:30.998670Z | {
"verified": true,
"answer": 33478,
"timestamp": "2026-02-08T18:13:32.786254Z"
} | 12a8b5 | 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": 1371
},
"timestamp": "2026-02-18T15:16:07.268Z",
"answer": 33478
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
fa73a7 | nt_count_coprime_v1_124444284_10322 | Let $r$ be the number of positive integers $n$ such that $1 \le n \le 51984$ and $\gcd(n, 24) = 1$. Let $s$ be the number of positive integers $t$ such that $18 \le t \le 9550$ and there exist positive integers $a \le 209$ and $b \le 1656$ for which $t = 14a + 4b$. Compute the remainder when $r^2 + 16r + s$ is divided ... | 53,364 | graphs = [
Graph(
let={
"upper": Const(51984),
"k": Const(24),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(GCD(a=Var("n"), b=Ref("k")), Const(1))))),
"Q": Mod(value=Sum(Pow(Ref("r... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 2ba0ea | nt_count_coprime_v1 | quadratic_mod | 6 | 0 | [
"LIN_FORM"
] | 1 | 7.209 | 2026-02-08T12:58:29.818344Z | {
"verified": true,
"answer": 53364,
"timestamp": "2026-02-08T12:58:37.026976Z"
} | c68c4d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 167,
"completion_tokens": 4854
},
"timestamp": "2026-02-15T09:00:11.306Z",
"answer": 53364
},
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status"... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
b7f5ad | nt_max_prime_below_v1_1440796553_85 | Let $p_{\max}$ be the largest prime number not exceeding $45369$. Let $A$ be the number of ordered pairs $(p, q)$ of positive integers such that $p < q$, $\gcd(p, q) = 1$, and $pq = 16978500$. Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 90000$. Let $m$ be the minimum value of $... | 21,627 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": Const(45369),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("upper")), IsPrime(Var("n"))))),
"Q": Mod(value=Sum(Pow(Ref("result"), Ref("_n")), Mul(C... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS",
"B3"
] | 1e3e48 | nt_max_prime_below_v1 | quadratic_mod | 7 | 0 | [
"B3",
"COPRIME_PAIRS"
] | 2 | 2.23 | 2026-02-08T11:34:39.468128Z | {
"verified": true,
"answer": 21627,
"timestamp": "2026-02-08T11:34:41.698532Z"
} | c875bc | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 183,
"completion_tokens": 3448
},
"timestamp": "2026-02-14T15:53:15.822Z",
"answer": 21627
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
150437 | alg_poly4_min_v1_1218484723_5904 | Let $Q$ be the minimum value of
$$1020a^{4} -261120a b^{3} + 343740 b^{4} + 97920 a^{2} b^{2} -16320 a^{3} b$$
over all ordered pairs $(a, b)$ of positive integers where
$$1 \le a \le \max\{n : n \ge 2,\ n \le 374,\ n \text{ is prime}\}$$
and
$$1 \le b \le \left|\left\{ t : \text{there exist integers } a, b \text{ with... | 82,620 | graphs = [
Graph(
let={
"_m": Const(3),
"_n": Const(2),
"result": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n")... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW",
"LIN_FORM"
] | d530e2 | alg_poly4_min_v1 | null | 7 | 0 | [
"LIN_FORM",
"MAX_PRIME_BELOW"
] | 2 | 0.327 | 2026-02-25T07:28:55.571583Z | {
"verified": true,
"answer": 82620,
"timestamp": "2026-02-25T07:28:55.898883Z"
} | 59e5f3 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 306,
"completion_tokens": 4199
},
"timestamp": "2026-03-29T23:19:15.607Z",
"answer": 82620
},
{
"... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},... | {
"lo": -3.33,
"mid": 1.03,
"hi": 5.26
} | ||
3e1db8 | nt_count_divisors_in_range_v1_1978505735_7715 | Let $n = 25200$, $a = 7$, and $b = 4207$. Compute the number of positive integers $d$ such that $d$ divides $n$ and $a \leq d \leq b$. | 79 | graphs = [
Graph(
let={
"n": Const(25200),
"a": Const(7),
"b": Const(4207),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Divides(divisor=Var("d"), dividend=Ref("n")), Geq(Var("d"), Ref("a")), Leq(Var("d"), Ref("b"))))),
},
... | NT | null | COUNT | sympy | VIETA_SUM | [
"B3"
] | 0cd20d | nt_count_divisors_in_range_v1 | null | 3 | 0 | [
"B3",
"VIETA_SUM"
] | 2 | 0.31 | 2026-02-08T20:24:13.747840Z | {
"verified": true,
"answer": 79,
"timestamp": "2026-02-08T20:24:14.058273Z"
} | a324eb | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 97,
"completion_tokens": 2809
},
"timestamp": "2026-02-19T00:31:24.546Z",
"answer": 79
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
706cce | algebra_quadratic_discriminant_v1_397696148_917 | Let $a = 2$, $b = \sum_{k=1}^{2} k$, and $c = \sum_{k=1}^{4} \phi(k) \left\lfloor \frac{4}{k} \right\rfloor$, where $\phi$ denotes Euler's totient function. Let $D = b^2 - 4ac$. Compute the remainder when $69562 \cdot D$ is divided by 93609. | 22,375 | graphs = [
Graph(
let={
"_n": Const(4),
"a": Const(2),
"b": Summation(var="k", start=Const(1), end=Const(2), expr=Var("k")),
"c": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(4), Var("k"))))),
"re... | NT | null | COMPUTE | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC",
"K2"
] | 2a0f86 | algebra_quadratic_discriminant_v1 | null | 6 | 0 | [
"K2",
"SUM_ARITHMETIC"
] | 2 | 0.002 | 2026-02-08T11:57:24.824302Z | {
"verified": true,
"answer": 22375,
"timestamp": "2026-02-08T11:57:24.826203Z"
} | abcb00 | 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": 955
},
"timestamp": "2026-02-14T21:05:32.923Z",
"answer": 22375
},
{... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
444aa6 | antilemma_sum_equals_v1_151522320_1730 | Let $x$ be the number of ordered pairs $(i,j)$ of positive integers such that $i + j = 46$, $1 \leq i \leq 45$, and $1 \leq j \leq 46$. Let $d_k$ denote the $k$-th decimal digit of $|x|$, starting from $k=0$ for the units digit. Let $m$ be the number of digits in $|x|$. Compute the value of $$\sum_{i=0}^{m-1} d_i (i+1)... | 149 | graphs = [
Graph(
let={
"_n": Const(46),
"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(45)), right=IntegerRange(start=Const(1), end=Con... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS",
"ONE_FACTORIAL_0"
] | 5b61d1 | antilemma_sum_equals_v1 | null | 4 | 0 | [
"COUNT_SUM_EQUALS",
"ONE_FACTORIAL_0"
] | 2 | 0.008 | 2026-02-08T04:19:06.146810Z | {
"verified": true,
"answer": 149,
"timestamp": "2026-02-08T04:19:06.154350Z"
} | 2ca91b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 237,
"completion_tokens": 888
},
"timestamp": "2026-02-24T00:21:57.665Z",
"answer": 149
},
{
"id"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "ONE_FACTORIAL_0",
"status": "ok"
},
{
"lemma": "V7",
... | {
"lo": -4.92,
"mid": -2.9,
"hi": -0.7
} | ||
b566f3 | nt_min_coprime_above_v1_2051736721_3796 | Let $S$ be the set of all ordered pairs $(p, q)$ of positive integers such that $pq = 24$, $\gcd(p, q) = 1$, and $p < q$. Let $d_0$ be the number of elements in $S$. Let $m$ be the smallest positive integer $d \geq d_0$ that divides $5676989$. Find the smallest integer $n$ such that $24649 < n \leq 24702$ and $\gcd(n, ... | 24,650 | graphs = [
Graph(
let={
"start": Const(24649),
"upper": Const(24702),
"modulus": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condit... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/MIN_PRIME_FACTOR"
] | 52cee2 | nt_min_coprime_above_v1 | null | 5 | 0 | [
"COPRIME_PAIRS",
"MIN_PRIME_FACTOR"
] | 2 | 0.049 | 2026-02-08T17:33:18.911650Z | {
"verified": true,
"answer": 24650,
"timestamp": "2026-02-08T17:33:18.960821Z"
} | 35f5fa | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 160,
"completion_tokens": 2237
},
"timestamp": "2026-02-18T04:22:36.226Z",
"answer": 24650
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"s... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
5604a5 | comb_count_derangements_v1_48377204_3152 | Let $P$ be the set of all positive integers $p$ such that there exists an integer $q > p$ with $pq = 108$ and $\gcd(p,q) = 1$. Let $m$ be the number of elements in $P$. Let $D$ be the smallest positive divisor $d$ of $11011$ such that $d \ge m$. Let $!D$ denote the number of derangements of $D$ elements. Compute the re... | 49,446 | graphs = [
Graph(
let={
"_n": Const(11011),
"n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), 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=... | NT | COMB | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/MIN_PRIME_FACTOR"
] | 52cee2 | comb_count_derangements_v1 | null | 6 | 0 | [
"COPRIME_PAIRS",
"MIN_PRIME_FACTOR"
] | 2 | 0.002 | 2026-02-08T17:13:08.982742Z | {
"verified": true,
"answer": 49446,
"timestamp": "2026-02-08T17:13:08.984677Z"
} | d20dd6 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 163,
"completion_tokens": 2171
},
"timestamp": "2026-02-17T21:40:42.445Z",
"answer": 49446
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
df2af4_n | algebra_poly_eval_v1_1419126231_1705 | A game uses two resource types: A and B, with values 7 and 3 respectively. Players can spend 1 to 8 of A and 1 to 12 of B to form total values $t = 7a + 3b$, but only totals from 10 to 92 count. Let $D$ be the number of distinct such totals. Separately, a power-up's base strength is $49 \cdot 12^3 - 49 \cdot 12^2 - 141... | 1,071 | ALG | null | COMPUTE | sympy | POLY3_MIN | [
"POLY3_MIN",
"LIN_FORM"
] | 59aee9 | algebra_poly_eval_v1 | null | 6 | null | [
"LIN_FORM",
"POLY3_MIN"
] | 2 | 0.006 | 2026-02-25T11:14:28.226125Z | null | ed4859 | df2af4 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 265,
"completion_tokens": 2540
},
"timestamp": "2026-03-31T05:01:09.333Z",
"answer": 1071
},
{
"i... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY3_MIN",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | |
7dd685 | diophantine_sum_product_min_v1_717093673_1589 | Let $S=34$ and $P=288$. Let $x$ be an integer with $1 \le x \le 33$ such that
\[x( S - x ) = P.
\]
Assume there is at least one such integer $x$, and let $r$ be the smallest such $x$.
Write $|r|$ in base $10$. For each integer $i$ with $0 \le i \le d-1$, where $d$ is the number of decimal digits of $|r|$, let $D_i$ be... | 7,570 | graphs = [
Graph(
let={
"S": Const(34),
"P": Const(288),
"result": MinOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), Const(1)), Leq(Var("x"), Const(33)), Eq(Mul(Var("x"), Sub(Ref("S"), Var("x"))), Ref("P"))))),
"Q": Sum(Summation(var="i", s... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS",
"B3"
] | 8d50ad | diophantine_sum_product_min_v1 | digits_weighted_mod | 8 | 0 | [
"B3",
"COPRIME_PAIRS"
] | 2 | 0.02 | 2026-02-08T16:11:26.365397Z | {
"verified": true,
"answer": 7570,
"timestamp": "2026-02-08T16:11:26.385005Z"
} | 2d2e4c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 363,
"completion_tokens": 1515
},
"timestamp": "2026-02-16T23:11:06.973Z",
"answer": 7570
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "V5",
"status": "... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
fb03bf | comb_factorial_compute_v1_1918700295_2720 | Let $n = 65728$. Let $S$ be the set of all nonnegative integers $j$ such that $0 \leq j \leq n$ and $\binom{n}{j} \equiv 1 \pmod{d}$, where $d$ is the number of positive integers $p$ for which there exists an integer $q > p$ such that $pq = 24$ and $\gcd(p, q) = 1$. Let $N$ be the number of elements in $S$. Define $f =... | 36,420 | graphs = [
Graph(
let={
"_n": Const(65728),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(65728)), Eq(Mod(value=Binom(n=Ref("_n"), k=Var("j")), modulus=CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(a... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/V8"
] | 93b9b8 | comb_factorial_compute_v1 | null | 7 | 0 | [
"COPRIME_PAIRS",
"V8"
] | 2 | 0.003 | 2026-02-08T08:10:41.294458Z | {
"verified": true,
"answer": 36420,
"timestamp": "2026-02-08T08:10:41.297188Z"
} | df9ea4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 178,
"completion_tokens": 2296
},
"timestamp": "2026-02-13T15:42:04.841Z",
"answer": 36420
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V1",
"status... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
dc16a6 | antilemma_sum_equals_v1_1125832087_187 | Let $x$ be the number of ordered pairs $(i,j)$ of positive integers such that $1 \leq i \leq 35$, $1 \leq j \leq 35$, and $i + j = 35$.
Let $Q$ be the remainder when $44121x$ is divided by $68687$. Compute $Q$. | 57,687 | graphs = [
Graph(
let={
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(35)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(35)), right=IntegerRange(start=Const(1), end=Const(35))))),
"Q": ... | COMB | GEOM | COMPUTE | sympy | COMB1 | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 2 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS"
] | 2 | 0.031 | 2026-02-08T02:55:37.100099Z | {
"verified": true,
"answer": 57687,
"timestamp": "2026-02-08T02:55:37.130989Z"
} | d8d0ff | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 187,
"completion_tokens": 771
},
"timestamp": "2026-02-10T11:48:00.235Z",
"answer": 57687
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"stat... | {
"lo": -1.87,
"mid": 0.05,
"hi": 1.73
} | ||
f8493c | nt_count_divisible_v1_1470522791_613 | Let $\phi$ denote Euler's totient function. Define
$$
d = \sum_{k=1}^{6} \phi(k) \left\lfloor \frac{6}{k} \right\rfloor.
$$
Let $N$ be the number of positive integers $n$ such that $1 \leq n \leq 67600$ and $n$ is divisible by $d$. Compute the value of $N$. | 3,219 | graphs = [
Graph(
let={
"_n": Const(6),
"upper": Const(67600),
"divisor": Summation(var="k", start=Const(1), end=Const(6), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Ref("_n"), Var("k"))))),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq... | NT | null | COUNT | sympy | K2 | [
"K2"
] | 6897ab | nt_count_divisible_v1 | null | 5 | 0 | [
"K2"
] | 1 | 3.719 | 2026-02-08T13:08:09.020117Z | {
"verified": true,
"answer": 3219,
"timestamp": "2026-02-08T13:08:12.739514Z"
} | c708ad | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 157,
"completion_tokens": 621
},
"timestamp": "2026-02-16T04:25:59.286Z",
"answer": 3224
},
{
"id": 11,... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
}
] | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
4d9955 | antilemma_k3_v1_1978505735_4223 | Let $m = 9909$. Define $\tau(d)$ as Euler's totient function $\phi(d)$. Let $n$ be the sum of $\phi(d)$ over all positive divisors $d$ of $m$. Let $x$ be the sum of $\phi(d_1)$ over all positive divisors $d_1$ of the sum of $\phi(d_2)$ over all positive divisors $d_2$ of $n$. Compute $x$. | 9,909 | graphs = [
Graph(
let={
"_m": Const(9909),
"_n": SumOverDivisors(n=Ref(name='_m'), var='d', expr=EulerPhi(n=Var(name='d'))),
"x": SumOverDivisors(n=SumOverDivisors(n=Ref(name='_n'), var='d2', expr=EulerPhi(n=Var(name='d2'))), var='d1', expr=EulerPhi(n=Var(name='d1'))),
... | NT | COMB | COMPUTE | sympy | K3 | [
"K3/K3",
"K3"
] | 79f53d | antilemma_k3_v1 | null | 5 | 0 | [
"K3"
] | 1 | 0.002 | 2026-02-08T18:05:05.356291Z | {
"verified": true,
"answer": 9909,
"timestamp": "2026-02-08T18:05:05.357903Z"
} | 449573 | 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": 1216
},
"timestamp": "2026-02-18T13:46:36.315Z",
"answer": 9909
},
{... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
c0386c | comb_bell_compute_v1_809748730_1453 | Let $n$ be a positive integer. A pair of positive integers $(p, q)$ is called \emph{amicable} if $p < q$, $\gcd(p, q) = 1$, and $pq = 147000$. Let $A$ be the number of such amicable pairs.
Let $B$ be the $A$-th Bell number, which counts the number of partitions of a set of size $A$.
Compute the remainder when $44121 ... | 26,312 | graphs = [
Graph(
let={
"_n": Const(66148),
"n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=147000)), Eq(left=GCD(a=Var(name='p'), b=Var(... | NT | COMB | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_bell_compute_v1 | null | 6 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.002 | 2026-02-08T12:25:58.377971Z | {
"verified": true,
"answer": 26312,
"timestamp": "2026-02-08T12:25:58.379619Z"
} | 22f184 | 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": 2043
},
"timestamp": "2026-02-15T01:20:33.084Z",
"answer": 26312
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
ba4b61 | nt_count_intersection_v1_1918700295_3204 | Let $N$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 6250000$. Let $a = 7$, and let $b$ 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 $n$ such that $1 \leq n \l... | 12,884 | graphs = [
Graph(
let={
"_n": Const(44121),
"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(6250000)))), expr=Sum(Var("x"), Var("y")... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | nt_count_intersection_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.198 | 2026-02-08T08:27:28.825925Z | {
"verified": true,
"answer": 12884,
"timestamp": "2026-02-08T08:27:29.023840Z"
} | 094ad7 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 199,
"completion_tokens": 1635
},
"timestamp": "2026-02-13T19:05:46.926Z",
"answer": 12884
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
ff3459 | comb_catalan_compute_v1_655260480_4149 | Let $n$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 20$. Let $\text{result}$ be the $n$-th Catalan number. Let $Q = 59049 - \text{result}$. Compute $Q$. | 42,253 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2")), Const(20))))),
"res... | COMB | null | COMPUTE | sympy | COMB1 | [
"COMB1"
] | 567f58 | comb_catalan_compute_v1 | null | 4 | 0 | [
"COMB1"
] | 1 | 0.004 | 2026-02-08T17:45:50.221788Z | {
"verified": true,
"answer": 42253,
"timestamp": "2026-02-08T17:45:50.225578Z"
} | 87e0a5 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 116,
"completion_tokens": 1620
},
"timestamp": "2026-02-18T07:46:54.174Z",
"answer": 42253
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
... | {
"lo": -8,
"mid": -4.75,
"hi": -2.28
} | ||
f88b4a | nt_max_prime_below_v1_655260480_4822 | Let $\text{result}$ be the largest prime number $n$ such that $2 \leq n \leq 11449$. Let $p_{\max}$ be the largest prime number $n_1$ such that $2 \leq n_1 \leq 252$. Define $Q$ to be the remainder when $$\left(\text{result} \bmod p_{\max}\right) + 2003 \cdot \left(\text{result} \bmod 397\right)$$ is divided by $94890$... | 93,805 | graphs = [
Graph(
let={
"_n": Const(252),
"upper": Const(11449),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("upper")), IsPrime(Var("n"))))),
"_c": Const(2003),
"Q": Mod(value=Sum(Mod... | NT | null | EXTREMUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | 08a653 | nt_max_prime_below_v1 | two_moduli | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 3.805 | 2026-02-08T18:07:39.724275Z | {
"verified": true,
"answer": 93805,
"timestamp": "2026-02-08T18:07:43.528941Z"
} | 680261 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 164,
"completion_tokens": 2245
},
"timestamp": "2026-02-18T14:09:40.270Z",
"answer": 93805
},
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
b5f323 | lte_diff_endings_v1_1248542787_34 | Let $a = 25$, $b = 5$, $p = 2$, and $n = 112$. Define $a^n$ and $b^n$ as the $n$th powers of $a$ and $b$, respectively, and let $d = a^n - b^n$. Let $v_p$ be the largest integer $k$ such that $p^k$ divides $d$. Let $x$ be the remainder when $13901 \cdot v_p$ is divided by $100000$. Compute the value of $x$. | 83,406 | graphs = [
Graph(
let={
"a_val": Const(25),
"b_val": Const(5),
"p_val": Const(2),
"n_val": Const(112),
"a_pow": Pow(Ref("a_val"), Ref("n_val")),
"b_pow": Pow(Ref("b_val"), Ref("n_val")),
"pow_diff": Sub(Ref("a_pow"), Ref("b_... | NT | null | COMPUTE | sympy | LTE_DIFF | [
"LTE_DIFF"
] | cf8260 | lte_diff_endings_v1 | null | 6 | null | [
"LTE_DIFF"
] | 1 | 0.001 | 2026-02-08T02:55:15.772753Z | {
"verified": true,
"answer": 83406,
"timestamp": "2026-02-08T02:55:15.773632Z"
} | d0440f | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 236,
"completion_tokens": 2239
},
"timestamp": "2026-02-08T23:27:00.197Z",
"answer": 83406
},
{
"... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"statu... | {
"lo": -6.51,
"mid": -0.31,
"hi": 5.43
} | ||
0fe6b2 | nt_num_divisors_compute_v1_784195855_9374 | Let $n = 25600$. Let $d(n)$ denote the number of positive divisors of $n$.
Compute $d(n)$. | 33 | graphs = [
Graph(
let={
"n": Const(25600),
"result": NumDivisors(n=Ref("n")),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | B3 | [
"B3/V5/MOBIUS_SQUAREFREE/EULER_TOTIENT_SUM",
"LIN_FORM/EULER_TOTIENT_SUM"
] | 174eef | nt_num_divisors_compute_v1 | null | 2 | 0 | [
"B3",
"EULER_TOTIENT_SUM",
"LIN_FORM",
"MOBIUS_SQUAREFREE",
"V5"
] | 5 | 0.202 | 2026-02-08T16:45:29.667318Z | {
"verified": true,
"answer": 33,
"timestamp": "2026-02-08T16:45:29.869563Z"
} | 7a9909 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 75,
"completion_tokens": 363
},
"timestamp": "2026-02-17T11:29:31.030Z",
"answer": 33
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "EULER_TOTIENT_SUM",
"status": "ok_later"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
5d28ab | sequence_count_fib_divisible_v1_1439011603_1317 | Let $d = 18$ and $\text{upper} = 531$. Compute the number of positive integers $n$ such that $1 \le n \le \text{upper}$ and $d$ divides the $n$th Fibonacci number. | 44 | graphs = [
Graph(
let={
"upper": Const(531),
"d": Const(18),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Divides(divisor=Ref("d"), dividend=Fibonacci(arg=Var(name='n')))))),
},
g... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW/K14/L3B"
] | a1794c | sequence_count_fib_divisible_v1 | null | 5 | 0 | [
"K14",
"L3B",
"MAX_PRIME_BELOW"
] | 3 | 0.094 | 2026-02-08T16:01:59.366813Z | {
"verified": true,
"answer": 44,
"timestamp": "2026-02-08T16:01:59.460416Z"
} | 177c9f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 101,
"completion_tokens": 2149
},
"timestamp": "2026-02-16T19:19:31.408Z",
"answer": 44
},
{
... | 1 | [
{
"lemma": "K14",
"status": "ok_later"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3B",
"status": "ok_later"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
2a6846 | comb_count_surjections_v1_124444284_1144 | Let $n$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 10$. Let $k = 5$. Define $S$ to be the Stirling number of the second kind $S(n, k)$, and let $r = k! \cdot S$. Let $c = 79061$. Compute the remainder when $c \cdot r$ is divided by $73857$. | 33,624 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2")), Const(10))))),
"k":... | COMB | null | COUNT | sympy | COMB1 | [
"COMB1"
] | 567f58 | comb_count_surjections_v1 | null | 5 | 0 | [
"COMB1"
] | 1 | 0.001 | 2026-02-08T03:42:25.395305Z | {
"verified": true,
"answer": 33624,
"timestamp": "2026-02-08T03:42:25.396542Z"
} | 977ac0 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 213,
"completion_tokens": 737
},
"timestamp": "2026-02-10T03:21:06.132Z",
"answer": 33624
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
5e868f | algebra_poly_eval_v1_865884756_3254 | Let $m = 16$. Compute the value of $$7m^3 + \left(\sum_{k=1}^{4} k\right) m^2 - 5m + 2.$$ | 31,154 | graphs = [
Graph(
let={
"_n": Const(3),
"m": Const(16),
"result": Sum(Mul(Const(7), Pow(Ref("m"), Ref("_n"))), Mul(Summation(var="k", start=Const(1), end=Const(4), expr=Var("k")), Pow(Ref("m"), Const(2))), Mul(Const(-5), Ref("m")), Const(2)),
},
goal=Ref("... | NT | null | COMPUTE | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | algebra_poly_eval_v1 | null | 2 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.002 | 2026-02-08T17:14:55.198225Z | {
"verified": true,
"answer": 31154,
"timestamp": "2026-02-08T17:14:55.200343Z"
} | 1b4084 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 90,
"completion_tokens": 354
},
"timestamp": "2026-02-17T22:14:43.312Z",
"answer": 31154
},
{
... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
11f944 | sequence_fibonacci_compute_v1_655260480_3364 | Let $n$ be the largest positive integer $k$ such that $3^k \leq 54916076071$. Compute the $n$-th Fibonacci number, where the Fibonacci sequence is defined by $F_1 = 1$, $F_2 = 1$, and $F_m = F_{m-1} + F_{m-2}$ for $m \geq 3$. | 17,711 | graphs = [
Graph(
let={
"_n": Const(3),
"n": MaxOverSet(set=SolutionsSet(var=Var("k"), condition=Leq(Pow(Ref("_n"), Var("k")), Const(54916076071)))),
"result": Fibonacci(arg=Ref(name='n')),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | MAX_VAL | [
"MAX_VAL"
] | 1da621 | sequence_fibonacci_compute_v1 | null | 2 | 0 | [
"MAX_VAL"
] | 1 | 0.001 | 2026-02-08T17:20:07.672924Z | {
"verified": true,
"answer": 17711,
"timestamp": "2026-02-08T17:20:07.673978Z"
} | 4b9036 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 130,
"completion_tokens": 844
},
"timestamp": "2026-02-17T23:47:14.282Z",
"answer": 17711
},
{... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "same_pattern_wrong"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "ok"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
dfe92a | lin_form_endings_v1_151522320_1679 | Let $a = 105$ and $b = 30$. Define $g = \gcd(a, b)$, and let $a' = \left\lfloor \frac{a}{g} \right\rfloor$ and $b' = \left\lfloor \frac{b}{g} \right\rfloor$. Let $A = 45$ and $B = 29$. Define $s = a'A + b'B - a'b'$. Let $k = 12335$ and $M = 62117$. Compute the remainder when $k \cdot s$ is divided by $M$. | 17,958 | graphs = [
Graph(
let={
"a_coeff": Const(105),
"b_coeff": Const(30),
"A_val": Const(45),
"B_val": Const(29),
"g_step": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"ap_node": Floor(Div(Ref("a_coeff"), Ref("g_step"))),
"bp_node":... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 4 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T04:11:49.054275Z | {
"verified": true,
"answer": 17958,
"timestamp": "2026-02-08T04:11:49.055728Z"
} | 3503c6 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 245,
"completion_tokens": 678
},
"timestamp": "2026-02-10T15:38:40.273Z",
"answer": 17958
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
6a2a9c | geo_count_lattice_rect_v1_865884756_4850 | Let $a = 240$ and $b = 166$. Define $L$ to be the number of lattice points $(x, y)$ with $0 \leq x \leq a$ and $0 \leq y \leq b$. Let $c = 74328$. Determine the value of
$$
(c \cdot L) \bmod 93629.
$$ | 32,466 | graphs = [
Graph(
let={
"a": Const(240),
"b": Const(166),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"_c": Const(74328),
"Q": Mod(value=Mul(Ref("_c"), Ref("result")), modulus=Const(93629)),
},
goal=Ref("Q"),
... | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.001 | 2026-02-08T18:12:59.381657Z | {
"verified": true,
"answer": 32466,
"timestamp": "2026-02-08T18:12:59.382570Z"
} | be79c6 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 124,
"completion_tokens": 2000
},
"timestamp": "2026-02-18T14:52:17.330Z",
"answer": 32466
},
... | 1 | [] | {
"lo": -3.12,
"mid": 1.47,
"hi": 6.57
} | ||||
5b31f1 | comb_count_partitions_v1_717093673_864 | Let $n$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 78$. Determine the value of the number of integer partitions of $n$. | 31,185 | graphs = [
Graph(
let={
"_n": Const(78),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2")), Re... | COMB | null | COUNT | sympy | COMB1 | [
"COMB1"
] | 567f58 | comb_count_partitions_v1 | null | 4 | 0 | [
"COMB1"
] | 1 | 0.002 | 2026-02-08T15:43:59.780056Z | {
"verified": true,
"answer": 31185,
"timestamp": "2026-02-08T15:43:59.781788Z"
} | 0c9f31 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 160,
"completion_tokens": 1205
},
"timestamp": "2026-02-24T18:26:25.988Z",
"answer": 31185
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -2.4,
"mid": 1.57,
"hi": 5.75
} | ||
27caff | nt_min_with_divisor_count_v1_397696148_1973 | Let $n$ be a positive integer such that the number of positive divisors of $n$ is equal to $\sum_{k=1}^{3} k$. Determine the smallest such $n$ that does not exceed $36481$.
Compute the value of $n$. | 12 | graphs = [
Graph(
let={
"upper": Const(36481),
"div_count": Summation(var="k", start=Const(1), end=Const(3), expr=Var("k")),
"result": MinOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(NumDivisors(n=Var("n")),... | NT | null | EXTREMUM | sympy | ONE_PHI_2 | [
"SUM_ARITHMETIC"
] | eb34f0 | nt_min_with_divisor_count_v1 | null | 3 | 0 | [
"ONE_PHI_2",
"SUM_ARITHMETIC"
] | 2 | 28.754 | 2026-02-08T12:52:21.755462Z | {
"verified": true,
"answer": 12,
"timestamp": "2026-02-08T12:52:50.509515Z"
} | 1e5e07 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 102,
"completion_tokens": 1117
},
"timestamp": "2026-02-15T06:39:55.141Z",
"answer": 12
},
{
... | 1 | [
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
7586ba | comb_count_surjections_v1_48377204_1141 | Let $n$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 14$. Let $k = 3$. Define $r = k! \cdot S(n, k)$, where $S(n, k)$ is the Stirling number of the second kind. Compute the remainder when $44121 \cdot r$ is divided by $98545$. | 58,166 | graphs = [
Graph(
let={
"_n": Const(98545),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2")),... | COMB | null | COUNT | sympy | COMB1 | [
"COMB1"
] | 567f58 | comb_count_surjections_v1 | null | 3 | 0 | [
"COMB1"
] | 1 | 0.002 | 2026-02-08T15:54:53.680660Z | {
"verified": true,
"answer": 58166,
"timestamp": "2026-02-08T15:54:53.682899Z"
} | ffb0b6 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 205,
"completion_tokens": 1898
},
"timestamp": "2026-02-24T19:01:34.286Z",
"answer": 58166
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V8",
"statu... | {
"lo": -2.4,
"mid": 1.57,
"hi": 5.75
} |
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