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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
f964d0 | nt_count_divisors_in_range_v1_1353956133_26 | Let $a = 1$ and $n = 27720$. Let $b$ be the number of positive integers $m$ such that $1 \leq m \leq 60683$, $7$ divides $m$, and $\gcd(m, 10) = 1$. Let $c$ be the number of positive divisors $d$ of $n$ such that $a \leq d \leq b$. Find the remainder when $25849 \cdot c$ is divided by $75954$. | 21,941 | graphs = [
Graph(
let={
"_n": Const(10),
"n": Const(27720),
"a": Const(1),
"b": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(60683)), Divides(divisor=Const(7), dividend=Var("n")), Eq(GCD(a=Var("n"), b=R... | NT | null | COUNT | sympy | C5 | [
"C5"
] | 1d9668 | nt_count_divisors_in_range_v1 | null | 5 | 0 | [
"C5"
] | 1 | 0.035 | 2026-02-08T11:16:29.982510Z | {
"verified": true,
"answer": 21941,
"timestamp": "2026-02-08T11:16:30.017895Z"
} | a1dddc | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 153,
"completion_tokens": 2562
},
"timestamp": "2026-02-14T11:24:49.488Z",
"answer": 21941
},
... | 1 | [
{
"lemma": "C5",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
3d31a3 | modular_product_range_v1_601307018_9235 | Let $S = \left\{ v \mid 4 \le v \le 2624,\ \exists\, a,b \in \mathbb{Z},\ 1 \le a,b \le 11\ \text{such that}\ 25a^2 - 38ab + 17b^2 = v \right\}$. Let $M = \prod_{i=4}^{|S|} i$. Find the remainder when $M$ is divided by $10427$. | 6,123 | graphs = [
Graph(
let={
"_n": Const(4),
"prod": MathProduct(expr=Var("i"), var="i", start=Const(4), end=CountOverSet(set=SolutionsSet(var=Var("v"), condition=And(Geq(Var("v"), Ref("_n")), Leq(Var("v"), Const(2624)), Exists(var=Tuple(elements=[Var(name='a'), Var(name='b')]), condition... | NT | null | COMPUTE | sympy | QF_PSD_DISTINCT | [
"QF_PSD_DISTINCT"
] | a8f9cb | modular_product_range_v1 | null | 4 | 0 | [
"QF_PSD_DISTINCT"
] | 1 | 0.008 | 2026-03-10T09:36:53.741828Z | {
"verified": true,
"answer": 6123,
"timestamp": "2026-03-10T09:36:53.749673Z"
} | 3c92d1 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 216,
"completion_tokens": 22852
},
"timestamp": "2026-04-19T10:55:59.449Z",
"answer": 6123
},
{
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "QF_PSD_DISTINCT",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
586252 | geo_count_lattice_triangle_v1_1419126231_331 | Let $M = \left|100 \cdot 144 + 12 \cdot (0 - 300)\right|$. Let $R = \gcd\left(100, \sum_{\substack{(a, b, c),\, a^2 + b^2 + c^2 = ab + bc + ca,\\ 4a + 3b + 5c = 120,\, a \geq 1, b \geq 1, c \geq 1}} (a^2 + b^2 + c^2)\right) + \gcd(|12 - 100|, |144 - 300|) + \gcd(|0 - 12|, |0 - 144|)$. Let $S = \frac{M + 2 - R}{2}$. Com... | 57,157 | graphs = [
Graph(
let={
"_n": Const(2),
"area_2x": Abs(arg=Sum(Mul(Const(value=100), Const(value=144)), Mul(Const(value=12), Sub(left=Const(value=0), right=Const(value=300))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=100)), b=Abs(arg=SumOverSet(set=MapOverSet(set=Solut... | GEOM | NT | COUNT | sympy | SUM_SQUARES_IDENTITY | [
"SUM_SQUARES_IDENTITY"
] | 9879b8 | geo_count_lattice_triangle_v1 | null | 5 | 0 | [
"SUM_SQUARES_IDENTITY"
] | 1 | 0.006 | 2026-02-25T09:50:40.042462Z | {
"verified": true,
"answer": 57157,
"timestamp": "2026-02-25T09:50:40.048690Z"
} | b5f9b0 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 296,
"completion_tokens": 1101
},
"timestamp": "2026-03-30T08:04:28.855Z",
"answer": 57157
},
{
"... | 1 | [
{
"lemma": "SUM_SQUARES_IDENTITY",
"status": "ok"
}
] | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | ||
dde0b5 | nt_min_coprime_above_v1_1248542787_150 | Let $A$ be the set of all ordered pairs $(i,j)$ where $i$ is an integer from 1 to 20, $j$ is an integer from 1 to 29, and $\gcd(i,j) = 1$. Let $m$ be the number of elements in $A$. Let $n_0$ be the smallest integer $n$ such that $85849 < n \leq 86230$ and $\gcd(n, m) = 1$. Compute the remainder when $\sum_{k=1}^{n_0} \... | 41,263 | graphs = [
Graph(
let={
"start": Const(85849),
"upper": Const(86230),
"modulus": 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=Cons... | NT | null | EXTREMUM | sympy | COUNT_COPRIME_GRID | [
"COUNT_COPRIME_GRID"
] | 20ec03 | nt_min_coprime_above_v1 | null | 6 | 0 | [
"COUNT_COPRIME_GRID"
] | 1 | 0.043 | 2026-02-08T02:58:21.432795Z | {
"verified": true,
"answer": 41263,
"timestamp": "2026-02-08T02:58:21.475411Z"
} | de7196 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 257,
"completion_tokens": 32768
},
"timestamp": "2026-02-23T21:15:58.945Z",
"answer": null
},
{
... | 0 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
... | {
"lo": 4.56,
"mid": 6.51,
"hi": 9.5
} | ||
2c9252 | nt_max_prime_below_v1_1915831931_3920 | Let $S$ be the set of all positive integers $p$ such that there exists a positive integer $q$ with $pq = 12$, $\gcd(p, q) = 1$, and $p < q$. Let $c$ be the number of elements in $S$. Let $n$ be a prime number satisfying $c \leq n \leq 80656$. Determine the value of the largest such $n$. | 80,651 | graphs = [
Graph(
let={
"upper": Const(80656),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), V... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_max_prime_below_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 1.923 | 2026-02-08T18:01:06.375685Z | {
"verified": true,
"answer": 80651,
"timestamp": "2026-02-08T18:01:08.298250Z"
} | f35fc7 | 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": 4507
},
"timestamp": "2026-02-18T11:59:41.015Z",
"answer": 80651
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V8_SUM",
"s... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
d2ba81 | nt_count_divisible_v1_677425708_2170 | Let $n = 2$. Define $T$ as the set of all integers $t$ such that $7 \leq t \leq 20$ and there exist positive integers $a \leq 5$ and $b \leq 2$ satisfying $t = 2a + 5b$. Let $d$ be the largest prime number $n$ such that $n \geq 2$ and $n \leq |T|$. Define $r$ as the number of positive integers $m$ such that $1 \leq m \... | 7,296 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": Const(51076),
"divisor": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=V... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/MAX_PRIME_BELOW",
"ONE_PHI_1"
] | fc144b | nt_count_divisible_v1 | null | 4 | 0 | [
"LIN_FORM",
"MAX_PRIME_BELOW",
"ONE_PHI_1"
] | 3 | 3.489 | 2026-02-08T04:49:54.859676Z | {
"verified": true,
"answer": 7296,
"timestamp": "2026-02-08T04:49:58.348660Z"
} | beea66 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 234,
"completion_tokens": 600
},
"timestamp": "2026-02-18T14:03:39.415Z",
"answer": 7296
}
] | 2 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "ONE_PHI_1",
"s... | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
4d64a7 | comb_sum_binomial_row_v1_784195855_7684 | Let $\_n = 2$. Let $n$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 11205810$, $\gcd(p, q) = 1$, and $p < q$. Compute $\_n^n$. | 65,536 | graphs = [
Graph(
let={
"_n": Const(2),
"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=11205810)), Eq(left=GCD(a=Var(name='p'), b=Var(na... | NT | null | SUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_sum_binomial_row_v1 | null | 3 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.001 | 2026-02-08T09:26:42.836500Z | {
"verified": true,
"answer": 65536,
"timestamp": "2026-02-08T09:26:42.837982Z"
} | 9fca18 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 113,
"completion_tokens": 1507
},
"timestamp": "2026-02-14T04:20:50.282Z",
"answer": 65536
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
25a1b4 | diophantine_sum_product_min_v1_1742523217_952 | Let $c=2$ and $m=2$. Consider all integers $x$ such that
$$x^2-102x-208=0.$$
Let $S_0$ be the set of all such integers $x$, and let
$$T=\sum_{x\in S_0} x.$$
Let $n$ be the largest prime number with $2\le n\le T$.
Let $A$ be the set of all integers $t$ such that there exist integers $a$ and $b$ with $1\le a\le 10$, $1... | 39 | graphs = [
Graph(
let={
"_c": Const(2),
"_m": Const(2),
"_n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_m")), Leq(Var("n"), SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Ref("_c")), Mul(Const(-102), Var("x")), C... | NT | null | EXTREMUM | sympy | K13 | [
"VIETA_SUM/MAX_PRIME_BELOW/LIN_FORM"
] | 65772e | diophantine_sum_product_min_v1 | null | 8 | 0 | [
"K13",
"LIN_FORM",
"MAX_PRIME_BELOW",
"VIETA_SUM"
] | 4 | 0.484 | 2026-02-08T03:22:02.911995Z | {
"verified": true,
"answer": 39,
"timestamp": "2026-02-08T03:22:03.395981Z"
} | a644b4 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 425,
"completion_tokens": 20343
},
"timestamp": "2026-02-23T18:18:39.905Z",
"answer": 39
},
{
"i... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok_later"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "o... | {
"lo": 2.84,
"mid": 4.91,
"hi": 7.14
} | ||
255394 | antilemma_k2_v1_1915831931_3169 | Let $x = \sum_{k=1}^{66} \phi(k) \left\lfloor \frac{66}{k} \right\rfloor$, where $\phi$ denotes Euler's totient function. Let $c = 62648$. Compute the remainder when $c \cdot x$ is divided by 83733. Find the value of $Q$, where $Q$ is this remainder. | 20,346 | graphs = [
Graph(
let={
"_n": Const(66),
"x": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(66), Var("k"))))),
"_c": Const(62648),
"Q": Mod(value=Mul(Ref("_c"), Ref("x")), modulus=Const(83733)),
},
... | NT | COMB | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | antilemma_k2_v1 | null | 5 | 0 | [
"K2"
] | 1 | 0.001 | 2026-02-08T17:24:26.169159Z | {
"verified": true,
"answer": 20346,
"timestamp": "2026-02-08T17:24:26.170149Z"
} | a254cc | 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": 2471
},
"timestamp": "2026-02-18T01:11:57.587Z",
"answer": 20346
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
2eaa35 | algebra_poly_eval_v1_124444284_907 | Let $n = 3$ and $x = 10$. Define $r = 5x^n + 7x^2 + 7x - 3$. Let $c$ be the number of integers $t$ such that $7 \leq t \leq 2411$ and there exist positive integers $a$, $b$ with $1 \leq a \leq 321$, $1 \leq b \leq 403$, and $t = 5a + 2b$. Compute the remainder when $r^2 + 47r + c$ is divided by $61269$. | 17,596 | graphs = [
Graph(
let={
"_n": Const(3),
"x": Const(10),
"result": Sum(Mul(Const(5), Pow(Ref("x"), Ref("_n"))), Mul(Const(7), Pow(Ref("x"), Const(2))), Mul(Const(7), Ref("x")), Const(-3)),
"_c": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=V... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 2ba0ea | algebra_poly_eval_v1 | quadratic_mod | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T03:35:45.528862Z | {
"verified": true,
"answer": 17596,
"timestamp": "2026-02-08T03:35:45.531030Z"
} | 077dc1 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 244,
"completion_tokens": 2150
},
"timestamp": "2026-02-09T23:43:40.753Z",
"answer": 17600
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V5",
"status... | {
"lo": 1.71,
"mid": 5.04,
"hi": 8.38
} | ||
d7fcc4 | diophantine_sum_product_min_v1_1520064083_5769 | Let $S=45$. Consider all ordered pairs $(x,y)$ of positive integers such that $xy=63504$. Let $P$ be the minimum possible value of $x+y$ over all such pairs.
Let $T$ be the set of all integers $z$ such that
$$z^2-484z+34848=0.$$
Let $U$ be the sum of all elements of $T$.
Consider all ordered pairs $(u,v)$ of positiv... | 86,121 | graphs = [
Graph(
let={
"_n": Const(21505),
"S": Const(45),
"P": 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(63504)))), e... | NT | null | EXTREMUM | sympy | VIETA_SUM | [
"VIETA_SUM/B3"
] | d036a4 | diophantine_sum_product_min_v1 | null | 8 | 0 | [
"B3",
"VIETA_SUM"
] | 2 | 0.019 | 2026-02-08T07:37:18.840446Z | {
"verified": true,
"answer": 86121,
"timestamp": "2026-02-08T07:37:18.859716Z"
} | f7b3ed | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 272,
"completion_tokens": 1699
},
"timestamp": "2026-02-13T11:11:46.143Z",
"answer": 86121
},
... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
... | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
6c8b84 | algebra_quadratic_discriminant_v1_655260480_407 | Let $a = 1$, $b = 11$, and $c = 18$. Define the discriminant $D = b^2 - 4ac$. Let $r = 2$ if $D > 0$, $r = 1$ if $D = 0$, and $r = 0$ otherwise. Compute the Bell number $B_k$, where $k = |r| \bmod 11$. | 2 | graphs = [
Graph(
let={
"a": Const(1),
"b": Const(11),
"c": Const(18),
"D": Sub(Pow(Ref("b"), Const(2)), Mul(Const(4), Ref("a"), Ref("c"))),
"result": Sum(Mul(Const(2), Iverson(condition=Gt(Ref("D"), Const(0)))), Iverson(condition=Eq(Ref("D"), Cons... | COMB | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"B3/L3C"
] | 345f3b | algebra_quadratic_discriminant_v1 | null | 2 | 0 | [
"B3",
"L3C",
"MAX_PRIME_BELOW"
] | 3 | 0.036 | 2026-02-08T15:22:14.698158Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-02-08T15:22:14.734156Z"
} | e9a784 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 202,
"completion_tokens": 289
},
"timestamp": "2026-02-24T20:38:36.923Z",
"answer": 2
},
{
"id": ... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
... | {
"lo": -8.52,
"mid": -5.43,
"hi": -3.2
} | ||
cb1e28_l | antilemma_sum_equals_v1_124444284_2022 | Let $x$ be the number of ordered pairs $(i,j)$ of positive integers with $1 \leq i \leq 56$, $1 \leq j \leq 56$, and $i + j = 58$. Compute the remainder when $12 - x$ is divided by $53960$. | 53,916 | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 2 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.006 | 2026-02-08T04:15:32.376915Z | {
"verified": false,
"answer": 53917,
"timestamp": "2026-02-08T04:15:32.382692Z"
} | 24b2e3 | cb1e28 | legacy_text | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 177,
"completion_tokens": 764
},
"timestamp": "2026-02-23T23:56:25.261Z",
"answer": 53917
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status"... | {
"lo": -3.83,
"mid": -1.68,
"hi": 1.09
} | |
3642ef | nt_count_divisible_v1_1520064083_3801 | Let $ S $ be the sum
$$
S = \sum_{k=0}^{9} (-1)^k \binom{9}{k}.
$$
Let $ A $ be the set of all positive integers $ n $ such that $ 1 \leq n \leq 39204 $ and $ n \equiv S \pmod{19} $. Compute $ 10731 $ minus the number of elements in $ A $. | 8,668 | graphs = [
Graph(
let={
"upper": Const(39204),
"divisor": Const(19),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(value=Var("n"), modulus=Ref("divisor")), Summation(var="k", start=Const(0)... | COMB | null | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING"
] | c21569 | nt_count_divisible_v1 | null | 5 | 0 | [
"BINOMIAL_ALTERNATING"
] | 1 | 1.27 | 2026-02-08T05:53:01.258768Z | {
"verified": true,
"answer": 8668,
"timestamp": "2026-02-08T05:53:02.528370Z"
} | a46e2a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 204,
"completion_tokens": 707
},
"timestamp": "2026-02-24T04:50:08.181Z",
"answer": 8668
},
{
"id... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"stat... | {
"lo": -5.98,
"mid": -3.97,
"hi": -1.94
} | ||
cced62 | comb_count_derangements_v1_1915831931_1635 | Let $m = 93505$. Let $d_{\text{min}}$ be the smallest divisor of $437$ that is at least $2$. Let $n$ be the number of prime numbers less than or equal to $d_{\text{min}}$ and at least $2$. Compute the remainder when $83872 \cdot !n$ is divided by $m$, where $!n$ denotes the subfactorial of $n$. Enter your answer as an ... | 82,856 | graphs = [
Graph(
let={
"_m": Const(93505),
"_n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(437))))),
"n": CountOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(2)), ... | NT | COMB | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/COUNT_PRIMES"
] | 56ea03 | comb_count_derangements_v1 | null | 4 | 0 | [
"COUNT_PRIMES",
"MIN_PRIME_FACTOR"
] | 2 | 0.002 | 2026-02-08T16:19:00.765795Z | {
"verified": true,
"answer": 82856,
"timestamp": "2026-02-08T16:19:00.768145Z"
} | e29d72 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 153,
"completion_tokens": 2692
},
"timestamp": "2026-02-17T02:00:47.231Z",
"answer": 82856
},
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "ok_later"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V1",
"status... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
1af727 | comb_bell_compute_v1_677425708_2813 | Let $N = 2054$. Let $n$ be the number of integers $j$ with $0 \le j \le N$ such that
$$\binom{2054}{j} \equiv 1 \pmod{2}.$$
Let $Q$ be the $n$th Bell number, that is, the number of ways to partition a set of $n$ elements into nonempty subsets.
Compute $Q$. | 4,140 | graphs = [
Graph(
let={
"_n": Const(2054),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Ref("_n")), Eq(Mod(value=Binom(n=Const(2054), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')),
"res... | COMB | null | COMPUTE | sympy | V8 | [
"V8"
] | 86348e | comb_bell_compute_v1 | null | 8 | 0 | [
"V8"
] | 1 | 0.004 | 2026-02-08T05:17:25.636832Z | {
"verified": true,
"answer": 4140,
"timestamp": "2026-02-08T05:17:25.640530Z"
} | 74b03c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 204,
"completion_tokens": 734
},
"timestamp": "2026-02-11T23:38:55.162Z",
"answer": 4140
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -1.7,
"mid": 0.37,
"hi": 2.2
} | ||
e85c4a | modular_sum_quadratic_residues_v1_1439011603_2538 | Let $p$ be the smallest prime divisor of $77837$. Define $r = \frac{p(p-1)}{4}$. Let $Q$ be the remainder when $44121 \cdot r$ is divided by $86701$.
Find the value of $Q$. | 30,747 | graphs = [
Graph(
let={
"_n": Const(4),
"p": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(77837))))),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), Ref("_n")),
"Q": Mod(value=... | 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 | 2026-02-08T16:51:15.291955Z | {
"verified": true,
"answer": 30747,
"timestamp": "2026-02-08T16:51:15.293388Z"
} | a63d72 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 103,
"completion_tokens": 2399
},
"timestamp": "2026-02-17T13:35:51.629Z",
"answer": 30747
},
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
27f30c | nt_count_coprime_v1_677425708_443 | Let $n$ be a positive integer such that $1 \leq n \leq 20160$ and $\gcd(n, 19) = 1$. Let $A$ be the number of such integers $n$. Compute the value of $$ A + \phi(|A| + 1) + \tau(|A| + 1), $$ where $\phi$ denotes Euler's totient function and $\tau(k)$ denotes the number of positive divisors of $k$. | 26,717 | graphs = [
Graph(
let={
"upper": Const(20160),
"k": Const(19),
"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": Sum(Ref("result"), Euler... | NT | null | COUNT | sympy | ONE_PHI_1 | [
"ONE_PHI_1"
] | f6b5a5 | nt_count_coprime_v1 | null | 4 | 0 | [
"ONE_PHI_1"
] | 1 | 1.546 | 2026-02-08T03:33:00.696057Z | {
"verified": true,
"answer": 26717,
"timestamp": "2026-02-08T03:33:02.242447Z"
} | 9d9ce0 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 216,
"completion_tokens": 1244
},
"timestamp": "2026-02-08T20:34:56.095Z",
"answer": 26717
},
{
"... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "ONE_PHI_1",
"status": "ok"
}
] | {
"lo": -6.51,
"mid": -0.31,
"hi": 5.43
} | ||
e58c9d | nt_max_prime_below_v1_1456120455_14 | Let $c$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq = 72$, $\gcd(p, q) = 1$, and $p < q$. Let $R$ be the largest prime number $n$ such that $c \leq n \leq 46225$. Compute the remainder when $44121 \cdot R$ is divided by $95734$. | 94,299 | graphs = [
Graph(
let={
"upper": Const(46225),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), V... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_max_prime_below_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.98 | 2026-02-08T02:48:33.214207Z | {
"verified": true,
"answer": 94299,
"timestamp": "2026-02-08T02:48:34.193865Z"
} | c13b5d | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 204,
"completion_tokens": 32768
},
"timestamp": "2026-02-23T17:42:53.657Z",
"answer": 94299
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_SUB",
... | {
"lo": 1.88,
"mid": 3.52,
"hi": 5.13
} | ||
2fb64d | comb_binomial_compute_v1_1520064083_2233 | Let $n$ be the largest prime number satisfying $2 \leq n \leq 15$. Let $k$ be the largest prime number satisfying $2 \leq k \leq 6$. Compute the value of $\binom{n}{k}$. | 1,287 | graphs = [
Graph(
let={
"_m": Const(6),
"_n": Const(2),
"n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(15)), IsPrime(Var("n"))))),
"k": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | comb_binomial_compute_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.004 | 2026-02-08T04:35:26.471050Z | {
"verified": true,
"answer": 1287,
"timestamp": "2026-02-08T04:35:26.474991Z"
} | caabe6 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 167,
"completion_tokens": 461
},
"timestamp": "2026-02-10T17:09:05.161Z",
"answer": 1287
},
{
"i... | 2 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -9.14,
"mid": -6.05,
"hi": -3.73
} | ||
dc8b9d | comb_count_permutations_fixed_v1_168721529_2034 | Let $N$ be the smallest positive integer $n$ such that $7^{140}$ divides $n!$. Let $d_{\min}$ be the smallest integer $d \geq 2$ that divides $N$. Define $n = d_{\min}$. Compute the value of $$ \binom{n}{3} \cdot !(n - 3), $$ where $!k$ denotes the number of derangements of $k$ elements. Let $m = 44121$. Find the remai... | 8,921 | graphs = [
Graph(
let={
"_m": Const(44121),
"_n": Const(2),
"n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=MinOverSet(set=SolutionsSet(var=Var("n"), condition=Geq(MaxKDivides(target=Factorial(Var("... | NT | COMB | COUNT | sympy | V5 | [
"V5/MIN_PRIME_FACTOR"
] | da0dce | comb_count_permutations_fixed_v1 | null | 7 | 0 | [
"MIN_PRIME_FACTOR",
"V5"
] | 2 | 0.004 | 2026-02-08T14:03:35.762408Z | {
"verified": true,
"answer": 8921,
"timestamp": "2026-02-08T14:03:35.766611Z"
} | bc6904 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 231,
"completion_tokens": 1543
},
"timestamp": "2026-02-10T01:09:24.026Z",
"answer": 8921
}
] | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok_later"
... | {
"lo": -10,
"mid": -1.96,
"hi": 6.09
} | ||
5a5fbb | algebra_poly_eval_v1_601307018_1004 | Let $n$ be the number of ordered pairs $(a, b)$ of positive integers with
$$1 \le a \le \left|\left\{(a1, b1) : 1 \le a1 \le 40,\ 1 \le b1 \le 40,\ 68a1^{3}b1 + 17b1^{4} + \min\{ |x - y| : x > 0,\ y > 0,\ xy = 21115 \} \cdot a1^{2} b1^{\left|\{ p : p > 0,\ \exists q \in \mathbb{Z} \text{ with } pq = 72,\ \gcd(p, q) = 1... | 23,872 | graphs = [
Graph(
let={
"_d": Const(4),
"_c": Const(2),
"_m": Const(3),
"_n": Const(3),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), CountOverSet(set=SolutionsSet(... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/POLY4_COUNT/QF_PSD_COUNT",
"B3_DIFF/POLY4_COUNT/QF_PSD_COUNT"
] | e9a352 | algebra_poly_eval_v1 | null | 8 | 0 | [
"B3_DIFF",
"COPRIME_PAIRS",
"POLY4_COUNT",
"QF_PSD_COUNT"
] | 4 | 0.048 | 2026-03-10T01:34:43.584379Z | {
"verified": true,
"answer": 23872,
"timestamp": "2026-03-10T01:34:43.632752Z"
} | 4612f7 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 389,
"completion_tokens": 3363
},
"timestamp": "2026-04-19T00:45:22.442Z",
"answer": 23872
},
{
... | 1 | [
{
"lemma": "B3_DIFF",
"status": "ok"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
... | {
"lo": -1.06,
"mid": 2.32,
"hi": 5.24
} | ||
4233e4 | antilemma_k2_v1_1915831931_3349 | Let $m = 17$. Define $n$ to be
$$
\sum_{k=1}^{m} \phi(k) \left\lfloor \frac{17}{k} \right\rfloor.
$$
Compute
$$
\sum_{k=1}^{n} \phi(k) \left\lfloor \frac{1 + 2 + \cdots + 17}{k} \right\rfloor.
$$ | 11,781 | graphs = [
Graph(
let={
"_m": Const(17),
"_n": Summation(var="k", start=Const(1), end=Ref("_m"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(17), Var("k"))))),
"x": Summation(var="k1", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k1")), Floor(Div(Summation(v... | NT | COMB | COMPUTE | sympy | K2 | [
"K2/SUM_ARITHMETIC/K2",
"K2"
] | 85b706 | antilemma_k2_v1 | null | 4 | 0 | [
"K2",
"SUM_ARITHMETIC"
] | 2 | 0.002 | 2026-02-08T17:34:31.753626Z | {
"verified": true,
"answer": 11781,
"timestamp": "2026-02-08T17:34:31.755645Z"
} | 599f8b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 132,
"completion_tokens": 1292
},
"timestamp": "2026-02-18T04:37:34.649Z",
"answer": 11781
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok_later"
},
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
b63672_l | nt_min_coprime_above_v1_1116507919_202 | Let $\text{modulus}$ be the number of integers $t$ such that $18 \leq t \leq 334$ and $t = 8a + 10b$ for some integers $a$ and $b$ with $1 \leq a \leq 8$ and $1 \leq b \leq 27$. Compute the smallest integer $n$ such that $73984 < n \leq 74141$ and $\gcd(n, \text{modulus}) = 1$. | 73,987 | NT | null | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_min_coprime_above_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.025 | 2026-02-08T02:27:52.498778Z | {
"verified": false,
"answer": 73985,
"timestamp": "2026-02-08T02:27:52.523602Z"
} | 1be7df | b63672 | legacy_text | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 224,
"completion_tokens": 32768
},
"timestamp": "2026-02-23T13:51:18.546Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": 1.42,
"mid": 2.89,
"hi": 4.27
} | |
e74120 | sequence_lucas_compute_v1_784195855_5286 | Let $n$ be the smallest integer $d \geq 2$ that divides $6982823$. Compute the $n$th Lucas number. | 9,349 | graphs = [
Graph(
let={
"_n": Const(2),
"n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(6982823))))),
"result": Lucas(arg=Ref(name='n')),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | sequence_lucas_compute_v1 | null | 4 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.001 | 2026-02-08T07:49:09.404500Z | {
"verified": true,
"answer": 9349,
"timestamp": "2026-02-08T07:49:09.405131Z"
} | 33b71c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 78,
"completion_tokens": 1621
},
"timestamp": "2026-02-13T12:31:04.213Z",
"answer": 9349
},
{
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
72cbad | modular_min_linear_v1_1520064083_6423 | Let $ S $ be the set of all integers $ t $ such that there exist integers $ a $ and $ b $ satisfying $ 1 \leq a \leq 283 $, $ 1 \leq b \leq 859 $, $ 9 \leq t \leq 3699 $, and $ t = 7a + 2b $. Let $ b $ be the number of elements in $ S $. Let $ a = 16435 $ and $ m = 38593 $. Define $ x $ to be the smallest positive inte... | 49,458 | graphs = [
Graph(
let={
"_n": Const(57140),
"a": Const(16435),
"b": 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'), rig... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | modular_min_linear_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 1.522 | 2026-02-08T08:03:44.684938Z | {
"verified": true,
"answer": 49458,
"timestamp": "2026-02-08T08:03:46.207370Z"
} | 59574c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 217,
"completion_tokens": 5506
},
"timestamp": "2026-02-13T14:23:58.280Z",
"answer": 49458
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
b893fd_n | alg_telescope_v1_1218484723_2844 | A robot computes a cumulative score by summing the values $4k^3 + 6k^2 + 4k + 1$ for $k = 0$ to $1549$, then takes the remainder modulo the sum of $4k_1 + 199$ for $k_1 = 0$ to $17$. Let $M$ be this final value. The robot then multiplies $M$ by $44121$ and computes the remainder when divided by $50306$. What is this fi... | 37,450 | ALG | null | COMPUTE | sympy | SUM_AP | [
"SUM_AP"
] | ff6f57 | alg_telescope_v1 | null | 4 | null | [
"SUM_AP"
] | 1 | 0.124 | 2026-02-25T04:34:51.445663Z | null | ecd788 | b893fd | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 221,
"completion_tokens": 5244
},
"timestamp": "2026-03-30T19:08:36.909Z",
"answer": 37450
},
{
"... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_AP",
"status": "ok"
}
] | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | |
679b8b | antilemma_cartesian_v1_1125832087_2416 | Let $S$ be the set of all ordered pairs $(a,b)$ such that $a$ is an integer with $1 \leq a \leq 18$ and $b$ is an integer with $1 \leq b \leq 21$. Compute the number of elements in $S$. | 378 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(18)), right=IntegerRange(start=Const(1), end=Const(21)))),
},
goal=Ref("x"),
)
] | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | antilemma_cartesian_v1 | null | 2 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.002 | 2026-02-08T04:35:40.956564Z | {
"verified": true,
"answer": 378,
"timestamp": "2026-02-08T04:35:40.958575Z"
} | 4f245f | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 175,
"completion_tokens": 231
},
"timestamp": "2026-02-24T01:17:49.147Z",
"answer": 378
},
{
"id"... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": ... | {
"lo": -10,
"mid": -7.79,
"hi": -5.57
} | ||
0b6e31 | sequence_count_fib_divisible_v1_1470522791_1191 | Let $T$ be the set of all integers $t$ with $18 \leq t \leq 1834$ for which there exist positive integers $a \leq 123$ and $b \leq 85$ such that $t = 8a + 10b$. Let $u$ be the number of elements in $T$. Let $d$ be the largest prime number at most 16. Determine the number of positive integers $n \leq u$ such that $d$ di... | 128 | graphs = [
Graph(
let={
"_n": Const(16),
"upper": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=123)), Geq(left... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW",
"LIN_FORM"
] | d530e2 | sequence_count_fib_divisible_v1 | null | 6 | 0 | [
"LIN_FORM",
"MAX_PRIME_BELOW"
] | 2 | 0.042 | 2026-02-08T13:29:40.745269Z | {
"verified": true,
"answer": 128,
"timestamp": "2026-02-08T13:29:40.787758Z"
} | 53348b | 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": 4941
},
"timestamp": "2026-02-15T16:59:12.535Z",
"answer": 128
},
{
... | 1 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
693f13 | modular_modexp_compute_v1_677425708_2065 | Let $a = 47$. Let $e$ be the number of positive integers $j$ such that $1 \leq j \leq 2304$ and $j^2 \leq 5308416$. Let $m = 11449$. Define $\text{result}$ to be $a^e \bmod m$, that is, the remainder when $a^e$ is divided by $m$. Compute $\text{result}$. | 7,148 | graphs = [
Graph(
let={
"a": Const(47),
"e": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(1)), Leq(Var("j"), Const(2304)), Leq(Pow(Var("j"), Const(2)), Const(5308416))), domain='positive_integers')),
"m": Const(11449),
"result"... | NT | null | COMPUTE | sympy | C3 | [
"C3"
] | 8a214c | modular_modexp_compute_v1 | null | 4 | 0 | [
"C3"
] | 1 | 0.001 | 2026-02-08T04:44:15.165219Z | {
"verified": true,
"answer": 7148,
"timestamp": "2026-02-08T04:44:15.166059Z"
} | 29d03f | 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": 5238
},
"timestamp": "2026-02-11T07:25:44.164Z",
"answer": 7148
},
{
"... | 1 | [
{
"lemma": "C3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
94fb44 | modular_mod_compute_v1_153355830_1705 | Let $a = -61009$ and $m = 69169$. Compute $r$, the remainder when $a$ is divided by $m$. Let $T$ be the set of all integers $t$ such that $12 \leq t \leq 334$ and there exist integers $a$ and $b$ with $1 \leq a \leq 25$, $1 \leq b \leq 78$, and $t = 7a + 2b + 3$. Find the remainder when
$$
(r \bmod 307) + 5003 \cdot (r... | 12,794 | graphs = [
Graph(
let={
"a": Const(-61009),
"m": Const(69169),
"result": Mod(value=Ref("a"), modulus=Ref("m")),
"Q": Mod(value=Sum(Mod(value=Ref("result"), modulus=Const(307)), Mul(Const(5003), Mod(value=Ref("result"), modulus=CountOverSet(set=SolutionsSet(var... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | d6c893 | modular_mod_compute_v1 | two_moduli | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T06:34:07.208550Z | {
"verified": true,
"answer": 12794,
"timestamp": "2026-02-08T06:34:07.209833Z"
} | 180bb6 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 187,
"completion_tokens": 3049
},
"timestamp": "2026-02-13T01:48:37.436Z",
"answer": 12794
},
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
10d441 | modular_min_linear_v1_124444284_1931 | Let $A$ be the set of all integers $n$ with $1 \leq n \leq 31239$ such that $n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{11}$. Let $a = |A|$. Let $B$ be the set of all integers $t$ with $10 \leq t \leq 2300$ such that there exist positive integers $a \leq 74$ and $b \leq 594$ satisfying $t = 7a + 3b$. Let $b ... | 3,275 | graphs = [
Graph(
let={
"_n": Const(63454),
"a": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(31239)), Congruent(a=Var(name='n'), b=Floor(arg=Div(left=Var(name='n'), right=Const(value=2))), modulus=Const(value=11))))),
... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM",
"L3C"
] | ecf77f | modular_min_linear_v1 | null | 7 | 0 | [
"L3C",
"LIN_FORM"
] | 2 | 0.669 | 2026-02-08T04:12:51.080237Z | {
"verified": true,
"answer": 3275,
"timestamp": "2026-02-08T04:12:51.749155Z"
} | 0cd854 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 232,
"completion_tokens": 5877
},
"timestamp": "2026-02-11T22:41:24.615Z",
"answer": 3275
},
{... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
598a13 | modular_min_modexp_v1_1125832087_1083 | Let $x$ be the smallest positive integer such that $1 \leq x \leq 52$ and $2^x \equiv 7 \pmod{157}$. Let $r$ be the remainder when $x$ is divided by 11. Compute the $r$-th Bell number. | 1 | graphs = [
Graph(
let={
"a": Const(2),
"b": Const(7),
"m": Const(157),
"upper": Const(52),
"result": MinOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), Const(1)), Leq(Var("x"), Ref("upper")), Eq(ModExp(base=Ref("a"), exp=Var("x")... | NT | COMB | EXTREMUM | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | 58d7e9 | modular_min_modexp_v1 | bell_mod | 6 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 1.749 | 2026-02-08T03:30:49.187233Z | {
"verified": true,
"answer": 1,
"timestamp": "2026-02-08T03:30:50.936258Z"
} | 58728f | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 177,
"completion_tokens": 627
},
"timestamp": "2026-02-10T14:51:08.687Z",
"answer": 1
},
{
"id": ... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
... | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
61535d | geo_count_lattice_triangle_v1_1978505735_2877 | Let $A$ be the area of the triangle with vertices at $(0,0)$, $(180,66)$, and $(111,128)$, multiplied by $2$. Let $B$ be the sum of the greatest common divisors of the absolute differences in coordinates along each side of the triangle:
- $\gcd(|180 - 0|, |66 - 0|)$,
- $\gcd(|111 - 180|, |128 - 66|)$,
- $\gcd(|0 - 111|... | 78,842 | graphs = [
Graph(
let={
"area_2x": Abs(arg=Sum(Mul(Const(value=180), Const(value=128)), Mul(Const(value=111), Sub(left=Const(value=0), right=Const(value=66))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=180)), b=Abs(arg=Const(value=66))), GCD(a=Abs(arg=Sub(left=Const(value=111), rig... | ALG | NT | COUNT | sympy | [] | geo_count_lattice_triangle_v1 | null | 5 | 0 | null | null | 0.003 | 2026-02-08T17:13:54.752218Z | {
"verified": true,
"answer": 78842,
"timestamp": "2026-02-08T17:13:54.755499Z"
} | a07bf7 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 241,
"completion_tokens": 598
},
"timestamp": "2026-02-16T09:10:58.753Z",
"answer": null
},
{
"id": 11,... | 1 | [] | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||||
b953ec | sequence_count_fib_divisible_v1_1918700295_1964 | Let $S$ be the set of positive integers $n$ such that $1 \le n \le 6160$ and $n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{11}$. Let $N = |S|$. Compute the number of positive integers $n$ such that $1 \le n \le N$ and the $n$th Fibonacci number is divisible by 11. | 56 | graphs = [
Graph(
let={
"_n": Const(6160),
"upper": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_n")), Congruent(a=Var(name='n'), b=Floor(arg=Div(left=Var(name='n'), right=Const(value=2))), modulus=Const(value=11))))),
... | NT | null | COUNT | sympy | L3C | [
"L3C"
] | 73f8b0 | sequence_count_fib_divisible_v1 | null | 6 | 0 | [
"L3C"
] | 1 | 0.085 | 2026-02-08T06:12:00.697666Z | {
"verified": true,
"answer": 56,
"timestamp": "2026-02-08T06:12:00.782944Z"
} | 90d469 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 140,
"completion_tokens": 1183
},
"timestamp": "2026-02-13T11:27:19.652Z",
"answer": 55
},
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8",
"status": "no"... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
5aaee8 | antilemma_k3_v1_784195855_9458 | Let $x = \sum_{d \mid 50724} \phi(d)$, where $\phi$ denotes Euler's totient function. Compute the remainder when $28226 \cdot x$ is divided by $64983$. | 30,168 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=50724), var='d', expr=EulerPhi(n=Var(name='d'))),
"_c": Const(28226),
"Q": Mod(value=Mul(Ref("_c"), Ref("x")), modulus=Const(64983)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T16:50:37.472333Z | {
"verified": true,
"answer": 30168,
"timestamp": "2026-02-08T16:50:37.473006Z"
} | de661b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 93,
"completion_tokens": 1395
},
"timestamp": "2026-02-17T13:44:02.425Z",
"answer": 30168
},
{... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
5ede2d | comb_bell_compute_v1_655260480_4830 | Let $n$ be the sum of all real solutions $x$ to the equation $x^2 - 8x - 9588 = 0$. Compute the Bell number $B_n$, which counts the number of partitions of a set of $n$ elements. | 4,140 | graphs = [
Graph(
let={
"_n": Const(2),
"n": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Ref("_n")), Mul(Const(-8), Var("x")), Const(-9588)), Const(0)))),
"result": Bell(Ref("n")),
},
goal=Ref("result"),
)
] | COMB | null | COMPUTE | sympy | K2 | [
"VIETA_SUM"
] | b33a7a | comb_bell_compute_v1 | null | 3 | 0 | [
"K2",
"VIETA_SUM"
] | 2 | 0.008 | 2026-02-08T18:08:53.591186Z | {
"verified": true,
"answer": 4140,
"timestamp": "2026-02-08T18:08:53.599452Z"
} | 5c512f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 103,
"completion_tokens": 678
},
"timestamp": "2026-02-18T14:53:44.069Z",
"answer": 4140
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "VIETA_SUM",
"status": "o... | {
"lo": -3.12,
"mid": 1.47,
"hi": 6.57
} | ||
00ec85 | diophantine_product_count_v1_677425708_2816 | Let $k = 180$ and $u = 47$. Compute the number of positive integers $x$ such that $1 \leq x \leq u$, $x$ divides $k$, and $\frac{k}{x} \leq u$. Find the value of this count. | 12 | graphs = [
Graph(
let={
"k": Const(180),
"upper": Const(47),
"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 | LIN_FORM | [
"LIN_FORM",
"B3"
] | 688dbe | diophantine_product_count_v1 | null | 3 | 0 | [
"B3",
"LIN_FORM"
] | 2 | 0.062 | 2026-02-08T05:17:26.202808Z | {
"verified": true,
"answer": 12,
"timestamp": "2026-02-08T05:17:26.264896Z"
} | 718605 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 106,
"completion_tokens": 778
},
"timestamp": "2026-02-12T06:31:40.406Z",
"answer": 12
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
0e31b5 | antilemma_k3_v1_1520064083_8723 | Let $n = 32830$. Compute the remainder when $44121$ times the sum $\sum_{d \mid n} \phi(d)$ is divided by $79654$, where $\phi$ denotes Euler's totient function. | 64,094 | graphs = [
Graph(
let={
"_n": Const(32830),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Mod(value=Mul(Const(44121), Ref("x")), modulus=Const(79654)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 4 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T10:20:43.902473Z | {
"verified": true,
"answer": 64094,
"timestamp": "2026-02-08T10:20:43.903444Z"
} | 2ede5e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 95,
"completion_tokens": 1081
},
"timestamp": "2026-02-14T07:09:05.883Z",
"answer": 64094
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
01677e | antilemma_cartesian_v1_124444284_1582 | Compute the remainder when $48512$ times the number of ordered pairs $(i,j)$ with $1 \leq i \leq 34$ and $1 \leq j \leq 39$ is divided by $78933$. | 75,450 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(34)), right=IntegerRange(start=Const(1), end=Const(39)))),
"Q": Mod(value=Mul(Const(48512), Ref("x")), modulus=Const(78933)),
},
goal=Ref("Q"),
)
] | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | antilemma_cartesian_v1 | null | 2 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.001 | 2026-02-08T04:01:43.978596Z | {
"verified": true,
"answer": 75450,
"timestamp": "2026-02-08T04:01:43.979473Z"
} | f22377 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 161,
"completion_tokens": 984
},
"timestamp": "2026-02-11T15:47:49.685Z",
"answer": 75450
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status":... | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
92e60e | nt_count_coprime_v1_2051736721_162 | Let $n = 5$ and let $k$ be the value of $$\sum_{k=1}^{5} \phi(k) \left\lfloor \frac{5}{k} \right\rfloor,$$ where $\phi$ denotes Euler's totient function. Let $S$ be the set of all positive integers $n$ such that $1 \leq n \leq 58564$ and $\gcd(n, k) = 1$. Compute the number of elements in $S$. | 31,235 | graphs = [
Graph(
let={
"_n": Const(5),
"upper": Const(58564),
"k": Summation(var="k1", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k1")), Floor(Div(Const(5), Var("k1"))))),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Va... | NT | null | COUNT | sympy | K2 | [
"K2"
] | 6897ab | nt_count_coprime_v1 | null | 5 | 0 | [
"K2"
] | 1 | 7.965 | 2026-02-08T15:15:47.665392Z | {
"verified": true,
"answer": 31235,
"timestamp": "2026-02-08T15:15:55.630867Z"
} | a72d1c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 150,
"completion_tokens": 1535
},
"timestamp": "2026-02-16T02:30:47.405Z",
"answer": 31235
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
849007 | diophantine_fbi2_min_v1_397696148_2635 | Let $k = 12$ and $\text{upper} = 22$. Define $\text{result}$ to be the smallest integer $d$ such that $2 \le d \le \text{upper}$, $d$ divides $k$, and $\frac{k}{d}$ is at least the number of nonnegative integers $j$ with $0 \le j \le 4128$ for which $\binom{4128}{j} \equiv 1 \pmod{2}$. Compute $\text{result}$. | 2 | graphs = [
Graph(
let={
"_n": Const(2),
"k": Const(12),
"upper": Const(22),
"result": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Leq(Var("d"), Ref("upper")), Divides(divisor=Var("d"), dividend=Ref("k")), Geq(Div(Ref("k"), ... | NT | null | EXTREMUM | sympy | V8 | [
"V8"
] | 86348e | diophantine_fbi2_min_v1 | null | 6 | 0 | [
"V8"
] | 1 | 0.007 | 2026-02-08T13:27:06.956038Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-02-08T13:27:06.963488Z"
} | c41826 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 156,
"completion_tokens": 1437
},
"timestamp": "2026-02-15T15:30:17.367Z",
"answer": 2
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
ef03ec | algebra_vieta_sum_v1_1742523217_5160 | Let $f(x) = -x^3 - 7x^2 - 4x + c$, where $c$ is the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 24$. Find the product of all real roots of the equation $f(x) = 0$. | 12 | graphs = [
Graph(
let={
"_n": Const(3),
"result": ProductOverSet(set=SolutionsSet(var=Var(name='x'), condition=Eq(left=Sum(Mul(Const(value=-1), Pow(base=Var(name='x'), exp=Ref(name='_n'))), Mul(Const(value=-7), Pow(base=Var(name='x'), exp=Const(value=2))), Mul(Const(value=-4), Var(na... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"COMB1"
] | 567f58 | algebra_vieta_sum_v1 | null | 6 | 0 | [
"COMB1",
"MAX_PRIME_BELOW"
] | 2 | 0.024 | 2026-02-08T10:50:31.071306Z | {
"verified": true,
"answer": 12,
"timestamp": "2026-02-08T10:50:31.095180Z"
} | cdd4df | 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": 764
},
"timestamp": "2026-02-14T08:58:14.559Z",
"answer": 12
},
{
... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
a6e23e | alg_linear_system_2x2_v1_1218484723_5100 | Let $\det = 16 \cdot 4 - 15 \cdot 16$ and $M = 483456 \cdot 4 - 452151 \cdot 16$. Let $R = \min\{ 29b^2 + 29a^2 - 42ab \mid 1 \leq a \leq 5,\ 1 \leq b \leq 5\} \cdot 452151 - 15 \cdot 483456$. Compute $\frac{M}{\det} + \frac{R}{\det}$. | 30,216 | graphs = [
Graph(
let={
"_n": Const(16),
"num_x": Sub(Mul(Const(483456), Const(4)), Mul(Const(452151), Const(16))),
"num_y": Sub(Mul(MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), C... | ALG | null | COMPUTE | sympy | QF_PSD_MIN | [
"QF_PSD_MIN"
] | c66ce3 | alg_linear_system_2x2_v1 | null | 3 | 0 | [
"QF_PSD_MIN"
] | 1 | 0.002 | 2026-02-25T06:43:54.084754Z | {
"verified": true,
"answer": 30216,
"timestamp": "2026-02-25T06:43:54.087181Z"
} | 156611 | 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": 2055
},
"timestamp": "2026-03-29T19:26:03.791Z",
"answer": 30216
},
{
"... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_MIN",
"status": "ok"
}
] | {
"lo": -3.33,
"mid": 1.03,
"hi": 5.26
} | ||
bbaaea | comb_count_partitions_v1_1470522791_1195 | Let $n$ be the number of integers $t$ such that $15 \le t \le 138$ and there exist positive integers $a$ and $b$ with $1 \le a \le 11$, $1 \le b \le 8$, and $t = 6a + 9b$. Define $p(n)$ to be the number of integer partitions of $n$. Compute $p(n)$. | 37,338 | 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=11)), Geq(left=Var(name='b'), right=Const(value=... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_count_partitions_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T13:30:44.713356Z | {
"verified": true,
"answer": 37338,
"timestamp": "2026-02-08T13:30:44.715213Z"
} | 195d77 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 201,
"completion_tokens": 2393
},
"timestamp": "2026-02-24T18:31:35.361Z",
"answer": 37338
},
{
"... | 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_SUM",
"status": "no"
... | {
"lo": 1.15,
"mid": 4.18,
"hi": 6.61
} | ||
c11e1b | diophantine_product_count_v1_124444284_8446 | Let $k = 840$. Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = 30$. Define $M$ to be the maximum value of $xy$ over all such pairs. Compute the number of positive integers $x \leq M$ such that $x$ divides $k$ and $\frac{k}{x} \leq M$. Let this count be $c$. Find $85849 - c$. | 85,823 | graphs = [
Graph(
let={
"k": Const(840),
"upper": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Const(30)))), expr=Mul(Var("x"), Var("y")))),... | NT | null | COUNT | sympy | B1 | [
"B1"
] | 5b950e | diophantine_product_count_v1 | null | 5 | 0 | [
"B1"
] | 1 | 0.01 | 2026-02-08T09:42:40.666850Z | {
"verified": true,
"answer": 85823,
"timestamp": "2026-02-08T09:42:40.676562Z"
} | 4a11a8 | 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": 1352
},
"timestamp": "2026-02-14T05:44:28.149Z",
"answer": 85823
},
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
992ec2 | v1_endings_v1_1248542787_302 | Let $n = 35340$ and $p = 5$. Let $n!$ denote the factorial of $n$, and let $v_p(n!)$ be the largest integer $k$ such that $p^k$ divides $n!$. Compute the remainder when $v_p(n!)$ is divided by $50761$. | 8,832 | graphs = [
Graph(
let={
"n_val": Const(35340),
"p_val": Const(5),
"n_fact": Factorial(Ref("n_val")),
"vp": MaxKDivides(target=Ref("n_fact"), base=Ref("p_val")),
"mod_val": Const(50761),
"x": Mod(value=Ref("vp"), modulus=Ref("mod_val")),... | NT | null | COMPUTE | sympy | V1 | [
"V1"
] | dae96f | v1_endings_v1 | null | 5 | null | [
"V1"
] | 1 | 0 | 2026-02-08T03:03:13.265201Z | {
"verified": true,
"answer": 8832,
"timestamp": "2026-02-08T03:03:13.265632Z"
} | 2b8e26 | 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": 825
},
"timestamp": "2026-02-09T02:32:35.270Z",
"answer": 8832
},
{
"id... | 1 | [
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "same_pattern_wrong"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"st... | {
"lo": -6.51,
"mid": -0.31,
"hi": 5.43
} | ||
539079 | antilemma_coprime_grid_v1_168721529_861 | Let $x$ be the number of ordered pairs $(i,j)$ of integers with $1 \leq i \leq 10$ and $1 \leq j \leq 130$ such that $\gcd(i,j) = \phi(1)$, where $\phi$ denotes Euler's totient function. Compute the remainder when $28343x$ is divided by $52718$. | 25,500 | graphs = [
Graph(
let={
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(GCD(a=Var("i"), b=Var("j")), EulerPhi(n=Const(1))), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(10)), right=IntegerRange(start=Const(1), end=Const(130))))),
... | NT | COMB | COMPUTE | sympy | COUNT_COPRIME_GRID | [
"COUNT_COPRIME_GRID",
"ONE_PHI_1"
] | 3d404c | antilemma_coprime_grid_v1 | null | 3 | 0 | [
"COUNT_COPRIME_GRID",
"ONE_PHI_1"
] | 2 | 0.002 | 2026-02-08T13:19:25.485479Z | {
"verified": true,
"answer": 25500,
"timestamp": "2026-02-08T13:19:25.487673Z"
} | fea7c1 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 198,
"completion_tokens": 3110
},
"timestamp": "2026-02-09T10:00:51.806Z",
"answer": 25500
},
{
"... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "ONE_PHI_1",
"status": "ok"
},
... | {
"lo": -1.99,
"mid": 2.14,
"hi": 6.33
} | ||
c42be0 | antilemma_sum_equals_v1_48377204_1985 | Let $t$ be an integer satisfying $5 \leq t \leq 103$. Let $n$ be the number of such integers $t$ for which there exist positive integers $a$ and $b$, with $1 \leq a \leq 26$ and $1 \leq b \leq 17$, such that $t = 2a + 3b$. Compute the number of ordered pairs $(i, j)$ of integers such that $1 \leq i \leq 96$, $1 \leq j ... | 96 | 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=26)), Geq(left=Var(name='b'), right=Const(value... | COMB | GEOM | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | ada383 | antilemma_sum_equals_v1 | null | 4 | 0 | [
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 2 | 0.006 | 2026-02-08T16:32:24.453421Z | {
"verified": true,
"answer": 96,
"timestamp": "2026-02-08T16:32:24.459246Z"
} | 732569 | 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": 3729
},
"timestamp": "2026-02-17T06:25:36.438Z",
"answer": 96
},
{
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": ... | {
"lo": -5.64,
"mid": -3.17,
"hi": -0.81
} | ||
ae7d74 | antilemma_sum_equals_v1_1918700295_3978 | Let $c = 160$. Consider the set of all ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = c$. Let $m$ be the number of such pairs. Now consider the set of all ordered pairs $(i, j)$ of integers with $1 \leq i \leq 80$ and $1 \leq j \leq 80$ such that $i + j = m$. Let $n$ be the number of such pa... | 78 | graphs = [
Graph(
let={
"_c": Const(160),
"_m": 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 | GEOM | COMPUTE | sympy | LIN_FORM | [
"COUNT_SUM_EQUALS/COUNT_SUM_EQUALS",
"COMB1/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | a57484 | antilemma_sum_equals_v1 | null | 6 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 3 | 0.05 | 2026-02-08T09:04:07.413572Z | {
"verified": true,
"answer": 78,
"timestamp": "2026-02-08T09:04:07.463805Z"
} | 6a24ca | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 313,
"completion_tokens": 2620
},
"timestamp": "2026-02-24T10:27:10.683Z",
"answer": 78
},
{
"id"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V8",
"status": ... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
943402 | diophantine_fbi2_count_v1_1978505735_23 | Let $k = 240$. Determine the number of positive integers $d$ such that $6 \leq d \leq 116$, $d$ divides $k$, and $6 \leq \frac{k}{d} \leq 116$. Let $r$ be this count. Compute the remainder when $44121 \cdot r$ is divided by $77965$. | 51,385 | graphs = [
Graph(
let={
"_n": Const(44121),
"k": Const(240),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(6)), Leq(Var("d"), Const(116)), Divides(divisor=Var("d"), dividend=Ref("k")), Geq(Div(Ref("k"), Var("d")), Const(6)), Leq(D... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | diophantine_fbi2_count_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.009 | 2026-02-08T15:08:47.466309Z | {
"verified": true,
"answer": 51385,
"timestamp": "2026-02-08T15:08:47.475412Z"
} | 7f8725 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 192,
"completion_tokens": 1631
},
"timestamp": "2026-02-10T06:44:23.548Z",
"answer": 51485
},
{
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
}
] | {
"lo": 1.69,
"mid": 5.03,
"hi": 8.38
} | ||
8cd155 | comb_binomial_compute_v1_1915831931_2619 | Let $n = 13$. Let $k$ be the smallest divisor of 35 that is at least 2. Compute $\binom{n}{k}$. | 1,287 | graphs = [
Graph(
let={
"n": Const(13),
"k": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(35))))),
"result": Binom(n=Ref("n"), k=Ref("k")),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | comb_binomial_compute_v1 | null | 2 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.001 | 2026-02-08T16:59:22.161133Z | {
"verified": true,
"answer": 1287,
"timestamp": "2026-02-08T16:59:22.162561Z"
} | df266e | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 92,
"completion_tokens": 610
},
"timestamp": "2026-02-16T08:54:43.474Z",
"answer": 1287
},
{
"id": 11,
... | 2 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "VAL_SUM_EQ",
"status": ... | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
b09421 | antilemma_k3_v1_971394319_1090 | Let $n = 57641$. Compute the sum of $\phi(d)$ over all positive divisors $d$ of $n$, where $\phi(d)$ denotes Euler's totient function. | 57,641 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=57641), var='d', expr=EulerPhi(n=Var(name='d'))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T13:29:45.566777Z | {
"verified": true,
"answer": 57641,
"timestamp": "2026-02-08T13:29:45.567314Z"
} | 33096b | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 102,
"completion_tokens": 837
},
"timestamp": "2026-02-16T04:47:43.676Z",
"answer": 30795
},
{
"id": 11,... | 1 | [
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
8d0bf7 | alg_sum_powers_v1_1218484723_4527 | Let $c = \left|\{ (a, b) : 1 \leq a \leq b \leq 35,\ 2a^2 - 4ab + 2b^2 = 50 \}\right|$, and let $d = \left|\{ n : 1 \leq n \leq 109260,\ c \mid F_n \}\right|$ where $F_n$ is the $n$-th Fibonacci number. Let $R = \left( \sum_{k=1}^{1388} k^2 \right) \bmod d$. Find the remainder when $83161 \cdot R$ is divided by $93616$... | 10,915 | graphs = [
Graph(
let={
"_n": Const(1388),
"result": Mod(value=Summation(var="k", start=Const(1), end=Ref("_n"), expr=Pow(Var("k"), Const(2))), modulus=CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(109260)), Divides(divisor=Cou... | NT | null | COMPUTE | sympy | QF_PSD_ORBIT | [
"QF_PSD_ORBIT/COUNT_FIB_DIVISIBLE"
] | 50cefd | alg_sum_powers_v1 | null | 5 | 0 | [
"COUNT_FIB_DIVISIBLE",
"QF_PSD_ORBIT"
] | 2 | 0.057 | 2026-02-25T06:11:44.891247Z | {
"verified": true,
"answer": 10915,
"timestamp": "2026-02-25T06:11:44.947895Z"
} | 55640e | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 259,
"completion_tokens": 8906
},
"timestamp": "2026-03-29T16:06:56.207Z",
"answer": 57212
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok_later"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "QF_PSD_ORBIT",
"status": "... | {
"lo": 3.81,
"mid": 6.33,
"hi": 9.49
} | ||
f615cc | antilemma_k3_v1_784195855_7594 | Let $S$ be the set of all positive integers $x$ such that $x^2 - 2087x - 2088 = 0$. Let $x = \sum_{d \mid s} \phi(d)$, where $s$ is the sum of all elements in $S$, and the sum is taken over all positive divisors $d$ of $s$. Compute the remainder when $8 - x$ is divided by $84311$. | 82,232 | graphs = [
Graph(
let={
"_n": Const(84311),
"x": SumOverDivisors(n=SumOverSet(set=SolutionsSet(var=Var(name='x'), condition=Eq(left=Sum(Pow(base=Var(name='x'), exp=Const(value=2)), Mul(Const(value=-2087), Var(name='x')), Const(value=-2088)), right=Const(value=0)))), var='d', expr=Eul... | NT | COMB | COMPUTE | sympy | K13 | [
"VIETA_SUM/K3",
"K3"
] | 78a626 | antilemma_k3_v1 | null | 4 | 0 | [
"K13",
"K3",
"VIETA_SUM"
] | 3 | 0.002 | 2026-02-08T09:24:36.444823Z | {
"verified": true,
"answer": 82232,
"timestamp": "2026-02-08T09:24:36.446338Z"
} | 82fb94 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 142,
"completion_tokens": 617
},
"timestamp": "2026-02-14T03:46:28.165Z",
"answer": 82231
},
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
672ddc | antilemma_sum_equals_v1_349078426_403 | Let $m = 43$ and $n = 83$. Define $x$ to be the number of ordered pairs $(i, j)$ of positive integers such that $i + j = n$ and $1 \leq i, j \leq 81$. Let $k$ be the number of integers $t$ with $9 \leq t \leq 52$ for which there exist positive integers $a$ and $b$ such that $1 \leq a \leq 8$, $1 \leq b \leq 4$, and $t ... | 9,003 | graphs = [
Graph(
let={
"_m": Const(43),
"_n": Const(83),
"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(81)), right=Integer... | COMB | GEOM | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM",
"COUNT_SUM_EQUALS"
] | a464cd | antilemma_sum_equals_v1 | quadratic_mod | 3 | 0 | [
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 2 | 0.009 | 2026-02-08T13:01:19.796658Z | {
"verified": true,
"answer": 9003,
"timestamp": "2026-02-08T13:01:19.805476Z"
} | 31a04e | 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": 8924
},
"timestamp": "2026-02-24T16:58:48.474Z",
"answer": 9003
},
{
"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": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"st... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
6e5190 | sequence_lucas_compute_v1_677425708_280 | Let $n$ be the number of positive integers $k$ such that $1 \leq k \leq 1539$ and $81$ divides $k$. Let $L_n$ denote the $n$-th Lucas number, defined by $L_1 = 1$, $L_2 = 3$, and $L_m = L_{m-1} + L_{m-2}$ for $m \geq 3$. Compute the remainder when $13994 \cdot L_n$ is divided by $93527$. | 79,160 | graphs = [
Graph(
let={
"_n": Const(93527),
"n": CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(1)), Leq(Var("k"), Const(1539)), Divides(divisor=Const(81), dividend=Var("k"))), domain='positive_integers')),
"result": Lucas(arg=Ref(name='n'))... | ALG | NT | COMPUTE | sympy | C2 | [
"C2"
] | 9685eb | sequence_lucas_compute_v1 | null | 3 | 0 | [
"C2"
] | 1 | 0.002 | 2026-02-08T03:12:40.715278Z | {
"verified": true,
"answer": 79160,
"timestamp": "2026-02-08T03:12:40.716857Z"
} | ab0326 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 230,
"completion_tokens": 1788
},
"timestamp": "2026-02-08T20:26:16.236Z",
"answer": 79160
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V7",
"status":... | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
0030f8 | sequence_lucas_compute_v1_349078426_771 | Let $S$ be the set of all prime numbers $n$ such that $2 \leq n \leq 19$. Let $n$ be the sum of $\phi(d)$ over all positive divisors $d$ of the largest element in $S$. Let $L_n$ denote the $n$-th Lucas number, defined by $L_1 = 1$, $L_2 = 3$, and $L_k = L_{k-1} + L_{k-2}$ for $k \geq 3$. Compute the remainder when $856... | 3,007 | graphs = [
Graph(
let={
"_n": Const(75758),
"n": SumOverDivisors(n=MaxOverSet(set=SolutionsSet(var=Var(name='n'), condition=And(Geq(left=Var(name='n'), right=Const(value=2)), Leq(left=Var(name='n'), right=Const(value=19)), IsPrime(arg=Var(name='n'))))), var='d', expr=EulerPhi(n=Var(n... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW/K3"
] | 6b6e89 | sequence_lucas_compute_v1 | null | 4 | 0 | [
"K3",
"MAX_PRIME_BELOW"
] | 2 | 0.003 | 2026-02-08T13:17:31.982993Z | {
"verified": true,
"answer": 3007,
"timestamp": "2026-02-08T13:17:31.986318Z"
} | 8414c3 | 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": 1235
},
"timestamp": "2026-02-15T12:22:29.533Z",
"answer": 3007
},
{... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K3",
"status": "ok_later"
},
{
"lemma": "K5",
"statu... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
0aa431 | modular_modexp_compute_v1_1742523217_1867 | Let $n$ be an integer such that $2 \leq n \leq 242$ and $n$ is prime. Define $e$ to be the maximum value of such $n$. Let $a = 13$ and $m = 21025$. Compute the remainder when $a^e$ is divided by $m$. | 9,563 | graphs = [
Graph(
let={
"_n": Const(2),
"a": Const(13),
"e": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Const(242)), IsPrime(Var("n"))))),
"m": Const(21025),
"result": ModExp(base=Ref("a"), exp=R... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | modular_modexp_compute_v1 | null | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.003 | 2026-02-08T04:18:46.492692Z | {
"verified": true,
"answer": 9563,
"timestamp": "2026-02-08T04:18:46.495331Z"
} | 27a75f | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 182,
"completion_tokens": 3007
},
"timestamp": "2026-02-10T16:10:20.537Z",
"answer": 9563
},
{
"... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
2ce9b0 | comb_count_surjections_v1_397696148_1139 | Let $n = 7$. Let $k$ be the number of ordered pairs $(i,j)$ of integers such that $1 \leq i \leq 5$, $1 \leq j \leq 5$, and $i + j = 6$. Compute $k! \cdot S(n, k)$, where $S(n, k)$ denotes the Stirling number of the second kind. Find the value of this expression. | 16,800 | graphs = [
Graph(
let={
"n": Const(7),
"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(5)), right=IntegerRange(start=Const(1), end=Const(5... | COMB | null | COUNT | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | comb_count_surjections_v1 | null | 5 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.012 | 2026-02-08T12:22:30.516106Z | {
"verified": true,
"answer": 16800,
"timestamp": "2026-02-08T12:22:30.528331Z"
} | d1f8e1 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 205,
"completion_tokens": 871
},
"timestamp": "2026-02-24T15:37:21.064Z",
"answer": 16800
},
{
"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": "V7",
"status": "no"
},
{
"lemma": "V8",
"status":... | {
"lo": -3.84,
"mid": -1.67,
"hi": 1.32
} | ||
c4fab5_l | modular_product_range_v1_548369836_52 | Let $m = 8$ and $n = 2130$. Define $a$ to be the sum of $\phi(d)$ over all positive divisors $d$ of $99$. Let $b$ be the number of positive integers $k$ such that $1 \leq k \leq n$ and $m$ divides $F_k$, where $F_k$ denotes the $k$th Fibonacci number. Compute the remainder when the product $\prod_{i=a}^{b} i$ is divide... | 0 | NT | null | COMPUTE | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE",
"K3"
] | 1c15c3 | modular_product_range_v1 | null | 6 | 0 | [
"COUNT_FIB_DIVISIBLE",
"K3"
] | 2 | 0.003 | 2026-02-08T02:44:41.983706Z | {
"verified": false,
"answer": 209,
"timestamp": "2026-02-08T02:44:41.986737Z"
} | 6b92d2 | c4fab5 | legacy_text | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 222,
"completion_tokens": 32768
},
"timestamp": "2026-02-23T16:01:24.118Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V5",
"status": "n... | {
"lo": 3.82,
"mid": 5.54,
"hi": 7.58
} | |
0d3173 | comb_bell_compute_v1_1431428450_409 | Let $n$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 16$. Let $Q = 11449 - B_n$, where $B_n$ denotes the $n$th Bell number, which counts the number of partitions of a set of size $n$. Compute $Q$. | 7,309 | graphs = [
Graph(
let={
"_n": Const(11449),
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(16)))), expr=Sum(Var("x"), Var("y")))),
... | COMB | null | COMPUTE | sympy | SUM_ARITHMETIC | [
"B3"
] | 0cd20d | comb_bell_compute_v1 | null | 3 | 0 | [
"B3",
"SUM_ARITHMETIC"
] | 2 | 0.015 | 2026-02-08T13:27:01.696907Z | {
"verified": true,
"answer": 7309,
"timestamp": "2026-02-08T13:27:01.711735Z"
} | a98f10 | 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": 1448
},
"timestamp": "2026-02-24T18:10:48.311Z",
"answer": 7309
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "n... | {
"lo": -3.84,
"mid": -1.67,
"hi": 1.32
} | ||
619d9b | comb_binomial_compute_v1_784195855_6637 | Let $n$ be the number of positive integers less than or equal to 25 such that the sum of the digits of $n$ leaves a remainder of 1 when divided by 2. Let $k = 6$. Compute the remainder when $88834 \times \binom{n}{k}$ is divided by 79263. | 16,395 | graphs = [
Graph(
let={
"_n": Const(2),
"n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(25)), Eq(Mod(value=DigitSum(Var("n")), modulus=Ref("_n")), Const(1))))),
"k": Const(6),
"result": Binom(n=Ref("n... | ALG | COMB | COMPUTE | sympy | L3B | [
"L3B"
] | cc148f | comb_binomial_compute_v1 | null | 4 | 0 | [
"L3B"
] | 1 | 0.001 | 2026-02-08T08:46:22.680336Z | {
"verified": true,
"answer": 16395,
"timestamp": "2026-02-08T08:46:22.681372Z"
} | b94241 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 181,
"completion_tokens": 32768
},
"timestamp": "2026-02-24T09:58:24.263Z",
"answer": 16395
},
{
... | 1 | [
{
"lemma": "L3B",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
3f3dc8 | comb_count_surjections_v1_898971024_1536 | Let $n = 5$ and $k = 4$. Compute $30634$ times $k!$ multiplied by the number of ways to partition a set of $n$ elements into $k$ nonempty unlabeled subsets, and then take the result modulo $93495$. | 59,550 | graphs = [
Graph(
let={
"n": Const(5),
"k": Const(4),
"result": Mul(Factorial(Ref("k")), Stirling2(n=Ref(name='n'), k=Ref(name='k'))),
"Q": Mod(value=Mul(Const(30634), Ref("result")), modulus=Const(93495)),
},
goal=Ref("Q"),
)
] | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/COUNT_SUM_EQUALS"
] | 8a3f7a | comb_count_surjections_v1 | null | 3 | 0 | [
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 2 | 0.037 | 2026-02-08T16:11:32.486622Z | {
"verified": true,
"answer": 59550,
"timestamp": "2026-02-08T16:11:32.524045Z"
} | 63aeae | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 169,
"completion_tokens": 743
},
"timestamp": "2026-02-24T20:05:43.137Z",
"answer": 59550
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok_later"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"... | {
"lo": -2.4,
"mid": 1.57,
"hi": 5.75
} | ||
419c99 | comb_binomial_compute_v1_1218484723_4685 | Let $k$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 25$ satisfying
\[
17a^4 + 68a^3b + 102a^2b^2 + 68ab^3 + 17b^4 = 69632.
\]
Compute $\binom{13}{k}$. | 1,716 | graphs = [
Graph(
let={
"_n": Const(2),
"n": Const(13),
"k": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(25)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(25)), Eq(Sum(Mul(Const(102), ... | COMB | null | COMPUTE | sympy | POLY4_COUNT | [
"POLY4_COUNT"
] | 861d91 | comb_binomial_compute_v1 | null | 4 | 0 | [
"POLY4_COUNT"
] | 1 | 0.002 | 2026-02-25T06:21:24.193341Z | {
"verified": true,
"answer": 1716,
"timestamp": "2026-02-25T06:21:24.195382Z"
} | 6196d1 | 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": 795
},
"timestamp": "2026-03-29T16:59:30.679Z",
"answer": 1716
},
{
"id... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "POLY4_COUNT",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": ... | {
"lo": -3.33,
"mid": 1.03,
"hi": 5.26
} | ||
297e60_n | geo_visible_lattice_v1_1218484723_1886 | A digital art canvas has dimensions $n \times n$, where $n = \sum_{k=1}^{18} \varphi(k) \cdot \left\lfloor \frac{18}{k} \right\rfloor$. A pixel at position $(x,y)$ lights up only if $\gcd(x,y) = 1$. How many pixels light up? | 17,875 | GEOM | GEOM | COUNT | sympy | K2 | [
"K2"
] | 6897ab | geo_visible_lattice_v1 | null | 3 | null | [
"K2"
] | 1 | 0.597 | 2026-02-25T03:35:31.752451Z | null | 852701 | 297e60 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 189,
"completion_tokens": 29161
},
"timestamp": "2026-03-30T17:31:52.028Z",
"answer": 17875
},
{
... | 1 | [
{
"lemma": "K2",
"status": "ok"
}
] | {
"lo": 1.5,
"mid": 4.69,
"hi": 7.23
} | |
91de3e | antilemma_k3_v1_1520064083_4071 | Compute the sum of $\phi(d)$ over all positive divisors $d$ of 31795, where $\phi(d)$ denotes Euler's totient function. | 31,795 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=31795), var='d', expr=EulerPhi(n=Var(name='d'))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T06:03:19.369695Z | {
"verified": true,
"answer": 31795,
"timestamp": "2026-02-08T06:03:19.370370Z"
} | 654871 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 78,
"completion_tokens": 5633
},
"timestamp": "2026-02-12T19:16:07.126Z",
"answer": 31795
},
{... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
4cf72b | comb_count_partitions_v1_865884756_3379 | Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = N$, where $N$ is the number of positive integers $n_1$ at most $M$ that are divisible by 5 and relatively prime to 6, and $M$ is the number of integers $t$ with $8 \le t \le 6620$ that can be expressed as $t = 3a + 5b$ for some integer... | 28,259 | graphs = [
Graph(
let={
"_n": Const(5),
"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")), CountOverSet(set=SolutionsSet(var=Var("n1"), condi... | NT | COMB | COUNT | sympy | LIN_FORM | [
"LIN_FORM/C5/B3"
] | 88b3fd | comb_count_partitions_v1 | null | 7 | 0 | [
"B3",
"C5",
"LIN_FORM"
] | 3 | 0.005 | 2026-02-08T17:19:20.420060Z | {
"verified": true,
"answer": 28259,
"timestamp": "2026-02-08T17:19:20.425421Z"
} | 6087d8 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 234,
"completion_tokens": 6566
},
"timestamp": "2026-02-17T23:42:34.863Z",
"answer": 28259
},
... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "C5",
"status": "ok_later"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
5beb1c | sequence_count_fib_divisible_v1_1918700295_3678 | Let $d$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $x \cdot y = 9$. Define $A$ to be the set of all positive integers $n$ such that $1 \leq n \leq 266$ and the $n$-th Fibonacci number is divisible by $d$. Let $r = |A|$, the number of elements in $A$. Compute the remai... | 30,800 | graphs = [
Graph(
let={
"_n": Const(52838),
"upper": Const(266),
"d": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(9)))), ... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | sequence_count_fib_divisible_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.064 | 2026-02-08T08:49:38.733603Z | {
"verified": true,
"answer": 30800,
"timestamp": "2026-02-08T08:49:38.797243Z"
} | 4e0183 | 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": 1687
},
"timestamp": "2026-02-13T21:44:59.048Z",
"answer": 30800
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
5ee09f | nt_count_gcd_equals_v1_1520064083_1368 | Let $S$ be the set of all ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 19208$. Let $N$ be the number of elements in $S$. Compute the number of positive integers $n$ such that $1 \leq n \leq N$ and $\gcd(n, 153) = 17$. | 376 | graphs = [
Graph(
let={
"upper": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2")), Const(19208))))),
... | NT | null | COUNT | sympy | COMB1 | [
"COMB1"
] | 567f58 | nt_count_gcd_equals_v1 | null | 6 | 0 | [
"COMB1"
] | 1 | 4.522 | 2026-02-08T03:56:56.218911Z | {
"verified": true,
"answer": 376,
"timestamp": "2026-02-08T03:57:00.740987Z"
} | d78726 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 197,
"completion_tokens": 1166
},
"timestamp": "2026-02-10T16:13:26.208Z",
"answer": 376
},
{
"id... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
3fe39d | alg_poly_orbit_count_v1_1218484723_5358 | For each non-negative integer $a$ with $0 \leq a \leq 43035$, define
\begin{align*}
N &= 3a^3 - 3 \bmod 53, \\
M &= 3N^3 - 3 \bmod 53, \\
R &= 3M^3 - 3 \bmod 53, \\
S &= 3R^3 - 3 \bmod 53, \\
T &= 3S^3 - 3 \bmod 53.
\end{align*}
Let $Q$ be the number of such $a$ for which $T = a$, but $N \neq a$, $M \neq a$, $R \neq a$... | 4,060 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Mul(Const(3), Pow(Var("a"), Const(3))), Const(-3)), modulus=Const(53)),
"p2": Mod(value=Sum(Mul(Const(3), Pow(Ref("p1"), Const(3))), Const(-3)), modulus=Const(53)),
"p3": Mod(value=Sum(Mul(Const(3), Pow(Ref("p2"), Const(3))), Co... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_orbit_count_v1 | null | 6 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.023 | 2026-02-25T06:57:10.633870Z | {
"verified": true,
"answer": 4060,
"timestamp": "2026-02-25T06:57:10.656751Z"
} | d94fdf | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 283,
"completion_tokens": 8220
},
"timestamp": "2026-03-29T20:43:23.325Z",
"answer": 5
},
{
"i... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 3.81,
"mid": 6.33,
"hi": 9.49
} | ||
62cae2 | algebra_poly_eval_v1_1520064083_5592 | Let $n = 11$. Define
$$
Q = 6n^4 + 2n^k + 3n^2 - 2n - 2,
$$
where $k$ is the smallest divisor of $75$ that is at least $2$. Compute the value of $Q$. | 90,847 | graphs = [
Graph(
let={
"_n": Const(6),
"n": Const(11),
"result": Sum(Mul(Ref("_n"), Pow(Ref("n"), Const(4))), Mul(Const(2), Pow(Ref("n"), MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(75))))))), ... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | algebra_poly_eval_v1 | null | 3 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.003 | 2026-02-08T07:26:56.023178Z | {
"verified": true,
"answer": 90847,
"timestamp": "2026-02-08T07:26:56.026292Z"
} | f1763b | 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": 571
},
"timestamp": "2026-02-13T10:24:10.420Z",
"answer": 90847
},
{... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": ... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
f8dc48 | antilemma_sum_equals_v1_153355830_2237 | Let $n = 31$. Let $x$ be the number of ordered pairs $(i, j)$ of integers such that $1 \leq i \leq 30$, $1 \leq j \leq 30$, and $i + j = n$. Let $Q$ be the Bell number $B_r$, where $r$ is the remainder when $|x|$ is divided by $11$. Compute $Q$. | 4,140 | graphs = [
Graph(
let={
"_n": Const(31),
"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(30)), 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 | 0.011 | 2026-02-08T07:00:12.023136Z | {
"verified": true,
"answer": 4140,
"timestamp": "2026-02-08T07:00:12.033889Z"
} | 51e61e | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 203,
"completion_tokens": 1278
},
"timestamp": "2026-02-24T07:31:14.565Z",
"answer": 4140
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V8_SU... | {
"lo": -5.97,
"mid": -3.97,
"hi": -1.93
} | ||
7a62e4 | nt_sum_totient_over_divisors_v1_151522320_48 | Let $N$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that
\[pq = 18,\quad \gcd(p,q)=1,\quad p<q.\]
Let $n=27619$, and define
\[R = \sum_{d\mid n} \varphi(d),\]
where $\varphi$ is Euler's totient function.
Let $T$ be the set of all integers $t$ for which there exist integer... | 21,147 | graphs = [
Graph(
let={
"_n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=18)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(value=1)), ... | NT | COMB | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/LIN_FORM/MAX_PRIME_BELOW"
] | 8f4fb8 | nt_sum_totient_over_divisors_v1 | bell_mod | 7 | 0 | [
"COPRIME_PAIRS",
"LIN_FORM",
"MAX_PRIME_BELOW"
] | 3 | 0.004 | 2026-02-08T02:56:17.370930Z | {
"verified": true,
"answer": 21147,
"timestamp": "2026-02-08T02:56:17.375402Z"
} | 12edf0 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 413,
"completion_tokens": 1686
},
"timestamp": "2026-02-10T11:57:21.393Z",
"answer": 21147
},
{
"... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok_later"
},
{
"lemma": "LTE_SUM",
"status": "no"
... | {
"lo": -1.94,
"mid": 0.57,
"hi": 2.67
} | ||
30e542 | algebra_poly_eval_v1_1218484723_1679 | Let $R$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 15$ such that $5b^2 - 2ab + 34a^2 = 1690$. Let $S$ be the set of integers $t1$ for which there exist integers $a, b$ with $1 \le a \le 163$, $1 \le b \le 19$, $18 \le t1 \le 918$, and $t1 = 4a + 14b$. Let $U = |S|$. Let $t$ be the... | 30,079 | graphs = [
Graph(
let={
"_d": Const(15),
"_m": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Ref("_d")), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(15)), Eq(Sum(Mul(Const(5), Pow(Var("b"), Const(2))), Mu... | ALG | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/QF_PSD_DISTINCT",
"QF_PSD_COUNT/LIN_FORM"
] | 23714a | algebra_poly_eval_v1 | null | 6 | 0 | [
"LIN_FORM",
"QF_PSD_COUNT",
"QF_PSD_DISTINCT"
] | 3 | 0.015 | 2026-02-25T03:22:03.546457Z | {
"verified": true,
"answer": 30079,
"timestamp": "2026-02-25T03:22:03.561820Z"
} | 81dbe5 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 339,
"completion_tokens": 5601
},
"timestamp": "2026-03-29T00:46:17.070Z",
"answer": 30079
},
{
"... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT",
"status": "ok"
},
{
"lemma": "QF_PSD_DISTINCT",
"status": "ok_later"
}
] | {
"lo": -2.47,
"mid": 1.2,
"hi": 4.81
} | ||
24cb4f | sequence_count_fib_divisible_v1_865884756_602 | Let $d$ be the largest prime number $n$ such that $2 \leq n \leq 18$. Determine the value of the number of positive integers $n_1$ less than or equal to 983 for which $d$ divides the $n_1$-th Fibonacci number. | 109 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": Const(983),
"d": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Const(18)), IsPrime(Var("n"))))),
"result": CountOverSet(set=SolutionsSet(var=Var("n1"), condition... | NT | null | COUNT | sympy | ONE_PHI_2 | [
"MAX_PRIME_BELOW"
] | dc3ad3 | sequence_count_fib_divisible_v1 | null | 6 | 0 | [
"MAX_PRIME_BELOW",
"ONE_PHI_2"
] | 2 | 0.188 | 2026-02-08T15:31:38.733605Z | {
"verified": true,
"answer": 109,
"timestamp": "2026-02-08T15:31:38.922015Z"
} | 819738 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 108,
"completion_tokens": 2234
},
"timestamp": "2026-02-16T07:42:01.393Z",
"answer": 109
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
5d2a6a | algebra_poly_eval_v1_124444284_6703 | Let $k = 8$. Define $s$ to be the maximum value of $xy$ over all ordered pairs $(x, y)$ of positive integers such that $x + y = 4$. Let $r$ be the value of the expression
$$
\frac{81 \cdot k^s + 1341 \cdot k^3 - 660 \cdot k^2 - 825 \cdot k - 153}{25 \cdot 75}.
$$
Compute the remainder when $10085r$ is divided by $78026... | 64,229 | graphs = [
Graph(
let={
"_n": Const(2),
"k": Const(8),
"result": Div(Sum(Mul(Const(81), Pow(Ref("k"), 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(Va... | NT | null | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN",
"B1"
] | 36c577 | algebra_poly_eval_v1 | null | 6 | 0 | [
"B1",
"COUNT_CARTESIAN"
] | 2 | 0.003 | 2026-02-08T08:35:45.290680Z | {
"verified": true,
"answer": 64229,
"timestamp": "2026-02-08T08:35:45.294004Z"
} | a07c28 | 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": 1249
},
"timestamp": "2026-02-13T19:46:17.346Z",
"answer": 64229
},
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
0585ec | nt_min_coprime_above_v1_397696148_742 | Let $S$ be the set of integers $t$ such that $7 \leq t \leq 205$ and there exist integers $a$ and $b$ with $1 \leq a \leq 25$, $1 \leq b \leq 40$, and $t = 5a + 2b$. Let $m$ be the number of elements in $S$. Determine the value of the smallest integer $n$ such that $71631 < n \leq 71836$ and $\gcd(n, m) = 1$. | 71,632 | graphs = [
Graph(
let={
"start": Const(71631),
"upper": Const(71836),
"modulus": 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(n... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_min_coprime_above_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.043 | 2026-02-08T11:43:03.736127Z | {
"verified": true,
"answer": 71632,
"timestamp": "2026-02-08T11:43:03.779197Z"
} | a2b9c9 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 162,
"completion_tokens": 3557
},
"timestamp": "2026-02-14T18:03:28.579Z",
"answer": 71632
},
... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
0a0b22 | alg_qf_psd_min_v1_1419126231_530 | Find the minimum value of $19850a^2 + 39700ab + 23026b^2$ over all ordered pairs $(a, b)$ of positive integers with $1 \leq a \leq 99$ and $1 \leq b \leq B$, where $B$ is the number of integers $v$ such that $4 \leq v \leq C$ and there exist integers $a, b$ with $1 \leq a, b \leq 14$ satisfying $8a^2 + 4b^2 - 8ab = v$,... | 82,576 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(2),
"result": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(99)), Geq(Var("b"), Const(1)), Leq(Var("b"), CountOverSet(set=... | ALG | null | COMPUTE | sympy | QF_PSD_COUNT_LEQ | [
"QF_PSD_COUNT_LEQ/QF_PSD_DISTINCT"
] | 0cf842 | alg_qf_psd_min_v1 | null | 6 | 0 | [
"QF_PSD_COUNT_LEQ",
"QF_PSD_DISTINCT"
] | 2 | 0.339 | 2026-02-25T10:03:40.358839Z | {
"verified": true,
"answer": 82576,
"timestamp": "2026-02-25T10:03:40.697640Z"
} | 48d1e3 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 309,
"completion_tokens": 17850
},
"timestamp": "2026-03-30T08:54:05.197Z",
"answer": 82576
},
{
... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
},
{
"lemma": "QF_PSD_DISTINCT",
"status": "ok_later"
}
] | {
"lo": 1.5,
"mid": 4.69,
"hi": 7.23
} | ||
b1cb55 | comb_count_permutations_fixed_v1_1918700295_2740 | Let $\_n = 5$. Define $n$ to be the sum of all positive integers $m$ such that $1 \leq m \leq \_n$ and $$m \equiv \sum_{k=0}^{7} (-1)^k \binom{7}{k} \pmod{5}.$$ Let $k = 0$ and define $\text{result} = \binom{n}{k} \cdot !(n - k)$, where $!r$ denotes the number of derangements of $r$ elements. Compute the remainder when... | 20,540 | graphs = [
Graph(
let={
"_n": Const(5),
"n": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_n")), Eq(Mod(value=Var("n"), modulus=Const(5)), Summation(var="k", start=Const(0), end=Const(7), expr=Mul(Pow(Const(-1), Var("k")), Binom(... | COMB | null | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING",
"SUM_DIVISIBLE"
] | 7f5b8a | comb_count_permutations_fixed_v1 | null | 5 | 0 | [
"BINOMIAL_ALTERNATING",
"SUM_DIVISIBLE"
] | 2 | 0.152 | 2026-02-08T08:11:08.693902Z | {
"verified": true,
"answer": 20540,
"timestamp": "2026-02-08T08:11:08.845940Z"
} | f6c288 | 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": 1196
},
"timestamp": "2026-02-24T09:01:23.539Z",
"answer": 20540
},
{
"... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "SUM_DIVISIBLE",
"status": "ok"
},
{
"lemma": "V7",
... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
44af55 | modular_sum_quadratic_residues_v1_1520064083_6458 | Let $p = 181$. Let $N$ be the number of positive integers $p'$ such that there exists a positive integer $q$ with $p'q = 750$, $\gcd(p', q) = 1$, and $p' < q$. Compute $\frac{p(p-1)}{N}$. Determine the remainder when $44121$ times this value is divided by $82394$. | 45,311 | graphs = [
Graph(
let={
"p": Const(181),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), 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... | NT | null | SUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | modular_sum_quadratic_residues_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.001 | 2026-02-08T08:05:52.071935Z | {
"verified": true,
"answer": 45311,
"timestamp": "2026-02-08T08:05:52.073315Z"
} | b298d6 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 132,
"completion_tokens": 3045
},
"timestamp": "2026-02-13T15:06:34.037Z",
"answer": 45311
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
6d9249 | algebra_poly_eval_v1_784195855_7947 | Let $n = 7$ and let $\_n = 2$. Define
$$
\text{result} = 7 \cdot n^{\_n} + \left( \sum_{k=1}^{4} \phi(k) \left\lfloor \frac{4}{k} \right\rfloor \right) \cdot n + 6,
$$
where $\phi(k)$ denotes Euler's totient function. Compute the value of $\text{result}$. | 419 | graphs = [
Graph(
let={
"_n": Const(2),
"n": Const(7),
"result": Sum(Mul(Const(7), Pow(Ref("n"), Ref("_n"))), Mul(Summation(var="k", start=Const(1), end=Const(4), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(4), Var("k"))))), Ref("n")), Const(6)),
},
goa... | NT | null | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | algebra_poly_eval_v1 | null | 3 | 0 | [
"K2"
] | 1 | 0.001 | 2026-02-08T09:38:00.270660Z | {
"verified": true,
"answer": 419,
"timestamp": "2026-02-08T09:38:00.271779Z"
} | 9db2f1 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 163,
"completion_tokens": 444
},
"timestamp": "2026-02-15T20:47:34.472Z",
"answer": 419
},
{
"id": 11,
... | 2 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.71,
"hi": -5.43
} | ||
3ceef0 | comb_sum_binomial_row_v1_2051736721_1520 | Let $n$ be the number of positive integers $k$ such that $1 \leq k \leq 1260$ and $90$ divides $k$. Define $r = 2^n$. Compute the value of $$r + \phi(|r| + 1) + \tau(|r| + 1),$$ where $\phi$ denotes Euler's totient function and $\tau(m)$ denotes the number of positive divisors of $m$. | 28,936 | graphs = [
Graph(
let={
"_n": Const(1260),
"n": CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(1)), Leq(Var("k"), Ref("_n")), Divides(divisor=Const(90), dividend=Var("k"))), domain='positive_integers')),
"result": Pow(Const(2), Ref("n")),
... | NT | null | SUM | sympy | C2 | [
"C2"
] | 9685eb | comb_sum_binomial_row_v1 | null | 3 | 0 | [
"C2"
] | 1 | 0.002 | 2026-02-08T16:05:07.340973Z | {
"verified": true,
"answer": 28936,
"timestamp": "2026-02-08T16:05:07.343378Z"
} | 35686d | 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": 990
},
"timestamp": "2026-02-16T20:44:24.772Z",
"answer": 28936
},
{... | 1 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
de72df | comb_factorial_compute_v1_124444284_7018 | Let $n$ be the smallest integer greater than or equal to 2 that divides 77. Compute $n!$. | 5,040 | graphs = [
Graph(
let={
"_n": Const(2),
"n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(77))))),
"result": Factorial(Ref("n")),
"Q": Ref("result"),
},
goal=Ref("Q")... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | comb_factorial_compute_v1 | null | 2 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.001 | 2026-02-08T08:46:04.116728Z | {
"verified": true,
"answer": 5040,
"timestamp": "2026-02-08T08:46:04.117761Z"
} | f37a5b | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 82,
"completion_tokens": 437
},
"timestamp": "2026-02-15T20:21:35.118Z",
"answer": 5040
},
{
"id": 11,
... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.73,
"hi": -5.46
} | ||
dcd4a7 | nt_min_coprime_above_v1_397696148_869 | Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 1000000$. Let $T$ be the set of all values $x + y$ where $(x,y) \in S$. Let $a$ be the minimum value in $T$.
Let $U$ be the set of all integers $n$ such that $a < n \leq 2303$ and $\gcd(n, 293) = 1$. Let $b$ be the minimum element of ... | 16,768 | graphs = [
Graph(
let={
"start": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(1000000)))), expr=Sum(Var("x"), Var("y")))),
"upper": Co... | NT | null | EXTREMUM | sympy | B3 | [
"B3"
] | 0cd20d | nt_min_coprime_above_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.054 | 2026-02-08T11:47:19.805328Z | {
"verified": true,
"answer": 16768,
"timestamp": "2026-02-08T11:47:19.859760Z"
} | 9e76a2 | 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": 1079
},
"timestamp": "2026-02-14T21:00:15.314Z",
"answer": 16768
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": ... | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
106e2c | sequence_lucas_compute_v1_1915831931_2629 | Let $m = 2$. Define $D$ as the set of all divisors $d$ of $5538101$ such that $d \geq m$. Let $n$ be the smallest element of $D$. Define $s = \sum_{d_1 \mid n} \phi(d_1)$, where $\phi$ denotes Euler's totient function. Compute the $s$-th Lucas number. | 9,349 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_m")), Divides(divisor=Var("d"), dividend=Const(5538101))))),
"n": SumOverDivisors(n=Ref(name='_n'), var='d1', expr=EulerPhi(n=Var(name='d1'))),
... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/K3"
] | 54b4a9 | sequence_lucas_compute_v1 | null | 6 | 0 | [
"K3",
"MIN_PRIME_FACTOR"
] | 2 | 0.002 | 2026-02-08T17:00:39.347606Z | {
"verified": true,
"answer": 9349,
"timestamp": "2026-02-08T17:00:39.349506Z"
} | b63b06 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 132,
"completion_tokens": 1670
},
"timestamp": "2026-02-17T17:13:17.855Z",
"answer": 9349
},
{... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K3",
"status": "ok_later"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
a7602a | geo_count_lattice_rect_v1_784195855_4260 | Let $a = 136$ and $b = 433$. Define $R$ to be the rectangle $[0, a] \times [0, b]$. Compute the number of lattice points $(x, y)$ with integer coordinates that lie inside or on the boundary of $R$. Let this count be $L$. Find the remainder when $1600 - L$ is divided by $89369$. | 31,511 | graphs = [
Graph(
let={
"a": Const(136),
"b": Const(433),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"_c": Const(1600),
"Q": Mod(value=Sub(Ref("_c"), Ref("result")), modulus=Const(89369)),
},
goal=Ref("Q"),
)... | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 4 | 0 | null | null | 0.002 | 2026-02-08T06:56:49.507954Z | {
"verified": true,
"answer": 31511,
"timestamp": "2026-02-08T06:56:49.509747Z"
} | 354e1a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 195,
"completion_tokens": 614
},
"timestamp": "2026-02-24T07:27:56.209Z",
"answer": 31511
},
{
"i... | 1 | [] | {
"lo": -5.97,
"mid": -3.97,
"hi": -1.93
} | ||||
2e73d1 | geo_count_lattice_rect_v1_1248542787_127 | Let $a = 300$ and $b = 88$. Compute the number of lattice points $(x, y)$ such that $0 \leq x \leq a$ and $0 \leq y \leq b$. Find the value of this count. | 26,789 | graphs = [
Graph(
let={
"a": Const(300),
"b": Const(88),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 2 | 0 | null | null | 0.001 | 2026-02-08T02:57:56.324818Z | {
"verified": true,
"answer": 26789,
"timestamp": "2026-02-08T02:57:56.326188Z"
} | 8a9f9c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 171,
"completion_tokens": 246
},
"timestamp": "2026-02-09T00:26:54.116Z",
"answer": 26789
},
{
"i... | 1 | [] | {
"lo": -9.23,
"mid": -6.17,
"hi": -4.06
} | ||||
f2ecda | sequence_count_fib_divisible_v1_2051736721_488 | Let $d = 13$. Determine the number of positive integers $n$ such that $1 \leq n \leq 882$ and $d$ divides the $n$-th Fibonacci number. | 126 | graphs = [
Graph(
let={
"upper": Const(882),
"d": Const(13),
"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 | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | sequence_count_fib_divisible_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.089 | 2026-02-08T15:28:14.458476Z | {
"verified": true,
"answer": 126,
"timestamp": "2026-02-08T15:28:14.547291Z"
} | aec5b8 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 88,
"completion_tokens": 2156
},
"timestamp": "2026-02-16T06:41:30.136Z",
"answer": 126
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
e9a330 | comb_count_surjections_v1_1431428450_1428 | Let $n$ be the number of ordered pairs $(i, j)$ of positive integers such that $1 \leq i \leq 7$, $1 \leq j \leq 7$, and $i + j = 7$. Let $k = 5$. Compute $k! \cdot S(n, k)$, where $S(n, k)$ denotes the Stirling number of the second kind. | 1,800 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(7)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(7)), right=IntegerRange(start=Const(1), end=Const(7))))),
"k": Con... | COMB | null | COUNT | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | comb_count_surjections_v1 | null | 3 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.052 | 2026-02-08T14:05:52.718968Z | {
"verified": true,
"answer": 1800,
"timestamp": "2026-02-08T14:05:52.770785Z"
} | 807f8c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 200,
"completion_tokens": 772
},
"timestamp": "2026-02-24T19:45:51.441Z",
"answer": 1800
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status"... | {
"lo": -4.1,
"mid": -1.76,
"hi": 1.26
} | ||
8aaaeb | comb_count_surjections_v1_1419126231_1724 | Let $k = 4$ and $N = k! \cdot S(7, k)$, where $S(7, k)$ denotes the Stirling number of the second kind. Find the remainder when $196 - N$ is divided by $50385$. | 42,181 | graphs = [
Graph(
let={
"n": Const(7),
"k": Const(4),
"result": Mul(Factorial(Ref("k")), Stirling2(n=Ref(name='n'), k=Ref(name='k'))),
"Q": Mod(value=Sub(Const(196), Ref("result")), modulus=Const(50385)),
},
goal=Ref("Q"),
)
] | COMB | null | COUNT | sympy | K3 | [
"K3/BINOMIAL_ALTERNATING"
] | 49270b | comb_count_surjections_v1 | negation_mod | 3 | 0 | [
"BINOMIAL_ALTERNATING",
"K3"
] | 2 | 0.029 | 2026-02-25T11:14:46.517101Z | {
"verified": true,
"answer": 42181,
"timestamp": "2026-02-25T11:14:46.545885Z"
} | de8631 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 167,
"completion_tokens": 818
},
"timestamp": "2026-03-30T13:38:02.614Z",
"answer": 42181
},
{
"i... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok_later"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemm... | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | ||
1deba4 | alg_poly3_sum_v1_1218484723_7342 | Find the remainder when $$\sum_{\substack{a=1 \\ b=1 \\ c=1}}^{31} \left( -480abc + \min_{\substack{a_1=1 \\ b_1=1}}^{23} (58a_1b_1 + 26a_1^2 + 41b_1^2) \cdot a^3 + 240ac^2 + 390bc^2 + 240ab^2 + 300a^2b + 125c^3 - 300a^2c - 120b^2c + 73b^3 \right)$$ is divided by $84873$. | 44,087 | graphs = [
Graph(
let={
"_n": Const(23),
"result": Mod(value=SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b"), Var("c")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(31)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(31)), Geq(Var("c")... | ALG | null | COMPUTE | sympy | QF_PSD_MIN | [
"QF_PSD_MIN"
] | c66ce3 | alg_poly3_sum_v1 | null | 5 | 0 | [
"QF_PSD_MIN"
] | 1 | 0.111 | 2026-02-25T08:44:58.270441Z | {
"verified": true,
"answer": 44087,
"timestamp": "2026-02-25T08:44:58.381509Z"
} | a4a533 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 257,
"completion_tokens": 6364
},
"timestamp": "2026-03-30T04:06:38.550Z",
"answer": 13232
},
{
... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_MIN",
"status": "ok"
}
] | {
"lo": 1.53,
"mid": 4.7,
"hi": 7.23
} | ||
135b5d | alg_poly_orbit_count_v1_1218484723_1361 | Define a sequence recursively by $N = (a^2 + a + 5) \bmod 17$, $M = (N^2 + N + 5) \bmod 17$, $R = (M^2 + M + 5) \bmod 17$, $S = (R^2 + R + 5) \bmod 17$, $T = (S^2 + S + 5) \bmod 17$, $K = (T^2 + T + 5) \bmod 17$. Find the number of integers $a$ with $0 \le a \le 662$ such that $K = a$, but $a$ does not appear in the se... | 234 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Pow(Var("a"), Const(2)), Var("a"), Const(5)), modulus=Const(17)),
"p2": Mod(value=Sum(Pow(Ref("p1"), Const(2)), Ref("p1"), Const(5)), modulus=Const(17)),
"p3": Mod(value=Sum(Pow(Ref("p2"), Const(2)), Ref("p2"), Const(5)), modulu... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_orbit_count_v1 | null | 6 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.037 | 2026-02-25T03:04:46.734838Z | {
"verified": true,
"answer": 234,
"timestamp": "2026-02-25T03:04:46.772111Z"
} | 8a942b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 276,
"completion_tokens": 3950
},
"timestamp": "2026-03-10T06:38:15.272Z",
"answer": 234
},
{
"id... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 2.68,
"mid": 4.77,
"hi": 6.68
} | ||
9e9fdd | algebra_quadratic_discriminant_v1_601307018_4336 | Let $m = \min\{ |x - y| : x > 0,\, y > 0,\, x \cdot y = 1891 \}$. Let $c$ be the number of ordered pairs $(a_1, b_1)$ of positive integers with $1 \leq a_1 \leq m$ and $1 \leq b_1 \leq 30$ satisfying
$$
512a_1^4 - 2048a_1^3b_1 + 3072a_1^2b_1^2 - 2048a_1b_1^3 + 512b_1^4 = 320000.
$$
Compute $5^2 - 4(-1) \cdot c$. | 225 | graphs = [
Graph(
let={
"_n": Const(4),
"a": Const(-1),
"b": Const(5),
"c": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a1"), Var("b1")]), condition=And(Geq(Var("a1"), Const(1)), Leq(Var("a1"), MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(el... | ALG | null | COMPUTE | sympy | SUM_GEOM | [
"B3_DIFF/POLY4_COUNT"
] | 848bcb | algebra_quadratic_discriminant_v1 | null | 6 | 0 | [
"B3_DIFF",
"POLY4_COUNT",
"SUM_GEOM"
] | 3 | 0.225 | 2026-03-10T04:54:46.423497Z | {
"verified": true,
"answer": 225,
"timestamp": "2026-03-10T04:54:46.648266Z"
} | a919d1 | 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": 1492
},
"timestamp": "2026-03-29T11:52:10.859Z",
"answer": 225
},
{
"id... | 1 | [
{
"lemma": "B3_DIFF",
"status": "ok"
},
{
"lemma": "POLY4_COUNT",
"status": "ok_later"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -6.2,
"mid": -2.87,
"hi": 0.44
} | ||
4a7dc9 | modular_count_residue_v1_1918700295_679 | Let $m$ be the largest prime number in the interval $[2, 8]$. Determine the number of positive integers $n \leq 65025$ such that $n \equiv 1 \pmod{m}$. | 9,290 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": Const(65025),
"m": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Const(8)), IsPrime(Var("n"))))),
"r": Const(1),
"result": CountOverSet(set=Solutions... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | modular_count_residue_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 2.681 | 2026-02-08T03:22:50.841384Z | {
"verified": true,
"answer": 9290,
"timestamp": "2026-02-08T03:22:53.522615Z"
} | 13db61 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 161,
"completion_tokens": 925
},
"timestamp": "2026-02-10T14:10:46.950Z",
"answer": 9290
},
{
"id... | 1 | [
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
d1d2eb | comb_catalan_compute_v1_458359167_1878 | Let $m$ be the number of integers $t$ with $9 \leq t \leq 64$ such that there exist positive integers $a$, $b$ with $1 \leq a \leq 6$, $1 \leq b \leq 8$, and $t = 4a + 5b$. Let $n$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = m$. Define $p$ to be the number of ordered pair... | 58,786 | graphs = [
Graph(
let={
"_m": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=6)), Geq(left=Var(name='b'), right=Const(value=... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/COMB1",
"COMB1/COMB1"
] | 818a72 | comb_catalan_compute_v1 | null | 7 | 0 | [
"COMB1",
"LIN_FORM"
] | 2 | 0.005 | 2026-02-08T04:55:14.516335Z | {
"verified": true,
"answer": 58786,
"timestamp": "2026-02-08T04:55:14.521020Z"
} | cab436 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 268,
"completion_tokens": 6037
},
"timestamp": "2026-02-11T22:27:09.535Z",
"answer": 58786
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
... | {
"lo": -0.05,
"mid": 2.89,
"hi": 5.27
} | ||
f1d50b | antilemma_k2_v1_153355830_2196 | Let $n = 64$. Compute the value of
$$
\sum_{k=1}^{d(n)} \varphi(k) \left\lfloor \frac{64}{k} \right\rfloor,
$$
where $d(n) = \sum_{d \mid n} \varphi(d)$ and $\varphi$ denotes Euler's totient function. | 2,080 | graphs = [
Graph(
let={
"_n": Const(64),
"x": Summation(var="k", start=Const(1), end=SumOverDivisors(n=SumOverDivisors(n=Const(value=64), var='d', expr=EulerPhi(n=Var(name='d'))), var='d', expr=EulerPhi(n=Var(name='d'))), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Ref("_n"), Var("k")))... | NT | COMB | COMPUTE | sympy | K3 | [
"K3/K3/K2",
"K2"
] | d92398 | antilemma_k2_v1 | null | 5 | 0 | [
"K2",
"K3"
] | 2 | 0.001 | 2026-02-08T06:57:52.094241Z | {
"verified": true,
"answer": 2080,
"timestamp": "2026-02-08T06:57:52.095412Z"
} | 2ab932 | 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": 655
},
"timestamp": "2026-02-13T06:42:30.024Z",
"answer": 2080
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"le... | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
eed70e | antilemma_k3_v1_1874849503_721 | Let $x = \sum_{d \mid 82629} \phi(d)$. Compute the remainder when $44121x$ is divided by $68993$. | 14,996 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=82629), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Mod(value=Mul(Const(44121), Ref("x")), modulus=Const(68993)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T13:16:21.458533Z | {
"verified": true,
"answer": 14996,
"timestamp": "2026-02-08T13:16:21.459468Z"
} | 43b3a2 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 145,
"completion_tokens": 6128
},
"timestamp": "2026-02-09T20:15:47.451Z",
"answer": 14996
},
{
"... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.03,
"hi": 6.12
} | ||
cddfcb | nt_count_primes_v1_1456120455_9 | Let $r$ be the sum of all real solutions to the equation $x^2 - 2x - 5928 = 0$. Let $T$ be the set of all prime numbers $n$ such that $r \leq n \leq 10609$. Compute the number of elements in $T$. | 1,294 | graphs = [
Graph(
let={
"upper": Const(10609),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Const(2)), Mul(Const(-2), Var("x")), Const(-5928)), Const(0))))), Leq(Var("n"), Re... | NT | null | COUNT | sympy | VIETA_SUM | [
"VIETA_SUM"
] | b33a7a | nt_count_primes_v1 | null | 4 | 0 | [
"VIETA_SUM"
] | 1 | 0.936 | 2026-02-08T02:48:30.342688Z | {
"verified": true,
"answer": 1294,
"timestamp": "2026-02-08T02:48:31.278550Z"
} | aa2b51 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 178,
"completion_tokens": 32768
},
"timestamp": "2026-02-23T17:42:53.492Z",
"answer": null
},
{
... | 0 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "VIETA_SUM",
"status": "ok"
}
] | {
"lo": 5.42,
"mid": 7.53,
"hi": 10
} | ||
6dadeb | sequence_lucas_compute_v1_48377204_1572 | Let $S$ be the set of all ordered pairs of positive integers $(x, y)$ such that $xy = 81$. Let $n$ be the minimum value of $x + y$ over all pairs $(x, y) \in S$. Compute the $n$-th Lucas number, and then find the remainder when $44121$ times this number is divided by $87581$. | 70,428 | 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(81)))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | sequence_lucas_compute_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.002 | 2026-02-08T16:12:34.782397Z | {
"verified": true,
"answer": 70428,
"timestamp": "2026-02-08T16:12:34.784504Z"
} | e39b8a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 129,
"completion_tokens": 1148
},
"timestamp": "2026-02-16T23:28:00.918Z",
"answer": 70428
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} |
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