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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
cf8bbc | nt_count_coprime_v1_168721529_1425 | Let $m = 3$. Let $n$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 40000$. Let $k$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = n$. Let $U = 59536$. Compute the number of positive integers $n$ with $1 \le n \l... | 23,814 | graphs = [
Graph(
let={
"_m": Const(3),
"_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(40000)))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | COUNT | sympy | MOBIUS_COPRIME | [
"MOBIUS_COPRIME",
"B3/B3"
] | 570ef1 | nt_count_coprime_v1 | null | 5 | 0 | [
"B3",
"MOBIUS_COPRIME"
] | 2 | 5.022 | 2026-02-08T13:41:52.589868Z | {
"verified": true,
"answer": 23814,
"timestamp": "2026-02-08T13:41:57.611879Z"
} | 9e67dd | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 264,
"completion_tokens": 1913
},
"timestamp": "2026-02-09T16:55:22.885Z",
"answer": 23814
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok"
},
... | {
"lo": -6.69,
"mid": -2.39,
"hi": 1.83
} | ||
be2340 | alg_poly4_min_v1_1419126231_1327 | Let $Q$ be the minimum value of
$$
3444a^4 + 9072a^3b + 672b^4 + 9072a^2b^2 + ab^3 \cdot \min\{x + y : x,y > 0,\ xy = 4064256\}
$$
over all positive integers $a, b$ with $1 \le a, b \le 294$. Find $Q$. | 26,292 | graphs = [
Graph(
let={
"_n": Const(294),
"result": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(294)), Geq(Var("b"), Const(1)), Leq(Var("b"), Ref("_n")))), expr=Sum(Mul(Const(672), Pow... | ALG | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | alg_poly4_min_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.199 | 2026-02-25T10:44:59.007519Z | {
"verified": true,
"answer": 26292,
"timestamp": "2026-02-25T10:44:59.206285Z"
} | 73d5bd | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 208,
"completion_tokens": 4147
},
"timestamp": "2026-03-30T12:06:21.592Z",
"answer": 17892
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 1.5,
"mid": 4.69,
"hi": 7.23
} | ||
b1ff67 | diophantine_fbi2_min_v1_458359167_807 | Let $k = 360$ and $n = 5$. Define $T$ to be the set of all integers $t$ such that $7 \leq t \leq 382$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 118$, $1 \leq b \leq 7$, and $t = 3a + 4b$. Let $u$ be the number of elements in $T$. Now let $S$ be the set of all integers $d$ such that $6 \leq d \le... | 6 | graphs = [
Graph(
let={
"_n": Const(5),
"k": Const(360),
"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... | NT | null | EXTREMUM | sympy | K2 | [
"LIN_FORM"
] | 7b2633 | diophantine_fbi2_min_v1 | null | 6 | 0 | [
"K2",
"LIN_FORM"
] | 2 | 0.026 | 2026-02-08T03:33:17.040547Z | {
"verified": true,
"answer": 6,
"timestamp": "2026-02-08T03:33:17.066417Z"
} | 9c6054 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 271,
"completion_tokens": 5241
},
"timestamp": "2026-02-10T13:44:06.820Z",
"answer": 6
},
{
"id"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -9.14,
"mid": -6.05,
"hi": -3.73
} | ||
f5533e_l | comb_count_permutations_fixed_v1_784195855_8365 | Let $n = 8$ and let $k$ be the number of nonnegative integers $j$ such that $0 \le j \le 544$ and $\binom{544}{j}$ is odd. Compute $\binom{n}{k} \cdot !(n - k)$, where $!m$ denotes the number of derangements of $m$ elements. | 0 | COMB | null | COUNT | sympy | LIN_FORM | [
"V8"
] | 86348e | comb_count_permutations_fixed_v1 | null | 7 | 0 | [
"LIN_FORM",
"V8"
] | 2 | 0.011 | 2026-02-08T16:01:58.319484Z | {
"verified": false,
"answer": 630,
"timestamp": "2026-02-08T16:01:58.330572Z"
} | cedd0f | f5533e | legacy_text | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 191,
"completion_tokens": 819
},
"timestamp": "2026-02-24T19:31:28.535Z",
"answer": 630
},
{
"id... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
}
] | {
"lo": -2.4,
"mid": 1.57,
"hi": 5.75
} | |
bbea12 | algebra_quadratic_discriminant_v1_349078426_701 | Let $n = 4$, $a = -1$, and $c = -16$. Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy$ equals the number of positive integers $p$ for which there exists a positive integer $q$ satisfying $pq = 113190$, $\gcd(p, q) = 1$, and $p < q$. Define $b$ to be the minimum value of $x + y$ over ... | 0 | graphs = [
Graph(
let={
"_n": Const(4),
"a": Const(-1),
"b": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), CountOverSet(set=Solut... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/B3"
] | 3f0fb0 | algebra_quadratic_discriminant_v1 | null | 6 | 0 | [
"B3",
"COPRIME_PAIRS"
] | 2 | 0.003 | 2026-02-08T13:13:26.787671Z | {
"verified": true,
"answer": 0,
"timestamp": "2026-02-08T13:13:26.790705Z"
} | aefe3c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 179,
"completion_tokens": 1228
},
"timestamp": "2026-02-15T11:29:42.571Z",
"answer": 0
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
b25af5 | alg_poly_orbit_hensel_v1_1218484723_2810 | For a non-negative integer $a$, define the sequence $N = (a^2 + 12) \bmod 289$, $M = (N^2 + 12) \bmod 289$, $R = (M^2 + 12) \bmod 289$. Let $Q$ be the number of integers $a$ in $[0, 491877]$ such that $R = a$, $N \ne a$, and $M \ne a$. Find $Q$. | 5,106 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Pow(Var("a"), Const(2)), Const(12)), modulus=Const(289)),
"p2": Mod(value=Sum(Pow(Ref("p1"), Const(2)), Const(12)), modulus=Const(289)),
"p3": Mod(value=Sum(Pow(Ref("p2"), Const(2)), Const(12)), modulus=Const(289)),
... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_orbit_hensel_v1 | null | 6 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.01 | 2026-02-25T04:31:56.026803Z | {
"verified": true,
"answer": 5106,
"timestamp": "2026-02-25T04:31:56.036984Z"
} | b21204 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 218,
"completion_tokens": 13379
},
"timestamp": "2026-03-29T06:44:48.270Z",
"answer": 0
},
{
"... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 3.81,
"mid": 6.33,
"hi": 9.49
} | ||
8365ff | alg_sym_quad_system_v1_601307018_8502 | Let $R$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \leq a \leq b \leq 15$ such that $5a^2 - 8ab + 5b^2 = 450$. Let $N$ be the number of integer solutions $(a_1, b_1, c)$ with $a_1, b_1, c \geq 1$ to the system
\[
a_1^2 + b_1^2 + c^2 = a_1b_1 + b_1c + ca_1 \quad \text{and} \quad 7a_1 + 6b_1 + 8... | 1,485 | graphs = [
Graph(
let={
"_c": Const(2),
"_m": Const(7),
"_n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(15)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(15)), Leq(Var("a"), Var("b")... | ALG | null | COMPUTE | sympy | QF_PSD_ORBIT | [
"QF_PSD_ORBIT/LIN_FORM",
"QF_PSD_COUNT_LEQ"
] | 11b15e | alg_sym_quad_system_v1 | null | 8 | 0 | [
"LIN_FORM",
"QF_PSD_COUNT_LEQ",
"QF_PSD_ORBIT"
] | 3 | 0.027 | 2026-03-10T08:59:02.218476Z | {
"verified": true,
"answer": 1485,
"timestamp": "2026-03-10T08:59:02.245119Z"
} | fe41a1 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 471,
"completion_tokens": 11581
},
"timestamp": "2026-04-19T09:11:07.921Z",
"answer": 1485
},
{
... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok_later"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
},
{
"lemma": "QF_PSD_ORBIT",
"status": "ok"
}
] | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
9756f3 | nt_min_coprime_above_v1_397696148_246 | Let $\mathcal{T}$ be the set of all integers $t$ with $9 \leq t \leq 379$ for which there exist positive integers $a \leq 35$ and $b \leq 67$ such that $t = 7a + 2b$. Let $m$ be the number of elements in $\mathcal{T}$. Let $n_0$ be the smallest integer $n$ such that $26796 < n \leq 27171$ and $\gcd(n, m) = 1$. Compute ... | 71,879 | graphs = [
Graph(
let={
"_n": Const(44121),
"start": Const(26796),
"upper": Const(27171),
"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... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_min_coprime_above_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.052 | 2026-02-08T11:23:45.042954Z | {
"verified": true,
"answer": 71879,
"timestamp": "2026-02-08T11:23:45.094609Z"
} | 897258 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 177,
"completion_tokens": 4919
},
"timestamp": "2026-02-14T13:32:49.763Z",
"answer": 71879
},
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
67dfc0 | geo_count_lattice_rect_v1_655260480_427 | Let $a = 144$ and $b = 55$. Define $R$ to be the number of lattice points in the rectangle $[0, a] \times [0, b]$, including the boundary. Let $Q$ be the Bell number of the remainder when $|R|$ is divided by 11. Compute $Q$. | 2 | graphs = [
Graph(
let={
"a": Const(144),
"b": Const(55),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"Q": Bell(Mod(value=Abs(arg=Ref(name='result')), modulus=Const(11))),
},
goal=Ref("Q"),
)
] | GEOM | COMB | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.003 | 2026-02-08T15:22:44.507910Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-02-08T15:22:44.511249Z"
} | e1b5e8 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 183,
"completion_tokens": 541
},
"timestamp": "2026-02-24T20:46:00.759Z",
"answer": 2
},
{
"id": ... | 1 | [] | {
"lo": -8,
"mid": -4.75,
"hi": -2.29
} | ||||
634fe9 | antilemma_k3_v1_1520064083_2165 | Let $x = \sum_{d \mid 78042} \phi(d)$. Compute the remainder when $44121 \cdot x$ is divided by $91096$. | 44,474 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=78042), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Mod(value=Mul(Const(44121), Ref("x")), modulus=Const(91096)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0 | 2026-02-08T04:32:29.563455Z | {
"verified": true,
"answer": 44474,
"timestamp": "2026-02-08T04:32:29.563898Z"
} | 0730ea | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 148,
"completion_tokens": 2629
},
"timestamp": "2026-02-10T17:07:47.037Z",
"answer": 44474
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
3a7709 | nt_sum_gcd_range_mod_v1_1918700295_4063 | Let $N$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 19749136$. Let $k = 96$ and $M = 10193$. Define $$
S = \sum_{n=1}^{N} \gcd(n, k).$$ Let $r$ be the remainder when $S$ is divided by $M$, and let $Q$ be the remainder when $44121 \cdot r$ is divided by $59288$. Find the ... | 52,141 | graphs = [
Graph(
let={
"N": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(19749136)))), expr=Sum(Var("x"), Var("y")))),
"k": Const(96)... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_gcd_range_mod_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.406 | 2026-02-08T09:07:20.491049Z | {
"verified": true,
"answer": 52141,
"timestamp": "2026-02-08T09:07:20.897464Z"
} | f73412 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 164,
"completion_tokens": 2415
},
"timestamp": "2026-02-14T00:43:42.167Z",
"answer": 52141
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "... | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
b97fe2 | antilemma_k2_v1_349078426_964 | Let $x = \sum_{k=1}^{163} \phi(k) \left\lfloor \frac{163}{k} \right\rfloor$, where $\phi$ denotes Euler's totient function. Compute the value of $(1597 - x) \bmod 77296$. | 65,527 | graphs = [
Graph(
let={
"_n": Const(163),
"x": Summation(var="k", start=Const(1), end=Const(163), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Ref("_n"), Var("k"))))),
"Q": Mod(value=Sub(Const(1597), Ref("x")), modulus=Const(77296)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K13 | [
"K2"
] | 6897ab | antilemma_k2_v1 | null | 5 | 0 | [
"K13",
"K2"
] | 2 | 0.002 | 2026-02-08T13:21:12.917609Z | {
"verified": true,
"answer": 65527,
"timestamp": "2026-02-08T13:21:12.919765Z"
} | 883480 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 107,
"completion_tokens": 809
},
"timestamp": "2026-02-15T13:26:21.569Z",
"answer": 65527
},
{... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
fe808a | diophantine_fbi2_count_v1_1742523217_5411 | Let $k = 480$. Let $m$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $x \cdot y = 2500$. Compute the number of integers $d$ such that $6 \leq d \leq 104$, $d$ divides $k$, and $2 \leq k/d \leq m$. Then, find the remainder when this count is multiplied by 44121 and divide... | 78,285 | graphs = [
Graph(
let={
"_n": Const(6),
"k": Const(480),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Leq(Var("d"), Const(104)), Divides(divisor=Var("d"), dividend=Ref("k")), Geq(Div(Ref("k"), Var("d")), Const(2)), Leq(Div(... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | diophantine_fbi2_count_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.008 | 2026-02-08T10:59:00.351900Z | {
"verified": true,
"answer": 78285,
"timestamp": "2026-02-08T10:59:00.359830Z"
} | 0c08c4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 151,
"completion_tokens": 1562
},
"timestamp": "2026-02-14T09:42:40.501Z",
"answer": 78285
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
26302d | algebra_poly_eval_v1_717093673_3685 | Let $t = 13$ and $n = 112$. Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 2304$. Define $s = \min\{x + y \mid (x, y) \in S\}$. Compute the value of
$$
r = \frac{64t^4 - 224t^3 + s \cdot t^2 + n \cdot t + 120}{84},
$$
and let $Q$ be the remainder when $24194 \cdot r$ is divided by... | 71,318 | graphs = [
Graph(
let={
"_n": Const(112),
"t": Const(13),
"result": Div(Sum(Mul(Const(64), Pow(Ref("t"), Const(4))), Mul(Const(-224), Pow(Ref("t"), Const(3))), Mul(MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositiv... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | algebra_poly_eval_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.003 | 2026-02-08T17:45:44.432914Z | {
"verified": true,
"answer": 71318,
"timestamp": "2026-02-08T17:45:44.435862Z"
} | 6b0536 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 178,
"completion_tokens": 1088
},
"timestamp": "2026-02-18T07:17:40.445Z",
"answer": 71318
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
5620fc | nt_min_with_divisor_count_v1_1918700295_694 | Let $A$ be the set of all positive integers $n$ such that $1 \le n \le 19321$ and $\tau(n) = 2$, where $\tau(n)$ is the number of positive divisors of $n$. Let $r$ be the smallest element of $A$. Let $d_0$ be the smallest divisor of $3490067079293$ that is at least $2$. Compute $ (r \bmod 307) + 2003 \cdot (r \bmod d_0... | 4,008 | graphs = [
Graph(
let={
"_n": Const(307),
"upper": Const(19321),
"div_count": Const(2),
"result": MinOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(NumDivisors(n=Var("n")), Ref("div_count"))))),
... | NT | null | EXTREMUM | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | cffc20 | nt_min_with_divisor_count_v1 | two_moduli | 4 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.749 | 2026-02-08T03:23:15.583671Z | {
"verified": true,
"answer": 4008,
"timestamp": "2026-02-08T03:23:16.332996Z"
} | 60eb85 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 241,
"completion_tokens": 18391
},
"timestamp": "2026-02-23T18:58:35.655Z",
"answer": 4008
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
}
... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
a5c085 | modular_sum_quadratic_residues_v1_48377204_2667 | Let $p$ be the smallest integer greater than or equal to $2$ that divides $40577833$. Define $r = \frac{p(p-1)}{4}$.
Compute the remainder when $44121 \cdot r$ is divided by $61856$. | 42,772 | graphs = [
Graph(
let={
"_n": Const(2),
"p": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(40577833))))),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), Const(4)),
"Q": Mod(val... | NT | null | SUM | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | modular_sum_quadratic_residues_v1 | null | 4 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.003 | 2026-02-08T16:54:48.884511Z | {
"verified": true,
"answer": 42772,
"timestamp": "2026-02-08T16:54:48.887019Z"
} | 910bf7 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 102,
"completion_tokens": 3709
},
"timestamp": "2026-02-17T14:34:57.369Z",
"answer": 42772
},
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "VAL_SUM_EQ",
"stat... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
1a5ba2 | comb_sum_binomial_row_v1_865884756_3841 | Let $c = 768$. Define $m$ to be the number of positive integers $k$ such that $1 \leq k \leq c$ and $64$ divides $k$. Let $n$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = M$, where $M$ is the maximum value of $x_1 y_1$ over all ordered pairs $(x_1, y_1)$ of positi... | 4,096 | graphs = [
Graph(
let={
"_c": Const(768),
"_m": CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(1)), Leq(Var("k"), Ref("_c")), Divides(divisor=Const(64), dividend=Var("k"))), domain='positive_integers')),
"_n": Const(2),
"n": MinO... | ALG | NT | SUM | sympy | C2 | [
"C2/B1/B3"
] | 5125d5 | comb_sum_binomial_row_v1 | null | 6 | 0 | [
"B1",
"B3",
"C2"
] | 3 | 0.003 | 2026-02-08T17:35:28.469908Z | {
"verified": true,
"answer": 4096,
"timestamp": "2026-02-08T17:35:28.473158Z"
} | c35f7a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 170,
"completion_tokens": 727
},
"timestamp": "2026-02-18T05:25:20.907Z",
"answer": 4096
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
286f6d | diophantine_fbi2_count_v1_1742523217_1357 | Let $k = 60$. Compute the number of integers $d$ such that $6 \leq d \leq 60$, $d$ divides $k$, and $6 \leq \frac{k}{d} \leq 60$. | 2 | graphs = [
Graph(
let={
"k": Const(60),
"a": Const(5),
"b": Const(5),
"upper": Const(55),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(6)), Leq(Var("d"), Const(60)), Divides(divisor=Var("d"), dividend=Ref(... | NT | null | COUNT | sympy | ONE_PHI_1 | [
"ONE_PHI_1",
"C2"
] | a5611a | diophantine_fbi2_count_v1 | null | 3 | 0 | [
"C2",
"ONE_PHI_1"
] | 2 | 0.077 | 2026-02-08T03:41:26.616119Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-02-08T03:41:26.692890Z"
} | 9e497e | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 164,
"completion_tokens": 557
},
"timestamp": "2026-02-10T15:20:18.135Z",
"answer": 2
},
{
"id": ... | 1 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "ONE_PHI_1",
"status": "ok"
},
{
"lemma": "VAL... | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
57e49c | comb_count_surjections_v1_349078426_19 | Let $n = 8$ and $k = 4$. Compute $k! \cdot S(n, k)$, where $S(n, k)$ denotes the number of ways to partition a set of $n$ elements into $k$ nonempty unlabeled subsets.
Find the value of this quantity. | 40,824 | graphs = [
Graph(
let={
"n": Const(8),
"k": Const(4),
"result": Mul(Factorial(Ref("k")), Stirling2(n=Ref(name='n'), k=Ref(name='k'))),
},
goal=Ref("result"),
)
] | COMB | null | COUNT | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | comb_count_surjections_v1 | null | 3 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.083 | 2026-02-08T12:46:53.322253Z | {
"verified": true,
"answer": 40824,
"timestamp": "2026-02-08T12:46:53.405356Z"
} | 5c312c | 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": 729
},
"timestamp": "2026-02-24T16:20:31.218Z",
"answer": 40824
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "n... | {
"lo": -3.84,
"mid": -1.67,
"hi": 1.32
} | ||
384571 | antilemma_k3_v1_865884756_5146 | Let $m = 94874$ and $n = 70303$. Define $x$ to be the sum of $\phi(d)$ over all positive divisors $d$ of $m$. Let $y$ be the sum of $\phi(d)$ over all positive divisors $d$ of $196$. Define $z$ to be the sum of $\phi(d)$ over all positive divisors $d$ of $y$. Compute the remainder when $z - x$ is divided by $n$. | 45,928 | graphs = [
Graph(
let={
"_m": Const(94874),
"_n": Const(70303),
"x": SumOverDivisors(n=Ref(name='_m'), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Mod(value=Sub(SumOverDivisors(n=SumOverDivisors(n=Const(value=196), var='d2', expr=EulerPhi(n=Var(name='d2')))... | NT | COMB | COMPUTE | sympy | K13 | [
"K3/K3",
"K3"
] | 229767 | antilemma_k3_v1 | negation_mod | 4 | 0 | [
"K13",
"K3"
] | 2 | 0.003 | 2026-02-08T18:23:41.591204Z | {
"verified": true,
"answer": 45928,
"timestamp": "2026-02-08T18:23:41.594444Z"
} | dae956 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 149,
"completion_tokens": 868
},
"timestamp": "2026-02-18T16:40:39.511Z",
"answer": 45928
},
{... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
5b539d | nt_count_divisors_in_range_v1_865884756_495 | Let $n = 166320$, $a = 31$, and $b = 1326$. Let $r$ be the number of positive divisors $d$ of $n$ such that $a \leq d \leq b$. Define $$
Q = r + \varphi(|r| + 1) + \tau(|r| + 1),
$$
where $\varphi$ denotes Euler's totient function and $\tau(m)$ denotes the number of positive divisors of $m$. Compute the value of $Q$. | 135 | graphs = [
Graph(
let={
"n": Const(166320),
"a": Const(31),
"b": Const(1326),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Divides(divisor=Var("d"), dividend=Ref("n")), Geq(Var("d"), Ref("a")), Leq(Var("d"), Ref("b"))))),
"Q"... | NT | null | COUNT | sympy | DIVISOR_PARITY | [
"DIVISOR_PARITY",
"BIG_OMEGA_ONE"
] | 47ec5c | nt_count_divisors_in_range_v1 | null | 3 | 0 | [
"BIG_OMEGA_ONE",
"DIVISOR_PARITY"
] | 2 | 0.054 | 2026-02-08T15:26:17.411185Z | {
"verified": true,
"answer": 135,
"timestamp": "2026-02-08T15:26:17.465174Z"
} | ddcfb4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 154,
"completion_tokens": 4014
},
"timestamp": "2026-02-16T06:24:00.523Z",
"answer": 135
},
{
... | 1 | [
{
"lemma": "BIG_OMEGA_ONE",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DIVISOR_PARITY",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
75e314 | lin_form_endings_v1_784195855_9514 | Let $a = 24$, $b = 36$, $A = 16$, and $B = 4$. Let $g = \gcd(a, b)$, and define $a' = \left\lfloor \frac{a}{g} \right\rfloor$ and $b' = \left\lfloor \frac{b}{g} \right\rfloor$. Let $T$ be a set of lattice points defined such that the number of points in $T$ is $|T| = a'A + b'B - a'b'$. The total number of lattice point... | 33,183 | graphs = [
Graph(
let={
"a_coeff": Const(24),
"b_coeff": Const(36),
"A_val": Const(16),
"B_val": Const(4),
"g_step": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"ap_node": Floor(Div(Ref("a_coeff"), Ref("g_step"))),
"bp_node": F... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 5 | null | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T16:52:14.154346Z | {
"verified": true,
"answer": 33183,
"timestamp": "2026-02-08T16:52:14.156734Z"
} | cede26 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 222,
"completion_tokens": 939
},
"timestamp": "2026-02-17T13:52:45.973Z",
"answer": 33183
},
{... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"sta... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
081fb7 | algebra_poly_eval_v1_1218484723_124 | Let $M$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \leq a, b \leq 25$ such that $10a^2 + 25b^2 - 18ab \leq 7400$. Let $R = 8 \cdot 13^2 - 7 \cdot 13 - 5$. Find the remainder when $R^2 + 25R + M$ is divided by $92071$. | 44,213 | graphs = [
Graph(
let={
"_n": Const(25),
"t": Const(13),
"result": Sum(Mul(Const(8), Pow(Ref("t"), Const(2))), Mul(Const(-7), Ref("t")), Const(-5)),
"_c": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const... | ALG | null | COMPUTE | sympy | QF_PSD_COUNT_LEQ | [
"QF_PSD_COUNT_LEQ"
] | e34ff7 | algebra_poly_eval_v1 | quadratic_mod | 3 | 0 | [
"QF_PSD_COUNT_LEQ"
] | 1 | 0.002 | 2026-02-25T01:49:57.779626Z | {
"verified": true,
"answer": 44213,
"timestamp": "2026-02-25T01:49:57.781845Z"
} | b57847 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 214,
"completion_tokens": 13086
},
"timestamp": "2026-03-10T08:28:08.161Z",
"answer": 44213
},
{
... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
}
] | {
"lo": 1.22,
"mid": 3.76,
"hi": 5.73
} | ||
ac1d08 | diophantine_fbi2_count_v1_1978505735_7332 | Let $k$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 396900$. Let $T$ be the set of all integers $t$ such that $10 \leq t \leq 112$ and $t = 3a + 7b$ for some positive integers $a \leq 7$ and $b \leq 13$. Let $m$ be the number of elements in $T$. Determine the number of d... | 16 | graphs = [
Graph(
let={
"_n": Const(94),
"k": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(396900)))), expr=Sum(Var("x"), Var("y")))),... | NT | null | COUNT | sympy | SUM_ARITHMETIC | [
"LIN_FORM",
"B3"
] | 688dbe | diophantine_fbi2_count_v1 | null | 6 | 0 | [
"B3",
"LIN_FORM",
"SUM_ARITHMETIC"
] | 3 | 0.034 | 2026-02-08T20:12:36.541289Z | {
"verified": true,
"answer": 16,
"timestamp": "2026-02-08T20:12:36.575300Z"
} | 9040f3 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 196,
"completion_tokens": 4324
},
"timestamp": "2026-02-19T00:06:51.461Z",
"answer": 16
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lem... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
1dec43 | nt_count_divisible_and_v1_655260480_920 | Let $d_1 = \sum_{k=1}^{3} k$ and $d_2 = 8$. Let $N$ be the number of positive integers $n$ such that $1 \leq n \leq 64008$, $n$ is divisible by $d_1$, and $n$ is divisible by $d_2$. Compute the remainder when $22148 \cdot N$ is divided by $95093$. | 15,963 | graphs = [
Graph(
let={
"_n": Const(3),
"upper": Const(64008),
"d1": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Var("k")),
"d2": Const(8),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(... | NT | null | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | nt_count_divisible_and_v1 | null | 3 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 11.92 | 2026-02-08T15:44:55.186620Z | {
"verified": true,
"answer": 15963,
"timestamp": "2026-02-08T15:45:07.106724Z"
} | b3ff11 | 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": 1050
},
"timestamp": "2026-02-16T12:53:46.253Z",
"answer": 15963
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
}... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
a4f15f | comb_catalan_compute_v1_898971024_561 | Let $n$ be the number of ordered pairs $(i, j)$ where $i$ is an integer with $1 \leq i \leq 2$ and $j$ is an integer with $1 \leq j \leq 5$. Let $C_n$ denote the $n$-th Catalan number. Compute $65025 - C_n$. | 48,229 | graphs = [
Graph(
let={
"n": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(2)), right=IntegerRange(start=Const(1), end=Const(5)))),
"result": Catalan(Ref("n")),
"_c": Const(65025),
"Q": Sub(Ref("_c"), Ref("result")),
},
... | COMB | null | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | comb_catalan_compute_v1 | null | 3 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.017 | 2026-02-08T15:32:28.990331Z | {
"verified": true,
"answer": 48229,
"timestamp": "2026-02-08T15:32:29.007365Z"
} | bdfdef | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 189,
"completion_tokens": 462
},
"timestamp": "2026-02-24T17:57:13.517Z",
"answer": 48229
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V8",
... | {
"lo": -8,
"mid": -4.75,
"hi": -2.28
} | ||
b66345 | diophantine_product_count_v1_238844314_963 | Let $k = 720$ and define $U = 464$. Let $\mathcal{X}$ be the set of all positive integers $x$ such that $1 \leq x \leq U$, $x$ divides $k$, and $\frac{k}{x} \leq U$. Find the number of elements in $\mathcal{X}$. | 28 | graphs = [
Graph(
let={
"k": Const(720),
"upper": Const(464),
"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 | [
"B3"
] | 0cd20d | diophantine_product_count_v1 | null | 3 | 0 | [
"B3",
"LIN_FORM"
] | 2 | 0.259 | 2026-02-08T13:50:06.022802Z | {
"verified": true,
"answer": 28,
"timestamp": "2026-02-08T13:50:06.281765Z"
} | acd143 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 116,
"completion_tokens": 1672
},
"timestamp": "2026-02-15T20:47:09.879Z",
"answer": 28
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
806237 | nt_count_primes_v1_655260480_5283 | Let $p$ and $q$ be positive integers such that $pq = 36$, $\gcd(p, q) = 1$, and $p < q$. Let $A$ be the number of such pairs $(p, q)$. Let $n$ be a prime number satisfying $n \geq A$ and $n \leq 24649$. Compute the number of such prime numbers $n$. | 2,729 | graphs = [
Graph(
let={
"upper": Const(24649),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'),... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_count_primes_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.551 | 2026-02-08T18:23:43.133819Z | {
"verified": true,
"answer": 2729,
"timestamp": "2026-02-08T18:23:43.684990Z"
} | 5fcde5 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 131,
"completion_tokens": 2674
},
"timestamp": "2026-02-18T16:52:29.325Z",
"answer": 2729
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
ca5748 | nt_count_intersection_v1_677425708_1197 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 6250000$. Let $N$ be the minimum value of $x + y$ over all such pairs. Let $b$ be the number of integers $t$ with $14 \le t \le 48$ for which there exist integers $a$ and $b$ such that $1 \le a \le 2$, $1 \le b \le 7$, and $t = 10a + ... | 714 | graphs = [
Graph(
let={
"N": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(6250000)))), expr=Sum(Var("x"), Var("y")))),
"a": Const(3),
... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM",
"B3"
] | 688dbe | nt_count_intersection_v1 | null | 5 | 0 | [
"B3",
"LIN_FORM"
] | 2 | 0.237 | 2026-02-08T04:01:42.837322Z | {
"verified": true,
"answer": 714,
"timestamp": "2026-02-08T04:01:43.074238Z"
} | 7090b0 | 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": 2663
},
"timestamp": "2026-02-09T16:52:31.469Z",
"answer": 714
},
{
"id... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
}... | {
"lo": -3.53,
"mid": 1.02,
"hi": 5.49
} | ||
f11e35 | antilemma_count_primes_v1_168721529_1755 | Let $x$ be the number of prime numbers $p$ such that $2 \leq p \leq 1249$. Compute the remainder when $|x|$ is divided by $52406$. | 204 | graphs = [
Graph(
let={
"_n": Const(1249),
"x": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))),
"Q": Mod(value=Abs(arg=Ref(name='x')), modulus=Const(52406)),
},
goal=Ref("Q"... | NT | null | COMPUTE | sympy | COUNT_PRIMES | [
"COUNT_PRIMES"
] | 07c874 | antilemma_count_primes_v1 | null | 2 | 0 | [
"COUNT_PRIMES"
] | 1 | 0.001 | 2026-02-08T13:54:20.981474Z | {
"verified": true,
"answer": 204,
"timestamp": "2026-02-08T13:54:20.982394Z"
} | 1d2ea1 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 154,
"completion_tokens": 6663
},
"timestamp": "2026-02-09T21:12:34.322Z",
"answer": 204
},
{
"id... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
... | {
"lo": -6.5,
"mid": -0.2,
"hi": 6.11
} | ||
7f208a | nt_count_gcd_equals_v1_1439011603_77 | Let $u$ be the number of positive integers $k_1$ such that $1 \leq k_1 \leq 198744$ and $24$ divides $k_1$. Let $k = 273$ and $d = 39$. Compute the number of positive integers $n$ such that $1 \leq n \leq u$ and $\gcd(n, 273) = 39$. | 182 | graphs = [
Graph(
let={
"upper": CountOverSet(set=SolutionsSet(var=Var("k1"), condition=And(Geq(Var("k1"), Const(1)), Leq(Var("k1"), Const(198744)), Divides(divisor=Const(24), dividend=Var("k1"))), domain='positive_integers')),
"k": Const(273),
"d": Const(39),
... | NT | null | COUNT | sympy | C2 | [
"C2"
] | 9685eb | nt_count_gcd_equals_v1 | null | 4 | 0 | [
"C2"
] | 1 | 0.717 | 2026-02-08T15:11:01.225649Z | {
"verified": true,
"answer": 182,
"timestamp": "2026-02-08T15:11:01.942204Z"
} | 0621a5 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 133,
"completion_tokens": 970
},
"timestamp": "2026-02-16T01:17:14.558Z",
"answer": 182
},
{
... | 1 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
98c454 | diophantine_product_count_v1_48377204_2578 | Let $k = 180$ and let $u = 174$. Define $r$ to be the number of positive integers $x$ such that $1 \leq x \leq u$, $x$ divides $180$, and $\frac{180}{x} \leq u$. Compute the smallest positive integer $n$ such that the $n$-th Fibonacci number is divisible by $r + 2$. That is, compute the Fibonacci entry point of $r + 2$... | 12 | graphs = [
Graph(
let={
"k": Const(180),
"upper": Const(174),
"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 | COUNT_COPRIME_GRID | [
"COUNT_COPRIME_GRID",
"MOBIUS_COPRIME"
] | db308f | diophantine_product_count_v1 | null | 4 | 0 | [
"COUNT_COPRIME_GRID",
"MOBIUS_COPRIME"
] | 2 | 0.06 | 2026-02-08T16:49:46.847844Z | {
"verified": true,
"answer": 12,
"timestamp": "2026-02-08T16:49:46.908204Z"
} | d3e632 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 180,
"completion_tokens": 417
},
"timestamp": "2026-02-16T07:57:20.902Z",
"answer": 15
},
{
"id": 11,
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok"
},
{
"lemma": "V3",
"... | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
de315d | comb_count_permutations_fixed_v1_1431428450_1266 | Let $f = \sum_{k=0}^{1} (-1)^k \binom{1}{k}$, $u = 9$, $n_1 = u + 1$, and $c = \sum_{k=0}^{n_1} (-1)^k \binom{n_1}{k}$. Let $n = 6$ and $k = f + c$. Compute $\binom{n}{k} \cdot !(n - k)$, where $!m$ denotes the number of derangements of $m$ elements. | 265 | graphs = [
Graph(
let={
"n2": Const(1),
"f": Summation(var="k", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n2"), k=Var("k")))),
"u": Const(9),
"n1": Sum(Ref("u"), Const(1)),
"c": Summation(var="k", start=Const(0)... | COMB | null | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING"
] | c21569 | comb_count_permutations_fixed_v1 | null | 4 | 2 | [
"BINOMIAL_ALTERNATING"
] | 1 | 0.002 | 2026-02-08T13:59:10.424547Z | {
"verified": true,
"answer": 265,
"timestamp": "2026-02-08T13:59:10.426130Z"
} | 5aa444 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 232,
"completion_tokens": 739
},
"timestamp": "2026-02-24T19:25:35.771Z",
"answer": 265
},
{
"id"... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",... | {
"lo": -8.52,
"mid": -5.43,
"hi": -3.2
} | ||
fd74f0 | nt_sum_over_divisible_v1_153355830_2219 | Compute the sum of all positive integers $n$ such that $n$ is a multiple of $186$ and $1 \leq n \leq 5737$. | 86,490 | graphs = [
Graph(
let={
"upper": Const(5737),
"divisor": Const(186),
"result": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(value=Var("n"), modulus=Ref("divisor")), Const(0))))),
},
go... | NT | null | SUM | sympy | ONE_PHI_1 | [
"MAX_PRIME_BELOW"
] | dc3ad3 | nt_sum_over_divisible_v1 | null | 2 | 0 | [
"MAX_PRIME_BELOW",
"ONE_PHI_1"
] | 2 | 13.148 | 2026-02-08T06:59:19.430036Z | {
"verified": true,
"answer": 86490,
"timestamp": "2026-02-08T06:59:32.577662Z"
} | a3efd5 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 94,
"completion_tokens": 530
},
"timestamp": "2026-02-15T18:48:27.600Z",
"answer": 86490
},
{
"id": 11,
... | 2 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -9.14,
"mid": -6.05,
"hi": -3.73
} | ||
e19e18 | lin_form_endings_v1_784195855_9654 | Let $a = 21$ and $b = 28$. Compute the value of $\left\lfloor \frac{21}{\gcd(a,b)} \right\rfloor$. Multiply this value by $15269$, and let the result be $N$. Find the remainder when $N$ is divided by $81326$. | 45,807 | graphs = [
Graph(
let={
"a_coeff": Const(21),
"b_coeff": Const(28),
"_inner_result": Floor(Div(Const(21), GCD(a=Ref("a_coeff"), b=Ref("b_coeff")))),
"_scale_k": Const(15269),
"_scaled": Mul(Ref("_scale_k"), Ref("_inner_result")),
"_mod_... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 2 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T16:58:04.520904Z | {
"verified": true,
"answer": 45807,
"timestamp": "2026-02-08T16:58:04.521659Z"
} | 3d832d | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 137,
"completion_tokens": 328
},
"timestamp": "2026-02-16T08:41:27.094Z",
"answer": 45807
},
{
"id": 11,
... | 2 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"s... | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
9944b3 | comb_binomial_compute_v1_1520064083_6294 | Let $n$ be the number of ordered pairs $(i, j)$ of positive integers such that $i + j = 17$, $1 \leq i \leq 15$, and $1 \leq j \leq 15$. Let $k$ be the number of positive integers $p$ for which there exists a positive integer $q > p$ such that $p \cdot q = 630$ and $\gcd(p, q) = 1$. Compute $\binom{n}{k}$. | 3,003 | graphs = [
Graph(
let={
"_n": Const(17),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref("_n")), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(15)), right=IntegerRange(start=Const(1), end=Con... | NT | null | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS",
"COPRIME_PAIRS"
] | e64e7a | comb_binomial_compute_v1 | null | 5 | 0 | [
"COPRIME_PAIRS",
"COUNT_SUM_EQUALS"
] | 2 | 0.011 | 2026-02-08T08:00:28.968828Z | {
"verified": true,
"answer": 3003,
"timestamp": "2026-02-08T08:00:28.980041Z"
} | bb6b93 | 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": 2639
},
"timestamp": "2026-02-13T13:58:29.672Z",
"answer": 3003
},
{... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"stat... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
acdbc9 | nt_count_primes_v1_1116507919_298 | Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 18$, $\gcd(p, q) = 1$, and $p < q$. Let $L$ be the number of elements in $S$. Let $T$ be the set of all prime numbers $n$ such that $L \leq n \leq 65536$. Compute the number of elements in $T$. | 6,542 | graphs = [
Graph(
let={
"upper": Const(65536),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'),... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_count_primes_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 3.682 | 2026-02-08T02:30:34.229310Z | {
"verified": true,
"answer": 6542,
"timestamp": "2026-02-08T02:30:37.910870Z"
} | 77991d | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 214,
"completion_tokens": 2286
},
"timestamp": "2026-02-08T19:21:01.400Z",
"answer": 6542
},
{
"i... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -0.8,
"mid": 1.05,
"hi": 2.66
} | ||
140e70 | nt_count_divisible_v1_1918700295_1091 | Let $ A $ be the set of all positive integers $ n \leq 184 $ such that $ 4 $ divides $ n $ and $ \gcd(n, 21) = 1 $. Let $ d $ be the number of elements in $ A $. Let $ B $ be the set of all positive integers $ n \leq 31991 $ such that $ n \equiv 0 \pmod{d} $. Let $ r $ be the number of elements in $ B $. Compute the re... | 25,482 | graphs = [
Graph(
let={
"_n": Const(184),
"upper": Const(31991),
"divisor": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_n")), Divides(divisor=Const(4), dividend=Var("n")), Eq(GCD(a=Var("n"), b=Const(21)), Const(1)... | NT | null | COUNT | sympy | C5 | [
"C5"
] | 1d9668 | nt_count_divisible_v1 | null | 5 | 0 | [
"C5"
] | 1 | 0.994 | 2026-02-08T05:33:25.960612Z | {
"verified": true,
"answer": 25482,
"timestamp": "2026-02-08T05:33:26.955057Z"
} | e0f63d | 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": 1354
},
"timestamp": "2026-02-12T10:59:47.170Z",
"answer": 25482
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "C5",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
3a11f4 | nt_count_divisors_in_range_v1_168721529_1419 | Let $n$ be the number of ordered pairs $(i,j)$ such that $1 \leq i \leq 70$ and $1 \leq j \leq 72$. Let $a = 12$ and $b = 2525$. Compute the number of positive divisors $d$ of $n$ such that $a \leq d \leq b$. Let $Q$ be the remainder when $75271$ times this count is divided by $84060$. Find the value of $Q$. | 73,699 | graphs = [
Graph(
let={
"n": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(70)), right=IntegerRange(start=Const(1), end=Const(72)))),
"a": Const(12),
"b": Const(2525),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condit... | NT | null | COUNT | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | nt_count_divisors_in_range_v1 | null | 3 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.05 | 2026-02-08T13:41:29.425886Z | {
"verified": true,
"answer": 73699,
"timestamp": "2026-02-08T13:41:29.475931Z"
} | 9e1a4e | 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": 3446
},
"timestamp": "2026-02-09T16:46:45.324Z",
"answer": 64910
},
{
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V8",
"status": "n... | {
"lo": 1.84,
"mid": 5.05,
"hi": 8.38
} | ||
7a4a80 | sequence_lucas_compute_v1_601307018_4063 | Let $C$ be the number of ordered pairs $(a_1, b_1)$ of positive integers with $1 \leq a_1, b_1 \leq 25$ such that $10a_1^2 - 18a_1b_1 + 25b_1^2 \leq 4234$. Let $n$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \leq a \leq b \leq 35$ such that $2a^2 - 4ab + 2b^2 = C$. Let $S = L_n$ denote the $n$-... | 22,575 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(35),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(35)), Geq(Var("b"), Const(1)), Leq(Var("b"), Ref("_n")), Leq(Var("a"), Var("b")... | ALG | null | COMPUTE | sympy | QF_PSD_COUNT_LEQ | [
"QF_PSD_COUNT_LEQ/QF_PSD_ORBIT"
] | b96baf | sequence_lucas_compute_v1 | null | 7 | 0 | [
"QF_PSD_COUNT_LEQ",
"QF_PSD_ORBIT"
] | 2 | 0.006 | 2026-03-10T04:41:09.884006Z | {
"verified": true,
"answer": 22575,
"timestamp": "2026-03-10T04:41:09.889671Z"
} | f2e6f0 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 275,
"completion_tokens": 6177
},
"timestamp": "2026-03-29T10:52:41.827Z",
"answer": 22575
},
{
"... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
},
{
"lemma": "QF_PSD_ORBIT",
"status": "ok_later"
}
] | {
"lo": -3.34,
"mid": 0.9,
"hi": 4.9
} | ||
c4bd23 | nt_count_coprime_v1_784195855_9440 | Let $k$ be the number of nonnegative integers $j$ such that $0 \leq j \leq 4097$ and $\binom{4097}{j}$ is odd. Let $N$ be the number of positive integers $n$ such that $1 \leq n \leq 45796$ and $\gcd(n, k) = 1$. Compute $38025 - N$. | 15,127 | graphs = [
Graph(
let={
"_n": Const(4097),
"upper": Const(45796),
"k": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(4097)), Eq(Mod(value=Binom(n=Ref("_n"), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonneg... | NT | null | COUNT | sympy | V8 | [
"V8"
] | 86348e | nt_count_coprime_v1 | null | 6 | 0 | [
"V8"
] | 1 | 5.42 | 2026-02-08T16:48:51.074186Z | {
"verified": true,
"answer": 15127,
"timestamp": "2026-02-08T16:48:56.494502Z"
} | 096a8d | 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": 1243
},
"timestamp": "2026-02-17T13:41:38.962Z",
"answer": 15127
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
69a90b | antilemma_k3_v1_349078426_28 | Let $n = 46763$. Compute
$$
\sum_{d \mid n} \phi(d),
$$
where $\phi$ denotes Euler's totient function. Let $x$ be this sum. Let $m = \sum_{d \mid 11} \phi(d)$. Let $k$ be the absolute value of $x$ modulo $m$. Let $Q$ be the $k$-th Bell number, where the Bell number $B_k$ counts the number of partitions of a set of $k$ ... | 2 | graphs = [
Graph(
let={
"_n": Const(46763),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Bell(Mod(value=Abs(arg=Ref(name='x')), modulus=SumOverDivisors(n=Const(value=11), var='d', expr=EulerPhi(n=Var(name='d'))))),
},
... | NT | COMB | COMPUTE | sympy | K3 | [
"K3",
"K3"
] | 1dcb5e | antilemma_k3_v1 | bell_mod | 4 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T12:47:09.987340Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-02-08T12:47:09.988731Z"
} | 22c969 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 163,
"completion_tokens": 541
},
"timestamp": "2026-02-15T05:22:14.756Z",
"answer": 2
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
57ff22 | comb_count_partitions_v1_1218484723_5878 | Let $n$ be the number of integers $t$ with $31 \leq t \leq 129$ such that $t = 14a + 6b + 11$ for some integers $a, b$ with $1 \leq a \leq 5$ and $1 \leq b \leq 8$. Compute $p(n)$, where $p(n)$ denotes the number of partitions of $n$. | 26,015 | 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=5)), Geq(left=Var(name='b'), right=Const(value=1... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_count_partitions_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-25T07:27:08.216544Z | {
"verified": true,
"answer": 26015,
"timestamp": "2026-02-25T07:27:08.217923Z"
} | b71386 | 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": 4622
},
"timestamp": "2026-03-29T23:11:14.850Z",
"answer": 26015
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
... | {
"lo": 1.53,
"mid": 4.7,
"hi": 7.23
} | ||
3d11b7 | sequence_fibonacci_compute_v1_655260480_2609 | Let $ n $ be the value of the sum
$$
\sum_{k=1}^{m} \phi(k) \left\lfloor \frac{6}{k} \right\rfloor,
$$
where $ m $ is the number of integers $ t $ in the range $ 15 \leq t \leq 36 $ for which there exist integers $ a $ and $ b $ such that $ 1 \leq a \leq 3 $, $ 1 \leq b \leq 2 $, and $ t = 6a + 9b $.
Compute the $ n $... | 10,946 | graphs = [
Graph(
let={
"_n": Const(6),
"n": Summation(var="k", start=Const(1), end=CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'),... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/K2"
] | 506489 | sequence_fibonacci_compute_v1 | null | 5 | 0 | [
"K2",
"LIN_FORM"
] | 2 | 0.003 | 2026-02-08T16:51:49.463881Z | {
"verified": true,
"answer": 10946,
"timestamp": "2026-02-08T16:51:49.466976Z"
} | 591a83 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 220,
"completion_tokens": 1143
},
"timestamp": "2026-02-17T13:28:29.808Z",
"answer": 10946
},
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K2",
"status": "ok_later"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
bdcb91 | antilemma_sum_equals_v1_1520064083_555 | Let $m$ be the number of ordered pairs $(i, j)$ such that $1 \leq i \leq 8$ and $1 \leq j \leq 12$. Let $n$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = m$. Compute the number of ordered pairs $(i, j)$ such that $1 \leq i \leq 47$, $1 \leq j \leq 48$, and $i + j = n$. | 47 | graphs = [
Graph(
let={
"_m": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(8)), right=IntegerRange(start=Const(1), end=Const(12)))),
"_n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name=... | COMB | GEOM | COMPUTE | sympy | LIN_FORM | [
"COUNT_CARTESIAN/COMB1/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | 9b4db5 | antilemma_sum_equals_v1 | null | 5 | 0 | [
"COMB1",
"COUNT_CARTESIAN",
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 4 | 0.032 | 2026-02-08T03:28:23.627904Z | {
"verified": true,
"answer": 47,
"timestamp": "2026-02-08T03:28:23.659687Z"
} | 71b1c4 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 233,
"completion_tokens": 1254
},
"timestamp": "2026-02-10T14:35:51.019Z",
"answer": 47
},
{
"id"... | 1 | [
{
"lemma": "COMB1",
"status": "ok_later"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma... | {
"lo": -3.83,
"mid": -1.68,
"hi": 1.09
} | ||
c3b901 | sequence_count_fib_divisible_v1_1918700295_4100 | Let $n = 62$. Define $\text{upper}$ to be the maximum value of $xy$ over all ordered pairs $(x,y)$ of positive integers such that $x + y = n$. Let $d = 16$. Define $\text{result}$ to be the number of positive integers $n$ with $1 \leq n \leq \text{upper}$ such that $d$ divides the $n$-th Fibonacci number. Compute $$\te... | 139 | graphs = [
Graph(
let={
"_n": Const(62),
"upper": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Ref("_n")))), expr=Mul(Var("x"), Var("y")))),... | NT | null | COUNT | sympy | B1 | [
"B1"
] | 5b950e | sequence_count_fib_divisible_v1 | null | 5 | 0 | [
"B1"
] | 1 | 0.108 | 2026-02-08T09:08:59.333592Z | {
"verified": true,
"answer": 139,
"timestamp": "2026-02-08T09:08:59.441640Z"
} | 66be99 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 211,
"completion_tokens": 2827
},
"timestamp": "2026-02-14T00:42:51.901Z",
"answer": 139
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
16a3a0 | comb_factorial_compute_v1_124444284_7591 | Let $u_1 = 10$ and $n_2 = u_1 + 1$. Define $m = \sum_{k=0}^{n_2} (-1)^k \binom{n_2}{k}$. Let $n_1 = m$, and define $u = \sum_{k=0}^{n_1} (-1)^k \binom{n_1}{k}$. Let $n = 8u$. Compute $n!$. | 40,320 | graphs = [
Graph(
let={
"u1": Const(10),
"n2": Sum(Ref("u1"), Const(1)),
"m": Summation(var="k", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n2"), k=Var("k")))),
"n1": Ref("m"),
"u": Summation(var="k", start=Const... | COMB | null | COMPUTE | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING"
] | c21569 | comb_factorial_compute_v1 | null | 6 | 2 | [
"BINOMIAL_ALTERNATING"
] | 1 | 0.001 | 2026-02-08T09:11:59.656971Z | {
"verified": true,
"answer": 40320,
"timestamp": "2026-02-08T09:11:59.657851Z"
} | 871908 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 214,
"completion_tokens": 509
},
"timestamp": "2026-02-24T10:52:33.483Z",
"answer": 40320
},
{
"i... | 2 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"sta... | {
"lo": -10,
"mid": -7.79,
"hi": -5.57
} | ||
4aa36a | nt_count_with_divisor_count_v1_124444284_286 | Let $d$ be the number of positive integers $n$ such that $1 \leq n \leq 111$ and $$n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{7}.$$ Determine the number of positive integers $n$ such that $1 \leq n \leq 71824$ and the number of positive divisors of $n$ is equal to $d$. Compute the remainder when $44121$ time... | 68,638 | graphs = [
Graph(
let={
"upper": Const(71824),
"div_count": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(111)), Congruent(a=Var(name='n'), b=Floor(arg=Div(left=Var(name='n'), right=Const(value=2))), modulus=Const(value=7))))),... | NT | null | COUNT | sympy | L3C | [
"L3C"
] | 73f8b0 | nt_count_with_divisor_count_v1 | null | 5 | 0 | [
"L3C"
] | 1 | 3.208 | 2026-02-08T03:08:57.214517Z | {
"verified": true,
"answer": 68638,
"timestamp": "2026-02-08T03:09:00.422524Z"
} | 2085d1 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 226,
"completion_tokens": 4413
},
"timestamp": "2026-02-09T15:39:13.631Z",
"answer": 68638
},
{
"... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
}
] | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
2a7d01 | modular_count_residue_v1_809748730_1055 | Let $m$ be the number of integers $t$ with $18 \leq t \leq 42$ such that there exist positive integers $a \leq 4$ and $b \leq 3$ satisfying $t = 4a + 6b + 8$. Let $r$ be the smallest integer $d \geq 2$ that divides $539$. Let $N$ be the number of integers $n$ with $1 \leq n \leq 30727$ such that $n \equiv r \pmod{m}$. ... | 41,993 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(44121),
"upper": Const(30727),
"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=... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR",
"LIN_FORM"
] | 41af5a | modular_count_residue_v1 | null | 6 | 0 | [
"LIN_FORM",
"MIN_PRIME_FACTOR"
] | 2 | 1.021 | 2026-02-08T12:01:37.152227Z | {
"verified": true,
"answer": 41993,
"timestamp": "2026-02-08T12:01:38.173060Z"
} | c1a9b2 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 180,
"completion_tokens": 1757
},
"timestamp": "2026-02-14T21:35:58.742Z",
"answer": 41993
},
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
cde5fc | antilemma_k3_v1_784195855_2302 | Let $n$ be a positive integer. Define $\phi(n)$ as the number of positive integers less than or equal to $n$ that are relatively prime to $n$. Compute the sum of $\phi(d)$ over all positive divisors $d$ of 64462. | 64,462 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=64462), var='d', expr=EulerPhi(n=Var(name='d'))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0 | 2026-02-08T05:38:44.895606Z | {
"verified": true,
"answer": 64462,
"timestamp": "2026-02-08T05:38:44.896032Z"
} | d49f79 | 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": 1197
},
"timestamp": "2026-02-12T12:13:11.883Z",
"answer": 64462
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status":... | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
56f16c | nt_count_divisible_and_v1_1742523217_2219 | Let $m$ be the number of integers $n$ with $1\le n\le 5829$ such that
$$n\equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{11}.$$
Let $s$ be the minimum value of $x+y$ over all ordered pairs $(x,y)$ of positive integers such that $xy=m$.
Let $U=13788$, and let $d_1=4$ and $d_2=6$. Let $r$ be the number of integers $... | 68,177 | graphs = [
Graph(
let={
"_m": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(5829)), Congruent(a=Var(name='n'), b=Floor(arg=Div(left=Var(name='n'), right=Const(value=2))), modulus=Const(value=11))))),
"_n": MinOverSet(set=MapOve... | NT | null | COUNT | sympy | L3C | [
"L3C/B3/B1"
] | 598b6c | nt_count_divisible_and_v1 | negation_mod | 7 | 0 | [
"B1",
"B3",
"L3C"
] | 3 | 0.99 | 2026-02-08T04:35:49.964086Z | {
"verified": true,
"answer": 68177,
"timestamp": "2026-02-08T04:35:50.954439Z"
} | 19a2e3 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 330,
"completion_tokens": 1804
},
"timestamp": "2026-02-10T17:13:40.509Z",
"answer": 68177
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma":... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
96b9f4 | comb_catalan_compute_v1_48377204_1981 | Let $n = 11$. Define $C_n$ to be the $n$-th Catalan number. Let $S$ be the set of all ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 4232$. Let $c$ be the number of elements in $S$. Compute the sum
$$
\sum_{i=0}^{d-1} \left( \text{digit}_i(|C_n|) \cdot (i+1)^2 \right) + c,
$$
where $d$ is th... | 2,470 | graphs = [
Graph(
let={
"n": Const(11),
"result": Catalan(Ref("n")),
"_c": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name... | COMB | null | COMPUTE | sympy | COMB1 | [
"COMB1"
] | 43779f | comb_catalan_compute_v1 | digits_weighted_mod | 5 | 0 | [
"COMB1"
] | 1 | 0.004 | 2026-02-08T16:32:07.646287Z | {
"verified": true,
"answer": 2470,
"timestamp": "2026-02-08T16:32:07.649925Z"
} | 4b3294 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 215,
"completion_tokens": 1104
},
"timestamp": "2026-02-17T06:23:27.412Z",
"answer": 2470
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
... | {
"lo": -4.1,
"mid": -1.76,
"hi": 1.32
} | ||
051632 | algebra_quadratic_discriminant_v1_677425708_329 | Let $a = 2$, $b = -4$, and $m = 2$, $n = 4$. Let $S$ be the set of all ordered pairs $(k, j)$ where $k$ and $j$ are integers with $1 \leq k \leq 4$ and $1 \leq j \leq 4$. Define $c = \frac{8}{32} \sum_{(k,j) \in S} k$. Let $D = b^2 - 4ac$. Define
$$
r = 2 \cdot \begin{cases} 1 & \text{if } D > 0, \\ 0 & \text{otherwis... | 0 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(4),
"a": Const(2),
"b": Const(-4),
"c": Div(Mul(Const(8), SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("k"), Var("_j")]), condition=Const(1), domain=CartesianProduct(left=Int... | NT | null | COMPUTE | sympy | SUM_INDEPENDENT | [
"SUM_INDEPENDENT/SUM_ARITHMETIC"
] | 87e6cf | algebra_quadratic_discriminant_v1 | null | 6 | 0 | [
"SUM_ARITHMETIC",
"SUM_INDEPENDENT"
] | 2 | 0.007 | 2026-02-08T03:13:22.788486Z | {
"verified": true,
"answer": 0,
"timestamp": "2026-02-08T03:13:22.795058Z"
} | 150151 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 318,
"completion_tokens": 563
},
"timestamp": "2026-02-08T20:27:39.583Z",
"answer": 0
},
{
"id": ... | 2 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok_later"
},
{
"lemma": "SUM_INDEPENDENT",
"status": "ok"
},
{
"lemma": "V3",
"statu... | {
"lo": -10,
"mid": -7.73,
"hi": -5.46
} | ||
a5675e | nt_max_prime_below_v1_784195855_2556 | Let $ A $ be the number of positive integers $ p $ for which there exists a positive integer $ q $ such that $ p \cdot q = 18 $, $ \gcd(p, q) = 1 $, and $ p < q $. Let $ B $ be the largest prime number $ n $ such that $ A \leq n \leq 16129 $. Compute the remainder when $ 32503 \cdot B $ is divided by $ 87276 $. | 83,501 | graphs = [
Graph(
let={
"_n": Const(87276),
"upper": Const(16129),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_max_prime_below_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 5.604 | 2026-02-08T05:51:24.199272Z | {
"verified": true,
"answer": 83501,
"timestamp": "2026-02-08T05:51:29.803471Z"
} | 106697 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 145,
"completion_tokens": 3960
},
"timestamp": "2026-02-12T16:04:01.916Z",
"answer": 83501
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
74dfc8 | algebra_quadratic_discriminant_v1_865884756_6664 | Compute the value of $0^2 - 4(-8)(10)$. | 320 | graphs = [
Graph(
let={
"a": Const(-8),
"b": Const(0),
"c": Const(10),
"result": Sub(Pow(Ref("b"), Const(2)), Mul(Const(4), Ref("a"), Ref("c"))),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | algebra_quadratic_discriminant_v1 | null | 2 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.011 | 2026-02-08T19:20:40.731994Z | {
"verified": true,
"answer": 320,
"timestamp": "2026-02-08T19:20:40.742593Z"
} | 0131fa | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 63,
"completion_tokens": 309
},
"timestamp": "2026-02-18T22:00:23.035Z",
"answer": 320
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
fb5a20 | comb_factorial_compute_v1_677425708_3682 | Let $n = 8$ and $\text{result} = n!$. Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = 190$. Let $P$ be the maximum value of $xy$ over all pairs in $S$. Define $Q = (P - \text{result}) \mod 58285$. Compute $Q$. | 26,990 | graphs = [
Graph(
let={
"n": Const(8),
"result": Factorial(Ref("n")),
"Q": Mod(value=Sub(MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("... | ALG | COMB | COMPUTE | sympy | B1 | [
"B1"
] | d2b6e1 | comb_factorial_compute_v1 | negation_mod | 3 | 0 | [
"B1"
] | 1 | 0.001 | 2026-02-08T05:53:36.399535Z | {
"verified": true,
"answer": 26990,
"timestamp": "2026-02-08T05:53:36.400595Z"
} | 9fb6d4 | 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": 649
},
"timestamp": "2026-02-24T04:46:01.204Z",
"answer": 26990
},
{
"i... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -4.93,
"mid": -2.91,
"hi": -0.71
} | ||
da9c10 | antilemma_k3_v1_865884756_404 | Let $x$ be the sum of $\phi(d)$ over all positive divisors $d$ of $54005$. Let $c = 80053$. Compute the remainder when $c \cdot x$ is divided by $97268$. | 88,737 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=54005), var='d', expr=EulerPhi(n=Var(name='d'))),
"_c": Const(80053),
"Q": Mod(value=Mul(Ref("_c"), Ref("x")), modulus=Const(97268)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K13 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K13",
"K3"
] | 2 | 0.002 | 2026-02-08T15:21:05.358576Z | {
"verified": true,
"answer": 88737,
"timestamp": "2026-02-08T15:21:05.360740Z"
} | 5a574a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 96,
"completion_tokens": 2273
},
"timestamp": "2026-02-16T04:00:16.584Z",
"answer": 88737
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
c678d8 | antilemma_k2_v1_1439011603_766 | Compute the value of
$$
\sum_{k=1}^{332} \phi(k) \left\lfloor \frac{332}{k} \right\rfloor,
$$
where $\phi(k)$ denotes Euler's totient function. | 55,278 | graphs = [
Graph(
let={
"_n": Const(332),
"x": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(332), Var("k"))))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | antilemma_k2_v1 | null | 3 | 0 | [
"K2"
] | 1 | 0.001 | 2026-02-08T15:42:32.906318Z | {
"verified": true,
"answer": 55278,
"timestamp": "2026-02-08T15:42:32.907156Z"
} | 1b13d8 | 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": 492
},
"timestamp": "2026-02-16T12:37:23.184Z",
"answer": 55278
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8_SUM",
"status"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
7c7d9d | nt_count_coprime_and_v1_48377204_2103 | Let $A$ be the set of all even positive integers $n$ such that $1 \leq n \leq 2$. Let $m$ be the sum of all elements in $A$. Let $B$ be the set of all prime numbers $n_1$ such that $m \leq n_1 \leq 5$. Let $k$ be the maximum element of $B$. Compute the number of positive integers $n_2$ such that $1 \leq n_2 \leq 45725$... | 24,387 | graphs = [
Graph(
let={
"_n": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(2)), Eq(Mod(value=Var("n"), modulus=Const(2)), Const(0))))),
"upper": Const(45725),
"k1": Const(3),
"k2": MaxOverSet(set=Solution... | NT | null | COUNT | sympy | SUM_DIVISIBLE | [
"SUM_DIVISIBLE/MAX_PRIME_BELOW"
] | caf344 | nt_count_coprime_and_v1 | null | 5 | 0 | [
"MAX_PRIME_BELOW",
"SUM_DIVISIBLE"
] | 2 | 5.639 | 2026-02-08T16:35:59.376253Z | {
"verified": true,
"answer": 24387,
"timestamp": "2026-02-08T16:36:05.015479Z"
} | b89f0c | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 207,
"completion_tokens": 642
},
"timestamp": "2026-02-16T07:31:49.902Z",
"answer": 24387
},
{
"id": 11,
... | 2 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "SUM_DIVISIBLE",
"status": "ok"
},
{
"lemma": "V5",
"status"... | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
8d591a | comb_sum_binomial_row_v1_1918700295_4615 | Let $a_1 = 1$ and $b_1 = 2$. Define $n_2 = a_1 + b_1$. Let
$$
f = \sum_{k=0}^{n_2} (-1)^k \binom{n_2}{k}.
$$
Let $a = 4$ and $b = 4$. Define $n_1 = a + b$. Let
$$
w = \sum_{k=0}^{n_1} (-1)^k \binom{n_1}{k}.
$$
Let $n$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 26$.
Comp... | 8,192 | graphs = [
Graph(
let={
"a1": Const(1),
"b1": Const(2),
"n2": Sum(Ref("a1"), Ref("b1")),
"f": Summation(var="k", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n2"), k=Var("k")))),
"a": Const(4),
"b": Con... | COMB | null | SUM | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING",
"COMB1"
] | e741ba | comb_sum_binomial_row_v1 | null | 6 | 2 | [
"BINOMIAL_ALTERNATING",
"COMB1"
] | 2 | 0.002 | 2026-02-08T09:29:09.407778Z | {
"verified": true,
"answer": 8192,
"timestamp": "2026-02-08T09:29:09.409799Z"
} | 945a3b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 284,
"completion_tokens": 841
},
"timestamp": "2026-02-24T11:22:50.843Z",
"answer": 8192
},
{
"id... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma":... | {
"lo": -7.18,
"mid": -5,
"hi": -3.01
} | ||
17f7ea_l | nt_sum_divisors_range_v1_1742523217_142 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = 196$. Define $\alpha = \max\{xy \mid (x, y) \in S\}$. Let $T$ be the set of all positive integers $n$ such that $1 \leq n \leq \alpha$. For each $n \in T$, let $d(n)$ denote the number of positive divisors of $n$. Compute the sum o... | 0 | NT | null | SUM | sympy | B1 | [
"B1"
] | 5b950e | nt_sum_divisors_range_v1 | null | 6 | 0 | [
"B1"
] | 1 | 0.336 | 2026-02-08T02:53:36.752923Z | {
"verified": false,
"answer": 31965,
"timestamp": "2026-02-08T02:53:37.089066Z"
} | 057f10 | 17f7ea | legacy_text | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 256,
"completion_tokens": 32768
},
"timestamp": "2026-02-23T18:20:37.161Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
}
] | {
"lo": 3.7,
"mid": 5.49,
"hi": 7.55
} | |
41a7b3 | geo_visible_lattice_v1_784195855_1616 | Let $n = 64$. Define $L$ to be the number of ordered pairs $(x, y)$ of positive integers such that $1 \leq x, y \leq n$ and $\gcd(x, y) = 1$. Compute $|L|$. | 2,519 | graphs = [
Graph(
let={
"n": Const(64),
"result": VisibleLatticePoints(n=Ref(name='n')),
"Q": Abs(arg=Ref(name='result')),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 3 | 0 | null | null | 0.107 | 2026-02-08T05:10:23.144204Z | {
"verified": true,
"answer": 2519,
"timestamp": "2026-02-08T05:10:23.251161Z"
} | 680032 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 169,
"completion_tokens": 32768
},
"timestamp": "2026-02-24T02:56:58.222Z",
"answer": null
},
{
... | 1 | [] | {
"lo": 1.97,
"mid": 4.36,
"hi": 6.69
} | ||||
a2cda0 | antilemma_cartesian_v1_677425708_4289 | Let $x$ be the number of ordered pairs $(i, j)$ such that $1 \leq i \leq 6$ and $1 \leq j \leq 10$. Compute the remainder when $70453 \cdot x$ is divided by 92772. | 52,440 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(6)), right=IntegerRange(start=Const(1), end=Const(10)))),
"Q": Mod(value=Mul(Const(70453), Ref("x")), modulus=Const(92772)),
},
goal=Ref("Q"),
)
] | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | antilemma_cartesian_v1 | null | 2 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0 | 2026-02-08T06:31:54.469351Z | {
"verified": true,
"answer": 52440,
"timestamp": "2026-02-08T06:31:54.469821Z"
} | f9b08e | 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": 852
},
"timestamp": "2026-02-24T06:28:06.255Z",
"answer": 52440
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.84,
"mid": -1.69,
"hi": 1.09
} | ||
424212 | nt_count_coprime_and_v1_153355830_1723 | Let $S$ be the set of all integers $n$ such that $1 \le n \le 23056$ and
\[n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{11}.
\]
Let $K$ be the number of elements of $S$.
Let $k_1$ be the number of integers $j$ with $0 \le j \le 2096$ for which the binomial coefficient $\binom{K}{j}$ is odd. Let $k_2 = 15$.
L... | 25,596 | graphs = [
Graph(
let={
"upper": Const(57903),
"k1": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(2096)), Eq(Mod(value=Binom(n=CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Co... | NT | null | COUNT | sympy | L3C | [
"L3C/V8"
] | 2a9f26 | nt_count_coprime_and_v1 | null | 8 | 0 | [
"L3C",
"V8"
] | 2 | 7.464 | 2026-02-08T06:35:17.083535Z | {
"verified": true,
"answer": 25596,
"timestamp": "2026-02-08T06:35:24.547111Z"
} | c9f288 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 249,
"completion_tokens": 3419
},
"timestamp": "2026-02-13T02:30:38.217Z",
"answer": 25596
},
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"le... | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
edbe7f | diophantine_sum_product_min_v1_655260480_3847 | Let $S = 24$. Let $P$ be the number of integers $t$ such that $8 \le t \le 155$ and there exist positive integers $a$ and $b$ with $1 \le a \le 7$, $1 \le b \le 40$, and $t = 5a + 3b$. Let $d_{\text{min}}$ be the smallest divisor of $667$ that is at least $2$. Find the smallest positive integer $x$ such that $1 \le x \... | 1,901 | graphs = [
Graph(
let={
"_n": Const(59747),
"S": Const(24),
"P": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=... | NT | null | EXTREMUM | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR",
"LIN_FORM"
] | 41af5a | diophantine_sum_product_min_v1 | null | 6 | 0 | [
"LIN_FORM",
"MIN_PRIME_FACTOR"
] | 2 | 0.007 | 2026-02-08T17:34:38.920685Z | {
"verified": true,
"answer": 1901,
"timestamp": "2026-02-08T17:34:38.928159Z"
} | 7d452f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 216,
"completion_tokens": 4448
},
"timestamp": "2026-02-18T04:17:03.422Z",
"answer": 1901
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
672a6c | nt_sum_divisors_mod_v1_151522320_870 | Let $n$ be the number of ordered pairs of positive odd integers $(x_1, x_2)$ such that $x_1 + x_2 = 15120$. Let $\sigma$ be the sum of all positive divisors of $n$. Find the remainder when $\sigma$ is divided by $11839$. | 5,122 | graphs = [
Graph(
let={
"_n": Const(15120),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2")),... | NT | null | COMPUTE | sympy | COMB1 | [
"COMB1"
] | 567f58 | nt_sum_divisors_mod_v1 | null | 5 | 0 | [
"COMB1"
] | 1 | 0.002 | 2026-02-08T03:37:04.628824Z | {
"verified": true,
"answer": 5122,
"timestamp": "2026-02-08T03:37:04.630476Z"
} | 6a5a06 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 178,
"completion_tokens": 1575
},
"timestamp": "2026-02-10T15:12:16.366Z",
"answer": 5122
},
{
"i... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V5",
"status": "no... | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
71207d | comb_count_partitions_v1_1978505735_3560 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 484$. Define $n$ to be the minimum value of $x + y$ as $(x, y)$ ranges over $S$. Let $p(n)$ denote the number of integer partitions of $n$. Compute the remainder when $45106 \cdot p(n)$ is divided by $88601$. | 83,280 | graphs = [
Graph(
let={
"_n": Const(484),
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_n")))), expr=Sum(Var("x"), Var("y")))),
... | COMB | null | COUNT | sympy | COPRIME_PAIRS | [
"B3"
] | 0cd20d | comb_count_partitions_v1 | null | 4 | 0 | [
"B3",
"COPRIME_PAIRS"
] | 2 | 0.024 | 2026-02-08T17:43:04.900238Z | {
"verified": true,
"answer": 83280,
"timestamp": "2026-02-08T17:43:04.923758Z"
} | 1d81de | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 134,
"completion_tokens": 2414
},
"timestamp": "2026-02-18T07:24:08.961Z",
"answer": 83280
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V8",
"status": ... | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||
da390c | nt_sum_over_divisible_v1_898971024_1000 | Let $T$ be the set of all integers $t$ with $20 \leq t \leq 8223$ for which there exist positive integers $a \leq 1133$ and $b \leq 736$ such that $t = 4a + 5b + 11$. Let $N$ be the number of elements in $T$. Compute the remainder when $$
74223 \cdot \left( \sum_{\substack{n=1 \\ 34 \mid n}}^{N} n \right)
$$
is divided... | 18,792 | graphs = [
Graph(
let={
"_n": Const(74223),
"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=1133)), Geq(... | NT | null | SUM | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_sum_over_divisible_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.354 | 2026-02-08T15:49:44.893061Z | {
"verified": true,
"answer": 18792,
"timestamp": "2026-02-08T15:49:45.246935Z"
} | 4884a8 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 164,
"completion_tokens": 4795
},
"timestamp": "2026-02-16T15:52:09.468Z",
"answer": 18792
},
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
f29331 | antilemma_k3_v1_1520064083_6110 | Compute the sum of $\varphi(d)$ over all positive divisors $d$ of $90776$, where $\varphi$ denotes Euler's totient function. | 90,776 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=90776), 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 | 2026-02-08T07:52:37.151360Z | {
"verified": true,
"answer": 90776,
"timestamp": "2026-02-08T07:52:37.152020Z"
} | cd72f5 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 77,
"completion_tokens": 730
},
"timestamp": "2026-02-13T13:05:10.502Z",
"answer": 90776
},
{
... | 1 | [
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
c2fd19 | modular_sum_quadratic_residues_v1_717093673_827 | Let $p$ be the number of integers $t$ such that $9 \leq t \leq 177$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 28$, $1 \leq b \leq 13$, and $t = 4a + 5b$. Compute $\frac{p(p-1)}{4}$. | 6,123 | graphs = [
Graph(
let={
"_n": Const(4),
"p": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=28)), Geq(left=Var(n... | NT | null | SUM | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | modular_sum_quadratic_residues_v1 | null | 3 | 0 | [
"LIN_FORM"
] | 1 | 0.003 | 2026-02-08T15:42:16.615234Z | {
"verified": true,
"answer": 6123,
"timestamp": "2026-02-08T15:42:16.618277Z"
} | 6ee724 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 126,
"completion_tokens": 3705
},
"timestamp": "2026-02-16T11:48:45.415Z",
"answer": 6123
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
660160 | nt_count_coprime_v1_1742523217_5320 | Let $S$ be the set of all positive integers $n$ such that $1 \leq n \leq 16384$ and $\gcd(n, 38) = 1$. Let $r$ be the number of elements in $S$. Let $p$ be the largest prime number less than or equal to 2004. Compute the remainder when
$$
(r \bmod 307) + p \cdot (r \bmod 317)
$$
is divided by 97919. | 12,788 | graphs = [
Graph(
let={
"_n": Const(97919),
"upper": Const(16384),
"k": Const(38),
"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))))),
... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | 08a653 | nt_count_coprime_v1 | two_moduli | 5 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 1.708 | 2026-02-08T10:54:59.786571Z | {
"verified": true,
"answer": 12788,
"timestamp": "2026-02-08T10:55:01.494820Z"
} | 7631c0 | 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": 1210
},
"timestamp": "2026-02-14T09:15:27.029Z",
"answer": 12788
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V3"... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
f036bd | modular_sum_quadratic_residues_v1_717093673_3101 | Let $p$ be the number of ordered pairs $(i,j)$ with $1 \leq i \leq 5$ and $1 \leq j \leq 121$ such that $\gcd(i,j) = 1$. Compute $\frac{p(p-1)}{4}$. | 44,205 | graphs = [
Graph(
let={
"_n": Const(4),
"p": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(GCD(a=Var("i"), b=Var("j")), Const(1)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(5)), right=IntegerRange(start=Const(1), end=Co... | NT | null | SUM | sympy | COUNT_COPRIME_GRID | [
"COUNT_COPRIME_GRID"
] | 20ec03 | modular_sum_quadratic_residues_v1 | null | 3 | 0 | [
"COUNT_COPRIME_GRID"
] | 1 | 0.001 | 2026-02-08T17:22:32.287764Z | {
"verified": true,
"answer": 44205,
"timestamp": "2026-02-08T17:22:32.289142Z"
} | 5f0dcf | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 104,
"completion_tokens": 913
},
"timestamp": "2026-02-18T01:16:42.484Z",
"answer": 44205
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
6e10a3 | geo_count_lattice_rect_v1_151522320_2071 | Let $a = 144$ and $b = 458$. Compute the number of lattice points in the rectangle $[0, a] \times [0, b]$ including the boundaries. | 66,555 | graphs = [
Graph(
let={
"a": Const(144),
"b": Const(458),
"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 | 0.003 | 2026-02-08T04:34:10.078678Z | {
"verified": true,
"answer": 66555,
"timestamp": "2026-02-08T04:34:10.081435Z"
} | 55eaae | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 151,
"completion_tokens": 400
},
"timestamp": "2026-02-24T01:04:56.151Z",
"answer": 66555
},
{
"i... | 1 | [] | {
"lo": -3.83,
"mid": -1.68,
"hi": 1.09
} | ||||
311ce2 | geo_count_lattice_rect_v1_809748730_894 | Compute the number of lattice points in the rectangle $[0, 180] \times [0, 54]$, including the boundary. | 9,955 | graphs = [
Graph(
let={
"a": Const(180),
"b": Const(54),
"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 | 0.004 | 2026-02-08T11:48:01.483745Z | {
"verified": true,
"answer": 9955,
"timestamp": "2026-02-08T11:48:01.488239Z"
} | 62e676 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 139,
"completion_tokens": 160
},
"timestamp": "2026-02-24T14:47:36.982Z",
"answer": 9955
},
{
"id... | 1 | [] | {
"lo": -7.18,
"mid": -5,
"hi": -3.01
} | ||||
e9060d | lin_form_endings_v1_1742523217_1953 | Let $a = 84$ and $b = 60$. Let $\ell$ be the least common multiple of $a$ and $b$. Define $s = 1 \cdot \ell + a + b$. Let $t$ be the remainder when $10321 \cdot s$ is divided by 76896. Compute $t$. | 53,844 | graphs = [
Graph(
let={
"a_coeff": Const(84),
"b_coeff": Const(60),
"k_val": Const(1),
"lcm_node": LCM(a=Ref("a_coeff"), b=Ref("b_coeff")),
"_inner_result": Sum(Mul(Ref("k_val"), Ref("lcm_node")), Ref("a_coeff"), Ref("b_coeff")),
"_scal... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 2 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T04:21:54.186443Z | {
"verified": true,
"answer": 53844,
"timestamp": "2026-02-08T04:21:54.187001Z"
} | 448e9d | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 184,
"completion_tokens": 624
},
"timestamp": "2026-02-10T16:24:49.886Z",
"answer": 53844
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
896c8b | comb_count_derangements_v1_1218484723_3544 | Let $D_n$ denote the number of derangements of $n$ elements and $B_n$ the $n$-th Bell number. Let $N = D_7$. Let $S = \{ t : \text{there exist integers } a, b \text{ with } 1 \leq a \leq 3, 1 \leq b \leq 4 \text{ such that } t = 6a + 4b + 2,\ 12 \leq t \leq 36 \}$. Compute $B_{N \bmod |S|}$. | 203 | graphs = [
Graph(
let={
"n": Const(7),
"result": Subfactorial(arg=Ref(name='n')),
"Q": Bell(Mod(value=Abs(arg=Ref(name='result')), modulus=CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 1ae498 | comb_count_derangements_v1 | bell_mod | 4 | 0 | [
"LIN_FORM"
] | 1 | 2.24 | 2026-02-25T05:10:48.534979Z | {
"verified": true,
"answer": 203,
"timestamp": "2026-02-25T05:10:50.775110Z"
} | 4a2513 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 240,
"completion_tokens": 1359
},
"timestamp": "2026-03-29T10:51:21.740Z",
"answer": 203
},
{
"id... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"st... | {
"lo": -10,
"mid": -6.41,
"hi": -2.82
} | ||
e466da | antilemma_k3_v1_2051736721_1791 | Let $x$ be the sum of $\phi(d)$ over all positive divisors $d$ of $79405$, where $\phi$ denotes Euler's totient function. Find the remainder when $39385x$ is divided by $69688$. | 47,237 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=79405), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Mod(value=Mul(Const(39385), Ref("x")), modulus=Const(69688)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0.002 | 2026-02-08T16:12:44.310824Z | {
"verified": true,
"answer": 47237,
"timestamp": "2026-02-08T16:12:44.313118Z"
} | 25d6f3 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 97,
"completion_tokens": 2927
},
"timestamp": "2026-02-17T00:12:22.221Z",
"answer": 47237
},
{... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
303377 | nt_count_digit_sum_v1_458359167_3244 | Let $S$ be the set of all positive integers $n$ such that $1 \leq n \leq 72900$ and the sum of the decimal digits of $n$ is $24$. Let $c$ be the number of elements in $S$. Now, let $T$ be the set of all integers $t$ such that $5 \leq t \leq 17$ and there exist positive integers $a \leq 4$, $b \leq 3$ satisfying $t = 2a... | 4,140 | graphs = [
Graph(
let={
"upper": Const(72900),
"target_sum": Const(24),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(DigitSum(Var("n")), Ref("target_sum"))))),
"Q": Bell(Mod(value=... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 1ae498 | nt_count_digit_sum_v1 | bell_mod | 6 | 0 | [
"LIN_FORM"
] | 1 | 2.552 | 2026-02-08T08:14:30.901865Z | {
"verified": true,
"answer": 4140,
"timestamp": "2026-02-08T08:14:33.454299Z"
} | f0e9c6 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 269,
"completion_tokens": 21459
},
"timestamp": "2026-02-24T09:09:24.918Z",
"answer": 1
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"sta... | {
"lo": 3.25,
"mid": 5.68,
"hi": 8.81
} | ||
092c61 | antilemma_sum_factor_cartesian_v1_151522320_99 | Let $n = 98675$. Let $S$ be the set of all ordered pairs $(i, j)$ with $1 \le i \le 8$ and $1 \le j \le 26$ such that
$$
\sum_{d \mid \gcd\left(\max\left\{k : 3^k \mid (4^9 - 1^9)\right\}, 5\right)} \mu(d)
$$
is nonzero. Let $x$ be the sum of $i \cdot j$ over all pairs $(i, j)$ in $S$. Let $c = 61747$ and define $Q = (... | 11,867 | graphs = [
Graph(
let={
"_n": Const(98675),
"x": SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=SumOverDivisors(n=GCD(a=MaxKDivides(target=Sub(left=Pow(base=Const(value=4), exp=Const(value=9)), right=Pow(base=Const(value=1), exp=Const(v... | NT | null | COMPUTE | sympy | LTE_DIFF | [
"LTE_DIFF/MOBIUS_COPRIME/SUM_FACTOR_CARTESIAN",
"SUM_FACTOR_CARTESIAN"
] | fd51ee | antilemma_sum_factor_cartesian_v1 | null | 6 | 0 | [
"LTE_DIFF",
"MOBIUS_COPRIME",
"SUM_FACTOR_CARTESIAN"
] | 3 | 0.002 | 2026-02-08T02:58:16.481070Z | {
"verified": true,
"answer": 11867,
"timestamp": "2026-02-08T02:58:16.483288Z"
} | 5cd221 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 274,
"completion_tokens": 1639
},
"timestamp": "2026-02-08T23:01:56.398Z",
"answer": 11867
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "ok"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok_later"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD... | {
"lo": 3.31,
"mid": 6.77,
"hi": 10
} | ||
21904f | diophantine_sum_product_min_v1_784195855_6498 | Let $S = 65$ and $P = 1050$. Let $A$ be the set of all positive integers $x$ and $y$ such that $xy = 1024$, and let $m$ be the minimum value of $x + y$ over all pairs $(x, y) \in A$. Find the smallest positive integer $x$ such that $1 \leq x \leq m$ and $x(S - x) = P$. Compute the remainder when $39257$ times this valu... | 69,378 | graphs = [
Graph(
let={
"_n": Const(92361),
"S": Const(65),
"P": Const(1050),
"result": MinOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), Const(1)), Leq(Var("x"), MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var(... | NT | null | EXTREMUM | sympy | B3 | [
"B3"
] | 0cd20d | diophantine_sum_product_min_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.011 | 2026-02-08T08:42:05.818264Z | {
"verified": true,
"answer": 69378,
"timestamp": "2026-02-08T08:42:05.829130Z"
} | b05698 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 163,
"completion_tokens": 1127
},
"timestamp": "2026-02-13T20:35:05.808Z",
"answer": 69378
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
377178 | diophantine_fbi2_count_v1_1440796553_1312 | Let $k = 480$. Determine the number of integers $d$ such that $2 \leq d \leq 67$, $d$ divides $k$, and $2 \leq \frac{k}{d} \leq 67$. | 12 | graphs = [
Graph(
let={
"k": Const(480),
"a": Const(1),
"b": Const(1),
"upper": Const(66),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Leq(Var("d"), Const(67)), Divides(divisor=Var("d"), dividend=Ref... | NT | null | COUNT | sympy | B3 | [
"MAX_PRIME_BELOW",
"MAX_DIVISOR"
] | beffb0 | diophantine_fbi2_count_v1 | null | 3 | 0 | [
"B3",
"MAX_DIVISOR",
"MAX_PRIME_BELOW"
] | 3 | 0.268 | 2026-02-08T13:38:33.801950Z | {
"verified": true,
"answer": 12,
"timestamp": "2026-02-08T13:38:34.070404Z"
} | dc457c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 97,
"completion_tokens": 1675
},
"timestamp": "2026-02-15T19:27:34.178Z",
"answer": 12
},
{
... | 1 | [
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
713dfb | nt_count_with_divisor_count_v1_548369836_356 | Let $A$ be the number of positive integers $n$ such that $1 \leq n \leq 55696$ and $n$ has exactly 15 positive divisors. Let
$$
C = \sum_{k=1}^{139} \phi(k) \left\lfloor \frac{139}{k} \right\rfloor,
$$
where $\phi$ denotes Euler's totient function. Compute $A^2 + 17A + C$. | 11,140 | graphs = [
Graph(
let={
"upper": Const(55696),
"div_count": Const(15),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(NumDivisors(n=Var("n")), Ref("div_count"))))),
"_c": Summation(v... | NT | null | COUNT | sympy | K2 | [
"K2"
] | 598070 | nt_count_with_divisor_count_v1 | quadratic_mod | 6 | 0 | [
"K2"
] | 1 | 2.295 | 2026-02-08T02:52:59.649532Z | {
"verified": true,
"answer": 11140,
"timestamp": "2026-02-08T02:53:01.944927Z"
} | f91ed7 | 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": 2021
},
"timestamp": "2026-02-08T20:22:38.053Z",
"answer": 11140
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": 1.16,
"mid": 3.17,
"hi": 4.94
} | ||
34e2f3 | comb_factorial_compute_v1_124444284_6165 | Let $n$ be the smallest divisor of $77077$ that is at least $2$. Compute the remainder when $44121 \cdot n!$ is divided by $80833$. | 79,090 | graphs = [
Graph(
let={
"_n": Const(44121),
"n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(77077))))),
"result": Factorial(Ref("n")),
"Q": Mod(value=Mul(Ref("_n"), Ref("result")), ... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | comb_factorial_compute_v1 | null | 5 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.001 | 2026-02-08T08:10:43.941405Z | {
"verified": true,
"answer": 79090,
"timestamp": "2026-02-08T08:10:43.942115Z"
} | 6609c5 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 86,
"completion_tokens": 1375
},
"timestamp": "2026-02-13T15:30:18.379Z",
"answer": 79090
},
{... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
958ec6 | nt_sum_divisors_compute_v1_1918700295_2088 | Let $n = 27889$. Compute the sum of all positive divisors of $n$. | 28,057 | graphs = [
Graph(
let={
"n": Const(27889),
"result": SumDivisors(n=Ref("n")),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE/OMEGA_ZERO/BIG_OMEGA_ONE"
] | fe5d12 | nt_sum_divisors_compute_v1 | null | 2 | 0 | [
"BIG_OMEGA_ONE",
"COUNT_FIB_DIVISIBLE",
"OMEGA_ZERO"
] | 3 | 0.004 | 2026-02-08T07:40:57.496508Z | {
"verified": true,
"answer": 28057,
"timestamp": "2026-02-08T07:40:57.500931Z"
} | 3dec0f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 66,
"completion_tokens": 328
},
"timestamp": "2026-02-13T11:52:02.123Z",
"answer": 28057
},
{
... | 1 | [
{
"lemma": "BIG_OMEGA_ONE",
"status": "ok_later"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"s... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
402ffa | comb_binomial_compute_v1_48377204_1811 | Let $n = 15$. Consider the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 16$. Let $k$ be the minimum value of $x + y$ over all such pairs. Compute $\binom{n}{k}$. | 6,435 | graphs = [
Graph(
let={
"_n": Const(16),
"n": Const(15),
"k": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_n")))), expr=Su... | ALG | COMB | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | comb_binomial_compute_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.001 | 2026-02-08T16:26:23.977043Z | {
"verified": true,
"answer": 6435,
"timestamp": "2026-02-08T16:26:23.978509Z"
} | 7bbc9a | 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": 905
},
"timestamp": "2026-02-24T20:54:20.946Z",
"answer": 6435
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -8.52,
"mid": -5.43,
"hi": -3.2
} | ||
5f6347 | modular_mod_compute_v1_601307018_10523 | Let $T$ be the number of ordered pairs $(a_2, b_1)$ of positive integers with $1 \le a_2, b_1 \le 25$ such that $17a_2^2 + 34a_2b_1 + 17b_1^2 = 9792$. Let $m = \min\{10a_1^2 - 32a_1b + 32b^2 : 1 \le a_1 \le T,\, 1 \le b \le 23\}$. Let $a$ be the maximum value of $xy$ over all positive integers $x, y$ with $x + y = m$. ... | 44,594 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(2),
"a": 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")), MinOverSet(set=MapOver... | NT | null | COMPUTE | sympy | QF_PSD_COUNT | [
"QF_PSD_COUNT/QF_PSD_MIN/B1"
] | 7a1c2a | modular_mod_compute_v1 | null | 7 | 0 | [
"B1",
"QF_PSD_COUNT",
"QF_PSD_MIN"
] | 3 | 0.006 | 2026-03-10T10:58:27.380339Z | {
"verified": true,
"answer": 44594,
"timestamp": "2026-03-10T10:58:27.386625Z"
} | 508b78 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 289,
"completion_tokens": 2263
},
"timestamp": "2026-04-19T14:06:22.561Z",
"answer": 44594
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT",
"status": "ok"
},... | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
046973 | algebra_poly_eval_v1_124444284_750 | Let $x$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq = 92610$, $\gcd(p, q) = 1$, and $p < q$. Define $r = x^2 + 10x - 1$. Compute the remainder when $53837 \cdot r$ is divided by $94734$. | 25,237 | graphs = [
Graph(
let={
"_n": Const(10),
"x": 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=92610)), Eq(left=GCD(a=Var(name='p'), b=Var(name... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | algebra_poly_eval_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.002 | 2026-02-08T03:29:38.035019Z | {
"verified": true,
"answer": 25237,
"timestamp": "2026-02-08T03:29:38.037034Z"
} | cfe52a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 193,
"completion_tokens": 2285
},
"timestamp": "2026-02-09T21:31:24.312Z",
"answer": 25237
},
{
"... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
... | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
e1c8c6 | comb_count_derangements_v1_1520064083_5671 | Let $T$ be the set of all integers $t$ such that $7 \leq t \leq 16$ and there exist integers $a$ and $b$ with $1 \leq a \leq 2$, $1 \leq b \leq 4$, and $t = 3a + 2b + 2$. Let $n$ be the number of elements in $T$. Compute the subfactorial $!n$, which is the number of derangements of $n$ elements. | 14,833 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=2)), Geq(left=Var(name='b'), right=Const(value=1... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_count_derangements_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T07:32:44.380283Z | {
"verified": true,
"answer": 14833,
"timestamp": "2026-02-08T07:32:44.381409Z"
} | f8acf8 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 223,
"completion_tokens": 1284
},
"timestamp": "2026-02-24T08:09:05.776Z",
"answer": 14833
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"st... | {
"lo": -4.92,
"mid": -2.91,
"hi": -0.68
} | ||
d7e765_n | comb_bell_compute_v1_1218484723_4670 | A bakery prepares special gift boxes. Each box contains $a$ chocolate cakes ($a = 1$ or $2$) and $b$ vanilla cupcakes ($b = 1, 2, 3,$ or $4$). The total delight score of a box is calculated as $6a + 4b + 3$. Only boxes with scores between $13$ and $31$ inclusive are offered for sale. The manager wants to group the dist... | 4,140 | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_bell_compute_v1 | null | 2 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-25T06:21:13.794264Z | null | a5bfc0 | d7e765 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 235,
"completion_tokens": 965
},
"timestamp": "2026-03-30T22:05:53.008Z",
"answer": 4140
},
{
"id... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"statu... | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | |
d964cf | nt_sum_totient_over_divisors_v1_717093673_2466 | Let $n$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 1628176$. Compute the sum of $\phi(d)$ over all positive divisors $d$ of $n$. | 2,552 | graphs = [
Graph(
let={
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(1628176)))), expr=Sum(Var("x"), Var("y")))),
"result": SumOv... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_totient_over_divisors_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.016 | 2026-02-08T16:52:04.010206Z | {
"verified": true,
"answer": 2552,
"timestamp": "2026-02-08T16:52:04.026035Z"
} | 49683b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 102,
"completion_tokens": 1599
},
"timestamp": "2026-02-17T14:56:16.606Z",
"answer": 2552
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
4b2884 | comb_sum_binomial_row_v1_865884756_6068 | Let $p$ be a positive integer. Define $S$ to be the number of ordered pairs $(p, q)$ of positive integers such that $pq = 54$, $\gcd(p, q) = 1$, and $p < q$. Let $N = S^{11}$.
Compute the smallest positive integer $k$ such that the $k$-th Fibonacci number is divisible by $N + 2$. | 300 | graphs = [
Graph(
let={
"n": Const(11),
"result": Pow(CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=54)), Eq(left=GCD(a=Var(name='p'), b=Var... | NT | null | SUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_sum_binomial_row_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.002 | 2026-02-08T18:56:48.053433Z | {
"verified": true,
"answer": 300,
"timestamp": "2026-02-08T18:56:48.054993Z"
} | 760601 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 134,
"completion_tokens": 2623
},
"timestamp": "2026-02-18T20:40:00.891Z",
"answer": 300
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_ADD",
"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
eade3e | diophantine_product_count_v1_865884756_3995 | Let $k=60$ and $U=31$. Let $r$ be the number of integers $x$ such that $1\le x\le U$, $x$ divides $k$, and $\dfrac{k}{x}\le U$.
Let $B_n$ denote the $n$th Bell number, the number of partitions of a set with $n$ elements. Let
$$Q\equiv B_{\,|r|\bmod 11} \pmod{88036},$$
with $0\le Q<88036$.
Find the value of $Q$. | 27,939 | graphs = [
Graph(
let={
"k": Const(60),
"upper": Const(31),
"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 | COMB | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW/LIN_FORM",
"COUNT_SUM_EQUALS"
] | 29684e | diophantine_product_count_v1 | bell_mod | 4 | 0 | [
"COUNT_SUM_EQUALS",
"LIN_FORM",
"MAX_PRIME_BELOW"
] | 3 | 0.085 | 2026-02-08T17:41:16.416212Z | {
"verified": true,
"answer": 27939,
"timestamp": "2026-02-08T17:41:16.501646Z"
} | 43f668 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 168,
"completion_tokens": 4100
},
"timestamp": "2026-02-18T06:40:09.463Z",
"answer": 27939
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
79fabc | antilemma_k3_v1_124444284_6367 | Let $ n = 85314 $. Define $ x = \sum_{d \mid n} \phi(d) $, where $ \phi $ denotes Euler's totient function. Compute $ x $. | 85,314 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=85314), var='d', expr=EulerPhi(n=Var(name='d'))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0 | 2026-02-08T08:18:44.934451Z | {
"verified": true,
"answer": 85314,
"timestamp": "2026-02-08T08:18:44.934748Z"
} | 58dcf5 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 102,
"completion_tokens": 629
},
"timestamp": "2026-02-15T20:12:34.826Z",
"answer": 85314
},
{
"id": 11,
... | 2 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}... | {
"lo": -9.14,
"mid": -6.05,
"hi": -3.73
} | ||
d58a85 | modular_mod_compute_v1_2051736721_3380 | Let $a = 74529$. Let $m$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 16777216$. Compute the remainder when $a$ is divided by $m$. | 801 | graphs = [
Graph(
let={
"a": Const(74529),
"m": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(16777216)))), expr=Sum(Var("x"), Var("y")... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | modular_mod_compute_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.007 | 2026-02-08T17:17:12.555487Z | {
"verified": true,
"answer": 801,
"timestamp": "2026-02-08T17:17:12.562085Z"
} | a000f0 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 104,
"completion_tokens": 970
},
"timestamp": "2026-02-17T22:55:18.923Z",
"answer": 801
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
4f9bb0 | modular_sum_quadratic_residues_v1_798873815_104 | Let $p$ be the largest prime number satisfying $2 \leq p \leq 261$. Compute $\frac{p(p-1)}{4}$. | 16,448 | graphs = [
Graph(
let={
"_n": Const(2),
"p": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Const(261)), IsPrime(Var("n"))))),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), Const(4)),
"Q": Ref("result"),... | NT | null | SUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | modular_sum_quadratic_residues_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.001 | 2026-02-08T02:26:11.367060Z | {
"verified": true,
"answer": 16448,
"timestamp": "2026-02-08T02:26:11.368193Z"
} | 1333f2 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 149,
"completion_tokens": 230
},
"timestamp": "2026-02-08T19:00:01.185Z",
"answer": 16448
},
{
"i... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
... | {
"lo": -4.71,
"mid": -2.86,
"hi": -0.92
} | ||
9d3ef8 | alg_poly4_min_v1_601307018_6039 | Let $M$ be the largest positive divisor $d$ of $78481877$ such that $d^2 \le 78481877$. Find the minimum value of
$$
M \cdot a^4 - 8336a^3b + 50016a^2b^2 - 133376ab^3 + 133376b^4
$$
over all ordered pairs $(a, b)$ of positive integers with $1 \le a \le 448$ and $1 \le b \le \min\{x + y : x, y > 0,\, xy = 50176,\, x \l... | 50,537 | graphs = [
Graph(
let={
"_m": Const(50016),
"_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(448)), Geq(Var("b"), Const(1)), Leq(Var("b"), MinOverSet(s... | NT | null | COMPUTE | sympy | B3_CLOSEST | [
"B3_CLOSEST",
"B3"
] | a6b579 | alg_poly4_min_v1 | null | 6 | 0 | [
"B3",
"B3_CLOSEST"
] | 2 | 0.539 | 2026-03-10T06:37:44.459739Z | {
"verified": true,
"answer": 50537,
"timestamp": "2026-03-10T06:37:44.999040Z"
} | 629087 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 252,
"completion_tokens": 25700
},
"timestamp": "2026-04-19T03:31:09.641Z",
"answer": -20646689599488... | 0 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "B3_CLOSEST",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_ADD... | {
"lo": 2.1,
"mid": 5.36,
"hi": 8.63
} | ||
2cc7eb | nt_min_coprime_above_v1_1918700295_3229 | Let $\phi_n$ denote Euler's totient function. Define $m$ to be the number of positive integers $n \leq 1823$ such that $\gcd(n, 30) = 1$. Find the smallest integer $n > 11025$ such that $n \leq 11522$ and $\gcd(n, m) = 1$. | 11,026 | graphs = [
Graph(
let={
"_n": Const(30),
"start": Const(11025),
"upper": Const(11522),
"modulus": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(1823)), Eq(GCD(a=Var("n"), b=Ref("_n")), Const(1))))),
... | NT | null | EXTREMUM | sympy | C4 | [
"C4"
] | 08d162 | nt_min_coprime_above_v1 | null | 4 | 0 | [
"C4"
] | 1 | 0.04 | 2026-02-08T08:27:49.396206Z | {
"verified": true,
"answer": 11026,
"timestamp": "2026-02-08T08:27:49.436221Z"
} | 615cb3 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 122,
"completion_tokens": 1566
},
"timestamp": "2026-02-13T19:09:00.088Z",
"answer": 11026
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
f04f6e | sequence_lucas_compute_v1_784195855_1664 | Let $n$ be the number of integers $t$ such that $5 \leq t \leq 25$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 5$, $1 \leq b \leq 5$, and $t = 2a + 3b$. Compute the value of the $n$-th Lucas number. | 9,349 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=5)), Geq(left=Var(name='b'), right=Const(value=1... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | sequence_lucas_compute_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T05:12:13.333616Z | {
"verified": true,
"answer": 9349,
"timestamp": "2026-02-08T05:12:13.335844Z"
} | 8c5023 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 198,
"completion_tokens": 1820
},
"timestamp": "2026-02-11T23:03:29.106Z",
"answer": 9349
},
{
"... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
b03189_l | nt_sum_divisors_range_v1_151522320_51 | Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 17909824$. Let $T$ be the set of all values $x + y$ for $(x,y) \in S$. Let $m$ be the minimum value in $T$. Define $f(n)$ to be the number of positive divisors of $n$. Compute the sum of $f(n)$ for all positive integers $n$ from $1$ to... | 77,862 | NT | null | SUM | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_divisors_range_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.717 | 2026-02-08T02:56:17.453859Z | {
"verified": false,
"answer": 77864,
"timestamp": "2026-02-08T02:56:18.171047Z"
} | 41f195 | b03189 | 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": 216,
"completion_tokens": 10425
},
"timestamp": "2026-02-23T19:59:30.136Z",
"answer": 77860
},
{
... | 0 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
... | {
"lo": 5.41,
"mid": 7.53,
"hi": 10
} | |
f2a55c | comb_binomial_compute_v1_1742523217_3320 | Let $n$ be the number of integers $t$ such that $11 \leq t \leq 25$ and there exist integers $a$ and $b$ with $1 \leq a \leq 3$, $1 \leq b \leq 5$, and $t = 3a + 2b + 6$. Let $k = \sum_{k=1}^{3} \phi(k) \left\lfloor \frac{3}{k} \right\rfloor$, where $\phi$ denotes Euler's totient function. Compute $\binom{n}{k}$. Let $... | 1 | graphs = [
Graph(
let={
"_n": Const(11),
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=3)), Geq(left=Var(n... | NT | COMB | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM",
"K2"
] | b46b5e | comb_binomial_compute_v1 | null | 6 | 0 | [
"K2",
"LIN_FORM"
] | 2 | 0.002 | 2026-02-08T05:46:42.822753Z | {
"verified": true,
"answer": 1,
"timestamp": "2026-02-08T05:46:42.824823Z"
} | a157b4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 201,
"completion_tokens": 1643
},
"timestamp": "2026-02-12T14:51:30.920Z",
"answer": 1
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} |
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