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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
8f89db | nt_count_digit_sum_v1_1978505735_3179 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 81$. Define $s$ to be the minimum value of $x + y$ over all such pairs. Let $N$ be the number of positive integers $n$ such that $1 \leq n \leq 99999$ and the sum of the decimal digits of $n$ is equal to $s$. Compute $$\sum_{k=1}^{N} ... | 41,827 | graphs = [
Graph(
let={
"_n": Const(81),
"upper": Const(99999),
"target_sum": 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("... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | nt_count_digit_sum_v1 | null | 5 | 0 | [
"B3"
] | 1 | 3.519 | 2026-02-08T17:26:50.767570Z | {
"verified": true,
"answer": 41827,
"timestamp": "2026-02-08T17:26:54.286752Z"
} | 03a598 | 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": 5082
},
"timestamp": "2026-02-18T02:16:05.729Z",
"answer": 41827
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "LTE_SUM",
"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
} | ||
66d801 | alg_poly_orbit_hensel_v1_1218484723_4141 | For a non-negative integer $a$, define $N = (2a^3 + a) \bmod 2197$ and $M = (2N^3 + N) \bmod 2197$. Find the number of integers $a$ with $0 \le a \le 1278653$ such that $M = a$ and $N \ne a$. | 1,164 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Mul(Const(2), Pow(Var("a"), Const(3))), Var("a")), modulus=Const(2197)),
"p2": Mod(value=Sum(Mul(Const(2), Pow(Ref("p1"), Const(3))), Ref("p1")), modulus=Const(2197)),
"result": CountOverSet(set=SolutionsSet(var=Var("a"), condit... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_orbit_hensel_v1 | null | 6 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.021 | 2026-02-25T05:48:49.366768Z | {
"verified": true,
"answer": 1164,
"timestamp": "2026-02-25T05:48:49.387977Z"
} | 57dd44 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 191,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T14:03:32.760Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 1.55,
"mid": 4.7,
"hi": 7.23
} | ||
1c7abf | nt_count_digit_sum_v1_1520064083_607 | Let $n = 68681$. Let $d_{\min}$ be the smallest integer $d \geq 2$ that divides $143143$. Define $t = \sum_{k=1}^{d_{\min}} \varphi(k) \cdot \left\lfloor \frac{7}{k} \right\rfloor$, where $\varphi$ denotes Euler's totient function. Let $S$ be the set of all positive integers $a$ such that $a \leq 99999$ and the sum of ... | 56,631 | graphs = [
Graph(
let={
"_n": Const(68681),
"upper": Const(99999),
"target_sum": Summation(var="k", start=Const(1), end=MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(143143))))), expr=Mul(EulerPhi... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/K2"
] | 352a97 | nt_count_digit_sum_v1 | null | 5 | 0 | [
"K2",
"MIN_PRIME_FACTOR"
] | 2 | 4.188 | 2026-02-08T03:29:36.558434Z | {
"verified": true,
"answer": 56631,
"timestamp": "2026-02-08T03:29:40.746676Z"
} | 35e8b9 | 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": 3101
},
"timestamp": "2026-02-10T13:38:00.811Z",
"answer": 56631
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K2",
"status": "ok_later"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
... | {
"lo": -3.49,
"mid": 1.84,
"hi": 7.55
} | ||
feaa14 | antilemma_v8_lucas_677425708_392 | Let $m = 4$ and $n = 23763$. Let $p$ be the largest prime number less than or equal to $m$. Define $F_k$ to be the $k$-th Fibonacci number, where $F_1 = 1$, $F_2 = 1$, and $F_k = F_{k-1} + F_{k-2}$ for $k \geq 3$. Let $d$ be the greatest common divisor of $F_p$ and $8$. Determine the number of nonnegative integers $j$ ... | 512 | graphs = [
Graph(
let={
"_m": Const(4),
"_n": Const(23763),
"x": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Ref("_n")), Eq(Mod(value=Binom(n=Const(23763), k=Var("j")), modulus=CountOverSet(set=SolutionsSet(var=Var("n")... | NT | COMB | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW/COUNT_FIB_DIVISIBLE/V8",
"V8"
] | 213f9a | antilemma_v8_lucas | null | 7 | 0 | [
"COUNT_FIB_DIVISIBLE",
"MAX_PRIME_BELOW",
"V8"
] | 3 | 0.003 | 2026-02-08T03:30:21.619772Z | {
"verified": true,
"answer": 512,
"timestamp": "2026-02-08T03:30:21.622552Z"
} | 74b69e | 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": 1717
},
"timestamp": "2026-02-08T20:30:59.405Z",
"answer": 512
},
{
"id... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok_later"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V5",
"status": "no... | {
"lo": -6.51,
"mid": -0.31,
"hi": 5.43
} | ||
73fc3e | antilemma_k2_v1_677425708_2455 | Let $m = 10$. Define $n$ to be the sum
$$
\sum_{k=1}^{10} \phi(k) \left\lfloor \frac{m}{k} \right\rfloor,
$$
where $\phi$ denotes Euler's totient function. Let $s$ be the sum of $\phi(d)$ over all positive divisors $d$ of 55. Define $x$ to be the sum
$$
\sum_{k=1}^{s} \phi(k) \left\lfloor \frac{n}{k} \right\rfloor.
$$
... | 1,540 | graphs = [
Graph(
let={
"_m": Const(10),
"_n": Summation(var="k", start=Const(1), end=Const(10), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Ref("_m"), Var("k"))))),
"x": Summation(var="k", start=Const(1), end=SumOverDivisors(n=Const(value=55), var='d', expr=EulerPhi(n=Var(n... | NT | COMB | COMPUTE | sympy | K2 | [
"K2/K3/K2",
"K2"
] | 4d84e5 | antilemma_k2_v1 | null | 5 | 0 | [
"K2",
"K3"
] | 2 | 0.002 | 2026-02-08T05:04:00.016121Z | {
"verified": true,
"answer": 1540,
"timestamp": "2026-02-08T05:04:00.017778Z"
} | 330811 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 247,
"completion_tokens": 1941
},
"timestamp": "2026-02-11T22:49:43.934Z",
"answer": 1540
},
{
"i... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K3",
"status": "ok_later"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
... | {
"lo": -3.52,
"mid": 1.14,
"hi": 6.18
} | ||
ab1242 | sequence_lucas_compute_v1_784195855_5027 | Let $k$ be the number of ordered pairs $(p, q)$ of positive integers such that $p \cdot q = 72$, $\gcd(p, q) = 1$, and $p < q$. Let $n$ be the smallest divisor of $317205857$ that is at least $k$. Define $L_n$ to be the $n$th Lucas number, where $L_1 = 1$, $L_2 = 3$, and $L_n = L_{n-1} + L_{n-2}$ for $n \ge 3$. Find th... | 3,939 | graphs = [
Graph(
let={
"_n": Const(16384),
"n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name=... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/MIN_PRIME_FACTOR"
] | 52cee2 | sequence_lucas_compute_v1 | null | 6 | 0 | [
"COPRIME_PAIRS",
"MIN_PRIME_FACTOR"
] | 2 | 0.002 | 2026-02-08T07:35:51.782990Z | {
"verified": true,
"answer": 3939,
"timestamp": "2026-02-08T07:35:51.784600Z"
} | aa53a6 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 189,
"completion_tokens": 1764
},
"timestamp": "2026-02-13T11:19:20.901Z",
"answer": 3939
},
{... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok_later"
},
{
"lemma": "MOD_MUL",
"status": "no"
}... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
40ac01 | geo_count_lattice_rect_v1_1915831931_481 | Compute the number of lattice points $(x, y)$ such that $0 \leq x \leq 121$ and $0 \leq y \leq 219$. | 26,840 | graphs = [
Graph(
let={
"a": Const(121),
"b": Const(219),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.003 | 2026-02-08T15:28:50.243940Z | {
"verified": true,
"answer": 26840,
"timestamp": "2026-02-08T15:28:50.246822Z"
} | 3e2739 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 148,
"completion_tokens": 175
},
"timestamp": "2026-02-24T21:01:38.415Z",
"answer": 26840
},
{
"i... | 2 | [] | {
"lo": -10,
"mid": -7.42,
"hi": -4.85
} | ||||
698ea2 | algebra_poly_eval_v1_655260480_2277 | Let $p$ be the maximum prime number $n$ such that $2 \leq n \leq 3$. Compute the value of
$$
7^4 \cdot p - 3 \cdot 7^3 - 9 \cdot 7^2 - 2 \cdot 7 - 9.
$$ | 5,710 | graphs = [
Graph(
let={
"_n": Const(2),
"z": Const(7),
"result": Sum(Mul(MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(3)), IsPrime(Var("n"))))), Pow(Ref("z"), Const(4))), Mul(Const(-3), Pow(Ref("z"), Const(3))), Mul(... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | algebra_poly_eval_v1 | null | 2 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.003 | 2026-02-08T16:39:22.333869Z | {
"verified": true,
"answer": 5710,
"timestamp": "2026-02-08T16:39:22.337190Z"
} | c4072e | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 124,
"completion_tokens": 442
},
"timestamp": "2026-02-16T07:35:18.548Z",
"answer": 5710
},
{
"id": 11,
... | 2 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
310be4 | modular_min_linear_v1_1439011603_409 | Let $a$ be the largest prime number $n$ such that $2 \leq n \leq 1151$. Let $b = 1070$ and $m = 4133$. Consider the set of all integers $x$ such that $1 \leq x \leq m$ and
$$
ax \equiv b \pmod{m}.
$$
Let $r$ be the smallest such $x$. Compute $r$. | 2,001 | graphs = [
Graph(
let={
"a": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(1151)), IsPrime(Var("n"))))),
"b": Const(1070),
"m": Const(4133),
"result": MinOverSet(set=SolutionsSet(var=Var("x"), condition=An... | NT | null | EXTREMUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | modular_min_linear_v1 | null | 5 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.208 | 2026-02-08T15:27:23.508826Z | {
"verified": true,
"answer": 2001,
"timestamp": "2026-02-08T15:27:23.716894Z"
} | 9ccdb8 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 136,
"completion_tokens": 1523
},
"timestamp": "2026-02-16T06:31:36.618Z",
"answer": 2001
},
{... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
90e5b4 | algebra_quadratic_discriminant_v1_349078426_382 | Let $a = 2$, $b = -8$, and $m = 4$. Consider the set of all ordered pairs $(x,y)$ of positive integers such that $x + y = 8$. For each such pair, compute $xy$, and let $n$ be the maximum value of $xy$ over all such pairs. Now consider the set of all ordered pairs $(x,y)$ of positive integers such that $xy = n$. For eac... | 0 | graphs = [
Graph(
let={
"_m": Const(4),
"_n": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Const(8)))), expr=Mul(Var("x"), Var("y")))),
... | NT | null | COMPUTE | sympy | B1 | [
"B1/B3"
] | 80b49d | algebra_quadratic_discriminant_v1 | null | 4 | 0 | [
"B1",
"B3"
] | 2 | 0.003 | 2026-02-08T12:59:58.072511Z | {
"verified": true,
"answer": 0,
"timestamp": "2026-02-08T12:59:58.075258Z"
} | f9de5d | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 193,
"completion_tokens": 326
},
"timestamp": "2026-02-16T04:22:50.222Z",
"answer": 0
},
{
"id": 11,
"... | 2 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{... | {
"lo": -9.12,
"mid": -6.02,
"hi": -3.62
} | ||
a0bc2b | antilemma_sum_equals_v1_2051736721_4227 | Let $n = 83$. Define $x$ to be the number of ordered pairs $(i, j)$ of integers such that $1 \leq i \leq 83$, $1 \leq j \leq 83$, and $i + j = n$. Compute the remainder when $74771 \cdot x$ is divided by $70250$. | 19,472 | graphs = [
Graph(
let={
"_n": Const(83),
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref("_n")), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(83)), right=IntegerRange(start=Const(1), end=Con... | COMB | GEOM | COMPUTE | sympy | COMB1 | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 2 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS"
] | 2 | 0.021 | 2026-02-08T17:49:22.623045Z | {
"verified": true,
"answer": 19472,
"timestamp": "2026-02-08T17:49:22.643712Z"
} | cf4b1b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 120,
"completion_tokens": 668
},
"timestamp": "2026-02-18T08:33:03.517Z",
"answer": 19472
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V8_SU... | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||
d441f1 | comb_bell_compute_v1_168721529_266 | Let $n$ be the smallest positive integer such that the largest integer $k$ for which $3^k$ divides $n!$ is at least 4. Let $B_n$ be the $n$th Bell number, which counts the number of partitions of a set of $n$ elements. Compute the remainder when $11025 - B_n$ is divided by 72327. | 62,205 | graphs = [
Graph(
let={
"_n": Const(11025),
"n": MinOverSet(set=SolutionsSet(var=Var("n"), condition=Geq(MaxKDivides(target=Factorial(Var("n")), base=Const(3)), Const(4)), domain='Z_{>0}')),
"result": Bell(Ref("n")),
"Q": Mod(value=Sub(Ref("_n"), Ref("result")... | NT | COMB | COMPUTE | sympy | V5 | [
"V5"
] | 79df37 | comb_bell_compute_v1 | null | 6 | 0 | [
"V5"
] | 1 | 0.001 | 2026-02-08T12:56:11.963685Z | {
"verified": true,
"answer": 62205,
"timestamp": "2026-02-08T12:56:11.964900Z"
} | 986a35 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 196,
"completion_tokens": 986
},
"timestamp": "2026-02-09T03:02:33.258Z",
"answer": 62205
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "ok"
}
] | {
"lo": -6.69,
"mid": -2.4,
"hi": 1.77
} | ||
93d067 | antilemma_cartesian_v1_153355830_553 | Let $x$ be the number of ordered pairs $(a, b)$ of integers such that $1 \leq a \leq 32$ and $1 \leq b \leq 42$.
Find the remainder when $71453 \cdot x$ is divided by 96549.
Compute this remainder. | 63,126 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(32)), right=IntegerRange(start=Const(1), end=Const(42)))),
"Q": Mod(value=Mul(Const(71453), Ref("x")), modulus=Const(96549)),
},
goal=Ref("Q"),
)
] | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | antilemma_cartesian_v1 | null | 2 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.001 | 2026-02-08T03:09:44.284449Z | {
"verified": true,
"answer": 63126,
"timestamp": "2026-02-08T03:09:44.285001Z"
} | 1842ec | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 178,
"completion_tokens": 7007
},
"timestamp": "2026-02-23T23:13:55.996Z",
"answer": 89890
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -0.05,
"mid": 2.89,
"hi": 5.27
} | ||
91ad58_n | alg_sum_ap_v1_1218484723_3184 | A music sequencer generates a pattern over $5$ beats. For each beat length $k$ from $1$ to $5$, the number of unique rhythmic motifs of length $k$ that avoid repetition (given by $\varphi(k)$) is multiplied by how many times it fits in $5$ beats ($\lfloor 5/k \rfloor$). The total number of such motif contributions is $... | 44,745 | ALG | null | COMPUTE | sympy | K2 | [
"K2/L3C"
] | d90701 | alg_sum_ap_v1 | null | 5 | null | [
"K2",
"L3C"
] | 2 | 0.029 | 2026-02-25T04:54:25.592665Z | null | 6ac4bd | 91ad58 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 330,
"completion_tokens": 3458
},
"timestamp": "2026-03-30T19:46:14.459Z",
"answer": 44745
},
{
"... | 1 | [
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3C",
"status": "ok_later"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | |
6f274f | nt_sum_gcd_range_mod_v1_124444284_3561 | Let $N = 5776$, $k = 120$, and $M = 10463$. Define $s$ to be the sum
$$
\sum_{n=1}^{N} \gcd(n, k).
$$
Let $r$ be the remainder when $s$ is divided by $M$. Let $T$ be the set of all integers $t$ such that $8 \leq t \leq 42$ and there exist positive integers $a \leq 9$ and $b \leq 3$ for which $t = 3a + 5b$. Compute the ... | 37,121 | graphs = [
Graph(
let={
"N": Const(5776),
"k": Const(120),
"M": Const(10463),
"sum": Summation(var="n", start=Const(1), end=Ref("N"), expr=GCD(a=Var("n"), b=Ref("k"))),
"result": Mod(value=Ref("sum"), modulus=Ref("M")),
"Q": Mod(value=S... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 2ba0ea | nt_sum_gcd_range_mod_v1 | quadratic_mod | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.386 | 2026-02-08T05:27:06.782193Z | {
"verified": true,
"answer": 37121,
"timestamp": "2026-02-08T05:27:07.168553Z"
} | 865c69 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 198,
"completion_tokens": 2640
},
"timestamp": "2026-02-12T09:35:30.851Z",
"answer": 37121
},
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
a0dbbb | nt_num_divisors_compute_v1_124444284_2943 | Let $n = 11664$. Compute the number of positive divisors of $n$. | 35 | graphs = [
Graph(
let={
"n": Const(11664),
"result": NumDivisors(n=Ref("n")),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | MOBIUS_COPRIME | [
"MOBIUS_COPRIME",
"SUM_ARITHMETIC"
] | 2450cb | nt_num_divisors_compute_v1 | null | 2 | 0 | [
"MOBIUS_COPRIME",
"SUM_ARITHMETIC"
] | 2 | 0.011 | 2026-02-08T05:05:18.100280Z | {
"verified": true,
"answer": 35,
"timestamp": "2026-02-08T05:05:18.111127Z"
} | 86577a | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 129,
"completion_tokens": 442
},
"timestamp": "2026-02-11T22:52:12.972Z",
"answer": 35
},
{
"id"... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"l... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
e67bfc | sequence_lucas_compute_v1_1978505735_7842 | Let $n$ be the number of positive integers $n_1$ such that $1 \le n_1 \le 154$ and $n_1 \equiv \left\lfloor \frac{n_1}{2} \right\rfloor \pmod{7}$. Let $Q = L_n$, the $n$th Lucas number, where the Lucas sequence is defined by $L_1 = 1$, $L_2 = 3$, and $L_k = L_{k-1} + L_{k-2}$ for $k \ge 3$. Find the value of $Q$. | 39,603 | graphs = [
Graph(
let={
"_n": Const(154),
"n": CountOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(1)), Leq(Var("n1"), Ref("_n")), Congruent(a=Var(name='n1'), b=Floor(arg=Div(left=Var(name='n1'), right=Const(value=2))), modulus=Const(value=7))))),
... | NT | null | COMPUTE | sympy | L3C | [
"L3C"
] | 73f8b0 | sequence_lucas_compute_v1 | null | 6 | 0 | [
"L3C"
] | 1 | 0.002 | 2026-02-08T20:31:11.486907Z | {
"verified": true,
"answer": 39603,
"timestamp": "2026-02-08T20:31:11.488599Z"
} | fbe9ed | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 176,
"completion_tokens": 1128
},
"timestamp": "2026-02-19T00:38:31.659Z",
"answer": 39603
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V8_SUM",
"s... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
8dfc75 | nt_count_coprime_and_v1_1439011603_2294 | Let $k_1 = 5$ and let $k_2$ be the number of prime numbers between $2$ and $17$, inclusive. Let $S$ be the set of positive integers $n_1 \le 31238$ such that $\gcd(n_1, k_1) = 1$ and $\gcd(n_1, k_2) = 1$. Compute the remainder when $67883 \cdot |S|$ is divided by $53625$. | 26,243 | graphs = [
Graph(
let={
"_n": Const(53625),
"upper": Const(31238),
"k1": Const(5),
"k2": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(17)), IsPrime(Var("n"))))),
"result": CountOverSet(set=S... | NT | null | COUNT | sympy | COUNT_PRIMES | [
"COUNT_PRIMES"
] | 07c874 | nt_count_coprime_and_v1 | null | 4 | 0 | [
"COUNT_PRIMES"
] | 1 | 5.183 | 2026-02-08T16:40:23.852791Z | {
"verified": true,
"answer": 26243,
"timestamp": "2026-02-08T16:40:29.035427Z"
} | 4a8434 | 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": 2435
},
"timestamp": "2026-02-17T10:06:31.386Z",
"answer": 26243
},
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
94d0a7 | antilemma_cartesian_v1_677425708_1039 | Compute the number of ordered pairs $(a, b)$ where $a$ is an integer from 1 to 25 and $b$ is an integer from 1 to 40. | 1,000 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(25)), right=IntegerRange(start=Const(1), end=Const(40)))),
},
goal=Ref("x"),
)
] | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | antilemma_cartesian_v1 | null | 2 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.001 | 2026-02-08T03:57:31.012690Z | {
"verified": true,
"answer": 1000,
"timestamp": "2026-02-08T03:57:31.013507Z"
} | 3b4c08 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 152,
"completion_tokens": 142
},
"timestamp": "2026-02-09T15:03:09.444Z",
"answer": 1000
},
{
"id... | 2 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"statu... | {
"lo": -10,
"mid": -7.79,
"hi": -5.57
} | ||
468107 | diophantine_sum_product_min_v1_1440796553_703 | Let $S = 56$. Let $P$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 153664$. Determine the value of the smallest positive integer $x$ such that $1 \leq x \leq 55$ and $x(S - x) = P$. | 28 | graphs = [
Graph(
let={
"S": Const(56),
"P": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(153664)))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | EXTREMUM | sympy | B3 | [
"B3"
] | 0cd20d | diophantine_sum_product_min_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.006 | 2026-02-08T11:55:25.158738Z | {
"verified": true,
"answer": 28,
"timestamp": "2026-02-08T11:55:25.164618Z"
} | a1c553 | 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": 703
},
"timestamp": "2026-02-14T20:45:09.198Z",
"answer": 28
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
9bdce1 | diophantine_fbi2_min_v1_1874849503_1260 | Let $k$ be the number of integers $t$ such that $27 \le t \le 186$ and there exist positive integers $a$ and $b$ with $1 \le a \le 6$, $1 \le b \le 10$, and $t = 21a + 6b$. Let $d_0$ be the smallest divisor of 245 that is at least 2. Determine the smallest integer $d$ such that $d_0 \le d \le 58$, $d$ divides $k$, and ... | 39,595 | graphs = [
Graph(
let={
"_m": Const(4),
"_n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(245))))),
"k": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition... | NT | null | EXTREMUM | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/LIN_FORM"
] | 1d7298 | diophantine_fbi2_min_v1 | null | 4 | 0 | [
"LIN_FORM",
"MIN_PRIME_FACTOR"
] | 2 | 0.01 | 2026-02-08T13:43:38.507441Z | {
"verified": true,
"answer": 39595,
"timestamp": "2026-02-08T13:43:38.517216Z"
} | fe0a03 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 246,
"completion_tokens": 2063
},
"timestamp": "2026-02-10T02:49:50.928Z",
"answer": 39595
},
{
"... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok_later"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemm... | {
"lo": -5.49,
"mid": 0.03,
"hi": 6.12
} | ||
6d712b | comb_binomial_compute_v1_1978505735_1292 | Let $n = 13$. For each integer $k$ from $1$ to $3$ and each integer $j$ from $1$ to $10$, compute $\phi(k) \cdot \left\lfloor \frac{3}{k} \right\rfloor$, where $\phi$ denotes Euler's totient function. Let $s$ be the sum of these values over all $k$ and $j$. Define $k = \frac{3s}{30}$. Compute $\binom{n}{k}$. | 1,716 | graphs = [
Graph(
let={
"_m": Const(30),
"n": Const(13),
"k": Div(Mul(Const(3), SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("k1"), Var("_j")]), condition=Const(1), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(3)), right=Intege... | NT | null | COMPUTE | sympy | SUM_INDEPENDENT | [
"SUM_INDEPENDENT",
"K2"
] | d64c9f | comb_binomial_compute_v1 | null | 5 | 0 | [
"K2",
"SUM_INDEPENDENT"
] | 2 | 0.002 | 2026-02-08T16:00:26.405132Z | {
"verified": true,
"answer": 1716,
"timestamp": "2026-02-08T16:00:26.407076Z"
} | 553054 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 153,
"completion_tokens": 1016
},
"timestamp": "2026-02-16T20:49:26.805Z",
"answer": 1716
},
{... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "SUM_INDEPENDENT",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
f4a2e9 | comb_count_derangements_v1_1125832087_123 | Let $n$ be the number of integers $t$ such that $8 \leq t \leq 17$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 4$, $1 \leq b \leq 2$, and $t = 2a + 3b + 3$. Let $r$ be the number of derangements of $n$ elements, denoted $!n$. Compute the remainder when $42609 \cdot r$ is divided by $68750$. | 547 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=4)), Geq(left=Var(name='b'), right=Const(value=1... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_count_derangements_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T02:52:25.501059Z | {
"verified": true,
"answer": 547,
"timestamp": "2026-02-08T02:52:25.501987Z"
} | fcd6e5 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 229,
"completion_tokens": 2082
},
"timestamp": "2026-02-10T11:46:51.420Z",
"answer": 547
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
... | {
"lo": 0.42,
"mid": 2.15,
"hi": 3.61
} | ||
079c37 | diophantine_fbi2_min_v1_168721529_551 | Let $k = 6$ and let $d$ be a positive integer divisor of $k$ such that $\frac{k}{d} \ge 1$ and $d \le 16$. Among all such $d$, let $r$ be the smallest. Compute $$\sum_{n=\phi(2)}^{|r|} \tau(n),$$ where $\phi$ denotes Euler's totient function and $\tau(n)$ denotes the number of positive divisors of $n$. | 1 | graphs = [
Graph(
let={
"k": Const(6),
"a": Const(0),
"b": Const(0),
"upper": Const(16),
"result": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Leq(Var("d"), Ref("upper")), Divides(divisor=Var("d"), dividend=Ref(... | NT | null | EXTREMUM | sympy | K2 | [
"ONE_PHI_2"
] | e19278 | diophantine_fbi2_min_v1 | null | 3 | 0 | [
"K2",
"ONE_PHI_2"
] | 2 | 0.071 | 2026-02-08T13:08:25.635231Z | {
"verified": true,
"answer": 1,
"timestamp": "2026-02-08T13:08:25.706693Z"
} | 5b19ea | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 217,
"completion_tokens": 802
},
"timestamp": "2026-02-09T06:15:47.915Z",
"answer": 1
},
{
"id": ... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "ONE_PHI_2",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V5",
"status":... | {
"lo": -10,
"mid": -6.5,
"hi": -3.01
} | ||
0b5f26 | geo_visible_lattice_v1_1520064083_1028 | Let $n = 90$. Define $\text{result}$ to be the number of visible lattice points $(x, y)$ such that $1 \leq x, y \leq n$ and $\gcd(x, y) = 1$. Compute the sum $\sum_{k=1}^{\text{result}} \tau(k)$, where $\tau(k)$ is the number of positive divisors of $k$. Find the value of this sum. | 42,964 | graphs = [
Graph(
let={
"n": Const(90),
"result": VisibleLatticePoints(n=Ref(name='n')),
"Q": Summation(var="n", start=Const(1), end=Abs(arg=Ref(name='result')), expr=NumDivisors(n=Var("n"))),
},
goal=Ref("Q"),
)
] | GEOM | NT | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 5 | 0 | null | null | 0.383 | 2026-02-08T03:43:27.284181Z | {
"verified": true,
"answer": 42964,
"timestamp": "2026-02-08T03:43:27.667159Z"
} | 6020e0 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 206,
"completion_tokens": 7792
},
"timestamp": "2026-02-10T15:37:33.518Z",
"answer": 42962
},
{
... | 1 | [] | {
"lo": 3.43,
"mid": 5.73,
"hi": 8.84
} | ||||
8c7b63 | v1_endings_v1_168721529_1059 | Let $n = 98864$ and $p = 7$. Let $v_p(n!)$ denote the largest integer $k$ such that $p^k$ divides $n!$. Compute the value of $v_p(n!) - r$, where $r$ is the remainder when $v_p(n!) - 7$ is divided by 8. | 16,471 | graphs = [
Graph(
let={
"n_val": Const(98864),
"p_val": Const(7),
"n_fact": Factorial(Ref("n_val")),
"vp": MaxKDivides(target=Ref("n_fact"), base=Ref("p_val")),
"r_val": Const(7),
"s_val": Const(8),
"vp_minus_r": Sub(Ref("vp... | NT | null | COMPUTE | sympy | V1 | [
"V1"
] | dae96f | v1_endings_v1 | null | 4 | null | [
"V1"
] | 1 | 0.001 | 2026-02-08T13:26:31.023064Z | {
"verified": true,
"answer": 16471,
"timestamp": "2026-02-08T13:26:31.023999Z"
} | 438a75 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 190,
"completion_tokens": 1185
},
"timestamp": "2026-02-09T13:31:46.514Z",
"answer": 16471
},
{
"... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K5",
"status": "same_pattern_wrong"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status... | {
"lo": -6.69,
"mid": -2.39,
"hi": 1.83
} | ||
af8bec | diophantine_fbi2_count_v1_898971024_815 | Let $m = 2$ and $n = 4$. Let $k$ be the sum of all real solutions $x$ to the equation $x^2 - 480x - 23625 = 0$. Let $T$ be the set of all integers $t$ such that $5 \leq t \leq 189$ and there exist positive integers $a \leq 12$, $b \leq 55$ such that $t = 2a + 3b$. Let $C$ be the number of elements in $T$. Find the numb... | 51,289 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(4),
"k": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Ref("_m")), Mul(Const(-480), Var("x")), Const(-23625)), Const(0)))),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), con... | NT | null | COUNT | sympy | VIETA_SUM | [
"VIETA_SUM",
"LIN_FORM",
"B3"
] | 5c2159 | diophantine_fbi2_count_v1 | null | 7 | 0 | [
"B3",
"LIN_FORM",
"VIETA_SUM"
] | 3 | 0.02 | 2026-02-08T15:40:17.251338Z | {
"verified": true,
"answer": 51289,
"timestamp": "2026-02-08T15:40:17.271699Z"
} | 0f13c0 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 236,
"completion_tokens": 4382
},
"timestamp": "2026-02-16T11:57:14.647Z",
"answer": 51289
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
75faaf | geo_count_lattice_triangle_v1_784195855_44 | Consider the triangle with vertices at $(0,0)$, $(222,120)$, and $(289,121)$. Let $A$ be twice the area of this triangle, and let $B$ be the number of lattice points on the boundary of the triangle, computed as the sum of the greatest common divisors of the absolute differences in coordinates along each edge. Compute t... | 37,414 | graphs = [
Graph(
let={
"_n": Const(120),
"area_2x": Abs(arg=Sum(Mul(Const(value=222), Const(value=121)), Mul(Const(value=289), Sub(left=Const(value=0), right=Ref(name='_n'))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=222)), b=Abs(arg=Const(value=120))), GCD(a=Abs(arg=... | ALG | NT | COUNT | sympy | L3C | [
"L3C"
] | 73f8b0 | geo_count_lattice_triangle_v1 | null | 6 | 0 | [
"L3C"
] | 1 | 0.009 | 2026-02-08T02:55:23.624178Z | {
"verified": true,
"answer": 37414,
"timestamp": "2026-02-08T02:55:23.633602Z"
} | 442435 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 229,
"completion_tokens": 2606
},
"timestamp": "2026-02-10T11:54:13.671Z",
"answer": 37414
},
{
"... | 1 | [
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 2.04,
"mid": 3.6,
"hi": 5.17
} | ||
9f776c | nt_count_intersection_v1_1918700295_3854 | Let $N = 50000$, $a = 11$, and $b = 6$. Define $S$ as the set of all positive integers $n$ such that $1 \leq n \leq N$, $a$ divides $n$, and $\gcd(n, b) = 1$. Let $r$ be the number of elements in $S$. Let $A = \sum_{i=0}^{\text{NumDigits}(r) - 1} d_i \cdot (i+1)^2$, where $d_i$ is the $i$-th decimal digit of $r$ (start... | 6,470 | graphs = [
Graph(
let={
"N": Const(50000),
"a": Const(11),
"b": Const(6),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("N")), Divides(divisor=Ref("a"), dividend=Var("n")), Eq(GCD(a=Var("n"), b=R... | NT | null | COUNT | sympy | B1 | [
"B1"
] | 51a773 | nt_count_intersection_v1 | digits_weighted_mod | 5 | 0 | [
"B1"
] | 1 | 1.581 | 2026-02-08T09:00:27.032513Z | {
"verified": true,
"answer": 6470,
"timestamp": "2026-02-08T09:00:28.613301Z"
} | 9ed4ff | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 227,
"completion_tokens": 1132
},
"timestamp": "2026-02-13T23:20:31.015Z",
"answer": 6470
},
{... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
6a4d5d | antilemma_sum_equals_v1_1742523217_3277 | Let $m = 184$. Compute the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = m$. Denote this number by $n$. Now consider all ordered pairs $(i, j)$ with $1 \leq i \leq 91$ and $1 \leq j \leq 92$ such that $i + j = n$. Compute the number of such pairs. | 91 | graphs = [
Graph(
let={
"_m": Const(184),
"_n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2")), ... | COMB | GEOM | COMPUTE | sympy | COMB1 | [
"COMB1/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | 3e1adf | antilemma_sum_equals_v1 | null | 3 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS"
] | 2 | 0.004 | 2026-02-08T05:45:47.901355Z | {
"verified": true,
"answer": 91,
"timestamp": "2026-02-08T05:45:47.905247Z"
} | c5f6c5 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 209,
"completion_tokens": 2418
},
"timestamp": "2026-02-24T04:25:50.309Z",
"answer": 91
},
{
"id"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS... | {
"lo": -7.18,
"mid": -5,
"hi": -3.01
} | ||
470061 | comb_count_surjections_v1_1353956133_271 | Let $m = 7$. Let $n$ be the number of ordered pairs $(i, j)$ of integers such that $1 \le i \le 7$, $1 \le j \le 7$, and $i + j = n'$, where $n'$ is the number of ordered pairs $(u, v)$ with $1 \le u \le 2$ and $1 \le v \le 4$. Let $k$ be the number of ordered pairs $(i, j)$ of integers such that $1 \le i \le 6$, $1 \l... | 15,120 | graphs = [
Graph(
let={
"_m": Const(7),
"_n": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(2)), right=IntegerRange(start=Const(1), end=Const(4)))),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(S... | COMB | null | COUNT | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN/COUNT_SUM_EQUALS"
] | 1e820b | comb_count_surjections_v1 | null | 5 | 0 | [
"COUNT_CARTESIAN",
"COUNT_SUM_EQUALS"
] | 2 | 0.022 | 2026-02-08T11:22:34.357653Z | {
"verified": true,
"answer": 15120,
"timestamp": "2026-02-08T11:22:34.379903Z"
} | 54daa4 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 278,
"completion_tokens": 877
},
"timestamp": "2026-02-24T13:39:56.897Z",
"answer": 15120
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok_later"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"statu... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
7dc3f2 | comb_sum_binomial_row_v1_717093673_885 | Let $A$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 54$, $\gcd(p, q) = 1$, and $p < q$. Let $n = |A|$. Compute the value of $$\left( \sum_{d \mid n} \varphi(d) \right)^{10},$$ where $\varphi$ denotes Euler's totient function and the sum is taken over all positiv... | 1,024 | graphs = [
Graph(
let={
"_n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=54)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(value=1)), ... | NT | null | SUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/K3"
] | f9481c | comb_sum_binomial_row_v1 | null | 4 | 0 | [
"COPRIME_PAIRS",
"K3"
] | 2 | 0.002 | 2026-02-08T15:44:41.371365Z | {
"verified": true,
"answer": 1024,
"timestamp": "2026-02-08T15:44:41.373736Z"
} | 35f49a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 153,
"completion_tokens": 759
},
"timestamp": "2026-02-16T12:10:52.310Z",
"answer": 1024
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K3",
"status": "ok_later"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V7",
"st... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
c09681 | comb_catalan_compute_v1_458359167_4694 | Let $T$ be the set of all integers $t$ with $20 \leq t \leq 32$ for which there exist integers $a$ and $b$ such that $1 \leq a \leq 4$, $1 \leq b \leq 3$, and $t = 2a + 3b + 15$. Let $n$ be the number of elements in $T$. Compute the $n$-th Catalan number. | 58,786 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=4)), Geq(left=Var(name='b'), right=Const(value=1... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_catalan_compute_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T11:59:33.071255Z | {
"verified": true,
"answer": 58786,
"timestamp": "2026-02-08T11:59:33.072932Z"
} | 7c3ec1 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 213,
"completion_tokens": 1515
},
"timestamp": "2026-02-24T15:08:11.077Z",
"answer": 58786
},
{
"... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"st... | {
"lo": -3.84,
"mid": -1.67,
"hi": 1.32
} | ||
9f7e83 | antilemma_cartesian_v1_1918700295_3833 | Let $n = 16384$. Compute the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = n$. Let this number be $a$. Let $b$ be the number of ordered pairs $(i, j)$ with $1 \leq i \leq 28$ and $1 \leq j \leq 39$. Compute $a - b$. | 7,100 | graphs = [
Graph(
let={
"_n": Const(16384),
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(28)), right=IntegerRange(start=Const(1), end=Const(39)))),
"Q": Sub(CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), con... | COMB | GEOM | COMPUTE | sympy | COMB1 | [
"COMB1",
"COUNT_CARTESIAN"
] | 20f64e | antilemma_cartesian_v1 | negation_mod | 3 | 0 | [
"COMB1",
"COUNT_CARTESIAN"
] | 2 | 0.002 | 2026-02-08T08:58:59.492386Z | {
"verified": true,
"answer": 7100,
"timestamp": "2026-02-08T08:58:59.494273Z"
} | 31dca9 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 204,
"completion_tokens": 1305
},
"timestamp": "2026-02-24T10:17:57.316Z",
"answer": 7100
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS... | {
"lo": -5.97,
"mid": -3.97,
"hi": -1.93
} | ||
cd1ca1 | nt_sum_totient_over_divisors_v1_2051736721_997 | Let $n = 10846$. Define $\phi(d)$ as Euler's totient function. Let $S$ be the sum of $\phi(d)$ over all positive divisors $d$ of $n$.
Now consider all ordered pairs $(x, y)$ of positive integers such that $xy = 129600$. Let $M$ be the minimum value of $x + y$ over all such pairs.
Compute the remainder when $M - S$ is... | 55,225 | graphs = [
Graph(
let={
"_n": Const(65351),
"n": Const(10846),
"result": SumOverDivisors(n=Ref(name='n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Mod(value=Sub(MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), conditio... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | fc629c | nt_sum_totient_over_divisors_v1 | negation_mod | 5 | 0 | [
"B3"
] | 1 | 0.001 | 2026-02-08T15:47:12.213292Z | {
"verified": true,
"answer": 55225,
"timestamp": "2026-02-08T15:47:12.214702Z"
} | 45675e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 146,
"completion_tokens": 920
},
"timestamp": "2026-02-16T13:48:08.080Z",
"answer": 55225
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
b55152 | modular_mod_compute_v1_124444284_7229 | Let $a$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $x \cdot y = 777924$. Let $m$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $x \cdot y = 1375929$. Define $\text{result} = a \bmod m$. Find the value of $\text{result}$... | 1,764 | graphs = [
Graph(
let={
"a": 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(777924)))), expr=Sum(Var("x"), Var("y")))),
"m": MinOverSet(... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | modular_mod_compute_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.002 | 2026-02-08T08:57:43.759795Z | {
"verified": true,
"answer": 1764,
"timestamp": "2026-02-08T08:57:43.761812Z"
} | b87741 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 146,
"completion_tokens": 3536
},
"timestamp": "2026-02-13T22:30:30.424Z",
"answer": 1764
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
ed89f0 | algebra_quadratic_discriminant_v1_809748730_606 | Let $p$ be a positive integer. Suppose there exists a positive integer $q$ such that $pq = 6$, $\gcd(p, q) = 1$, and $p < q$. Let $e$ be the number of such values of $p$. Let $r = (-2)^e - 4 \cdot 2 \cdot (-40)$. Compute the remainder when $21119 \cdot r$ is divided by $85728$. | 70,044 | graphs = [
Graph(
let={
"a": Const(2),
"b": Const(-2),
"c": Const(-40),
"result": Sub(Pow(Ref("b"), 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(... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | algebra_quadratic_discriminant_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.002 | 2026-02-08T11:36:46.570947Z | {
"verified": true,
"answer": 70044,
"timestamp": "2026-02-08T11:36:46.573245Z"
} | 0e675b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 141,
"completion_tokens": 2874
},
"timestamp": "2026-02-14T17:05:42.396Z",
"answer": 70044
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8",
"status": "no... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
3f02b7 | nt_sum_totient_over_divisors_v1_1520064083_6645 | Let $A$ be the set of all ordered pairs $(i, j)$ of integers with $1 \le i \le 41$ and $1 \le j \le 53$. Define $n$ to be the number of pairs in $A$ such that $\gcd(i, j) = 1$. Let $S = \sum_{d \mid n} \phi(d)$, where the sum is taken over all positive divisors $d$ of $n$, and $\phi$ denotes Euler's totient function. F... | 56,335 | graphs = [
Graph(
let={
"_n": Const(93713),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(GCD(a=Var("i"), b=Var("j")), Const(1)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(41)), right=IntegerRange(start=Const(1), e... | NT | null | COMPUTE | sympy | COUNT_COPRIME_GRID | [
"COUNT_COPRIME_GRID"
] | 20ec03 | nt_sum_totient_over_divisors_v1 | null | 6 | 0 | [
"COUNT_COPRIME_GRID"
] | 1 | 0.006 | 2026-02-08T08:15:25.111898Z | {
"verified": true,
"answer": 56335,
"timestamp": "2026-02-08T08:15:25.117874Z"
} | 1360e6 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 173,
"completion_tokens": 4545
},
"timestamp": "2026-02-13T16:51:02.179Z",
"answer": 56335
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
1cf671 | modular_min_linear_v1_1742523217_151 | Let $a = 12505$. Let $b$ be the number of integers $t$ such that $36 \leq t \leq 20499$ and there exist positive integers $a'$ and $b'$ with $1 \leq a' \leq 324$, $1 \leq b' \leq 913$, and $t = 21a' + 15b'$. Let $m = 14398$. Compute the smallest positive integer $x$ such that $1 \leq x \leq m$ and
$$
12505x \equiv b \... | 7,184 | graphs = [
Graph(
let={
"a": Const(12505),
"b": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=324)), Geq(left=V... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | modular_min_linear_v1 | null | 7 | 0 | [
"LIN_FORM"
] | 1 | 0.526 | 2026-02-08T02:53:54.133800Z | {
"verified": true,
"answer": 7184,
"timestamp": "2026-02-08T02:53:54.659981Z"
} | 89516a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 246,
"completion_tokens": 29884
},
"timestamp": "2026-02-23T18:19:59.958Z",
"answer": 757
},
{
... | 0 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": 5.07,
"mid": 7.32,
"hi": 10
} | ||
a0ac01 | nt_count_gcd_equals_v1_1520064083_3594 | Let $k$ be the minimum value of $x + y$ over all ordered pairs of positive integers $(x, y)$ such that $xy = 121$. Let $d$ be the largest prime number less than or equal to $12$. Let $\text{result}$ be the number of positive integers $n$ less than or equal to $32400$ such that $\gcd(n, k) = d$. Compute the remainder wh... | 27,129 | graphs = [
Graph(
let={
"_m": Const(12),
"_n": Const(65224),
"upper": Const(32400),
"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... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW",
"B3"
] | 78ed98 | nt_count_gcd_equals_v1 | null | 5 | 0 | [
"B3",
"MAX_PRIME_BELOW"
] | 2 | 4.344 | 2026-02-08T05:46:04.459940Z | {
"verified": true,
"answer": 27129,
"timestamp": "2026-02-08T05:46:08.803875Z"
} | 35ecc7 | 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": 1130
},
"timestamp": "2026-02-12T13:53:24.934Z",
"answer": 27129
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma"... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
a81bdb | comb_count_surjections_v1_151522320_2227 | Let $n$ be the number of ordered pairs $(i, j)$ of integers such that $1 \leq i \leq 8$, $1 \leq j \leq 8$, and $i + j = 8$. Let $k = 2$. 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 subsets. | 126 | graphs = [
Graph(
let={
"_n": Const(8),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref("_n")), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(8)), right=IntegerRange(start=Const(1), end=Const... | COMB | null | COUNT | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | comb_count_surjections_v1 | null | 3 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.01 | 2026-02-08T04:42:11.919925Z | {
"verified": true,
"answer": 126,
"timestamp": "2026-02-08T04:42:11.930073Z"
} | 8d9802 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 211,
"completion_tokens": 842
},
"timestamp": "2026-02-24T01:31:13.038Z",
"answer": 126
},
{
"id"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status"... | {
"lo": -4.92,
"mid": -2.9,
"hi": -0.7
} | ||
9ed135 | lin_form_endings_v1_168721529_1818 | Let $a = 14$ and $b = 21$. Let $l = \mathrm{lcm}(a, b)$. Let $k = 13731$ and $s = k \cdot l$. Compute the remainder when $s$ is divided by $81342$. | 7,308 | graphs = [
Graph(
let={
"a_coeff": Const(14),
"b_coeff": Const(21),
"_inner_result": LCM(a=Ref("a_coeff"), b=Ref("b_coeff")),
"_scale_k": Const(13731),
"_scaled": Mul(Ref("_scale_k"), Ref("_inner_result")),
"_mod_M": Const(81342),
... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 2 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T13:56:45.741849Z | {
"verified": true,
"answer": 7308,
"timestamp": "2026-02-08T13:56:45.742751Z"
} | 30e658 | 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": 672
},
"timestamp": "2026-02-09T21:58:37.651Z",
"answer": 7308
},
{
"id... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status... | {
"lo": -5.49,
"mid": 0.03,
"hi": 6.12
} | ||
808975 | nt_count_digit_sum_v1_784195855_6293 | Let $T$ be the set of all ordered pairs of positive integers $(x, y)$ such that $x + y = 10$. Let $p_{\text{max}}$ be the maximum value of $xy$ over all such pairs. Let $C$ be the number of positive integers $n \le 99999$ such that the sum of the digits of $n$ equals $p_{\text{max}}$. Compute the remainder when $66235 ... | 39,297 | graphs = [
Graph(
let={
"_n": Const(10),
"upper": Const(99999),
"target_sum": 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("... | NT | null | COUNT | sympy | B1 | [
"B1"
] | 5b950e | nt_count_digit_sum_v1 | null | 4 | 0 | [
"B1"
] | 1 | 3.842 | 2026-02-08T08:32:57.390607Z | {
"verified": true,
"answer": 39297,
"timestamp": "2026-02-08T08:33:01.232510Z"
} | a9f688 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 153,
"completion_tokens": 2239
},
"timestamp": "2026-02-13T19:34:37.741Z",
"answer": 39297
},
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
e5215a | geo_count_lattice_rect_v1_677425708_931 | Let $a = 70$ and $b = 267$. The quantity $L$ is the number of lattice points $(x, y)$ such that $0 \le x \le a$ and $0 \le y \le b$. Let $c = 144$. Compute the remainder when $c - L$ is divided by $53703$. | 34,819 | graphs = [
Graph(
let={
"a": Const(70),
"b": Const(267),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"_c": Const(144),
"Q": Mod(value=Sub(Ref("_c"), Ref("result")), modulus=Const(53703)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0 | 2026-02-08T03:52:39.441320Z | {
"verified": true,
"answer": 34819,
"timestamp": "2026-02-08T03:52:39.441721Z"
} | 273d5b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 188,
"completion_tokens": 699
},
"timestamp": "2026-02-09T14:12:23.411Z",
"answer": 34819
},
{
"i... | 1 | [] | {
"lo": -4.92,
"mid": -2.9,
"hi": -0.7
} | ||||
feb68f | modular_count_residue_v1_1080341949_475 | Let $r = \sum_{k=0}^{10} (-1)^k \binom{10}{k}$. Let $m = 21$ and let $N$ be the number of positive integers $n$ such that $1 \leq n \leq 53361$ and $n \equiv r \pmod{m}$. Let $c = 95927$. Compute the remainder when $c \cdot N$ is divided by $85026$. | 65,991 | graphs = [
Graph(
let={
"upper": Const(53361),
"m": Const(21),
"r": Summation(var="k", start=Const(0), end=Const(10), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Const(10), k=Var("k")))),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(V... | COMB | null | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING"
] | c21569 | modular_count_residue_v1 | null | 5 | 0 | [
"BINOMIAL_ALTERNATING"
] | 1 | 2.229 | 2026-02-08T13:31:54.020381Z | {
"verified": true,
"answer": 65991,
"timestamp": "2026-02-08T13:31:56.248891Z"
} | 04da37 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 212,
"completion_tokens": 1365
},
"timestamp": "2026-02-24T18:34:40.515Z",
"answer": 65991
},
{
"... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
bfdd4e | geo_count_lattice_triangle_v1_2051736721_3127 | Let $n = 289$. The area of a triangle with vertices at $(0,0)$, $(111,121)$, and $(70,289)$ is equal to $\frac{1}{2} \cdot \text{area\_2x}$, where
$$
\text{area\_2x} = |111 \cdot 121 + 70 \cdot (0 - 289)|.
$$
Let $\text{boundary}$ be the sum of the number of lattice points on the three edges of the triangle (excluding ... | 3,399 | graphs = [
Graph(
let={
"_n": Const(289),
"area_2x": Abs(arg=Sum(Mul(Const(value=111), Const(value=121)), Mul(Const(value=70), Sub(left=Const(value=0), right=Const(value=289))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=111)), b=Abs(arg=Ref(name='_n'))), GCD(a=Abs(arg=S... | ALG | NT | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | geo_count_lattice_triangle_v1 | null | 3 | 0 | [
"LIN_FORM"
] | 1 | 0.011 | 2026-02-08T17:08:08.520770Z | {
"verified": true,
"answer": 3399,
"timestamp": "2026-02-08T17:08:08.531643Z"
} | 941bc4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 230,
"completion_tokens": 1480
},
"timestamp": "2026-02-17T19:07:26.576Z",
"answer": 3399
},
{... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
2474e0 | nt_min_crt_v1_1978505735_6161 | Let $n$ be a positive integer such that $1 \leq n \leq 72$, $n \equiv 2 \pmod{m}$, and $n \equiv 0 \pmod{9}$, where $m$ is the number of positive integers $p$ for which there exists a positive integer $q$ such that $p < q$, $\gcd(p, q) = 1$, and $pq = 1050$. Let $r$ be the smallest such $n$. Compute the value of
\[
\su... | 16,912 | graphs = [
Graph(
let={
"_n": Const(16900),
"m": 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=1050)), Eq(left=GCD(a=Var(name='p'), b=Var(na... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | a9a663 | nt_min_crt_v1 | digits_weighted_mod | 7 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.023 | 2026-02-08T19:27:28.710129Z | {
"verified": true,
"answer": 16912,
"timestamp": "2026-02-08T19:27:28.733590Z"
} | 3e9543 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 299,
"completion_tokens": 3476
},
"timestamp": "2026-02-18T22:27:46.352Z",
"answer": 16912
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
f33d31 | nt_num_divisors_compute_v1_1520064083_115 | Let $n$ be the smallest possible value of $x + y$ where $x$ and $y$ are positive integers such that $xy = 2500$. Compute the number of positive divisors of $n$. | 9 | graphs = [
Graph(
let={
"_n": Const(2500),
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_n")))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_num_divisors_compute_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.002 | 2026-02-08T03:00:28.267512Z | {
"verified": true,
"answer": 9,
"timestamp": "2026-02-08T03:00:28.269419Z"
} | f500bc | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 156,
"completion_tokens": 771
},
"timestamp": "2026-02-10T12:57:23.661Z",
"answer": 9
},
{
"id": ... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.02,
"hi": 0.3
} | ||
48c18d | nt_max_prime_below_v1_1526740231_325 | Let $n$ be the largest prime number less than or equal to $28561$. Define $$ Q = \left( 353702 \cdot (|n| \bmod 97) + 329703 \cdot \left( (|n|^2 + 1) \bmod 101 \right) + 215534 \cdot \left( (|n| + 8) \bmod d \right) \right) \bmod 1009091, $$ where $d$ is the smallest divisor of $130940501$ that is at least $2$. Compute... | 43,372 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": Const(28561),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("upper")), IsPrime(Var("n"))))),
"Q": Mod(value=Mod(value=Sum(Mul(Const(353702), Mod(val... | NT | null | EXTREMUM | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | b5b91a | nt_max_prime_below_v1 | crt_mix_3 | 4 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 2.991 | 2026-02-08T11:28:24.175490Z | {
"verified": true,
"answer": 43372,
"timestamp": "2026-02-08T11:28:27.166084Z"
} | 25db54 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 184,
"completion_tokens": 3009
},
"timestamp": "2026-02-14T15:02:55.394Z",
"answer": 43372
},
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
a925f3 | comb_catalan_compute_v1_1470522791_1277 | Let $T$ be the set of all integers $t$ such that $29 \leq t \leq 65$ and there exist positive integers $a$, $b$ with $1 \leq a \leq 3$, $1 \leq b \leq 4$, satisfying $t = 9a + 6b + 14$. Define $n$ to be the number of elements in $T$.
Compute the $n$-th Catalan number. | 58,786 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=3)), Geq(left=Var(name='b'), right=Const(value=1... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_catalan_compute_v1 | null | 3 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T13:33:01.517775Z | {
"verified": true,
"answer": 58786,
"timestamp": "2026-02-08T13:33:01.519677Z"
} | 185b07 | 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": 1798
},
"timestamp": "2026-02-24T18:32:06.289Z",
"answer": 58786
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
cbc8a3 | comb_sum_binomial_row_v1_124444284_1406 | Let $n$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 36$. Let $Q$ be the remainder when $69249 \cdot 2^n$ is divided by $75679$. Compute $Q$. | 74,691 | graphs = [
Graph(
let={
"_n": Const(69249),
"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(36)))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | SUM | sympy | B3 | [
"B3"
] | 0cd20d | comb_sum_binomial_row_v1 | null | 3 | 0 | [
"B3"
] | 1 | 0.001 | 2026-02-08T03:52:09.080755Z | {
"verified": true,
"answer": 74691,
"timestamp": "2026-02-08T03:52:09.082126Z"
} | c8d3e8 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 174,
"completion_tokens": 1467
},
"timestamp": "2026-02-10T15:57:04.396Z",
"answer": 74691
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
21de43 | nt_sum_divisors_range_v1_865884756_6873 | Let $T$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 64$. Let $s(x, y) = x + y$, and let $S$ be the set of all values of $s(x, y)$ as $(x, y)$ ranges over $T$. Let $d_{\min}$ be the smallest element of $S$.
Let $U$ be the set of all positive integers $k$ such that $1 \leq k \leq 82944$... | 45,158 | graphs = [
Graph(
let={
"_m": Const(64),
"_n": Const(82944),
"upper": CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(1)), Leq(Var("k"), Ref("_n")), Divides(divisor=MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var(... | NT | null | SUM | sympy | ONE_PHI_1 | [
"B3/C2"
] | dcbe93 | nt_sum_divisors_range_v1 | null | 5 | 0 | [
"B3",
"C2",
"ONE_PHI_1"
] | 3 | 3.256 | 2026-02-08T19:25:43.430075Z | {
"verified": true,
"answer": 45158,
"timestamp": "2026-02-08T19:25:46.686192Z"
} | e5bc20 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 257,
"completion_tokens": 3510
},
"timestamp": "2026-02-18T22:21:22.137Z",
"answer": 45158
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "ok_later"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
ad4b97 | comb_catalan_compute_v1_1520064083_2157 | Let $n$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = T$, where $T$ is the number of integers $t$ with $10 \leq t \leq 52$ for which there exist integers $a$ and $b$ satisfying $1 \leq a \leq 6$, $1 \leq b \leq 4$, and $t = 6a + 4b$. Let $C_n$ denote the $n$-th Catalan numb... | 40,494 | graphs = [
Graph(
let={
"_n": Const(92546),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2")),... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/COMB1"
] | 268a62 | comb_catalan_compute_v1 | null | 7 | 0 | [
"COMB1",
"LIN_FORM"
] | 2 | 0.002 | 2026-02-08T04:32:19.759717Z | {
"verified": true,
"answer": 40494,
"timestamp": "2026-02-08T04:32:19.761839Z"
} | 0e154c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 256,
"completion_tokens": 2305
},
"timestamp": "2026-02-24T01:01:34.852Z",
"answer": 40494
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok_later"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status": "n... | {
"lo": -0.05,
"mid": 2.89,
"hi": 5.27
} | ||
3a4a8b | comb_count_surjections_v1_677425708_2348 | Let $n = 6$ and $k = 6$. Define $A = k! \cdot S(n, k)$, where $S(n, k)$ denotes the Stirling number of the second kind. Let $B$ be the number of ordered pairs $(i, j)$ with $i \in \{1, 2\}$ and $j \in \{1, 2, 3\}$ such that $i + j = 3$. Compute the remainder when $B - A$ is divided by $86252$. | 85,534 | graphs = [
Graph(
let={
"_n": Const(3),
"n": Const(6),
"k": Const(6),
"result": Mul(Factorial(Ref("k")), Stirling2(n=Ref(name='n'), k=Ref(name='k'))),
"_c": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Va... | COMB | null | COUNT | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 1449d2 | comb_count_surjections_v1 | negation_mod | 3 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.011 | 2026-02-08T05:00:48.264968Z | {
"verified": true,
"answer": 85534,
"timestamp": "2026-02-08T05:00:48.275579Z"
} | 45ba1f | 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": 613
},
"timestamp": "2026-02-24T02:35:16.696Z",
"answer": 85534
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"stat... | {
"lo": -7.18,
"mid": -4.99,
"hi": -3
} | ||
e7c8e6 | antilemma_v7_kummer_124444284_459 | Let $m = 2$. Let $s$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 1369$. Let $x_0$ be the largest integer $k$ such that $5^k$ divides $\binom{185}{s}$. Define $Q$ to be $19600$ plus the sum $\sum_{i=0}^{d-1} d_i (i+1)^2$, where $d_i$ is the $i$-th decimal digit of... | 19,603 | graphs = [
Graph(
let={
"_m": Const(2),
"_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(1369)))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | COMPUTE | sympy | V7 | [
"B3/V7",
"V7"
] | 664b43 | antilemma_v7_kummer | null | 6 | 0 | [
"B3",
"V7"
] | 2 | 0.003 | 2026-02-08T03:17:59.118333Z | {
"verified": true,
"answer": 19603,
"timestamp": "2026-02-08T03:17:59.121444Z"
} | 59e7d0 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 274,
"completion_tokens": 1244
},
"timestamp": "2026-02-09T17:55:28.392Z",
"answer": 19603
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"... | {
"lo": -6.51,
"mid": -0.31,
"hi": 5.43
} | ||
e07a3a | sequence_fibonacci_compute_v1_1125832087_2334 | Let $n = 24$. Define $F_n$ to be the $n$th Fibonacci number, where $F_1 = 1$, $F_2 = 1$, and $F_k = F_{k-1} + F_{k-2}$ for $k \geq 3$. Let $c = \sum_{k=1}^{2} k$. Compute the remainder when $c - F_n$ is divided by $50478$. | 4,113 | graphs = [
Graph(
let={
"n": Const(24),
"result": Fibonacci(arg=Ref(name='n')),
"_c": Summation(var="k", start=Const(1), end=Const(2), expr=Var("k")),
"Q": Mod(value=Sub(Ref("_c"), Ref("result")), modulus=Const(50478)),
},
goal=Ref("Q"),
)
... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"SUM_ARITHMETIC"
] | 5c63b0 | sequence_fibonacci_compute_v1 | negation_mod | 2 | 0 | [
"COPRIME_PAIRS",
"SUM_ARITHMETIC"
] | 2 | 0.014 | 2026-02-08T04:33:02.178658Z | {
"verified": true,
"answer": 4113,
"timestamp": "2026-02-08T04:33:02.193022Z"
} | 22ec0a | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 208,
"completion_tokens": 502
},
"timestamp": "2026-02-10T17:05:25.688Z",
"answer": 4113
},
{
"i... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V1",
"status": ... | {
"lo": -5.92,
"mid": -3.14,
"hi": 0.27
} | ||
c46f0b | algebra_quadratic_discriminant_v1_124444284_9819 | Let $a = 2$, $b = 16$, and $c = 0$. Compute $b^2 - a \cdot c \cdot \min\{x + y \mid x, y \text{ are positive integers such that } xy = 4\}$. | 256 | graphs = [
Graph(
let={
"_n": Const(2),
"a": Const(2),
"b": Const(16),
"c": Const(0),
"result": Sub(Pow(Ref("b"), Ref("_n")), Mul(MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"B3"
] | 0cd20d | algebra_quadratic_discriminant_v1 | null | 3 | 0 | [
"B3",
"COPRIME_PAIRS"
] | 2 | 0.016 | 2026-02-08T12:41:38.521050Z | {
"verified": true,
"answer": 256,
"timestamp": "2026-02-08T12:41:38.536623Z"
} | 2e7b06 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 116,
"completion_tokens": 301
},
"timestamp": "2026-02-16T04:02:19.144Z",
"answer": 256
},
{
"id": 11,
... | 2 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.71,
"hi": -5.43
} | ||
620662 | nt_sum_gcd_range_mod_v1_655260480_1324 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 2250000$. Define $N$ to be the minimum value of $x + y$ over all pairs in $S$.
Let
$$
\sum_{n=1}^{N} \gcd(n, 90) = M.
$$
Let $R$ be the remainder when $M$ is divided by $11551$.
Compute the remainder when $44121 \cdot R$ is divided ... | 86,618 | 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(2250000)))), expr=Sum(Var("x"), Var("y")))),
"k": Const(90),... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_gcd_range_mod_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.145 | 2026-02-08T16:04:05.900219Z | {
"verified": true,
"answer": 86618,
"timestamp": "2026-02-08T16:04:06.045105Z"
} | b50950 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 156,
"completion_tokens": 3133
},
"timestamp": "2026-02-16T20:31:18.516Z",
"answer": 86618
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
93c118 | nt_count_with_divisor_count_v1_151522320_107 | Let $m = 7$. Consider the set of all ordered pairs $(i,j)$ of integers with $1 \leq i \leq 8$ and $1 \leq j \leq 17$ such that $\gcd(i,j) = 1$. Let $n$ be the number of such pairs. Let $d$ be the largest integer such that $m^d$ divides $n!$. Determine the number of positive integers $n'$ with $1 \leq n' \leq 54756$ suc... | 169 | graphs = [
Graph(
let={
"_m": Const(7),
"_n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(GCD(a=Var("i"), b=Var("j")), Const(1)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(8)), right=IntegerRange(start=Const(1), end=C... | NT | null | COUNT | sympy | COUNT_COPRIME_GRID | [
"COUNT_COPRIME_GRID/V1"
] | 95d765 | nt_count_with_divisor_count_v1 | null | 6 | 0 | [
"COUNT_COPRIME_GRID",
"V1"
] | 2 | 2.721 | 2026-02-08T02:58:43.070822Z | {
"verified": true,
"answer": 169,
"timestamp": "2026-02-08T02:58:45.792129Z"
} | 57db87 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 244,
"completion_tokens": 3821
},
"timestamp": "2026-02-08T23:05:11.687Z",
"answer": 169
},
{
"i... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "V1",
"status": "ok_later"
},
{
"lemma": "V3",
"status": "no"
... | {
"lo": -6.49,
"mid": 0.51,
"hi": 7.52
} | ||
d6f2ab | antilemma_k3_v1_784195855_7346 | Let $n = 81207$. Define $x$ to be the sum of $\phi(d)$ over all positive divisors $d$ of $n$, where $\phi$ denotes Euler's totient function. Compute the remainder when $44121 \cdot x$ is divided by $51773$. | 35,355 | graphs = [
Graph(
let={
"_n": Const(81207),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Mod(value=Mul(Const(44121), Ref("x")), modulus=Const(51773)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T09:13:41.965936Z | {
"verified": true,
"answer": 35355,
"timestamp": "2026-02-08T09:13:41.966876Z"
} | 382f5e | 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": 1901
},
"timestamp": "2026-02-14T01:27:50.168Z",
"answer": 35355
},
... | 1 | [
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
de3015 | nt_count_primes_v1_1978505735_1387 | Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 6$, $\gcd(p, q) = 1$, and $p < q$. Let $m$ be the number of elements in $S$. Let $T$ be the set of all prime numbers $n$ such that $m \leq n \leq 39601$. Compute the remainder when $39925 \cdot |T|$ is d... | 58,852 | graphs = [
Graph(
let={
"_n": Const(39925),
"upper": Const(39601),
"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'), conditio... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_count_primes_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 1.932 | 2026-02-08T16:06:46.048759Z | {
"verified": true,
"answer": 58852,
"timestamp": "2026-02-08T16:06:47.980392Z"
} | 4399f5 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 158,
"completion_tokens": 4727
},
"timestamp": "2026-02-16T21:00:51.359Z",
"answer": 58852
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
dfe153 | comb_count_partitions_v1_124444284_148 | Let $N$ be the number of positive integers $k$ such that
\[1 \le k \le M \quad \text{and} \quad 80 \mid k,
\]
where $M$ is defined as follows.
Consider all ordered pairs $(x,y)$ of positive integers such that
\[xy = 2433600.
\]
Let $M$ be the minimum value of $x+y$ over all such pairs $(x,y)$.
Let $p(N)$ denote the n... | 31,185 | graphs = [
Graph(
let={
"_n": Const(80),
"n": CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(1)), Leq(Var("k"), MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(... | NT | COMB | COUNT | sympy | B3 | [
"B3/C2"
] | dcbe93 | comb_count_partitions_v1 | null | 8 | 0 | [
"B3",
"C2"
] | 2 | 0.002 | 2026-02-08T03:01:21.160015Z | {
"verified": true,
"answer": 31185,
"timestamp": "2026-02-08T03:01:21.161875Z"
} | 4b9b87 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 231,
"completion_tokens": 5488
},
"timestamp": "2026-02-08T23:31:15.346Z",
"answer": 30848
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "ok_later"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma... | {
"lo": 1.28,
"mid": 3.39,
"hi": 5.27
} | ||
6bbe9c | modular_sum_quadratic_residues_v1_1918700295_2875 | Let $p = 149$ and define $\text{result} = \frac{p(p-1)}{4}$. Let $c$ be the number of prime numbers $n$ such that $2 \leq n \leq 6133$. Let $Q$ be the remainder when $c - \text{result}$ is divided by 96336. Compute $Q$. | 91,623 | graphs = [
Graph(
let={
"p": Const(149),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), Const(4)),
"_c": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(6133)), IsPrime(Var("n"))))),
"Q": Mod(value=... | NT | null | SUM | sympy | COUNT_PRIMES | [
"COUNT_PRIMES"
] | ad5c3c | modular_sum_quadratic_residues_v1 | negation_mod | 3 | 0 | [
"COUNT_PRIMES"
] | 1 | 0.002 | 2026-02-08T08:16:36.382449Z | {
"verified": true,
"answer": 91623,
"timestamp": "2026-02-08T08:16:36.384260Z"
} | c8ec7e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 124,
"completion_tokens": 3727
},
"timestamp": "2026-02-13T16:47:31.018Z",
"answer": 91623
},
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
af386f | comb_count_partitions_v1_1439011603_1213 | Let $n$ be the number of integers $t$ with $5 \leq t \leq 15$ that can be expressed as $3a + 2b$ for positive integers $a, b$ each at most $3$. Define $m = 9$ and let $s = \sum_{k=1}^{n} \phi(k) \left\lfloor \frac{m}{k} \right\rfloor$. Find the number of integer partitions of $s$. | 89,134 | graphs = [
Graph(
let={
"_m": Const(9),
"_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 | COUNT | sympy | LIN_FORM | [
"LIN_FORM/K2"
] | 506489 | comb_count_partitions_v1 | null | 6 | 0 | [
"K2",
"LIN_FORM"
] | 2 | 0.005 | 2026-02-08T15:58:46.079784Z | {
"verified": true,
"answer": 89134,
"timestamp": "2026-02-08T15:58:46.084966Z"
} | 45d5dd | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 147,
"completion_tokens": 1529
},
"timestamp": "2026-02-16T18:33:26.363Z",
"answer": 89134
},
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K2",
"status": "ok_later"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": ... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
ce56ed | nt_count_coprime_and_v1_677425708_2365 | Let $U = 27839$, $k_1 = 7$, and $k_2 = 9$. Determine the number of positive integers $n \leq U$ such that $\gcd(n, k_1) = 1$ and $\gcd(n, k_2) = 1$. Let this number be $r$. Let $N = 152$. Consider all pairs of positive integers $(x, y)$ such that $x + y = N$. Let $c$ be the maximum value of $xy$ over all such pairs. Fi... | 67,691 | graphs = [
Graph(
let={
"_n": Const(152),
"upper": Const(27839),
"k1": Const(7),
"k2": Const(9),
"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("k1"... | NT | null | COUNT | sympy | B1 | [
"B1"
] | d2b6e1 | nt_count_coprime_and_v1 | negation_mod | 4 | 0 | [
"B1"
] | 1 | 3.034 | 2026-02-08T05:01:16.746143Z | {
"verified": true,
"answer": 67691,
"timestamp": "2026-02-08T05:01:19.779770Z"
} | 4ff209 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 244,
"completion_tokens": 2049
},
"timestamp": "2026-02-11T22:44:41.525Z",
"answer": 67691
},
{
"... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status... | {
"lo": 1.71,
"mid": 5.04,
"hi": 8.38
} | ||
317049 | geo_count_lattice_rect_v1_1470522791_834 | Let $a = 128$ and $b = 110$. Define $\text{result}$ to be the number of lattice points $(x, y)$ such that $0 \leq x \leq a$ and $0 \leq y \leq b$. Compute the remainder when $44121 \cdot \text{result}$ is divided by $99394$. Determine the value of this remainder. | 20,335 | graphs = [
Graph(
let={
"a": Const(128),
"b": Const(110),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"Q": Mod(value=Mul(Const(44121), Ref("result")), modulus=Const(99394)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 2 | 0 | null | null | 0.006 | 2026-02-08T13:16:54.117021Z | {
"verified": true,
"answer": 20335,
"timestamp": "2026-02-08T13:16:54.122761Z"
} | 23a461 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 196,
"completion_tokens": 6801
},
"timestamp": "2026-02-24T17:42:15.775Z",
"answer": 20335
},
{
"... | 1 | [] | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||||
633845 | modular_min_modexp_v1_151522320_2560 | Let $a = 3$, $b = 546$, and $m = 887$. Let $S$ be the set of all positive integers $x$ such that $1 \leq x \leq 443$ and $a^x \equiv b \pmod{m}$. Find the value of the smallest element in $S$. | 282 | graphs = [
Graph(
let={
"a": Const(3),
"b": Const(546),
"m": Const(887),
"upper": Const(443),
"result": MinOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), Const(1)), Leq(Var("x"), Ref("upper")), Eq(ModExp(base=Ref("a"), exp=Var("... | NT | null | EXTREMUM | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | modular_min_modexp_v1 | null | 6 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.038 | 2026-02-08T04:52:53.145699Z | {
"verified": true,
"answer": 282,
"timestamp": "2026-02-08T04:52:53.183420Z"
} | 778402 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 185,
"completion_tokens": 5316
},
"timestamp": "2026-02-11T22:23:15.845Z",
"answer": 282
},
{
"i... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
... | {
"lo": -3.49,
"mid": 1.84,
"hi": 7.55
} | ||
43bb34 | sequence_count_fib_divisible_v1_1439011603_245 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 164025$. For each pair in $S$, compute $x + y$, and let $u$ be the minimum value among all such sums. Let $d = 13$. Determine the number of positive integers $n$ such that $1 \leq n \leq u$ and the $n$-th Fibonacci number is divisible... | 115 | graphs = [
Graph(
let={
"upper": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(164025)))), expr=Sum(Var("x"), Var("y")))),
"d": Const(1... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | sequence_count_fib_divisible_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.042 | 2026-02-08T15:22:13.310303Z | {
"verified": true,
"answer": 115,
"timestamp": "2026-02-08T15:22:13.352445Z"
} | 6b377a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 143,
"completion_tokens": 2342
},
"timestamp": "2026-02-16T05:17:20.777Z",
"answer": 115
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
a5ee24 | geo_count_lattice_triangle_v1_124444284_4069 | Let $A$ be the area of a triangle with vertices at $(0,0)$, $(144,49)$, and $(256,100)$, multiplied by 2. Let $B$ be the number of lattice points on the boundary of this triangle, computed using the formula
$$
B = \gcd(144, 49) + \gcd(256 - 144, 100 - 49) + \gcd(256, 100).
$$
Compute the value of $Q$, where $Q$ is the ... | 35,633 | graphs = [
Graph(
let={
"_n": Const(256),
"area_2x": Abs(arg=Sum(Mul(Const(value=144), Const(value=100)), Mul(Const(value=256), Sub(left=Const(value=0), right=Const(value=49))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=144)), b=Abs(arg=Const(value=49))), GCD(a=Abs(arg=... | ALG | NT | COUNT | sympy | B1 | [
"B1"
] | 5b950e | geo_count_lattice_triangle_v1 | null | 6 | 0 | [
"B1"
] | 1 | 0.005 | 2026-02-08T05:45:04.951409Z | {
"verified": true,
"answer": 35633,
"timestamp": "2026-02-08T05:45:04.956736Z"
} | 041a04 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 181,
"completion_tokens": 1225
},
"timestamp": "2026-02-12T14:22:21.779Z",
"answer": 35633
},
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
69e391 | modular_sum_quadratic_residues_v1_397696148_2077 | Let $A$ be the set of all positive integers $n$ such that $1 \leq n \leq 819$ and the sum of the decimal digits of $n$ is even. Let $D$ be the number of elements in $A$. Let $p$ be the largest positive divisor of 172189 that is less than or equal to $D$. Compute $\frac{p(p-1)}{4}$. | 41,718 | graphs = [
Graph(
let={
"_n": Const(4),
"p": MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Leq(Var("d"), CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(819)), Eq(Mod(value=DigitSum(Var("n")), m... | NT | null | SUM | sympy | L3B | [
"L3B/MAX_DIVISOR"
] | 22366c | modular_sum_quadratic_residues_v1 | null | 5 | 0 | [
"L3B",
"MAX_DIVISOR"
] | 2 | 0.004 | 2026-02-08T12:56:52.771261Z | {
"verified": true,
"answer": 41718,
"timestamp": "2026-02-08T12:56:52.775322Z"
} | e1130b | 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": 3211
},
"timestamp": "2026-02-15T07:43:00.074Z",
"answer": 41718
},
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3B",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok_later"
},
{
"lemma": "MAX_VAL",
"status": "no"
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
dad01c | sequence_fibonacci_compute_v1_1874849503_1026 | Let $T$ be the set of all integers $t$ such that $5 \leq t \leq 31$ and there exist positive integers $a \leq 8$ and $b \leq 5$ for which $t = 2a + 3b$. Let $n$ be the number of elements in $T$. Let $F_n$ be the $n$-th Fibonacci number. Let $S$ be the set of all integers $t$ such that $7 \leq t \leq 20$ and there exist... | 21,877 | graphs = [
Graph(
let={
"_n": Const(10),
"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=8)), Geq(left=Var(n... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/BINOMIAL_ALTERNATING"
] | cedb10 | sequence_fibonacci_compute_v1 | digits_weighted_mod | 7 | 0 | [
"BINOMIAL_ALTERNATING",
"LIN_FORM"
] | 2 | 0.012 | 2026-02-08T13:30:38.066827Z | {
"verified": true,
"answer": 21877,
"timestamp": "2026-02-08T13:30:38.079192Z"
} | de55b7 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 364,
"completion_tokens": 3212
},
"timestamp": "2026-02-10T00:00:07.733Z",
"answer": 21793
},
{
... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok_later"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
... | {
"lo": 3.25,
"mid": 5.68,
"hi": 8.81
} | ||
03697a | geo_count_lattice_rect_v1_865884756_6085 | Compute the number of lattice points $(x, y)$ such that $0 \leq x \leq 300$ and $0 \leq y \leq 246$. | 74,347 | graphs = [
Graph(
let={
"a": Const(300),
"b": Const(246),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.001 | 2026-02-08T18:57:37.650173Z | {
"verified": true,
"answer": 74347,
"timestamp": "2026-02-08T18:57:37.651136Z"
} | 5923df | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 81,
"completion_tokens": 437
},
"timestamp": "2026-02-18T20:41:38.456Z",
"answer": 74347
},
{
... | 1 | [] | {
"lo": -7.92,
"mid": -4.6,
"hi": -1.84
} | ||||
80fb54 | algebra_quadratic_discriminant_v1_601307018_4574 | Let $c$ be the number of ordered pairs $(a_1, b_1)$ of positive integers with $1 \le a_1, b_1 \le 30$ such that $13a_1^2 - 2a_1b_1 + 2b_1^2 \le 853$. Let $D = 36 + 2c \cdot \left| \left\{ (a_2, b_2) : 1 \le a_2, b_2 \le 20,\ 8a_2^3 - 24a_2^2b_2 + 24a_2b_2^2 = 13832 \right\} \right|$. Define $R = 2$ if $D > 0$, and $R =... | 37,634 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(2),
"a": Const(-2),
"b": Const(6),
"c": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a1"), Var("b1")]), condition=And(Geq(Var("a1"), Const(1)), Leq(Var("a1"), Const(30)), Geq(Var("b1"), ... | ALG | null | COMPUTE | sympy | QF_PSD_COUNT_LEQ | [
"QF_PSD_COUNT_LEQ",
"POLY3_COUNT"
] | 6b3631 | algebra_quadratic_discriminant_v1 | null | 6 | 0 | [
"POLY3_COUNT",
"QF_PSD_COUNT_LEQ"
] | 2 | 0.011 | 2026-03-10T05:12:56.510977Z | {
"verified": true,
"answer": 37634,
"timestamp": "2026-03-10T05:12:56.521484Z"
} | aeed3e | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 302,
"completion_tokens": 3976
},
"timestamp": "2026-03-29T12:44:45.424Z",
"answer": 37634
},
{
"... | 1 | [
{
"lemma": "POLY3_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
}
] | {
"lo": -6.2,
"mid": -2.87,
"hi": 0.44
} | ||
5d524b | antilemma_k2_v1_1520064083_7449 | Let $m = 298$ and let $n = \sum_{d \mid 298} \phi(d)$, where $\phi$ denotes Euler's totient function. Define $x = \sum_{k=1}^{n} \phi(k) \left\lfloor \frac{m}{k} \right\rfloor$. Compute the value of $x + \phi(|x| + 1) + \tau(|x| + 1)$, where $\tau(N)$ denotes the number of positive divisors of $N$. | 66,831 | graphs = [
Graph(
let={
"_m": Const(298),
"_n": SumOverDivisors(n=Const(value=298), var='d', expr=EulerPhi(n=Var(name='d'))),
"x": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Ref("_m"), Var("k"))))),
"Q": Sum(Ref(... | NT | COMB | COMPUTE | sympy | K3 | [
"K3/K2",
"K2"
] | c7f244 | antilemma_k2_v1 | null | 7 | 0 | [
"K2",
"K3"
] | 2 | 0.001 | 2026-02-08T09:03:19.805191Z | {
"verified": true,
"answer": 66831,
"timestamp": "2026-02-08T09:03:19.806252Z"
} | 8e8270 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 155,
"completion_tokens": 1609
},
"timestamp": "2026-02-13T23:37:06.945Z",
"answer": 66831
},
... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V5",
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
3327d5 | antilemma_cartesian_v1_1915831931_2419 | Let $x$ be the number of ordered pairs $(i, j)$ such that $1 \le i \le 47$ and $1 \le j \le 48$. Let $d_k$ denote the $k$-th decimal digit of $|x|$, where the units digit is at position $k=0$. Let $\ell$ be the number of digits in $|x|$. Compute
$$
\sum_{k=0}^{\ell-1} d_k (k+1)^2 + 3364.
$$ | 3,440 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(47)), right=IntegerRange(start=Const(1), end=Const(48)))),
"Q": Sum(Summation(var="i", start=Const(0), end=Sub(NumDigits(x=Abs(arg=Ref(name='x')), base=None), Const(1)), expr=Mu... | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | antilemma_cartesian_v1 | null | 5 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.001 | 2026-02-08T16:47:45.230731Z | {
"verified": true,
"answer": 3440,
"timestamp": "2026-02-08T16:47:45.232195Z"
} | bcbf4d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 158,
"completion_tokens": 865
},
"timestamp": "2026-02-17T12:18:32.084Z",
"answer": 3440
},
{
... | 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_SU... | {
"lo": -5.64,
"mid": -3.17,
"hi": -0.81
} | ||
aa5132 | geo_count_lattice_triangle_v1_1978505735_2220 | Let $A$ be the area of the triangle with vertices at $(0,0)$, $(120,66)$, and $(31,121)$. Let $B$ be the number of lattice points on the boundary of this triangle. Using the formula
$$
\text{Area} = \frac{1}{2} \left( 2A + 2 - B \right),
$$
compute the value of $37950$ minus the number of interior lattice points of the... | 31,716 | graphs = [
Graph(
let={
"_n": Const(121),
"area_2x": Abs(arg=Sum(Mul(Const(value=120), Const(value=121)), Mul(Const(value=31), Sub(left=Const(value=0), right=Const(value=66))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=120)), b=Abs(arg=Const(value=66))), GCD(a=Abs(arg=S... | ALG | NT | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | geo_count_lattice_triangle_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.011 | 2026-02-08T16:46:59.814139Z | {
"verified": true,
"answer": 31716,
"timestamp": "2026-02-08T16:46:59.824945Z"
} | 3d898a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 144,
"completion_tokens": 2462
},
"timestamp": "2026-02-17T11:20:07.696Z",
"answer": 31716
},
... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
6bb4aa | geo_count_lattice_triangle_v1_1978505735_7719 | Let the area of a certain triangle be such that twice the area is given by $$ |111 \cdot 128 + 240 \cdot (0 - 2)|. $$ Let the number of boundary lattice points on this triangle be $$ \gcd(|111|, 2) + \gcd\left(|N - 111|, |128 - 2|\right) + \gcd(|0 - 240|, |0 - 128|), $$ where $N$ is the number of pairs of positive odd ... | 62,773 | graphs = [
Graph(
let={
"_n": Const(2),
"area_2x": Abs(arg=Sum(Mul(Const(value=111), Const(value=128)), Mul(Const(value=240), Sub(left=Const(value=0), right=Const(value=2))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=111)), b=Abs(arg=Ref(name='_n'))), GCD(a=Abs(arg=Sub(... | NT | null | COUNT | sympy | COMB1 | [
"COMB1"
] | 567f58 | geo_count_lattice_triangle_v1 | null | 7 | 0 | [
"COMB1"
] | 1 | 0.006 | 2026-02-08T20:24:15.016082Z | {
"verified": true,
"answer": 62773,
"timestamp": "2026-02-08T20:24:15.021827Z"
} | 8e7482 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 244,
"completion_tokens": 3613
},
"timestamp": "2026-02-19T00:31:34.274Z",
"answer": 62773
},
... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
f58ed3 | diophantine_fbi2_min_v1_458359167_3462 | Let $n = 36$ and $k = 35$. Let $s$ be the sum of $\phi(d)$ over all positive divisors $d$ of $45$, where $\phi$ is Euler's totient function. Let $D$ be the set of all integers $d$ such that $2 \le d \le s$, $d$ divides $k$, and $\frac{k}{d} \ge 2$. Let $r = \min D$, the smallest element of $D$. Let $c = \sum_{k=1}^{36}... | 661 | graphs = [
Graph(
let={
"_n": Const(36),
"k": Const(35),
"upper": SumOverDivisors(n=Const(value=45), var='d', expr=EulerPhi(n=Var(name='d'))),
"result": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Leq(Var("d"), Ref("upper")... | NT | null | EXTREMUM | sympy | K2 | [
"K2",
"K3"
] | 37dde1 | diophantine_fbi2_min_v1 | negation_mod | 6 | 0 | [
"K2",
"K3"
] | 2 | 0.011 | 2026-02-08T08:22:50.218871Z | {
"verified": true,
"answer": 661,
"timestamp": "2026-02-08T08:22:50.229887Z"
} | 9120fb | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 191,
"completion_tokens": 983
},
"timestamp": "2026-02-13T18:01:02.422Z",
"answer": 661
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8",
"st... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
4f227e | antilemma_product_of_sums_v1_1742523217_1809 | Let $S_1$ be the sum of $i \cdot j$ over all ordered pairs $(i, j)$ where $1 \leq i \leq 4$ and $1 \leq j \leq 9$. Let $S_2$ be the sum of $k$ over all ordered pairs $(k, \_j)$ where $1 \leq k \leq 5$ and $1 \leq \_j \leq 3$. Compute $S_1 \cdot S_2$. | 20,250 | graphs = [
Graph(
let={
"S1": SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Const(1), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(4)), right=IntegerRange(start=Const(1), end=Const(9)))), expr=Mul(Var("i"), Var("j")))),
... | NT | null | COMPUTE | sympy | PRODUCT_OF_SUMS | [
"PRODUCT_OF_SUMS"
] | f2b2b0 | antilemma_product_of_sums_v1 | null | 2 | 0 | [
"PRODUCT_OF_SUMS"
] | 1 | 0.001 | 2026-02-08T04:15:31.183775Z | {
"verified": true,
"answer": 20250,
"timestamp": "2026-02-08T04:15:31.184628Z"
} | b9fcfe | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 198,
"completion_tokens": 497
},
"timestamp": "2026-02-18T10:21:05.992Z",
"answer": 20250
}
] | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "PRODUCT_OF_SUMS",
... | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
18529a | algebra_poly_eval_v1_809748730_611 | Let $t = 8$. Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = 4$. Define $m$ to be the maximum value of $xy$ over all $(x, y) \in S$. Compute the value of
$$
7t^m - 9t^3 + 6t^2 + 2t - 5.
$$ | 24,459 | graphs = [
Graph(
let={
"t": Const(8),
"result": Sum(Mul(Const(7), Pow(Ref("t"), MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Const(4)))), e... | NT | null | COMPUTE | sympy | B1 | [
"B1"
] | 5b950e | algebra_poly_eval_v1 | null | 2 | 0 | [
"B1"
] | 1 | 0.002 | 2026-02-08T11:37:18.796419Z | {
"verified": true,
"answer": 24459,
"timestamp": "2026-02-08T11:37:18.798369Z"
} | d98a48 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 138,
"completion_tokens": 601
},
"timestamp": "2026-02-14T16:59:11.835Z",
"answer": 24459
},
{... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8_SUM",
"... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
a7a175 | modular_min_linear_v1_717093673_1135 | Let $T$ be the set of all integers $t$ such that $27 \leq t \leq 9435$ and there exist positive integers $a \leq 283$, $b \leq 582$ satisfying $t = 21a + 6b$. Let $a_0$ be the number of elements in $T$. Let $F_n$ denote the $n$th Fibonacci number. Let $N$ be the number of positive integers $n_1 \leq 60192$ such that $6... | 3,233 | graphs = [
Graph(
let={
"_m": Const(6),
"_n": Const(3),
"a": 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=Cons... | NT | null | EXTREMUM | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE/C5",
"LIN_FORM"
] | 2abbcb | modular_min_linear_v1 | null | 7 | 0 | [
"C5",
"COUNT_FIB_DIVISIBLE",
"LIN_FORM"
] | 3 | 0.416 | 2026-02-08T15:52:17.077667Z | {
"verified": true,
"answer": 3233,
"timestamp": "2026-02-08T15:52:17.493417Z"
} | c880a9 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 242,
"completion_tokens": 6428
},
"timestamp": "2026-02-16T15:29:47.107Z",
"answer": 3233
},
{... | 1 | [
{
"lemma": "C5",
"status": "ok_later"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
b70bc2 | antilemma_sum_equals_v1_655260480_2177 | Let $m = 74$. Define $n$ to be the number of ordered pairs $(i, j)$ of positive integers such that $1 \leq i \leq 73$, $1 \leq j \leq 74$, and $i + j = m$.
Let $x$ be the number of ordered pairs $(i_1, j_1)$ of positive integers such that $1 \leq i_1 \leq 71$, $1 \leq j_1 \leq 71$, and $i_1 + j_1 = n$.
Find the remai... | 28,054 | graphs = [
Graph(
let={
"_m": Const(74),
"_n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref("_m")), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(73)), right=IntegerRange(start=Const(1), end=Co... | COMB | GEOM | COMPUTE | sympy | LIN_FORM | [
"COUNT_SUM_EQUALS/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | ae9919 | antilemma_sum_equals_v1 | null | 3 | 0 | [
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 2 | 0.052 | 2026-02-08T16:36:22.498675Z | {
"verified": true,
"answer": 28054,
"timestamp": "2026-02-08T16:36:22.550665Z"
} | 51dc9f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 181,
"completion_tokens": 1196
},
"timestamp": "2026-02-17T07:07:47.493Z",
"answer": 28054
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||
209a4d | modular_mod_compute_v1_601307018_1718 | Let $m$ be the maximum value of $xy$ over all ordered pairs $(x, y)$ of positive integers such that $x + y = 172$. Let $M = -67600 \bmod m$. Compute $20164 - M$. | 13,804 | graphs = [
Graph(
let={
"a": Const(-67600),
"m": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Const(172)))), expr=Mul(Var("x"), Var("y")))),... | NT | null | COMPUTE | sympy | B1 | [
"B1"
] | 5b950e | modular_mod_compute_v1 | null | 3 | 0 | [
"B1"
] | 1 | 0.005 | 2026-03-10T02:27:51.223178Z | {
"verified": true,
"answer": 13804,
"timestamp": "2026-03-10T02:27:51.228608Z"
} | 12f82d | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 163,
"completion_tokens": 577
},
"timestamp": "2026-03-29T03:11:12.706Z",
"answer": 13804
},
{
"i... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
}
] | {
"lo": -6.5,
"mid": -3.34,
"hi": -0.89
} | ||
7f5809 | diophantine_fbi2_min_v1_1080341949_285 | Let $m=169$. Let $r$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that
$$pq = 216, \quad \gcd(p,q) = 1, \quad p < q.$$
Let $n$ be the number of integers $j$ with $0 \le j \le 16648$ such that
$$\binom{16648}{j} \equiv 1 \pmod{r}.$$
For each ordered pair $(x,y)$ of positive... | 13 | graphs = [
Graph(
let={
"_m": Const(169),
"_n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(16648)), Eq(Mod(value=Binom(n=Const(16648), k=Var("j")), modulus=CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive... | NT | null | EXTREMUM | sympy | MAX_DIVISOR | [
"COPRIME_PAIRS/V8/SUM_ARITHMETIC",
"B3"
] | c5974e | diophantine_fbi2_min_v1 | null | 7 | 0 | [
"B3",
"COPRIME_PAIRS",
"MAX_DIVISOR",
"SUM_ARITHMETIC",
"V8"
] | 5 | 0.037 | 2026-02-08T13:24:06.287114Z | {
"verified": true,
"answer": 13,
"timestamp": "2026-02-08T13:24:06.324184Z"
} | 38fc58 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 278,
"completion_tokens": 2197
},
"timestamp": "2026-02-15T14:48:16.120Z",
"answer": 13
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
4dd6ff | sequence_fibonacci_compute_v1_1470522791_1337 | Let $n$ be the number of positive integers $m$ such that $1 \leq m \leq 38$ and the sum of the decimal digits of $m$ is odd. Let $F_n$ denote the $n$-th Fibonacci number, where $F_1 = F_2 = 1$ and $F_k = F_{k-1} + F_{k-2}$ for $k \geq 3$. Compute the remainder when $89648 \cdot F_n$ is divided by $56947$. | 40,117 | graphs = [
Graph(
let={
"_n": Const(2),
"n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(38)), Eq(Mod(value=DigitSum(Var("n")), modulus=Ref("_n")), Const(1))))),
"result": Fibonacci(arg=Ref(name='n')),
... | NT | null | COMPUTE | sympy | L3B | [
"L3B"
] | cc148f | sequence_fibonacci_compute_v1 | null | 4 | 0 | [
"L3B"
] | 1 | 0.002 | 2026-02-08T13:35:32.543088Z | {
"verified": true,
"answer": 40117,
"timestamp": "2026-02-08T13:35:32.544734Z"
} | bf7cbe | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 158,
"completion_tokens": 1665
},
"timestamp": "2026-02-15T18:17:18.935Z",
"answer": 40117
},
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3B",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
618923 | geo_visible_lattice_v1_548369836_240 | Let $n = 180$. Define $r$ to be the number of visible lattice points $(x, y)$ such that $1 \le x, y \le n$, where a point $(x, y)$ is visible if $\gcd(x, y) = 1$. Let $Q$ be the remainder when $91263 \cdot r$ is divided by $95453$. Find the value of $Q$. | 62,994 | graphs = [
Graph(
let={
"n": Const(180),
"result": VisibleLatticePoints(n=Ref(name='n')),
"_c": Const(91263),
"Q": Mod(value=Mul(Ref("_c"), Ref("result")), modulus=Const(95453)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 5 | 0 | null | null | 1.586 | 2026-02-08T02:49:26.172089Z | {
"verified": true,
"answer": 62994,
"timestamp": "2026-02-08T02:49:27.758161Z"
} | 2be459 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 199,
"completion_tokens": 30653
},
"timestamp": "2026-02-23T16:33:25.946Z",
"answer": 52780
},
{
... | 1 | [] | {
"lo": 4.43,
"mid": 5.71,
"hi": 7.12
} | ||||
92fb11 | nt_count_primes_v1_2080023795_67 | Let $P$ be the set of all positive integers $p$ such that there exists a positive integer $q$ with $pq = 108$, $\gcd(p, q) = 1$, and $p < q$. Let $\ell = |P|$. Determine the number of prime numbers $n$ such that $\ell \leq n \leq 20000$. | 2,262 | graphs = [
Graph(
let={
"upper": Const(20000),
"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 | 0.486 | 2026-02-08T11:31:16.335373Z | {
"verified": true,
"answer": 2262,
"timestamp": "2026-02-08T11:31:16.821754Z"
} | 94e77d | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 194,
"completion_tokens": 1469
},
"timestamp": "2026-02-08T20:39:56.312Z",
"answer": 2262
},
{
"i... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "V8_SUM",
"statu... | {
"lo": -5.3,
"mid": -2.05,
"hi": 1.82
} | ||
70bb32 | algebra_quadratic_discriminant_v1_601307018_5509 | Let $c$ be the number of ordered pairs $(a_1, b_1)$ of positive integers with $1 \leq a_1 \leq 30$ and $1 \leq b_1 \leq 30$ satisfying $-56a_1^3 - 6a_1b_1^2 + 36a_1^2b_1 = -728$. Compute $9^2 - 4(-8)c$. | 241 | graphs = [
Graph(
let={
"_n": Const(2),
"a": Const(-8),
"b": Const(9),
"c": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a1"), Var("b1")]), condition=And(Geq(Var("a1"), Const(1)), Leq(Var("a1"), Const(30)), Geq(Var("b1"), Const(1)), Leq(Var("b1"), Co... | ALG | null | COMPUTE | sympy | B3_CLOSEST | [
"POLY3_COUNT"
] | 355dbe | algebra_quadratic_discriminant_v1 | null | 4 | 0 | [
"B3_CLOSEST",
"POLY3_COUNT"
] | 2 | 0.039 | 2026-03-10T06:06:47.505777Z | {
"verified": true,
"answer": 241,
"timestamp": "2026-03-10T06:06:47.544515Z"
} | 5e2776 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 209,
"completion_tokens": 2920
},
"timestamp": "2026-04-19T02:15:18.316Z",
"answer": 241
},
{
"i... | 1 | [
{
"lemma": "POLY3_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -3.31,
"mid": 1.32,
"hi": 5.87
} | ||
3aa2d8 | modular_modexp_compute_v1_601307018_502 | Let $a$ be the minimum value of $|x - y|$ over all ordered pairs $(x, y)$ of positive integers such that $xy = \min\{ x_1 + y_1 \mid x_1, y_1 > 0,\, x_1 y_1 = 400,\, x_1 \le y_1 \}$. Let $M = a^{5000} \bmod 27495$. Find the remainder when $83125M$ is divided by $81398$. | 16,599 | graphs = [
Graph(
let={
"_n": Const(81398),
"a": 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")), MinOverSet(set=MapOverSet(set=SolutionsSet(var... | NT | null | COMPUTE | sympy | B3 | [
"B3/B3_DIFF"
] | 181426 | modular_modexp_compute_v1 | null | 5 | 0 | [
"B3",
"B3_DIFF"
] | 2 | 0.007 | 2026-03-10T01:00:36.871996Z | {
"verified": true,
"answer": 16599,
"timestamp": "2026-03-10T01:00:36.879162Z"
} | f56eba | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 222,
"completion_tokens": 7393
},
"timestamp": "2026-03-28T23:10:45.530Z",
"answer": 16599
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "B3_DIFF",
"status": "ok_later"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
... | {
"lo": -0.92,
"mid": 2.07,
"hi": 4.68
} | ||
7db24b | geo_count_lattice_triangle_v1_2051736721_3204 | The area of a triangle with vertices at $(0,0)$, $(233,169)$, and $(30,100)$ is to be computed using the shoelace formula. Let $A$ be twice the area of this triangle, given by
\[
A = \left| 233 \cdot 100 - 30 \cdot 169 \right|.
\]
Let $B$ be the number of lattice points on the boundary of the triangle, computed as the ... | 9,110 | graphs = [
Graph(
let={
"area_2x": Abs(arg=Sum(Mul(Const(value=233), Const(value=100)), Mul(Const(value=30), Sub(left=Const(value=0), right=Const(value=169))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=233)), b=Abs(arg=Const(value=169))), GCD(a=Abs(arg=Sub(left=Const(value=30), rig... | ALG | NT | COUNT | sympy | [] | geo_count_lattice_triangle_v1 | null | 4 | 0 | null | null | 0.003 | 2026-02-08T17:10:20.893446Z | {
"verified": true,
"answer": 9110,
"timestamp": "2026-02-08T17:10:20.896344Z"
} | 621b63 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 224,
"completion_tokens": 1587
},
"timestamp": "2026-02-17T20:46:59.112Z",
"answer": 9110
},
{... | 1 | [] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||||
74a1d3 | modular_modexp_compute_v1_1520064083_1651 | Let $a = 47$, $e = 406$, and $m = 55696$. Let $r$ be the remainder when $a^e$ is divided by $m$. Let $p$ be the largest prime number not exceeding $399$. Let $c$ be the number of ordered pairs $(x_1, x_2)$ of odd positive integers such that $x_1 + x_2 = 10006$. Compute the remainder when $\left(r \bmod 251\right) + c \... | 57,003 | graphs = [
Graph(
let={
"_m": Const(77921),
"_n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(399)), IsPrime(Var("n"))))),
"a": Const(47),
"e": Const(406),
"m": Const(55696),
"res... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW/COMB1"
] | 02f3da | modular_modexp_compute_v1 | two_moduli | 6 | 0 | [
"COMB1",
"MAX_PRIME_BELOW"
] | 2 | 0.005 | 2026-02-08T04:11:05.685178Z | {
"verified": true,
"answer": 57003,
"timestamp": "2026-02-08T04:11:05.690564Z"
} | cc49c4 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 239,
"completion_tokens": 5003
},
"timestamp": "2026-02-10T15:48:19.299Z",
"answer": 57003
},
{
... | 1 | [
{
"lemma": "COMB1",
"status": "ok_later"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
31f51a | nt_sum_gcd_range_mod_v1_1915831931_1995 | Let $m = 2$ and let $n = \sum_{k=1}^{5} \phi(k) \left\lfloor \frac{5}{k} \right\rfloor$, where $\phi$ denotes Euler's totient function. Let $N$ be the number of nonnegative integers $j$ with $0 \leq j \leq 85245$ such that $\binom{85245}{j}$ is odd. Define $k = 90$ and $M = 11489$. Let $\text{sum} = \sum_{n=1}^{N} \gcd... | 3,409 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Summation(var="k1", start=Const(1), end=Const(5), expr=Mul(EulerPhi(n=Var("k1")), Floor(Div(Const(5), Var("k1"))))),
"N": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(8... | NT | null | COMPUTE | sympy | K2 | [
"K2/V8"
] | b13751 | nt_sum_gcd_range_mod_v1 | mod_exp | 6 | 0 | [
"K2",
"V8"
] | 2 | 0.1 | 2026-02-08T16:33:27.893945Z | {
"verified": true,
"answer": 3409,
"timestamp": "2026-02-08T16:33:27.994440Z"
} | 8c4d21 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 224,
"completion_tokens": 3374
},
"timestamp": "2026-02-17T06:53:59.284Z",
"answer": 3409
},
{... | 1 | [
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8",
"status": "ok_later"
},
{
"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
4c9821 | comb_binomial_compute_v1_1918700295_416 | Let $T$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 36$. For each pair $(x, y)$ in $T$, compute $x + y$. Let $s$ be the smallest such sum. Compute $\binom{s}{7}$. Let $k$ be the absolute value of this binomial coefficient plus 2. Determine the smallest positive integer $t$ such that th... | 597 | graphs = [
Graph(
let={
"_n": Const(36),
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_n")))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | comb_binomial_compute_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.001 | 2026-02-08T03:13:05.920566Z | {
"verified": true,
"answer": 597,
"timestamp": "2026-02-08T03:13:05.921765Z"
} | 8f0263 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 215,
"completion_tokens": 6099
},
"timestamp": "2026-02-10T13:01:31.572Z",
"answer": 597
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
528c9c | modular_modexp_compute_v1_1742523217_1650 | Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 10000$. Let $e$ be the minimum value of $x + y$ over all such pairs. Compute the value of $17^e \mod 73984$. | 28,033 | graphs = [
Graph(
let={
"a": Const(17),
"e": 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(10000)))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | modular_modexp_compute_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.001 | 2026-02-08T04:05:42.627157Z | {
"verified": true,
"answer": 28033,
"timestamp": "2026-02-08T04:05:42.628122Z"
} | a1c025 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 170,
"completion_tokens": 1887
},
"timestamp": "2026-02-10T15:17:19.128Z",
"answer": 28033
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
736f68 | antilemma_cartesian_v1_1915831931_4092 | Compute the number of ordered pairs $(a,b)$ such that $a$ is an integer satisfying $1 \le a \le 31$ and $b$ is an integer satisfying $1 \le b \le 39$. | 1,209 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(31)), right=IntegerRange(start=Const(1), end=Const(39)))),
},
goal=Ref("x"),
)
] | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | antilemma_cartesian_v1 | null | 2 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.001 | 2026-02-08T18:06:27.631159Z | {
"verified": true,
"answer": 1209,
"timestamp": "2026-02-08T18:06:27.631935Z"
} | c2201b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 94,
"completion_tokens": 4481
},
"timestamp": "2026-02-24T23:27:07.221Z",
"answer": 30
},
{
... | 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": -8.52,
"mid": -5.43,
"hi": -3.2
} | ||
fb1608_l | comb_factorial_compute_v1_784195855_588 | Let $S$ be the set of all positive integers $n$ such that $1 \leq n \leq 1588$ and $\gcd(n, 15) = 1$. Let $d$ be the smallest integer greater than or equal to 2 that divides the number of elements in $S$. Compute $d!$. | 2 | NT | null | COMPUTE | sympy | C4 | [
"C4/MIN_PRIME_FACTOR"
] | 411729 | comb_factorial_compute_v1 | null | 5 | 0 | [
"C4",
"MIN_PRIME_FACTOR"
] | 2 | 0.002 | 2026-02-08T04:29:20.981518Z | {
"verified": false,
"answer": 5040,
"timestamp": "2026-02-08T04:29:20.983672Z"
} | b403c0 | fb1608 | 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": 182,
"completion_tokens": 752
},
"timestamp": "2026-02-10T16:51:14.120Z",
"answer": 5040
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok_later... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | |
2ff512 | geo_count_lattice_triangle_v1_238844314_540 | Let $A$ be the set of all positive integers $n$ such that $1 \leq n \leq 841$ and $\gcd(n, 14) = 1$. Let $a = |A|$. Define $$\text{area}_2 = |169a - 256^2|.$$ Let $$\text{boundary} = \gcd(361, 256) + \gcd(|256 - 361|, |169 - 256|) + \gcd(256, 169).$$ Compute $$\frac{\text{area}_2 + 2 - \text{boundary}}{2}.$$ | 2,262 | graphs = [
Graph(
let={
"_n": Const(256),
"area_2x": Abs(arg=Sum(Mul(CountOverSet(set=SolutionsSet(var=Var(name='n'), condition=And(Geq(left=Var(name='n'), right=Const(value=1)), Leq(left=Var(name='n'), right=Const(value=841)), Eq(left=GCD(a=Var(name='n'), b=Const(value=14)), right=C... | NT | null | COUNT | sympy | C4 | [
"C4"
] | 08d162 | geo_count_lattice_triangle_v1 | null | 4 | 0 | [
"C4"
] | 1 | 0.006 | 2026-02-08T13:23:38.403491Z | {
"verified": true,
"answer": 2262,
"timestamp": "2026-02-08T13:23:38.409760Z"
} | 94f2ce | 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": 1221
},
"timestamp": "2026-02-15T15:12:12.095Z",
"answer": 2262
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
af7b27 | v7_endings_v1_260342960_28 | For each integer $k$ with $0 \leq k \leq 4742$, let $e_k$ be the largest integer $e$ such that $2^e$ divides $\binom{4742}{k}$. Let $m$ be the maximum value of $e_k$ over all such $k$. Compute the remainder when $11419 \cdot m$ is divided by $91643$. | 45,385 | graphs = [
Graph(
let={
"_inner_result": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(0)), Leq(Var("k"), Const(4742)))), expr=MaxKDivides(target=Binom(n=Const(4742), k=Var("k")), base=Const(2)))),
"_scale_k": Const(11419),
"_s... | NT | null | COMPUTE | sympy | V7 | [
"V7"
] | 0672d4 | v7_endings_v1 | null | 7 | null | [
"V7"
] | 1 | 0.008 | 2026-02-08T11:11:13.554727Z | {
"verified": true,
"answer": 45385,
"timestamp": "2026-02-08T11:11:13.562312Z"
} | 79487e | 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": 7344
},
"timestamp": "2026-02-10T00:41:31.640Z",
"answer": 45385
},
{
... | 1 | [
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V7",
"status": "ok"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"... | {
"lo": -1.98,
"mid": 2.16,
"hi": 5.82
} | ||
6a66b8 | modular_sum_quadratic_residues_v1_2051736721_2061 | Let $n = 2$. Let $p$ be the smallest divisor of $123197$ that is at least $n$. Define $$
result = \frac{p(p - 1)}{4}.
$$ Compute the remainder when $44121 \cdot result$ is divided by $77621$. | 62,705 | 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(123197))))),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), Const(4)),
"Q": Mod(value... | 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 | 2026-02-08T16:25:43.906409Z | {
"verified": true,
"answer": 62705,
"timestamp": "2026-02-08T16:25:43.909481Z"
} | c481c7 | 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": 2194
},
"timestamp": "2026-02-17T04:15:48.041Z",
"answer": 62705
},
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"st... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
d40b5e | algebra_quadratic_discriminant_v1_1978505735_2080 | Let $m = 509$. Define $S$ as the set of all ordered pairs $(x, y)$ of positive integers such that $xy$ equals the number of integers $n$ with $1 \leq n \leq m$ and $n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{3}$. Let $b$ be the minimum value of $x + y$ over all pairs $(x, y) \in S$. Compute $b^2 - 4(-2)(-60)... | 196 | graphs = [
Graph(
let={
"_m": Const(509),
"_n": Const(2),
"a": Const(-2),
"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... | NT | null | COMPUTE | sympy | MOBIUS_SUM | [
"L3C/B3"
] | 4d8a41 | algebra_quadratic_discriminant_v1 | null | 6 | 0 | [
"B3",
"L3C",
"MOBIUS_SUM"
] | 3 | 0.017 | 2026-02-08T16:39:11.142158Z | {
"verified": true,
"answer": 196,
"timestamp": "2026-02-08T16:39:11.159403Z"
} | fa784a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 161,
"completion_tokens": 1116
},
"timestamp": "2026-02-17T08:53:36.684Z",
"answer": 196
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} |
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