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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
a38213 | algebra_poly_eval_v1_2051736721_2494 | Let $t = 6$. Let $c$ be the number of ordered pairs $(p, q)$ of positive integers such that $pq = 36$, $\gcd(p, q) = 1$, and $p < q$. Compute the value of $3t^4 - 4t^3 + 4t^c - t - 8$. | 3,154 | graphs = [
Graph(
let={
"_n": Const(3),
"t": Const(6),
"result": Sum(Mul(Const(3), Pow(Ref("t"), Const(4))), Mul(Const(-4), Pow(Ref("t"), Ref("_n"))), Mul(Const(4), Pow(Ref("t"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exis... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | algebra_poly_eval_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.004 | 2026-02-08T16:44:36.951498Z | {
"verified": true,
"answer": 3154,
"timestamp": "2026-02-08T16:44:36.955414Z"
} | 761ba1 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 123,
"completion_tokens": 1207
},
"timestamp": "2026-02-17T10:34:42.633Z",
"answer": 3154
},
{... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
d4cb65 | comb_count_derangements_v1_601307018_7853 | Let $D_n$ denote the number of derangements of $n$ elements. Let $N = D_8$. Find the remainder when $9711N$ is divided by $75628€. | 47,551 | graphs = [
Graph(
let={
"n": Const(8),
"result": Subfactorial(arg=Ref(name='n')),
"Q": Mod(value=Mul(Const(9711), Ref("result")), modulus=Const(75628)),
},
goal=Ref("Q"),
)
] | COMB | null | COUNT | sympy | STARS_BARS | [
"STARS_BARS"
] | a8801b | comb_count_derangements_v1 | affine_mod | 2 | 0 | [
"STARS_BARS"
] | 1 | 0.009 | 2026-03-10T08:23:49.926846Z | {
"verified": true,
"answer": 47551,
"timestamp": "2026-03-10T08:23:49.936271Z"
} | fb321a | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 151,
"completion_tokens": 1068
},
"timestamp": "2026-04-19T07:39:02.408Z",
"answer": 47551
},
{
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "STARS_BARS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"... | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
a707ee | algebra_vieta_sum_v1_168721529_1791 | Let $f(x) = -x^3 + x^2 + 34x + s$, where $s$ is the number of ordered pairs $(i,j)$ with $1 \leq i \leq 2$ and $1 \leq j \leq 37$ such that $\gcd(i,j) = 1$. Define $r$ to be the sum of all real numbers $x$ such that $f(x) = 0$. Compute $44121 \cdot r$. | 44,121 | graphs = [
Graph(
let={
"_n": Const(2),
"result": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Mul(Const(-1), Pow(Var("x"), Const(3))), Pow(Var("x"), Ref("_n")), Mul(Const(34), Var("x")), CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=... | NT | null | COMPUTE | sympy | COUNT_COPRIME_GRID | [
"COUNT_COPRIME_GRID"
] | 20ec03 | algebra_vieta_sum_v1 | null | 6 | 0 | [
"COUNT_COPRIME_GRID"
] | 1 | 0.012 | 2026-02-08T13:54:58.957360Z | {
"verified": true,
"answer": 44121,
"timestamp": "2026-02-08T13:54:58.969019Z"
} | 1ae7d2 | 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": 1632
},
"timestamp": "2026-02-09T21:39:22.246Z",
"answer": 44121
},
{
"... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_SUB",... | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
dffe36 | nt_min_coprime_above_v1_1978505735_5386 | Let $p$ be the largest prime number at most $1265$. Let $T$ be the number of integers $t$ in the interval $44 \leq t \leq 4595$ that can be written as $t = 9a + 21b + 14$ for some integers $a$ and $b$ with $1 \leq a \leq 243$ and $1 \leq b \leq 114$. Let $n_1$ be the smallest integer greater than $p$ and at most $T$ su... | 53,933 | graphs = [
Graph(
let={
"_n": Const(14901),
"start": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(1265)), IsPrime(Var("n"))))),
"upper": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'),... | NT | null | EXTREMUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW",
"LIN_FORM"
] | d530e2 | nt_min_coprime_above_v1 | null | 6 | 0 | [
"LIN_FORM",
"MAX_PRIME_BELOW"
] | 2 | 0.027 | 2026-02-08T18:58:01.992161Z | {
"verified": true,
"answer": 53933,
"timestamp": "2026-02-08T18:58:02.019021Z"
} | b9df32 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 195,
"completion_tokens": 5788
},
"timestamp": "2026-02-18T20:50:36.166Z",
"answer": 53933
},
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
d14fc9 | nt_count_divisible_v1_1431428450_322 | Let $N = 33072$ and $U = 55225$. Define $d$ to be the number of nonnegative integers $j \leq 33072$ for which $\binom{33072}{j}$ is odd. Compute the number of positive integers $n \leq 55225$ that are divisible by $d$. | 3,451 | graphs = [
Graph(
let={
"_n": Const(33072),
"upper": Const(55225),
"divisor": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(33072)), Eq(Mod(value=Binom(n=Ref("_n"), k=Var("j")), modulus=Const(2)), Const(1))), domain... | ALG | COMB | COUNT | sympy | V8 | [
"V8"
] | 86348e | nt_count_divisible_v1 | null | 6 | 0 | [
"V8"
] | 1 | 3.113 | 2026-02-08T13:23:27.139778Z | {
"verified": true,
"answer": 3451,
"timestamp": "2026-02-08T13:23:30.253228Z"
} | 4df266 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 183,
"completion_tokens": 972
},
"timestamp": "2026-02-24T17:56:57.408Z",
"answer": 3451
},
{
"id... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
}
] | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
1ea8f2 | antilemma_sum_factor_cartesian_v1_1116507919_227 | For each ordered pair $(i, j)$ with $1 \leq i \leq 17$ and $1 \leq j \leq 20$, compute the product $i \cdot j$. Let $x$ be the sum of all such products. Compute the remainder when $65922 \cdot x$ is divided by $94955$. | 7,630 | graphs = [
Graph(
let={
"x": SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Const(1), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(17)), right=IntegerRange(start=Const(1), end=Const(20)))), expr=Mul(Var("i"), Var("j")))),
... | NT | null | COMPUTE | sympy | SUM_FACTOR_CARTESIAN | [
"SUM_FACTOR_CARTESIAN"
] | d9e436 | antilemma_sum_factor_cartesian_v1 | null | 3 | 0 | [
"SUM_FACTOR_CARTESIAN"
] | 1 | 0.001 | 2026-02-08T02:29:19.105316Z | {
"verified": true,
"answer": 7630,
"timestamp": "2026-02-08T02:29:19.106027Z"
} | 491a56 | 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": 1642
},
"timestamp": "2026-02-08T19:15:15.845Z",
"answer": 7630
},
{
"i... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_FACTOR_CARTESIAN",
"status": "ok"
},
{
"lemma": "V1",
"s... | {
"lo": -4.6,
"mid": 0.19,
"hi": 4.77
} | ||
29598f | nt_lcm_compute_v1_124444284_5449 | Let $a = 2489$ and $b = 760$. Compute the least common multiple of $a$ and $b$. | 99,560 | graphs = [
Graph(
let={
"a": Const(2489),
"b": Const(760),
"result": LCM(a=Ref("a"), b=Ref("b")),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"MIN_PRIME_FACTOR",
"LIN_FORM"
] | 41af5a | nt_lcm_compute_v1 | null | 2 | 0 | [
"COUNT_SUM_EQUALS",
"LIN_FORM",
"MIN_PRIME_FACTOR"
] | 3 | 0.027 | 2026-02-08T06:35:35.858371Z | {
"verified": true,
"answer": 99560,
"timestamp": "2026-02-08T06:35:35.885293Z"
} | ef9c12 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 75,
"completion_tokens": 679
},
"timestamp": "2026-02-13T02:18:05.869Z",
"answer": 99560
},
{
... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
4628eb | nt_sum_gcd_range_mod_v1_865884756_1731 | Let $N = 2704$ and $k = 108$. Define
$$
S = \sum_{n=1}^{N} \gcd(n, k).
$$
Let $r$ be the remainder when $S$ is divided by $11833$.
Let $T$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 9253764$. Let $c$ be the minimum value of $x + y$ over all such pairs.
Compute $c - r$. | 1,707 | graphs = [
Graph(
let={
"N": Const(2704),
"k": Const(108),
"M": Const(11833),
"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")),
"_c": MinOverSet... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | fc629c | nt_sum_gcd_range_mod_v1 | negation_mod | 5 | 0 | [
"B3"
] | 1 | 0.237 | 2026-02-08T16:14:33.535592Z | {
"verified": true,
"answer": 1707,
"timestamp": "2026-02-08T16:14:33.772839Z"
} | 28fe1c | 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": 2087
},
"timestamp": "2026-02-17T00:16:44.538Z",
"answer": 1707
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
1f05ba | antilemma_sum_equals_v1_809748730_422 | Let $n = 42$. Define $x$ to be the number of ordered pairs $(i, j)$ of positive integers such that $i + j = n$, $1 \leq i \leq 40$, and $1 \leq j \leq 41$. Let $Q$ be the remainder when $44121 \cdot x$ is divided by $58579$. Find the value of $Q$. | 7,470 | graphs = [
Graph(
let={
"_n": Const(42),
"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(40)), right=IntegerRange(start=Const(1), end=Con... | COMB | GEOM | COMPUTE | sympy | LIN_FORM | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 2 | 0 | [
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 2 | 0.025 | 2026-02-08T11:30:49.964090Z | {
"verified": true,
"answer": 7470,
"timestamp": "2026-02-08T11:30:49.989554Z"
} | d045c7 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 200,
"completion_tokens": 836
},
"timestamp": "2026-02-24T14:00:35.270Z",
"answer": 7470
},
{
"id... | 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": -3.84,
"mid": -1.67,
"hi": 1.32
} | ||
b1db78 | modular_sum_quadratic_residues_v1_124444284_10024 | Let $p$ be the number of positive integers $k$ with $1 \leq k \leq 55400$ that are divisible by $200$. Compute the value of $\frac{p(p-1)}{4}$. | 19,113 | graphs = [
Graph(
let={
"_n": Const(4),
"p": CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(1)), Leq(Var("k"), Const(55400)), Divides(divisor=Const(200), dividend=Var("k"))), domain='positive_integers')),
"result": Div(Mul(Ref("p"), Sub(Ref(... | ALG | NT | SUM | sympy | C2 | [
"C2"
] | 9685eb | modular_sum_quadratic_residues_v1 | null | 2 | 0 | [
"C2"
] | 1 | 0.001 | 2026-02-08T12:47:27.798330Z | {
"verified": true,
"answer": 19113,
"timestamp": "2026-02-08T12:47:27.799803Z"
} | 92c185 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 92,
"completion_tokens": 413
},
"timestamp": "2026-02-15T05:27:48.380Z",
"answer": 19113
},
{
... | 1 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
3f6906 | nt_count_coprime_v1_124444284_2528 | Let $r$ be the number of positive integers $n \leq 31684$ such that $\gcd(n, 49) = 1$. Let $c$ be the number of ordered pairs $(i, j)$ with $1 \leq i \leq 38$ and $1 \leq j \leq 85$ such that $\gcd(i, j) = 1$. Compute the remainder when $r \bmod 251 + c \cdot (r \bmod 397)$ is divided by $82794$. | 76,154 | graphs = [
Graph(
let={
"_n": Const(397),
"upper": Const(31684),
"k": Const(49),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(GCD(a=Var("n"), b=Ref("k")), Const(1))))),
... | NT | null | COUNT | sympy | COUNT_COPRIME_GRID | [
"COUNT_COPRIME_GRID"
] | 283923 | nt_count_coprime_v1 | two_moduli | 5 | 0 | [
"COUNT_COPRIME_GRID"
] | 1 | 3.125 | 2026-02-08T04:44:42.233645Z | {
"verified": true,
"answer": 76154,
"timestamp": "2026-02-08T04:44:45.358474Z"
} | 21aa70 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 228,
"completion_tokens": 3106
},
"timestamp": "2026-02-11T22:02:18.463Z",
"answer": 76154
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"st... | {
"lo": -3.49,
"mid": 1.84,
"hi": 7.55
} | ||
204a6d | comb_bell_compute_v1_1520064083_4700 | Let $n$ be the number of integers $j$ with $0 \le j \le 8706$ such that $\binom{8706}{j}$ is odd. Let $B_n$ denote the $n$th Bell number, which counts the number of partitions of a set of $n$ elements. Let $c = 81941$ and $m = 71970$. Compute the remainder when $c \cdot B_n$ is divided by $m$. | 41,130 | graphs = [
Graph(
let={
"_n": Const(71970),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(8706)), Eq(Mod(value=Binom(n=Const(8706), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')),
"... | COMB | null | COMPUTE | sympy | V8 | [
"V8"
] | 86348e | comb_bell_compute_v1 | null | 6 | 0 | [
"V8"
] | 1 | 0.001 | 2026-02-08T06:23:19.578058Z | {
"verified": true,
"answer": 41130,
"timestamp": "2026-02-08T06:23:19.578851Z"
} | 47afcf | 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": 2399
},
"timestamp": "2026-02-24T06:06:28.645Z",
"answer": 41130
},
{
"... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
}
] | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
0492c3 | comb_count_partitions_v1_458359167_2476 | Let $n$ be the sum of all positive integers $k$ such that $1 \le k \le 40$ and $k$ is divisible by 40. Let $p(n)$ denote the number of integer partitions of $n$. Let $c = 18305$ and define $Q = (c \cdot p(n)) \mod 68347$. Compute $Q$. | 2,090 | graphs = [
Graph(
let={
"_n": Const(40),
"n": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(40)), Eq(Mod(value=Var("n"), modulus=Ref("_n")), Const(0))))),
"result": Partition(arg=Ref(name='n')),
"_c": Cons... | COMB | null | COUNT | sympy | SUM_DIVISIBLE | [
"SUM_DIVISIBLE"
] | 02dbe3 | comb_count_partitions_v1 | null | 5 | 0 | [
"SUM_DIVISIBLE"
] | 1 | 0.001 | 2026-02-08T05:26:28.850256Z | {
"verified": true,
"answer": 2090,
"timestamp": "2026-02-08T05:26:28.851182Z"
} | f1d03b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 192,
"completion_tokens": 19724
},
"timestamp": "2026-02-24T05:56:47.750Z",
"answer": 2090
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "SUM_DIVISIBLE",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "n... | {
"lo": -0.06,
"mid": 2.89,
"hi": 5.27
} | ||
fd2c21 | sequence_count_fib_divisible_v1_53965629_58 | Let $n$ be a positive integer such that $1 \leq n \leq 463$ and the $n$th Fibonacci number is divisible by 4. Compute the number of such integers $n$. | 77 | graphs = [
Graph(
let={
"upper": Const(463),
"d": Const(4),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Divides(divisor=Ref("d"), dividend=Fibonacci(arg=Var(name='n')))))),
},
go... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | sequence_count_fib_divisible_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.111 | 2026-02-08T11:15:45.797432Z | {
"verified": true,
"answer": 77,
"timestamp": "2026-02-08T11:15:45.908633Z"
} | 87b4aa | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 159,
"completion_tokens": 1066
},
"timestamp": "2026-02-09T11:28:51.163Z",
"answer": 77
},
{
"id"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
ef10b3 | diophantine_fbi2_min_v1_655260480_5088 | Let $d$ be an integer satisfying the following conditions:
\begin{itemize}
\item $d \geq \sum_{k_1=1}^{2} \varphi(k_1) \left\lfloor \frac{2}{k_1} \right\rfloor$,
\item $d \leq 16$,
\item $d$ divides $6$,
\item $\frac{6}{d} \geq 2$.
\end{itemize}
Let $r$ be the smallest such $d$. Compute $32761 - r$. | 32,758 | graphs = [
Graph(
let={
"_n": Const(2),
"k": Const(6),
"upper": Const(16),
"result": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Summation(var="k1", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k1")), Floor(Div(Const(2), Va... | NT | null | EXTREMUM | sympy | K2 | [
"K2"
] | 6897ab | diophantine_fbi2_min_v1 | null | 5 | 0 | [
"K2"
] | 1 | 0.004 | 2026-02-08T18:16:17.425923Z | {
"verified": true,
"answer": 32758,
"timestamp": "2026-02-08T18:16:17.429920Z"
} | ed38e1 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 183,
"completion_tokens": 639
},
"timestamp": "2026-02-16T12:14:49.832Z",
"answer": 32759
},
{
"id": 11... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
4af49b | antilemma_sum_equals_v1_784195855_9268 | Let $x$ be the number of ordered pairs $(i, j)$ of positive integers such that $i + j = 82$, $1 \leq i \leq 81$, and $1 \leq j \leq 82$. Let $y$ be the number of ordered pairs of positive odd integers $(x_1, x_2)$ such that $x_1 + x_2 = 9882$. Compute the remainder when $x \cdot y$ is divided by $93110$. Determine the ... | 27,781 | graphs = [
Graph(
let={
"_m": Const(93110),
"_n": Const(82),
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref("_n")), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(81)), right=Inte... | COMB | GEOM | COMPUTE | sympy | COMB1 | [
"COMB1",
"COUNT_SUM_EQUALS"
] | a8cbfb | antilemma_sum_equals_v1 | affine_mod | 3 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS"
] | 2 | 0.01 | 2026-02-08T16:40:20.349748Z | {
"verified": true,
"answer": 27781,
"timestamp": "2026-02-08T16:40:20.359519Z"
} | e044d7 | 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": 884
},
"timestamp": "2026-02-17T09:26:35.285Z",
"answer": 27781
},
{... | 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": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||
4b310f | nt_sum_gcd_range_mod_v1_677425708_3263 | Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 63504$. Let $T$ be the set of all values $x+y$ where $(x,y) \in S$. Let $k$ be the minimum value in $T$. Define $$\sum_{n=1}^{1225} \gcd(n, k).$$ Find the remainder when this sum is divided by $11393$. | 1,640 | graphs = [
Graph(
let={
"N": Const(1225),
"k": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(63504)))), expr=Sum(Var("x"), Var("y")))),... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_gcd_range_mod_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.056 | 2026-02-08T05:35:58.176676Z | {
"verified": true,
"answer": 1640,
"timestamp": "2026-02-08T05:35:58.232782Z"
} | c2a5c4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 140,
"completion_tokens": 3168
},
"timestamp": "2026-02-12T11:36:53.576Z",
"answer": 1640
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
b89808 | nt_sum_divisors_mod_v1_1742523217_2372 | Consider the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 14400$. For each such pair, compute the sum $x + y$. Let $n$ be the minimum value of these sums.
Let $\sigma$ denote the sum of all positive divisors of $n$, and let $M = 10687$. Define $r$ to be the remainder when $\sigma$ is divided b... | 24,035 | graphs = [
Graph(
let={
"_n": Const(84119),
"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(14400)))), expr=Sum(Var("x"), Var("y")))... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_divisors_mod_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.001 | 2026-02-08T04:43:11.077222Z | {
"verified": true,
"answer": 24035,
"timestamp": "2026-02-08T04:43:11.078642Z"
} | 0866ff | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 218,
"completion_tokens": 930
},
"timestamp": "2026-02-11T21:53:51.519Z",
"answer": 24035
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.49,
"mid": 1.84,
"hi": 7.55
} | ||
338602 | geo_visible_lattice_v1_1742523217_1218 | Let $ n = 128 $. Define $ L $ to be the number of ordered pairs $ (x, y) $ of positive integers such that $ 1 \leq x, y \leq n $ and $ \gcd(x, y) = 1 $. Compute $ 39601 - L $. | 29,558 | graphs = [
Graph(
let={
"n": Const(128),
"result": VisibleLatticePoints(n=Ref(name='n')),
"_c": Const(39601),
"Q": Sub(Ref("_c"), Ref("result")),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 5 | 0 | null | null | 0.735 | 2026-02-08T03:32:16.201853Z | {
"verified": true,
"answer": 29558,
"timestamp": "2026-02-08T03:32:16.936909Z"
} | 32b351 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 175,
"completion_tokens": 6385
},
"timestamp": "2026-02-10T05:16:01.341Z",
"answer": 29486
},
{
... | 1 | [] | {
"lo": 3.43,
"mid": 5.73,
"hi": 8.84
} | ||||
726cf5 | comb_count_surjections_v1_1218484723_5975 | Let $k = 6$ and $n = \sum_{k1=0}^{2} 2^{k1}$. Compute $k! \cdot S(n, k)$, where $S(n, k)$ denotes the Stirling number of the second kind. | 15,120 | graphs = [
Graph(
let={
"n": Summation(var="k1", start=Const(0), end=Const(2), expr=Pow(Const(2), Var("k1"))),
"k": Const(6),
"result": Mul(Factorial(Ref("k")), Stirling2(n=Ref(name='n'), k=Ref(name='k'))),
},
goal=Ref("result"),
)
] | COMB | null | COUNT | sympy | SUM_GEOM | [
"SUM_GEOM"
] | 04214c | comb_count_surjections_v1 | null | 2 | 0 | [
"SUM_GEOM"
] | 1 | 0.001 | 2026-02-25T07:34:09.671995Z | {
"verified": true,
"answer": 15120,
"timestamp": "2026-02-25T07:34:09.672897Z"
} | dd2360 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 168,
"completion_tokens": 659
},
"timestamp": "2026-03-29T23:40:45.692Z",
"answer": 15120
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "SUM_GEOM",
"status": "ok"
},
{
"lemma": "V8",
"sta... | {
"lo": -3.33,
"mid": 1.03,
"hi": 5.26
} | ||
b1b5d5 | diophantine_fbi2_count_v1_898971024_308 | Let $k$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 14400$. Let $m = 2$ and $n = 4$. Let $P$ be the set of prime numbers $p$ such that $2 \le p \le 131$. Let $q$ be the largest prime in $P$. Determine the number of positive integers $d$ such that $4 \le d \le 131... | 14 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(4),
"k": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(14400)))), expr=... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW/MAX_PRIME_BELOW",
"B3"
] | ca513e | diophantine_fbi2_count_v1 | null | 6 | 0 | [
"B3",
"MAX_PRIME_BELOW"
] | 2 | 0.021 | 2026-02-08T15:20:10.090947Z | {
"verified": true,
"answer": 14,
"timestamp": "2026-02-08T15:20:10.111497Z"
} | 74c82b | 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": 1367
},
"timestamp": "2026-02-16T03:17:46.940Z",
"answer": 14
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V8... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
3d387f | comb_binomial_compute_v1_1978505735_5522 | Let $n$ be the number of integers $t$ such that $10 \leq t \leq 38$ and there exist integers $a$ and $b$ with $1 \leq a \leq 5$, $1 \leq b \leq 3$, and $t = 4a + 6b$. Let $k$ be the number of positive integers $n_1$ at most $60$ such that $6$ divides the $n_1$-th Fibonacci number. Compute $\binom{n}{k}$. | 1,287 | graphs = [
Graph(
let={
"_n": Const(6),
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=5)), Geq(left=Var(na... | NT | null | COMPUTE | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE",
"LIN_FORM"
] | 0f3003 | comb_binomial_compute_v1 | null | 5 | 0 | [
"COUNT_FIB_DIVISIBLE",
"LIN_FORM"
] | 2 | 0.004 | 2026-02-08T19:02:40.184628Z | {
"verified": true,
"answer": 1287,
"timestamp": "2026-02-08T19:02:40.188692Z"
} | d87623 | 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": 1938
},
"timestamp": "2026-02-18T21:12:22.242Z",
"answer": 1287
},
{... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
f14cf3 | nt_min_coprime_above_v1_48377204_1323 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 33489$. Let $m$ be the minimum value of $x + y$ over all such pairs. Let $I$ be the interval of integers $n$ such that $57291 < n \leq 57667$ and $\gcd(n, m) = 1$. Compute the smallest element of $I$. | 57,293 | graphs = [
Graph(
let={
"start": Const(57291),
"upper": Const(57667),
"modulus": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Co... | NT | null | EXTREMUM | sympy | B3 | [
"B3"
] | 0cd20d | nt_min_coprime_above_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.04 | 2026-02-08T16:01:43.150917Z | {
"verified": true,
"answer": 57293,
"timestamp": "2026-02-08T16:01:43.190572Z"
} | 3186dd | 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": 1002
},
"timestamp": "2026-02-16T19:55:03.334Z",
"answer": 57293
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
7ad089 | diophantine_fbi2_count_v1_1520064083_57 | Let $k = 420$. Determine the number of integers $d$ such that $5 \leq d \leq 124$, $d$ divides $k$, and $6 \leq \frac{k}{d} \leq 125$. | 15 | graphs = [
Graph(
let={
"k": Const(420),
"a": Const(4),
"b": Const(5),
"upper": Const(120),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(5)), Leq(Var("d"), Const(124)), Divides(divisor=Var("d"), dividend=R... | NT | null | COUNT | sympy | LIN_FORM | [
"COMB1/COUNT_FIB_DIVISIBLE/C5"
] | e1b46c | diophantine_fbi2_count_v1 | null | 3 | 0 | [
"C5",
"COMB1",
"COUNT_FIB_DIVISIBLE",
"LIN_FORM"
] | 4 | 0.073 | 2026-02-08T02:58:35.437414Z | {
"verified": true,
"answer": 15,
"timestamp": "2026-02-08T02:58:35.510084Z"
} | a4c81e | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 164,
"completion_tokens": 3651
},
"timestamp": "2026-02-10T12:06:55.085Z",
"answer": 15
},
{
"id"... | 1 | [
{
"lemma": "C5",
"status": "ok_later"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok_later"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
... | {
"lo": -5.55,
"mid": -3.02,
"hi": 0.3
} | ||
b88f79 | comb_sum_binomial_row_v1_124444284_10083 | Let $S$ be the set of all ordered pairs $(p, q)$ of positive integers such that $pq = 36$, $\gcd(p, q) = 1$, and $p < q$. Let $N = |S|^{12}$. Compute the remainder when $15505 \cdot N$ is divided by $54258$. | 26,620 | graphs = [
Graph(
let={
"_n": Const(54258),
"n": Const(12),
"result": Pow(CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=36)), Eq... | NT | null | SUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_sum_binomial_row_v1 | null | 3 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.002 | 2026-02-08T12:49:15.094806Z | {
"verified": true,
"answer": 26620,
"timestamp": "2026-02-08T12:49:15.097287Z"
} | 5da5e8 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 117,
"completion_tokens": 1399
},
"timestamp": "2026-02-15T05:31:32.333Z",
"answer": 26620
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
673b0b | alg_linear_system_2x2_v1_601307018_2880 | Let $\det = 2 \cdot (-3) - (-10) \cdot (-15)$, $M = 21751 \cdot (-3) - (-79973) \cdot (-15)$, and $$R = \min\{ -96a b^{2} + 24 a^{2} b + 98 b^{3} : a, b \in \mathbb{Z}^+,\, 1 \leq a \leq 20,\, 1 \leq b \leq 20 \} \cdot (-79973) - (-10) \cdot 21751.$$ Compute $\frac{M}{\det} + \frac{R}{\det}$. | 7,739 | graphs = [
Graph(
let={
"_n": Const(21751),
"num_x": Sub(Mul(Ref("_n"), Const(-3)), Mul(Const(-79973), Const(-15))),
"num_y": Sub(Mul(MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), ... | ALG | null | COMPUTE | sympy | POLY3_MIN | [
"POLY3_MIN"
] | e2e279 | alg_linear_system_2x2_v1 | null | 5 | 0 | [
"POLY3_MIN"
] | 1 | 0.004 | 2026-03-10T03:29:55.669123Z | {
"verified": true,
"answer": 7739,
"timestamp": "2026-03-10T03:29:55.673035Z"
} | 8ef4a3 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 265,
"completion_tokens": 2960
},
"timestamp": "2026-03-29T06:48:02.056Z",
"answer": 7739
},
{
"i... | 1 | [
{
"lemma": "POLY3_MIN",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -2.46,
"mid": 1.23,
"hi": 4.93
} | ||
caf404 | antilemma_sum_equals_v1_1520064083_9972 | Let $n = 41$. Determine the number of ordered pairs $(i, j)$ of integers such that $1 \le i \le 40$, $1 \le j \le 40$, and $i + j = n$. Let $x$ be this number. Find the remainder when $83117x$ is divided by $61663$. | 56,541 | graphs = [
Graph(
let={
"_n": Const(41),
"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(40)), right=IntegerRange(start=Const(1), end=Con... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 3 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.007 | 2026-02-08T11:04:48.415303Z | {
"verified": true,
"answer": 56541,
"timestamp": "2026-02-08T11:04:48.422445Z"
} | cbc532 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 184,
"completion_tokens": 858
},
"timestamp": "2026-02-24T12:50:30.326Z",
"answer": 56541
},
{
"i... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
1a2db3 | nt_count_gcd_equals_v1_124444284_10354 | Let $k$ be the number of integers $t$ such that $30 \leq t \leq 558$ and $t = 9a + 21b$ for some integers $a$ and $b$ with $1 \leq a \leq 13$ and $1 \leq b \leq 21$. Determine the number of positive integers $n$ such that $1 \leq n \leq 23104$ and $\gcd(n, k) = 165$. | 140 | graphs = [
Graph(
let={
"upper": Const(23104),
"k": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=13)), Geq(lef... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_count_gcd_equals_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 3.867 | 2026-02-08T13:00:23.660313Z | {
"verified": true,
"answer": 140,
"timestamp": "2026-02-08T13:00:27.527519Z"
} | 3b2dbc | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 148,
"completion_tokens": 6019
},
"timestamp": "2026-02-15T09:04:14.641Z",
"answer": 140
},
{
... | 1 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
239350 | lin_form_endings_v1_1978505735_1987 | Let $a = 84$ and $b = 24$. Compute the least common multiple of $a$ and $b$, multiply it by $12431$, and then compute the remainder when this product is divided by $77520$. Find the value of this remainder. | 72,888 | graphs = [
Graph(
let={
"a_coeff": Const(84),
"b_coeff": Const(24),
"_inner_result": LCM(a=Ref("a_coeff"), b=Ref("b_coeff")),
"_scale_k": Const(12431),
"_scaled": Mul(Ref("_scale_k"), Ref("_inner_result")),
"_mod_M": Const(77520),
... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 2 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T16:35:22.484672Z | {
"verified": true,
"answer": 72888,
"timestamp": "2026-02-08T16:35:22.485387Z"
} | 009628 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 103,
"completion_tokens": 2772
},
"timestamp": "2026-02-17T07:17:55.247Z",
"answer": 72888
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8_SUM",
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
d07d3f | diophantine_fbi2_count_v1_784195855_8168 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 44100$. Let $k$ be the minimum value of $x + y$ over all pairs $(x, y) \in S$. Determine the number of positive divisors $d$ of $k$ such that $5 \leq d \leq 132$, and the quotient $k/d$ is an integer between 2 and 129, inclusive. | 17 | graphs = [
Graph(
let={
"_n": Const(5),
"k": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(44100)))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | diophantine_fbi2_count_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.028 | 2026-02-08T15:55:18.078108Z | {
"verified": true,
"answer": 17,
"timestamp": "2026-02-08T15:55:18.106150Z"
} | 66ace7 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 145,
"completion_tokens": 1846
},
"timestamp": "2026-02-16T16:12:54.702Z",
"answer": 17
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
ca570e | nt_count_gcd_equals_v1_1874849503_744 | Let $T$ be the set of all integers $t$ such that $27 \leq t \leq 705$ and $t = 6a + 21b$ for some positive integers $a \leq 51$ and $b \leq 19$. Let $k$ be the number of elements in $T$. Determine the number of positive integers $n$ such that $1 \leq n \leq 15129$ and $\gcd(n, k) = 221$. | 68 | graphs = [
Graph(
let={
"upper": Const(15129),
"k": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=51)), Geq(lef... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_count_gcd_equals_v1 | null | 7 | 0 | [
"LIN_FORM"
] | 1 | 3.507 | 2026-02-08T13:16:42.649866Z | {
"verified": true,
"answer": 68,
"timestamp": "2026-02-08T13:16:46.156582Z"
} | 707298 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 219,
"completion_tokens": 4909
},
"timestamp": "2026-02-09T20:29:58.226Z",
"answer": 68
},
{
"id"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V1",
"status": "n... | {
"lo": -9.12,
"mid": -6.02,
"hi": -3.62
} | ||
5344c3 | comb_count_surjections_v1_1440796553_1110 | Let $n$ be the number of elements in the Cartesian product of the sets $\{1, 2\}$ and $\{1, 2, 3\}$. Let $k$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 10$. Compute $k! \cdot S(n, k)$, where $S(n, k)$ denotes the Stirling number of the second kind. Find the remainder whe... | 35,688 | graphs = [
Graph(
let={
"_n": Const(97282),
"n": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(2)), right=IntegerRange(start=Const(1), end=Const(3)))),
"k": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition... | COMB | null | COUNT | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN",
"COMB1"
] | e44290 | comb_count_surjections_v1 | null | 5 | 0 | [
"COMB1",
"COUNT_CARTESIAN"
] | 2 | 0.003 | 2026-02-08T12:11:41.022721Z | {
"verified": true,
"answer": 35688,
"timestamp": "2026-02-08T12:11:41.026007Z"
} | 288ec5 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 232,
"completion_tokens": 2299
},
"timestamp": "2026-02-24T15:21:44.868Z",
"answer": 35688
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status":... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
409724 | nt_sum_divisors_range_v1_458359167_2273 | Let $ N $ be the number of positive integers $ n $ such that $ 1 \leq n \leq 210000 $ and $ 20 $ divides the $ n $-th Fibonacci number. Compute the sum of the number of positive divisors of all positive integers from $ 1 $ to $ N $. That is, compute $$
\sum_{k=1}^{N} \tau(k),$$ where $ \tau(k) $ is the number of positi... | 63,071 | graphs = [
Graph(
let={
"_n": Const(20),
"upper": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(210000)), Divides(divisor=Ref("_n"), dividend=Fibonacci(arg=Var(name='n')))))),
"result": SumOverSet(set=MapOverSet(set... | NT | null | SUM | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE"
] | 66de3c | nt_sum_divisors_range_v1 | null | 7 | 0 | [
"COUNT_FIB_DIVISIBLE"
] | 1 | 0.297 | 2026-02-08T05:17:14.554001Z | {
"verified": true,
"answer": 63071,
"timestamp": "2026-02-08T05:17:14.851061Z"
} | 31781b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 145,
"completion_tokens": 4093
},
"timestamp": "2026-02-12T06:03:01.560Z",
"answer": 63071
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V5",
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
77acde | geo_visible_lattice_v1_1918700295_1981 | Let $n = 77$. Define $S$ as the set of all ordered pairs $(x, y)$ of positive integers such that $1 \leq x, y \leq n$ and $\gcd(x, y) = 1$. Let $Q = 32768 - |S|$. Compute the value of $Q$. | 29,105 | graphs = [
Graph(
let={
"n": Const(77),
"result": VisibleLatticePoints(n=Ref(name='n')),
"Q": Sub(Const(32768), Ref("result")),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 3 | 0 | null | null | 0.126 | 2026-02-08T07:36:05.275586Z | {
"verified": true,
"answer": 29105,
"timestamp": "2026-02-08T07:36:05.401686Z"
} | 0d9f01 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 182,
"completion_tokens": 7206
},
"timestamp": "2026-02-24T08:19:41.636Z",
"answer": 29102
},
{
... | 1 | [] | {
"lo": 1.15,
"mid": 4.18,
"hi": 6.61
} | ||||
7ef3a6 | diophantine_product_count_v1_865884756_4316 | Let $k = 420$ and $n = 9$. Let $r$ be the number of positive integers $x$ such that $1 \leq x \leq 242$, $x$ divides $k$, and $\frac{k}{x} \leq 242$. Let $c$ be the number of integers $t$ such that $9 \leq t \leq 9045$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 1157$, $1 \leq b \leq 815$, and $t ... | 9,707 | graphs = [
Graph(
let={
"_n": Const(9),
"k": Const(420),
"upper": Const(242),
"result": CountOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), Const(1)), Leq(Var("x"), Ref("upper")), Divides(divisor=Var("x"), dividend=Ref("k")), Leq(Div(Ref("k... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 2ba0ea | diophantine_product_count_v1 | quadratic_mod | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.018 | 2026-02-08T17:53:11.971965Z | {
"verified": true,
"answer": 9707,
"timestamp": "2026-02-08T17:53:11.989472Z"
} | 70c980 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 188,
"completion_tokens": 5613
},
"timestamp": "2026-02-18T09:10:21.503Z",
"answer": 9707
},
{... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
8fab39 | antilemma_k2_v1_124444284_8596 | Define $x = \sum_{k=1}^{257} \phi(k) \left\lfloor \frac{257}{k} \right\rfloor$. Let $y$ be the sum of all real solutions to the equation $t^2 - 7001t - 288722 = 0$. Compute the remainder when $\left(x \bmod{199}\right) + \left(y \cdot \left(x \bmod{499}\right)\right)$ is divided by $64300$. | 54,438 | graphs = [
Graph(
let={
"_m": Const(64300),
"_n": Const(257),
"x": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(257), Var("k"))))),
"Q": Mod(value=Sum(Mod(value=Ref("x"), modulus=Const(199)), Mul(SumOverSet(s... | NT | COMB | COMPUTE | sympy | VIETA_SUM | [
"VIETA_SUM",
"K2"
] | 838ba1 | antilemma_k2_v1 | two_moduli | 7 | 0 | [
"K2",
"VIETA_SUM"
] | 2 | 0.001 | 2026-02-08T09:48:16.604208Z | {
"verified": true,
"answer": 54438,
"timestamp": "2026-02-08T09:48:16.605343Z"
} | 435842 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 152,
"completion_tokens": 939
},
"timestamp": "2026-02-14T19:40:12.537Z",
"answer": 54438
},
{... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
},
{
... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
7ed905 | nt_sum_over_divisible_v1_548369836_118 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 2829124$. Let $T$ be the set of all values $x + y$ where $(x, y) \in S$. Let $m$ be the minimum value in $T$. Now let $U$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = m$. Let $d$ be the minimum value o... | 48,442 | graphs = [
Graph(
let={
"_n": Const(70123),
"upper": Const(42849),
"divisor": 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")), MinOv... | COMB | null | SUM | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING",
"B3/B3",
"ONE_BINOM_N"
] | dedaf6 | nt_sum_over_divisible_v1 | null | 6 | 0 | [
"B3",
"BINOMIAL_ALTERNATING",
"ONE_BINOM_N"
] | 3 | 1.28 | 2026-02-08T02:46:10.761446Z | {
"verified": true,
"answer": 48442,
"timestamp": "2026-02-08T02:46:12.041512Z"
} | 0a8559 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 307,
"completion_tokens": 21372
},
"timestamp": "2026-02-23T16:09:13.609Z",
"answer": 48442
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "ONE_BINOM_N",
... | {
"lo": 1.81,
"mid": 3.24,
"hi": 4.6
} | ||
a482e0_n | modular_modexp_compute_v1_601307018_2267 | A factory produces items in batches of size $t = 21c + 6b$, where $c$ is the number of machines (1 or 2) and $b$ is the number of workers (from 1 to 9). Only batches between 27 and 96 units are valid. Let $N$ be the number of distinct valid batch sizes. The supervisor selects the largest prime number $M$ that does not ... | 27,673 | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/MAX_PRIME_BELOW",
"B3"
] | 2a7052 | modular_modexp_compute_v1 | null | 6 | null | [
"B3",
"LIN_FORM",
"MAX_PRIME_BELOW"
] | 3 | 0.007 | 2026-03-10T02:56:09.962748Z | null | facf9e | a482e0 | narrative | 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": 5204
},
"timestamp": "2026-03-29T16:00:23.657Z",
"answer": 27673
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"s... | {
"lo": -5.36,
"mid": 0.27,
"hi": 5.45
} | |
e0daf1 | comb_count_partitions_v1_655260480_1194 | Let $m = 6$. Let $n_0$ be the largest integer $k$ such that $2^k \leq m$. Let $n$ be the smallest divisor of $127434929$ that is at least $n_0$. Compute $50625 - p(n)$, where $p(n)$ denotes the number of integer partitions of $n$. Find the value of this expression. | 6,042 | graphs = [
Graph(
let={
"_m": Const(6),
"_n": MaxOverSet(set=SolutionsSet(var=Var("k"), condition=Leq(Pow(Const(2), Var("k")), Ref("_m")))),
"n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(127... | NT | COMB | COUNT | sympy | MAX_VAL | [
"MAX_VAL/MIN_PRIME_FACTOR"
] | 565dfa | comb_count_partitions_v1 | null | 5 | 0 | [
"MAX_VAL",
"MIN_PRIME_FACTOR"
] | 2 | 0.003 | 2026-02-08T15:59:09.703315Z | {
"verified": true,
"answer": 6042,
"timestamp": "2026-02-08T15:59:09.706780Z"
} | 3799d4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 129,
"completion_tokens": 1485
},
"timestamp": "2026-02-16T19:13:25.422Z",
"answer": 6042
},
{... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "same_pattern_wrong"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_VAL",
"statu... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
a81c84_n | comb_binomial_compute_v1_1218484723_1917 | A lab analyzes cell cultures on a $30 \times 30$ grid. A cell at position $(a,b)$ is active if $64a^3 + 27b^3 + 144a^2b + 108ab^2 = 1061208$. Let $S$ be the total number of active cells. Two researchers split a project of $S$ tasks into positive integer parts $x$ and $y$ such that $x + y = S$, maximizing their combined... | 11,440 | COMB | null | COMPUTE | sympy | POLY3_COUNT | [
"POLY3_COUNT/B1"
] | ede8bc | comb_binomial_compute_v1 | null | 6 | null | [
"B1",
"POLY3_COUNT"
] | 2 | 0.003 | 2026-02-25T03:39:22.380899Z | null | 8d147f | a81c84 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 249,
"completion_tokens": 1886
},
"timestamp": "2026-03-30T17:32:01.743Z",
"answer": 11440
},
{
"... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "POLY3_COUNT",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "... | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | |
cb8176 | comb_count_derangements_v1_1978505735_1016 | Let $n$ be the largest prime number such that $2 \leq n \leq 9$. Define $!n$ to be the number of derangements of $n$ objects. Compute $!n$. | 1,854 | graphs = [
Graph(
let={
"_n": Const(2),
"n": MaxOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Ref("_n")), Leq(Var("n1"), Const(9)), IsPrime(Var("n1"))))),
"result": Subfactorial(arg=Ref(name='n')),
},
goal=Ref("result"),
)
] | NT | COMB | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | comb_count_derangements_v1 | null | 2 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.001 | 2026-02-08T15:44:30.031667Z | {
"verified": true,
"answer": 1854,
"timestamp": "2026-02-08T15:44:30.033070Z"
} | 8addb4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 91,
"completion_tokens": 1165
},
"timestamp": "2026-02-16T13:02:26.293Z",
"answer": 1854
},
{
... | 1 | [
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
b78d1f | antilemma_k3_v1_168721529_562 | Let $x = \sum_{d \mid 2084} \phi(d)$, where $\phi$ denotes Euler's totient function. Let $D$ be the number of decimal digits of $|x|$, and for $i = 0, 1, \dots, D-1$, let $d_i$ denote the $i$-th digit of $|x|$ (starting from the units digit as $i=0$). Compute the value of $$ Q = \sum_{i=0}^{D-1} d_i \cdot (i+1)^2 + 360... | 3,668 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=2084), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Sum(Summation(var="i", start=Const(0), end=Sub(NumDigits(x=Abs(arg=Ref(name='x')), base=None), Const(1)), expr=Mul(Digit(x=Abs(arg=Ref(name='x')), k=Var(name='i'), base=No... | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 4 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T13:08:32.090968Z | {
"verified": true,
"answer": 3668,
"timestamp": "2026-02-08T13:08:32.092281Z"
} | 63d1a6 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 245,
"completion_tokens": 540
},
"timestamp": "2026-02-09T06:21:46.704Z",
"answer": 3668
},
{
"id... | 1 | [
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V3",
"status": "... | {
"lo": -5.3,
"mid": -2.04,
"hi": 1.84
} | ||
ce41e9 | algebra_poly_eval_v1_124444284_254 | Let $P$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 36$, $\gcd(p, q) = 1$, and $p < q$. Let $t$ be the number of elements in $P$. Define $y = 11$ and compute the value of $6y^3 + 2 \cdot y^t + 2y - 1$. Let $R$ be this value. Find the remainder when $44121 \cdot ... | 34,412 | graphs = [
Graph(
let={
"_n": Const(2),
"y": Const(11),
"result": Sum(Mul(Const(6), Pow(Ref("y"), Const(3))), Mul(Ref("_n"), Pow(Ref("y"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(l... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | algebra_poly_eval_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.003 | 2026-02-08T03:07:01.732500Z | {
"verified": true,
"answer": 34412,
"timestamp": "2026-02-08T03:07:01.735084Z"
} | 7bc1dc | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 237,
"completion_tokens": 2187
},
"timestamp": "2026-02-09T15:13:10.435Z",
"answer": 34412
},
{
"... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
e48b87 | diophantine_fbi2_count_v1_1918700295_3687 | Let $k$ be the number of integers $t$ in the range $49 \le t \le 442$ for which there exist positive integers $a$ and $b$ with $1 \le a \le 33$, $1 \le b \le 6$, and $t = 9a + 21b + 19$. Let $d_{\text{min}}$ be the largest prime number between $2$ and $4$, inclusive. Define $r$ to be the number of positive divisors $d$... | 24 | graphs = [
Graph(
let={
"_m": Const(3),
"_n": Const(57),
"k": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Con... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"MAX_PRIME_BELOW",
"LIN_FORM"
] | d530e2 | diophantine_fbi2_count_v1 | null | 6 | 0 | [
"COPRIME_PAIRS",
"LIN_FORM",
"MAX_PRIME_BELOW"
] | 3 | 0.074 | 2026-02-08T08:49:45.440182Z | {
"verified": true,
"answer": 24,
"timestamp": "2026-02-08T08:49:45.513742Z"
} | bec6b7 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 356,
"completion_tokens": 4592
},
"timestamp": "2026-02-13T21:47:43.304Z",
"answer": 24
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
05562b | comb_factorial_compute_v1_1915831931_367 | Let $m = 2$. Let $n'$ be the largest prime number such that $m \leq n' \leq 9$. Let $n$ be the largest prime number such that $2 \leq n \leq n'$. Compute $n!$. | 5,040 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": MaxOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Ref("_m")), Leq(Var("n1"), Const(9)), IsPrime(Var("n1"))))),
"n": MaxOverSet(set=SolutionsSet(var=Var("n2"), condition=And(Geq(Var("n2"), Const(2)), Leq(V... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW/MAX_PRIME_BELOW"
] | 15be89 | comb_factorial_compute_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.003 | 2026-02-08T15:23:12.035943Z | {
"verified": true,
"answer": 5040,
"timestamp": "2026-02-08T15:23:12.038636Z"
} | 1ad05b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 103,
"completion_tokens": 373
},
"timestamp": "2026-02-16T05:02:28.398Z",
"answer": 5040
},
{
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
196441 | antilemma_sum_equals_v1_151522320_1123 | Let $ x $ be the number of ordered pairs $ (i, j) $ of positive integers such that $ 1 \leq i \leq 24 $, $ 1 \leq j \leq 24 $, and $ i + j = 25 $. Compute the remainder when $ 44121 \cdot x $ is divided by $ 74384 $. | 17,528 | graphs = [
Graph(
let={
"_n": Const(25),
"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(24)), right=IntegerRange(start=Const(1), end=Con... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 3 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.011 | 2026-02-08T03:48:49.173673Z | {
"verified": true,
"answer": 17528,
"timestamp": "2026-02-08T03:48:49.184396Z"
} | 663725 | 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": 679
},
"timestamp": "2026-02-10T15:49:27.174Z",
"answer": 17528
},
{
"i... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status"... | {
"lo": -3.83,
"mid": -1.68,
"hi": 1.09
} | ||
5b4045 | geo_count_lattice_rect_v1_798873815_40 | Let $a = 512$ and $b = 160$. Consider the rectangle in the coordinate plane with vertices at $(0,0)$, $(a,0)$, $(0,b)$, and $(a,b)$. The number of lattice points (points with integer coordinates) inside and on the boundary of this rectangle is denoted by $R$. Compute the remainder when $44121 \cdot R$ is divided by $65... | 30,417 | graphs = [
Graph(
let={
"a": Const(512),
"b": Const(160),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"Q": Mod(value=Mul(Const(44121), Ref("result")), modulus=Const(65176)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 4 | 0 | null | null | 0.001 | 2026-02-08T02:24:46.856751Z | {
"verified": true,
"answer": 30417,
"timestamp": "2026-02-08T02:24:46.857332Z"
} | 08feef | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 206,
"completion_tokens": 2309
},
"timestamp": "2026-02-08T18:31:06.319Z",
"answer": 30417
},
{
"... | 1 | [] | {
"lo": -0.97,
"mid": 0.77,
"hi": 2.26
} | ||||
2e3ba6 | modular_mod_compute_v1_865884756_280 | Let $m$ be the smallest possible value of $x + y$ where $x$ and $y$ are positive integers such that $xy = 9801$. Let $p$ be the maximum value of $xy$ where $x$ and $y$ are positive integers such that $x + y = m$. Compute the remainder when $-128$ is divided by $p$. | 9,673 | graphs = [
Graph(
let={
"_m": Const(9801),
"_n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_m")))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | COMPUTE | sympy | B3 | [
"B3/B1"
] | 7f76f7 | modular_mod_compute_v1 | null | 4 | 0 | [
"B1",
"B3"
] | 2 | 0.004 | 2026-02-08T15:17:40.694397Z | {
"verified": true,
"answer": 9673,
"timestamp": "2026-02-08T15:17:40.698323Z"
} | 5df78a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 191,
"completion_tokens": 1167
},
"timestamp": "2026-02-10T06:29:09.748Z",
"answer": 9673
},
{
"i... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma":... | {
"lo": -7.09,
"mid": -0.49,
"hi": 6.1
} | ||
7de1b9 | diophantine_fbi2_count_v1_1978505735_7693 | Let $k = 360$. Let $t$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 4225$. Determine the number of positive integers $d$ such that $3 \leq d \leq 130$, $d$ divides $k$, $\frac{k}{d} \geq 3$, and $\frac{k}{d} \leq t$. | 20 | graphs = [
Graph(
let={
"k": Const(360),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(3)), Leq(Var("d"), Const(130)), Divides(divisor=Var("d"), dividend=Ref("k")), Geq(Div(Ref("k"), Var("d")), Const(3)), Leq(Div(Ref("k"), Var("d")), MinOverS... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | diophantine_fbi2_count_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.008 | 2026-02-08T20:23:36.375686Z | {
"verified": true,
"answer": 20,
"timestamp": "2026-02-08T20:23:36.383691Z"
} | 400ccb | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 139,
"completion_tokens": 2563
},
"timestamp": "2026-02-19T00:30:48.193Z",
"answer": 20
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
0c753c | algebra_quadratic_discriminant_v1_458359167_1491 | Let $a = \phi(1)$, $b = -7$, and $c = 8$. Let $s$ be the minimum value of $x + y$ over all ordered pairs $(x,y)$ of positive integers such that $xy = 4$. Define $D = b^2 - s \cdot a \cdot c$. Compute
$$
2 \cdot [D > 0] + [D = 0],
$$
where $[P]$ is the Iverson bracket, equal to $1$ if $P$ is true and $0$ otherwise. | 2 | graphs = [
Graph(
let={
"_n": Const(2),
"a": EulerPhi(n=Const(1)),
"b": Const(-7),
"c": Const(8),
"D": Sub(Pow(Ref("b"), Const(2)), Mul(MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(ar... | NT | null | COMPUTE | sympy | C4 | [
"ONE_PHI_1",
"B3"
] | d3bb9b | algebra_quadratic_discriminant_v1 | null | 5 | 0 | [
"B3",
"C4",
"ONE_PHI_1"
] | 3 | 0.025 | 2026-02-08T04:38:02.699679Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-02-08T04:38:02.725157Z"
} | 002145 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 217,
"completion_tokens": 430
},
"timestamp": "2026-02-18T13:04:19.031Z",
"answer": 2
}
] | 2 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "ONE_PHI_1",
"status": "ok"
... | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
e8d756 | alg_sum_powers_v1_1218484723_4259 | Find the remainder when $\sum_{k=1}^{1913} k^2$ is divided by the number of integers $t$ in the range $35 \le t \le 15741$ that can be expressed as $t = 14a + 6b + 15$ for some integers $a, b$ with $1 \le a \le 972$, $1 \le b \le 353$. | 4,933 | graphs = [
Graph(
let={
"_n": Const(2),
"result": Mod(value=Summation(var="k", start=Const(1), end=Const(1913), expr=Pow(Var("k"), Ref("_n"))), modulus=CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Ge... | ALG | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | alg_sum_powers_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.071 | 2026-02-25T05:54:24.808706Z | {
"verified": true,
"answer": 4933,
"timestamp": "2026-02-25T05:54:24.879522Z"
} | 0242b5 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 200,
"completion_tokens": 4875
},
"timestamp": "2026-03-29T14:35:01.108Z",
"answer": 4807
},
{
... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 3.81,
"mid": 6.33,
"hi": 9.49
} | ||
7b8cf9 | alg_qf_psd_sum_v1_1218484723_4345 | Let $M$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 11250$. Let $N$ be the number of integers $v$ with $0 \le v \le M$ such that there exist integers $a, b \in \{1, 2, \dots, 26\}$ satisfying $9a^2 - 18ab + 9b^2 = v$. Find the remainder when $$\sum_{\substack{1 \le a \le ... | 6,624 | graphs = [
Graph(
let={
"_m": Const(26),
"_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")), C... | ALG | null | COMPUTE | sympy | COMB1 | [
"COMB1/QF_PSD_DISTINCT"
] | 555ca3 | alg_qf_psd_sum_v1 | null | 6 | 0 | [
"COMB1",
"QF_PSD_DISTINCT"
] | 2 | 0.058 | 2026-02-25T05:58:12.047047Z | {
"verified": true,
"answer": 6624,
"timestamp": "2026-02-25T05:58:12.105131Z"
} | 76e3fe | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 296,
"completion_tokens": 2725
},
"timestamp": "2026-03-29T15:08:58.732Z",
"answer": 6624
},
{
"i... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_DISTINCT",
"status": "ok_later"
}
] | {
"lo": -2.45,
"mid": 1.37,
"hi": 5.29
} | ||
a8852a | nt_sum_over_divisible_v1_124444284_1033 | Let $n = 29161$. Let $u$ be the largest prime number less than or equal to $5572$. Consider the set of all positive integers $n$ from $1$ to $u$ that are divisible by $19$, and let $s$ be the sum of all such integers. Let $t$ be the number of positive integers $n$ from $1$ to $n$ such that $\gcd(n, 30) = 1$. Compute th... | 95,727 | graphs = [
Graph(
let={
"_n": Const(29161),
"upper": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(5572)), IsPrime(Var("n"))))),
"divisor": Const(19),
"result": SumOverSet(set=SolutionsSet(var=Var("n"), co... | NT | null | SUM | sympy | C4 | [
"C4",
"MAX_PRIME_BELOW"
] | 27f3c2 | nt_sum_over_divisible_v1 | two_stage_modexp | 6 | 0 | [
"C4",
"MAX_PRIME_BELOW"
] | 2 | 0.204 | 2026-02-08T03:39:39.835245Z | {
"verified": true,
"answer": 95727,
"timestamp": "2026-02-08T03:39:40.039564Z"
} | a4b97d | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 231,
"completion_tokens": 9389
},
"timestamp": "2026-02-23T21:02:39.871Z",
"answer": 95727
},
{
... | 1 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
... | {
"lo": 1.96,
"mid": 5.23,
"hi": 8.52
} | ||
289101 | modular_mod_compute_v1_124444284_5623 | Let $m = 196$. Let $S$ be the set of all ordered pairs of positive integers $(x, y)$ such that $x + y = m$. Let $P$ be the set of all products $xy$ where $(x, y) \in S$. Let $m_1$ be the maximum value in $P$. Let $r = 29161 \bmod{m_1}$. Compute $67593 \cdot r \bmod{76327}$. | 4,914 | graphs = [
Graph(
let={
"_n": Const(196),
"a": Const(29161),
"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")), Ref("_n")))), exp... | NT | null | COMPUTE | sympy | B1 | [
"B1"
] | 5b950e | modular_mod_compute_v1 | null | 4 | 0 | [
"B1"
] | 1 | 0.003 | 2026-02-08T06:45:19.547169Z | {
"verified": true,
"answer": 4914,
"timestamp": "2026-02-08T06:45:19.549686Z"
} | 939386 | 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": 613
},
"timestamp": "2026-02-13T04:18:30.975Z",
"answer": 4914
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
066d52 | modular_modexp_compute_v1_124444284_1137 | Let $n$ be the largest prime number less than or equal to the number of integers $t$ in the range $11 \le t \le 97$ for which there exist positive integers $a \le 12$ and $b \le 7$ such that $t = 4a + 7b$. Define
$$
e = \sum_{k=1}^{67} \phi(k) \left\lfloor \frac{n}{k} \right\rfloor,
$$
where $\phi(k)$ denotes Euler's t... | 1,225 | graphs = [
Graph(
let={
"_n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("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... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/MAX_PRIME_BELOW/K2"
] | a3f611 | modular_modexp_compute_v1 | null | 7 | 0 | [
"K2",
"LIN_FORM",
"MAX_PRIME_BELOW"
] | 3 | 0.003 | 2026-02-08T03:42:24.832013Z | {
"verified": true,
"answer": 1225,
"timestamp": "2026-02-08T03:42:24.834819Z"
} | 137c9e | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 263,
"completion_tokens": 8156
},
"timestamp": "2026-02-09T10:08:47.212Z",
"answer": 1225
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K2",
"status": "ok_later"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status":... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
be62d9 | diophantine_sum_product_min_v1_2051736721_6056 | Let $S$ be the number of integers $t$ with $16 \le t \le 98$ for which there exist positive integers $a$ and $b$ such that $1 \le a \le 5$, $1 \le b \le 8$, and $t = 10a + 6b$.
Let $P = 289$. Let $x_0$ be the smallest positive integer $x \le 33$ such that $x(S - x) = P$.
Let $Q$ be the Bell number $B_m$, where $m$ is... | 203 | graphs = [
Graph(
let={
"_n": Const(11),
"S": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=5)), Geq(left=Var(n... | COMB | null | EXTREMUM | sympy | MAX_PRIME_BELOW | [
"LIN_FORM"
] | 7b2633 | diophantine_sum_product_min_v1 | null | 6 | 0 | [
"LIN_FORM",
"MAX_PRIME_BELOW"
] | 2 | 0.064 | 2026-02-08T18:55:07.089101Z | {
"verified": true,
"answer": 203,
"timestamp": "2026-02-08T18:55:07.153113Z"
} | f168ae | 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": 2255
},
"timestamp": "2026-02-18T20:41:45.064Z",
"answer": 203
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -3.12,
"mid": 1.47,
"hi": 6.57
} | ||
623dc7 | nt_lcm_compute_v1_151522320_622 | Let $n = 70$. Define $a$ to be the maximum value of $xy$ over all ordered pairs $(x, y)$ of positive integers such that $x + y = n$. Define $b$ to be the sum of all real solutions $x$ to the equation $x^2 - 875x - 87906 = 0$. Compute $\mathrm{LCM}(a, b)$. | 6,125 | graphs = [
Graph(
let={
"_n": Const(70),
"a": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Ref("_n")))), expr=Mul(Var("x"), Var("y")))),
... | NT | null | COMPUTE | sympy | B3 | [
"VIETA_SUM",
"B1"
] | 928088 | nt_lcm_compute_v1 | null | 6 | 0 | [
"B1",
"B3",
"VIETA_SUM"
] | 3 | 0.005 | 2026-02-08T03:25:51.685461Z | {
"verified": true,
"answer": 6125,
"timestamp": "2026-02-08T03:25:51.690799Z"
} | a27814 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 197,
"completion_tokens": 703
},
"timestamp": "2026-02-10T14:18:27.858Z",
"answer": 6125
},
{
"id... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"... | {
"lo": -5.55,
"mid": -3.02,
"hi": 0.31
} | ||
1ff210 | algebra_poly_eval_v1_784195855_5562 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = 6$. Let $P$ be the maximum value of $xy$ over all pairs in $S$. Compute the value of $$
P \cdot 8^4 + 8 \cdot 8^3 - 3 \cdot 8^2 + 10 \cdot 8 - 8.
$$ | 40,840 | graphs = [
Graph(
let={
"_n": Const(3),
"y": Const(8),
"result": Sum(Mul(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(6)))... | NT | null | COMPUTE | sympy | B1 | [
"B1"
] | 5b950e | algebra_poly_eval_v1 | null | 3 | 0 | [
"B1"
] | 1 | 0.004 | 2026-02-08T07:58:06.959118Z | {
"verified": true,
"answer": 40840,
"timestamp": "2026-02-08T07:58:06.962958Z"
} | 03d312 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 137,
"completion_tokens": 635
},
"timestamp": "2026-02-13T13:35:32.934Z",
"answer": 40840
},
{... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
ce6dcc_l | comb_sum_binomial_row_v1_1116507919_146 | Let $m = 2$ and $n = 5$. For each integer $k$ from 1 to $n$, define $\phi(k)$ to be the number of positive integers at most $k$ that are relatively prime to $k$. For each such $k$, let $t_k$ be the smallest divisor of the number of integer solutions $(a, b)$ to the conditions $1 \leq a \leq 8$, $1 \leq b \leq 5$, and $... | 8 | NT | null | SUM | sympy | LIN_FORM | [
"LIN_FORM/MIN_PRIME_FACTOR/K2"
] | db5ec0 | comb_sum_binomial_row_v1 | null | 7 | 0 | [
"K2",
"LIN_FORM",
"MIN_PRIME_FACTOR"
] | 3 | 0.002 | 2026-02-08T02:26:49.117593Z | {
"verified": false,
"answer": 32768,
"timestamp": "2026-02-08T02:26:49.119882Z"
} | 05809a | ce6dcc | legacy_text | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 305,
"completion_tokens": 1721
},
"timestamp": "2026-02-08T19:07:22.275Z",
"answer": 8
},
{
"i... | 0 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K2",
"status": "ok_later"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lem... | {
"lo": 5.92,
"mid": 7.64,
"hi": 10
} | |
5536e1_n | alg_poly4_min_v1_1218484723_5405 | A biologist models a population where the $n$-th generation has $F_n$ individuals, the $n$-th Fibonacci number. She counts how many times the population is divisible by 21 over the first 58384 generations, calling this count $T$. She then designs a lab experiment with two parameters $a$ and $b$ (positive integers from ... | 29,993 | ALG | null | COMPUTE | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE"
] | 66de3c | alg_poly4_min_v1 | null | 6 | null | [
"COUNT_FIB_DIVISIBLE"
] | 1 | 0.294 | 2026-02-25T06:58:36.732700Z | null | f94ab4 | 5536e1 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 241,
"completion_tokens": 2796
},
"timestamp": "2026-03-30T23:24:07.192Z",
"answer": 29993
},
{
"... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
... | {
"lo": 1.5,
"mid": 4.69,
"hi": 7.23
} | |
a377ed | comb_catalan_compute_v1_2051736721_5385 | Let $n$ be the number of ordered pairs $(i, j)$ of positive integers such that $1 \leq i \leq 12$, $1 \leq j \leq 12$, and $i + j = 14$.
Let $C_n$ denote the $n$-th Catalan number, defined by
$$
C_n = \frac{1}{n+1} \binom{2n}{n}.
$$
Compute $73441 - C_n$. | 14,655 | graphs = [
Graph(
let={
"_n": Const(14),
"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(12)), right=IntegerRange(start=Const(1), end=Con... | COMB | null | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | comb_catalan_compute_v1 | null | 3 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.01 | 2026-02-08T18:31:39.555738Z | {
"verified": true,
"answer": 14655,
"timestamp": "2026-02-08T18:31:39.565620Z"
} | 959cf4 | 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": 1003
},
"timestamp": "2026-02-18T17:36:13.889Z",
"answer": 14655
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status":... | {
"lo": -7.92,
"mid": -4.6,
"hi": -1.84
} | ||
eeac6a | comb_count_permutations_fixed_v1_898971024_1705 | Let $k$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq = 24$, $\gcd(p, q) = 1$, and $p < q$. Compute $\binom{5}{k} \cdot !(5 - k)$, where $!m$ denotes the number of derangements of $m$ elements. | 20 | graphs = [
Graph(
let={
"n": Const(5),
"k": 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=24)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')... | NT | COMB | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_count_permutations_fixed_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.002 | 2026-02-08T16:15:10.775181Z | {
"verified": true,
"answer": 20,
"timestamp": "2026-02-08T16:15:10.777434Z"
} | 9531c0 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 127,
"completion_tokens": 1164
},
"timestamp": "2026-02-16T23:42:38.523Z",
"answer": 20
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
84345a | nt_count_divisible_v1_458359167_3755 | Let $n = 36$. Consider the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 36$. Let $\text{divisor}$ be the minimum value of $x + y$ over all such pairs. Let $\text{result}$ be the number of positive integers $n$ such that $1 \leq n \leq 71824$ and $n$ is divisible by $\text{divisor}$. Compute $\... | 5,985 | graphs = [
Graph(
let={
"_n": Const(36),
"upper": Const(71824),
"divisor": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_n"... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | nt_count_divisible_v1 | null | 4 | 0 | [
"B3"
] | 1 | 2.551 | 2026-02-08T11:18:55.881116Z | {
"verified": true,
"answer": 5985,
"timestamp": "2026-02-08T11:18:58.431895Z"
} | 1e33fc | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 164,
"completion_tokens": 330
},
"timestamp": "2026-02-15T21:47:10.002Z",
"answer": 4788
},
{
"id": 11,... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
8173d2 | nt_count_digit_sum_v1_168721529_1873 | Let $n = 44$ and $\text{upper} = 108900$. Define $\text{target\_sum}$ to be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = n$. Define $\text{result}$ to be the number of positive integers $n$ with $1 \leq n \leq \text{upper}$ such that the sum of the decimal digits of $n$ is eq... | 6,514 | graphs = [
Graph(
let={
"_n": Const(44),
"upper": Const(108900),
"target_sum": 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(... | NT | null | COUNT | sympy | COMB1 | [
"COMB1"
] | 567f58 | nt_count_digit_sum_v1 | null | 4 | 0 | [
"COMB1"
] | 1 | 4.14 | 2026-02-08T13:58:23.984867Z | {
"verified": true,
"answer": 6514,
"timestamp": "2026-02-08T13:58:28.124455Z"
} | fa1c8b | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 235,
"completion_tokens": 6286
},
"timestamp": "2026-02-11T08:06:16.138Z",
"answer": 6514
},
{
"... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
}
] | {
"lo": -5.48,
"mid": 0.74,
"hi": 7.52
} | ||
9bd4b0_l | nt_count_coprime_and_v1_1456120455_29 | Let $d$ be the smallest integer greater than or equal to 2 that divides
$$
\sum_{x} \left( x^{-7007} \cdot 629356 \right),
$$
defined over all positive integers $x$ for which there exist positive integers $p$ and $q$ with $pq = 54$, $\gcd(p, q) = 1$, and $p < q$. Let $k_1 = 3$ and $k_2 = d$. Compute the number of posit... | 11,803 | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/VIETA_SUM/MIN_PRIME_FACTOR"
] | c492f6 | nt_count_coprime_and_v1 | null | 7 | 0 | [
"COPRIME_PAIRS",
"MIN_PRIME_FACTOR",
"VIETA_SUM"
] | 3 | 12.106 | 2026-02-08T02:50:55.136830Z | {
"verified": false,
"answer": 20233,
"timestamp": "2026-02-08T02:51:07.243254Z"
} | 3c1919 | 9bd4b0 | legacy_text | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 259,
"completion_tokens": 3605
},
"timestamp": "2026-02-23T17:43:07.697Z",
"answer": 11803
},
{
... | 0 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok_later"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
... | {
"lo": 4.68,
"mid": 6.57,
"hi": 9.55
} | |
3630a8 | nt_count_coprime_v1_1915831931_2405 | Let $t$ be an integer. Define $n$ to be the number of integers $t$ such that $7 \leq t \leq 42$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 6$, $1 \leq b \leq 6$, and $t = 4a + 3b$. Let $k$ be the largest prime number not exceeding $n$. Determine the value of the number of positive integers $n_1$ ... | 26,287 | 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=6)), Geq(left=Var(name='b'), right=Const(value=... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/MAX_PRIME_BELOW"
] | 47006e | nt_count_coprime_v1 | null | 5 | 0 | [
"LIN_FORM",
"MAX_PRIME_BELOW"
] | 2 | 2.078 | 2026-02-08T16:46:26.832972Z | {
"verified": true,
"answer": 26287,
"timestamp": "2026-02-08T16:46:28.911248Z"
} | 2749d9 | 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": 1543
},
"timestamp": "2026-02-17T12:19:13.539Z",
"answer": 26287
},
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V8",
"sta... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
17b108 | antilemma_sum_equals_v1_238844314_966 | Let $t$ be an integer. Consider the set of all integers $t$ such that $27 \leq t \leq 315$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 20$, $1 \leq b \leq 5$, satisfying $t = 12a + 15b$. Let $S$ be the number of ordered pairs $(i, j)$ of positive integers, each at most $85$, such that $i + j = S$.... | 84 | 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=20)), Geq(left=Var(name='b'), right=Const(value... | COMB | GEOM | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | ada383 | antilemma_sum_equals_v1 | null | 5 | 0 | [
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 2 | 0.006 | 2026-02-08T13:50:18.290975Z | {
"verified": true,
"answer": 84,
"timestamp": "2026-02-08T13:50:18.296706Z"
} | 2c2046 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 231,
"completion_tokens": 12685
},
"timestamp": "2026-02-24T19:14:55.855Z",
"answer": 85
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
... | {
"lo": 1.15,
"mid": 4.18,
"hi": 6.61
} | ||
1b5da3 | nt_num_divisors_compute_v1_784195855_6794 | Let $n = 42436$. Let $\text{result}$ be the number of positive divisors of $n$. Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 82944$. Define $m$ to be the minimum value of $x + y$ over all such pairs. Compute the value of $$\sum_{i=0}^{\text{NumDigits}(|\text{result}|)-1} \left( ... | 585 | graphs = [
Graph(
let={
"n": Const(42436),
"result": NumDivisors(n=Ref("n")),
"Q": Sum(Summation(var="i", start=Const(0), end=Sub(NumDigits(x=Abs(arg=Ref(name='result')), base=None), Const(1)), expr=Mul(Digit(x=Abs(arg=Ref(name='result')), k=Var(name='i'), base=None), Pow... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 8e300c | nt_num_divisors_compute_v1 | digits_weighted_mod | 5 | 0 | [
"B3"
] | 1 | 0.003 | 2026-02-08T08:52:12.787575Z | {
"verified": true,
"answer": 585,
"timestamp": "2026-02-08T08:52:12.790529Z"
} | 8a0c93 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 174,
"completion_tokens": 986
},
"timestamp": "2026-02-13T22:14:29.168Z",
"answer": 585
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
6bd40e | antilemma_cartesian_v1_153355830_1606 | Let $x$ be the number of ordered pairs $(u,v)$ of integers such that $1\le u\le 35$ and $1\le v\le 42$.
Let $S$ be the set of all integers $t$ for which there exist integers $a$ and $b$ satisfying $1\le a\le 5$, $1\le b\le 2$, $22\le t\le 61$, and
$$t = 6a + 15b + 1.$$
Let $M$ be the number of elements in $S$.
Define... | 10,956 | graphs = [
Graph(
let={
"_n": Const(10),
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(35)), right=IntegerRange(start=Const(1), end=Const(42)))),
"Q": Summation(var="n", start=Factorial(Summation(var="k", start=Const(0), end=Ref("_n"),... | COMB | GEOM | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/BINOMIAL_ALTERNATING/ONE_FACTORIAL_0",
"COUNT_CARTESIAN"
] | e5f080 | antilemma_cartesian_v1 | sum_divisor_count | 7 | 0 | [
"BINOMIAL_ALTERNATING",
"COUNT_CARTESIAN",
"LIN_FORM",
"ONE_FACTORIAL_0"
] | 4 | 0.002 | 2026-02-08T06:31:37.005372Z | {
"verified": true,
"answer": 10956,
"timestamp": "2026-02-08T06:31:37.007596Z"
} | b4628d | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 317,
"completion_tokens": 3031
},
"timestamp": "2026-02-24T06:23:21.768Z",
"answer": 10960
},
{
... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma"... | {
"lo": 1.97,
"mid": 4.36,
"hi": 6.69
} | ||
26641b | nt_min_coprime_above_v1_971394319_112 | Let $s = 2048$. Let $u$ be the number of positive integers $j$ such that $1 \leq j \leq 2171$ and $j^5 \leq 48227985011979851$. Let $n$ be the smallest integer such that $n > s$, $n \leq u$, and $\gcd(n, 113) = 1$. Let $Q$ be the remainder when $36119 \cdot n$ is divided by $85660$. Find the value of $Q$. | 83,251 | graphs = [
Graph(
let={
"start": Const(2048),
"upper": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(1)), Leq(Var("j"), Const(2171)), Leq(Pow(Var("j"), Const(5)), Const(48227985011979851))), domain='positive_integers')),
"modulus": Const(11... | NT | null | EXTREMUM | sympy | C3 | [
"C3"
] | 8a214c | nt_min_coprime_above_v1 | null | 5 | 0 | [
"C3"
] | 1 | 0.015 | 2026-02-08T12:50:35.160828Z | {
"verified": true,
"answer": 83251,
"timestamp": "2026-02-08T12:50:35.175365Z"
} | b6d6da | 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": 2806
},
"timestamp": "2026-02-15T06:48:51.997Z",
"answer": 83251
},
... | 1 | [
{
"lemma": "C3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
34a40f | comb_count_surjections_v1_1918700295_2090 | Let $n$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2$ equals the number of integers $t$ in the interval $23 \leq t \leq 57$ for which there exist integers $a$ and $b$ with $1 \leq a \leq 2$, $1 \leq b \leq 7$, and $t = 10a + 4b + 9$. Let $k = 4$. Compute $k! \cdot S(n, k)$, ... | 8,400 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2")), CountOverSet(set=SolutionsSet(v... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/COMB1"
] | 268a62 | comb_count_surjections_v1 | null | 6 | 0 | [
"COMB1",
"LIN_FORM"
] | 2 | 0.002 | 2026-02-08T07:40:57.512243Z | {
"verified": true,
"answer": 8400,
"timestamp": "2026-02-08T07:40:57.514366Z"
} | 1f14d4 | 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": 1514
},
"timestamp": "2026-02-24T08:21:08.661Z",
"answer": 8400
},
{
"i... | 1 | [
{
"lemma": "COMB1",
"status": "ok_later"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
0cdf9d | diophantine_product_count_v1_1742523217_1933 | Let $k$ be the minimum value of $x + y$ over all ordered pairs of positive integers $(x, y)$ such that $xy = 8100$. Compute the number of positive integers $x$ such that $1 \leq x \leq 73$, $x$ divides $k$, and $\frac{k}{x} \leq 73$. | 14 | graphs = [
Graph(
let={
"k": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(8100)))), expr=Sum(Var("x"), Var("y")))),
"upper": Const(73)... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | diophantine_product_count_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.037 | 2026-02-08T04:21:13.177872Z | {
"verified": true,
"answer": 14,
"timestamp": "2026-02-08T04:21:13.215099Z"
} | 65d8fd | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 188,
"completion_tokens": 1453
},
"timestamp": "2026-02-10T16:24:25.286Z",
"answer": 14
},
{
"id... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.33
} | ||
939116 | nt_min_crt_v1_1978505735_7534 | Let $N$ be the number of positive integers $n$ at most $236$ that are even and relatively prime to $15$. Determine the smallest positive integer $n_1$ such that $n_1 \leq N$, $n_1 \equiv 1 \pmod{7}$, and $n_1 \equiv 5 \pmod{9}$. | 50 | graphs = [
Graph(
let={
"_n": Const(15),
"m": Const(7),
"k": Const(9),
"a": Const(1),
"b": Const(5),
"upper": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(236)), Divides(divisor=... | NT | null | EXTREMUM | sympy | B1 | [
"C5"
] | 1d9668 | nt_min_crt_v1 | null | 5 | 0 | [
"B1",
"C5"
] | 2 | 0.105 | 2026-02-08T20:18:15.922185Z | {
"verified": true,
"answer": 50,
"timestamp": "2026-02-08T20:18:16.027522Z"
} | b630a8 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 136,
"completion_tokens": 827
},
"timestamp": "2026-02-16T18:50:16.055Z",
"answer": 5
},
{
"id": 11,
... | 1 | [
{
"lemma": "C5",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V3",
"status": "n... | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
e54361 | comb_count_surjections_v1_1431428450_603 | Let $n = 7$. Let $k$ be the number of ordered pairs $(i, j)$ of integers with $1 \leq i \leq 6$, $1 \leq j \leq 6$, and $i + j = 7$. Define $S$ to be the product of $k!$ and the Stirling number of the second kind $S(n, k)$. Compute the remainder when $S$ multiplied by the number of elements in the Cartesian product of ... | 13,986 | graphs = [
Graph(
let={
"n": Const(7),
"k": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(7)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(6)), right=IntegerRange(start=Const(1), end=Const(6... | COMB | null | COUNT | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN",
"COUNT_SUM_EQUALS"
] | 81018e | comb_count_surjections_v1 | affine_mod | 4 | 0 | [
"COUNT_CARTESIAN",
"COUNT_SUM_EQUALS"
] | 2 | 0.013 | 2026-02-08T13:33:15.969226Z | {
"verified": true,
"answer": 13986,
"timestamp": "2026-02-08T13:33:15.982489Z"
} | d0420a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 251,
"completion_tokens": 1603
},
"timestamp": "2026-02-24T18:42:15.550Z",
"answer": 13986
},
{
"... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
df7b6d | lin_form_endings_v1_124444284_1519 | Let $ a = 30 $ and $ b = 45 $. Let $ d = \gcd(a,b) $. Let $ k = 8816 $. Compute the remainder when $ k \cdot \left\lfloor \frac{45}{d} \right\rfloor $ is divided by 97115. | 26,448 | graphs = [
Graph(
let={
"a_coeff": Const(30),
"b_coeff": Const(45),
"_inner_result": Floor(Div(Const(45), GCD(a=Ref("a_coeff"), b=Ref("b_coeff")))),
"_scale_k": Const(8816),
"_scaled": Mul(Ref("_scale_k"), Ref("_inner_result")),
"_mod_M... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 2 | null | [
"LIN_FORM"
] | 1 | 0 | 2026-02-08T03:58:06.418288Z | {
"verified": true,
"answer": 26448,
"timestamp": "2026-02-08T03:58:06.418783Z"
} | defcef | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 177,
"completion_tokens": 467
},
"timestamp": "2026-02-10T16:17:55.502Z",
"answer": 26448
},
{
"i... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
... | {
"lo": -9.14,
"mid": -6.05,
"hi": -3.74
} | ||
309add | nt_count_phi_equals_v1_809748730_708 | Let $n = 44121$. Let $r_1$ and $r_2$ be the two real solutions to the equation $x^2 - 3364x - 30357 = 0$. Define $S$ to be the set of all integers $x$ such that $x = r_1$ or $x = r_2$. Let $\text{upper}$ be the sum of all elements in $S$. Let $k = 48$. Define $T$ to be the set of all positive integers $n$ such that $1 ... | 30,346 | graphs = [
Graph(
let={
"_n": Const(44121),
"upper": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Const(2)), Mul(Const(-3364), Var("x")), Const(-30357)), Const(0)))),
"k": Const(48),
"result": CountOverSet(set=SolutionsSet(var=Var("... | NT | null | COUNT | sympy | VIETA_SUM | [
"VIETA_SUM"
] | b33a7a | nt_count_phi_equals_v1 | null | 6 | 0 | [
"VIETA_SUM"
] | 1 | 0.245 | 2026-02-08T11:42:05.559553Z | {
"verified": true,
"answer": 30346,
"timestamp": "2026-02-08T11:42:05.804909Z"
} | e97e95 | 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": 4432
},
"timestamp": "2026-02-14T17:32:49.302Z",
"answer": 30346
},
... | 1 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
},
{
"lemma": "VIETA_SUM",
"status": "ok"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
830b86 | comb_binomial_compute_v1_784195855_8004 | Let $f = \sum_{k=0}^{7} (-1)^k \binom{7}{k}$, and let $a = 1 + f$, $b = 0!$, and $n_1 = a + b$. Let $w = \sum_{k=0}^{n_1} (-1)^k \binom{n_1}{k}$. Let $\binom{16}{7}$ denote the binomial coefficient. Let $c$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 16200$. Let $Q$ be th... | 50,695 | graphs = [
Graph(
let={
"n2": Const(7),
"f": Summation(var="k", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n2"), k=Var("k")))),
"a": Sum(Const(1), Ref("f")),
"b": Factorial(Const(0)),
"n1": Sum(Ref("a"), Ref("b")... | COMB | null | COMPUTE | sympy | COMB1 | [
"COMB1",
"BINOMIAL_ALTERNATING",
"ONE_FACTORIAL_0"
] | bf0891 | comb_binomial_compute_v1 | negation_mod | 6 | 2 | [
"BINOMIAL_ALTERNATING",
"COMB1",
"ONE_FACTORIAL_0"
] | 3 | 0.004 | 2026-02-08T09:39:36.288006Z | {
"verified": true,
"answer": 50695,
"timestamp": "2026-02-08T09:39:36.292337Z"
} | 13832b | 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": 1828
},
"timestamp": "2026-02-24T12:14:01.214Z",
"answer": 50695
},
{
"... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "ONE_FACTORIAL_... | {
"lo": -5.97,
"mid": -3.97,
"hi": -1.93
} | ||
37ef2a | geo_visible_lattice_v1_124444284_5665 | Let $n = 91$. A visible lattice point $(x, y)$ is a point with integer coordinates such that $1 \leq x, y \leq n$ and $\gcd(x, y) = 1$. Compute the number of visible lattice points $(x, y)$ in the $n \times n$ grid. | 5,103 | graphs = [
Graph(
let={
"n": Const(91),
"result": VisibleLatticePoints(n=Ref(name='n')),
"Q": Ref("result"),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 4 | 0 | null | null | 0.184 | 2026-02-08T06:46:07.849368Z | {
"verified": true,
"answer": 5103,
"timestamp": "2026-02-08T06:46:08.033352Z"
} | 550700 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 181,
"completion_tokens": 5179
},
"timestamp": "2026-02-24T07:00:33.701Z",
"answer": 5103
},
{
"i... | 1 | [] | {
"lo": 1.97,
"mid": 4.36,
"hi": 6.69
} | ||||
4b3618 | nt_num_divisors_compute_v1_717093673_3394 | Let $n_0 = 2$. Let $n$ be the smallest integer $d$ such that $d \geq n_0$ and $d$ divides $115002253$. Define $\text{result} = \tau(n)$, the number of positive divisors of $n$. Compute $$\sum_{n_1=1}^{\left|\text{result}\right|} \phi(n_1),$$ where $\phi$ denotes Euler's totient function. | 2 | graphs = [
Graph(
let={
"_n": Const(2),
"n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(115002253))))),
"result": NumDivisors(n=Ref("n")),
"Q": Summation(var="n1", start=Const(1), ... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | nt_num_divisors_compute_v1 | null | 4 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.002 | 2026-02-08T17:34:40.643778Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-02-08T17:34:40.645675Z"
} | 29784b | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 164,
"completion_tokens": 376
},
"timestamp": "2026-02-16T11:21:38.044Z",
"answer": 2
},
{
"id": 11,
"... | 2 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V5",
"status... | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
bea585 | nt_min_crt_v1_784195855_1147 | Let $b$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq = 18$, $\gcd(p, q) = 1$, and $p < q$. Let $S$ be the set of all positive integers $n \leq 55$ such that $n \equiv 1 \pmod{5}$ and $n \equiv b \pmod{11}$. Determine the minimum element of $S$. | 46 | graphs = [
Graph(
let={
"m": Const(5),
"k": Const(11),
"a": Const(1),
"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(name='q')), right=Const(v... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_min_crt_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.017 | 2026-02-08T04:52:36.202734Z | {
"verified": true,
"answer": 46,
"timestamp": "2026-02-08T04:52:36.219923Z"
} | 031fd6 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 214,
"completion_tokens": 936
},
"timestamp": "2026-02-11T22:16:35.188Z",
"answer": 46
},
{
"id"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.33
} | ||
f44aaa | diophantine_fbi2_count_v1_124444284_7839 | Let $k$ be the number of positive integers from 1 to 13680 that are divisible by 19. Define a positive integer $d$ to be good if $2 \le d \le 78$, $d$ divides $k$, and $5 \le \frac{k}{d} \le 81$. Let $r$ be the number of good integers. Compute $36100 - r$. | 36,085 | graphs = [
Graph(
let={
"k": CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(1)), Leq(Var("k"), Const(13680)), Divides(divisor=Const(19), dividend=Var("k"))), domain='positive_integers')),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=A... | NT | null | COUNT | sympy | C2 | [
"C2"
] | 9685eb | diophantine_fbi2_count_v1 | null | 4 | 0 | [
"C2"
] | 1 | 0.016 | 2026-02-08T09:23:23.312202Z | {
"verified": true,
"answer": 36085,
"timestamp": "2026-02-08T09:23:23.327968Z"
} | 83918f | 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": 1057
},
"timestamp": "2026-02-14T03:40:37.355Z",
"answer": 36085
},
... | 1 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
afad30 | nt_sum_divisors_compute_v1_349078426_2018 | Let $p$ be the greatest prime number $n$ such that $2\le n\le 105$. Let
$$N=\sum_{d\mid p} \varphi(d),$$
where the sum is taken over all positive divisors $d$ of $p$ and $\varphi$ denotes Euler's totient function.
Let $n=20449$, and let $S$ be the sum of all positive divisors of $n$.
Let $c=48$. Let $L$ be the smalle... | 11,104 | graphs = [
Graph(
let={
"_d": Const(2),
"_m": Const(58218),
"_n": SumOverDivisors(n=MaxOverSet(set=SolutionsSet(var=Var(name='n'), condition=And(Geq(left=Var(name='n'), right=Const(value=2)), Leq(left=Var(name='n'), right=Const(value=105)), IsPrime(arg=Var(name='n'))))), ... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW/K3/MIN_PRIME_FACTOR"
] | e5ae1e | nt_sum_divisors_compute_v1 | crt_mix_3 | 5 | 0 | [
"K3",
"MAX_PRIME_BELOW",
"MIN_PRIME_FACTOR"
] | 3 | 0.006 | 2026-02-08T14:04:05.970080Z | {
"verified": true,
"answer": 11104,
"timestamp": "2026-02-08T14:04:05.975595Z"
} | 9c97f7 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 325,
"completion_tokens": 6169
},
"timestamp": "2026-02-15T23:20:42.455Z",
"answer": 11104
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K3",
"status": "ok_later"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma"... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
61f851 | antilemma_sum_equals_v1_151522320_516 | Let $n = 74$. Consider the set of all ordered pairs $(i, j)$ of positive integers such that $i + j = n$, where $1 \leq i \leq 72$ and $1 \leq j \leq 73$. Let $x$ be the number of such pairs. Compute $2209 - x$. | 2,137 | graphs = [
Graph(
let={
"_n": Const(74),
"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(72)), right=IntegerRange(start=Const(1), end=Con... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 2 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.004 | 2026-02-08T03:21:58.208770Z | {
"verified": true,
"answer": 2137,
"timestamp": "2026-02-08T03:21:58.212962Z"
} | 448a3b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 185,
"completion_tokens": 3297
},
"timestamp": "2026-02-10T13:59:52.114Z",
"answer": 2137
},
{
"i... | 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": -7.18,
"mid": -4.99,
"hi": -3
} | ||
fc1b04_l | comb_count_partitions_v1_798873815_9 | Let $n = 39$. Define $s = \sum_{d \mid n} \phi(d)$, where $\phi$ denotes Euler's totient function and the sum is over all positive divisors $d$ of $n$. Let $r$ be the number of integer partitions of $s$. Determine the value of $r$. | 31,044 | NT | COMB | COUNT | sympy | K3 | [
"K3"
] | 54c41e | comb_count_partitions_v1 | null | 4 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T02:23:38.882289Z | {
"verified": false,
"answer": 31185,
"timestamp": "2026-02-08T02:23:38.883574Z"
} | 025315 | fc1b04 | legacy_text | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 185,
"completion_tokens": 1127
},
"timestamp": "2026-02-08T18:28:23.658Z",
"answer": 31044
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
}
... | {
"lo": 3.15,
"mid": 4.33,
"hi": 5.51
} | |
155c5c | nt_min_phi_inverse_v1_677425708_2248 | Let $n_0$ be the sum of all positive integers $n \leq 20$ such that $n$ is divisible by the smallest divisor $d \geq 2$ of $35$. Let $n_1$ be the smallest positive integer $n \leq n_0$ such that $\phi(n) = 12$. Compute the value of $7^{|n_1|} + 50176$ modulo $99991$. | 81,376 | graphs = [
Graph(
let={
"_m": Const(35),
"_n": Const(20),
"upper": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_n")), Eq(Mod(value=Var("n"), modulus=MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"... | NT | null | EXTREMUM | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/SUM_DIVISIBLE"
] | 9f1b23 | nt_min_phi_inverse_v1 | null | 6 | 0 | [
"MIN_PRIME_FACTOR",
"SUM_DIVISIBLE"
] | 2 | 0.013 | 2026-02-08T04:52:23.280903Z | {
"verified": true,
"answer": 81376,
"timestamp": "2026-02-08T04:52:23.293415Z"
} | 6455e8 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 207,
"completion_tokens": 2094
},
"timestamp": "2026-02-11T22:35:26.391Z",
"answer": 81376
},
{
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "SUM_DIVISIBLE",
"status": "ok_... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
d8ecd9 | antilemma_sum_equals_v1_655260480_4337 | Let $m = 45$. Let $n$ be the number of ordered pairs $(i, j)$ of positive integers such that $1 \leq i \leq 44$, $1 \leq j \leq 45$, and $i + j = m$. Let $x$ be the number of ordered pairs $(i_1, j_1)$ of positive integers such that $1 \leq i_1 \leq 44$, $1 \leq j_1 \leq 44$, and $i_1 + j_1 = n$. Find the value of $x$. | 43 | graphs = [
Graph(
let={
"_m": Const(45),
"_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(44)), 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 | 0.1 | 2026-02-08T17:53:21.639288Z | {
"verified": true,
"answer": 43,
"timestamp": "2026-02-08T17:53:21.739187Z"
} | 5ce206 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 169,
"completion_tokens": 1355
},
"timestamp": "2026-02-24T23:08:22.545Z",
"answer": 43
},
{
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SU... | {
"lo": -8.52,
"mid": -5.43,
"hi": -3.2
} | ||
f1d5e6 | comb_sum_binomial_row_v1_601307018_514 | For each integer $a$ with $0 \leq a \leq 60$, define the sequence
\[
M = (a^2 - 2) \bmod 61,\quad R = (M^2 - 2) \bmod 61,\quad S = (R^2 - 2) \bmod 61,\quad T = (S^2 - 2) \bmod 61,\quad K = (T^2 - 2) \bmod 61.
\]
Let $n$ be the number of such $a$ for which $K = a$, but $M \neq a$, $R \neq a$, $S \neq a$, and $T \neq a$.... | 32,768 | graphs = [
Graph(
let={
"_n": Const(2),
"n": CountOverSet(set=SolutionsSet(var=Var("a"), condition=And(Geq(Var("a"), Const(0)), Leq(Var("a"), Const(60)), Eq(Ref("_po_p5"), Var("a")), Neq(Ref("_po_p1"), Var("a")), Neq(Ref("_po_p2"), Var("a")), Neq(Ref("_po_p3"), Var("a")), Neq(Ref("_p... | COMB | null | SUM | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | comb_sum_binomial_row_v1 | null | 7 | 0 | [
"POLY_ORBIT_COUNT"
] | 1 | 0.004 | 2026-03-10T01:00:39.707785Z | {
"verified": true,
"answer": 32768,
"timestamp": "2026-03-10T01:00:39.712250Z"
} | 3b583b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 272,
"completion_tokens": 28376
},
"timestamp": "2026-03-28T23:16:44.560Z",
"answer": 33554432
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "... | {
"lo": 4.01,
"mid": 6.11,
"hi": 9.15
} | ||
8b59de_n | alg_poly3_count_v1_1419126231_818 | A sculptor carves blocks of material into shapes whose volume is given by the expression $64a^3 - 96a^2b + 48ab^2 - 8b^3$ cubic units, where $a$ and $b$ are positive integers between 1 and 189. She wants to know how many distinct pairs $(a, b)$ will yield a volume of exactly 11,543,176 cubic units. How many such pairs ... | 95 | ALG | null | COUNT | sympy | MAX_DIVISOR | [
"B3/POLY4_COUNT"
] | a7d975 | alg_poly3_count_v1 | null | 4 | null | [
"B3",
"MAX_DIVISOR",
"POLY4_COUNT"
] | 3 | 5.132 | 2026-02-25T10:18:22.126701Z | null | 7f8032 | 8b59de | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 208,
"completion_tokens": 965
},
"timestamp": "2026-03-31T03:59:03.928Z",
"answer": 95
},
{
"id":... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY4_COUNT",
"status": "ok_later"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | |
4160a3 | comb_factorial_compute_v1_601307018_7498 | Let $n$ be the minimum value of $10a^2 - 32ab + 32b^2$ over all ordered pairs $(a, b)$ of positive integers with $1 \leq a \leq \left|\{ (a_1, b_1) : 1 \leq a_1 \leq 25,\ 1 \leq b_1 \leq 25,\ a_1 \leq b_1,\ 32a_1^2 - 64a_1b_1 + 32b_1^2 = \min\{ x + y : x > 0, y > 0, xy = 3748096 \} \}\right|$ and $1 \leq b \leq 14$. Co... | 40,320 | graphs = [
Graph(
let={
"_c": Const(2),
"_m": Const(32),
"_n": Const(2),
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), CountOverSet(set=SolutionsSet(var=Tuple(elem... | COMB | null | COMPUTE | sympy | B3 | [
"B3/QF_PSD_ORBIT/QF_PSD_MIN"
] | e708ee | comb_factorial_compute_v1 | null | 7 | 0 | [
"B3",
"QF_PSD_MIN",
"QF_PSD_ORBIT"
] | 3 | 0.011 | 2026-03-10T08:01:42.448556Z | {
"verified": true,
"answer": 40320,
"timestamp": "2026-03-10T08:01:42.459213Z"
} | 1cc7f8 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 283,
"completion_tokens": 3286
},
"timestamp": "2026-04-19T06:53:00.419Z",
"answer": 40320
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "QF_PSD_MIN",
"status": "ok_later"
},
{
"lemma": "QF_PSD_ORBIT",
"status": "ok_later"
},
{
"lemma": "V7",
"status": ... | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
e7362b_n | alg_qf_psd_sum_v1_1218484723_2413 | A game board has four positions, each of which can be filled with a tile numbered 1 through 4. A player rolls four dice to determine values $a$, $b$, $c$, and $d$. The score for a roll is computed using the formula: $27a^2 + 59b^2 + 30c^2 + 66d^2 + 40bc - 8ac - 40ad - 112bd - 66cd + K \cdot ab$, where $K$ is the smalle... | 36,221 | ALG | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | alg_qf_psd_sum_v1 | null | 4 | null | [
"B3"
] | 1 | 0.049 | 2026-02-25T04:12:50.595753Z | null | 863db2 | e7362b | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 257,
"completion_tokens": 1792
},
"timestamp": "2026-03-30T18:27:24.817Z",
"answer": 36121
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 1.5,
"mid": 4.69,
"hi": 7.23
} | |
30be3d | nt_count_divisible_and_v1_784195855_1250 | Let $d_1$ be the maximum value of $xy$ over all ordered pairs of positive integers $(x, y)$ such that $x + y = 6$. Let $d_2 = 12$. Let $s = \sum_{k=0}^{t} (-1)^k \binom{10}{k}$, where $t$ is the number of integers in the interval $[21, 60]$ that can be expressed as $15a + 6b$ for positive integers $a \in \{1,2\}$ and $... | 4,059 | graphs = [
Graph(
let={
"_n": Const(6),
"upper": Const(146124),
"d1": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Ref("_n")))),... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/BINOMIAL_ALTERNATING",
"B1"
] | c703bd | nt_count_divisible_and_v1 | null | 7 | 0 | [
"B1",
"BINOMIAL_ALTERNATING",
"LIN_FORM"
] | 3 | 4.888 | 2026-02-08T04:55:20.118145Z | {
"verified": true,
"answer": 4059,
"timestamp": "2026-02-08T04:55:25.006245Z"
} | a07975 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 295,
"completion_tokens": 1733
},
"timestamp": "2026-02-24T02:19:29.994Z",
"answer": 4059
},
{
"i... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "LIN_FORM",
... | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
ad7436 | nt_count_divisible_v1_865884756_6470 | Let $S$ be the set of all positive integers $n$ such that $1 \leq n \leq 49284$ and $n$ is divisible by $\sum_{k=1}^{5} k$. Compute the number of elements in $S$. | 3,285 | graphs = [
Graph(
let={
"upper": Const(49284),
"divisor": Summation(var="k", start=Const(1), end=Const(5), expr=Var("k")),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(value=Var("n"), modu... | NT | null | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | nt_count_divisible_v1 | null | 2 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 1.44 | 2026-02-08T19:13:29.935448Z | {
"verified": true,
"answer": 3285,
"timestamp": "2026-02-08T19:13:31.375872Z"
} | f5fd5f | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 114,
"completion_tokens": 286
},
"timestamp": "2026-02-16T18:36:01.384Z",
"answer": 3285
},
{
"id": 11,
... | 2 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
}
] | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
25dfb9 | v7_endings_v1_1248542787_189 | For each integer $k$ with $0 \le k \le 823$, let $e_k$ be the largest integer $e$ such that $2^e$ divides $\binom{823}{k}$. Let $m$ be the maximum value of $e_k$ over all such $k$. Compute the remainder when $13683 \cdot m$ is divided by $97183$. | 82,098 | graphs = [
Graph(
let={
"_inner_result": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(0)), Leq(Var("k"), Const(823)))), expr=MaxKDivides(target=Binom(n=Const(823), k=Var("k")), base=Const(2)))),
"_scale_k": Const(13683),
"_sca... | NT | null | COMPUTE | sympy | V7 | [
"V7"
] | 0672d4 | v7_endings_v1 | null | 7 | null | [
"V7"
] | 1 | 0.002 | 2026-02-08T03:00:44.696173Z | {
"verified": true,
"answer": 82098,
"timestamp": "2026-02-08T03:00:44.697806Z"
} | c8e676 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 198,
"completion_tokens": 7071
},
"timestamp": "2026-02-09T01:10:56.154Z",
"answer": 82098
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V7",
"status": "ok"
}
] | {
"lo": -6.5,
"mid": -0.2,
"hi": 6.11
} | ||
9eaf75 | nt_sum_totient_over_divisors_v1_458359167_4917 | Let $m = 30$, and let $n$ be the number of positive integers at most $21461$ that are relatively prime to $m$. Let $\text{result} = \sum_{d \mid 18891} \phi(d)$, where $\phi$ denotes Euler's totient function. Let $c$ be the largest positive divisor of $32832851$ that is at most $n$. Compute the remainder when $c \cdot ... | 49,241 | graphs = [
Graph(
let={
"_m": Const(30),
"_n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(21461)), Eq(GCD(a=Var("n"), b=Ref("_m")), Const(1))))),
"n": Const(18891),
"result": SumOverDivisors(n=Ref(nam... | NT | null | COMPUTE | sympy | C4 | [
"C4/MAX_DIVISOR"
] | 93b7fc | nt_sum_totient_over_divisors_v1 | affine_mod | 5 | 0 | [
"C4",
"MAX_DIVISOR"
] | 2 | 0.004 | 2026-02-08T12:07:34.798303Z | {
"verified": true,
"answer": 49241,
"timestamp": "2026-02-08T12:07:34.802654Z"
} | 1b7639 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 152,
"completion_tokens": 3171
},
"timestamp": "2026-02-14T22:23:23.729Z",
"answer": 49241
},
... | 1 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok_later"
},
{
"lemma": "MOD_MUL",
"status"... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
eca4a8 | comb_binomial_compute_v1_1978505735_7206 | Let $n$ be the number of ordered pairs $(i, j)$ of positive integers such that $i + j = 13$, $1 \le i \le 12$, and $1 \le j \le 13$. Compute $\binom{n}{5}$. | 792 | graphs = [
Graph(
let={
"_n": Const(13),
"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(12)), right=IntegerRange(start=Const(1), end=Con... | ALG | COMB | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | comb_binomial_compute_v1 | null | 3 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.011 | 2026-02-08T20:06:50.987210Z | {
"verified": true,
"answer": 792,
"timestamp": "2026-02-08T20:06:50.997874Z"
} | ad8f4c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 103,
"completion_tokens": 816
},
"timestamp": "2026-02-18T23:57:50.001Z",
"answer": 792
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status":... | {
"lo": -7.92,
"mid": -4.6,
"hi": -1.84
} | ||
0b77ad | nt_min_coprime_above_v1_784195855_9584 | Let $m$ be the largest positive divisor of $396899$ that does not exceed $629$. Let $n$ be the number of positive integers at most $m$ that are relatively prime to $10$. Let $c = 2$, and let $p_{\text{max}}$ be the largest prime number $n$ such that $c \leq n \leq n$. Compute the smallest integer $k$ such that $21609 <... | 21,610 | graphs = [
Graph(
let={
"_c": Const(2),
"_m": MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Leq(Var("d"), Const(629)), Divides(divisor=Var("d"), dividend=Const(396899))))),
"_n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(... | NT | null | EXTREMUM | sympy | MAX_DIVISOR | [
"MAX_DIVISOR/C4/MAX_PRIME_BELOW"
] | 139b52 | nt_min_coprime_above_v1 | null | 7 | 0 | [
"C4",
"MAX_DIVISOR",
"MAX_PRIME_BELOW"
] | 3 | 0.047 | 2026-02-08T16:54:07.616291Z | {
"verified": true,
"answer": 21610,
"timestamp": "2026-02-08T16:54:07.663770Z"
} | 3ae601 | 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": 1529
},
"timestamp": "2026-02-17T15:30:43.842Z",
"answer": 21610
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "C4",
"status": "ok_later"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "MAX_DIVIS... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
7ef2b6 | modular_count_residue_v1_151522320_1307 | Let $m = \sum_{d \mid 30} \phi(d)$, where $\phi$ denotes Euler's totient function. Let $r = 10$ and let $\text{upper} = 32057$. Define $\text{result}$ to be the number of positive integers $n$ such that $1 \leq n \leq \text{upper}$ and $n \equiv r \pmod{m}$. Let $\_n = 44121$. Compute $\_n \cdot \text{result}$, and the... | 15,890 | graphs = [
Graph(
let={
"_n": Const(44121),
"upper": Const(32057),
"m": SumOverDivisors(n=Const(value=30), var='d', expr=EulerPhi(n=Var(name='d'))),
"r": Const(10),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), C... | NT | null | COUNT | sympy | K3 | [
"K3"
] | 54c41e | modular_count_residue_v1 | null | 3 | 0 | [
"K3"
] | 1 | 1.046 | 2026-02-08T03:52:37.878739Z | {
"verified": true,
"answer": 15890,
"timestamp": "2026-02-08T03:52:38.924309Z"
} | bec544 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 248,
"completion_tokens": 1313
},
"timestamp": "2026-02-10T16:19:01.055Z",
"answer": 15890
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
a488c1 | lin_form_endings_v1_1742523217_1145 | Let $a = 15$ and $b = 25$. Define $g = \gcd(a, b)$. Let $a' = \left\lfloor \frac{a}{g} \right\rfloor$ and $b' = \left\lfloor \frac{b}{g} \right\rfloor$. Compute the value of
$$
(5437 \cdot (a' \cdot 17 + b' \cdot 37 - a' \cdot b')) \mod 61397.
$$ | 35,034 | graphs = [
Graph(
let={
"a_coeff": Const(15),
"b_coeff": Const(25),
"A_val": Const(17),
"B_val": Const(37),
"g_step": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"ap_node": Floor(Div(Ref("a_coeff"), Ref("g_step"))),
"bp_node": ... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 3 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T03:28:30.443198Z | {
"verified": true,
"answer": 35034,
"timestamp": "2026-02-08T03:28:30.443765Z"
} | 2c8e44 | 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": 650
},
"timestamp": "2026-02-10T04:06:41.414Z",
"answer": 35034
},
{
"i... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
6349bc | nt_lcm_compute_v1_865884756_3107 | Let $n = 38$. Let $a$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 173056$. Let $b = \sum_{k=1}^{n} k$. Compute the least common multiple of $a$ and $b$. | 47,424 | graphs = [
Graph(
let={
"_n": Const(38),
"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(173056)))), expr=Sum(Var("x"), Var("y")))),... | NT | null | COMPUTE | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC",
"B3"
] | dee757 | nt_lcm_compute_v1 | null | 5 | 0 | [
"B3",
"SUM_ARITHMETIC"
] | 2 | 0.002 | 2026-02-08T17:10:47.745120Z | {
"verified": true,
"answer": 47424,
"timestamp": "2026-02-08T17:10:47.747033Z"
} | b562cd | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 117,
"completion_tokens": 1323
},
"timestamp": "2026-02-17T20:56:03.128Z",
"answer": 47424
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"le... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
2ca0b6 | alg_poly3_min_v1_1218484723_5603 | Find the remainder when the minimum value of $-21a^2b + 21ab^2 - 91b^{\max \{ n : n \geq 2,\, n \leq 4,\, n \text{ is prime} \}}$ over all integers $a, b$ with $1 \leq a \leq 115$ and $1 \leq b \leq 115$ is divided by $65396$. | 43,707 | graphs = [
Graph(
let={
"_n": Const(65396),
"result": Mod(value=MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(115)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(115)))), expr=Sum(Mul(Co... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | alg_poly3_min_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.024 | 2026-02-25T07:05:40.082127Z | {
"verified": true,
"answer": 43707,
"timestamp": "2026-02-25T07:05:40.105797Z"
} | f68061 | 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": 5179
},
"timestamp": "2026-03-29T21:55:33.532Z",
"answer": 43707
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
... | {
"lo": -3.33,
"mid": 1.03,
"hi": 5.26
} |
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