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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
20c511 | alg_poly_orbit_count_v1_1218484723_658 | Let $f(x) = 3x^3 - 4x^2 - 5x - 2 \bmod 31$. For a non-negative integer $a$ with $0 \le a \le 4990$, define $N = f(a)$, $M = f(N)$, $R = f(M)$, $S = f(R)$, $T = f(S)$. Find the number of values of $a$ such that $T = a$, $N \ne a$, $M \ne a$, $R \ne a$, and $S \ne a$. | 805 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Mul(Const(3), Pow(Var("a"), Const(3))), Mul(Const(-4), Pow(Var("a"), Const(2))), Mul(Const(-5), Var("a")), Const(-2)), modulus=Const(31)),
"p2": Mod(value=Sum(Mul(Const(3), Pow(Ref("p1"), Const(3))), Mul(Const(-4), Pow(Ref("p1"), Const(2)))... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_orbit_count_v1 | null | 6 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.095 | 2026-02-25T02:24:13.180270Z | {
"verified": true,
"answer": 805,
"timestamp": "2026-02-25T02:24:13.274854Z"
} | 0c8f61 | 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": 12289
},
"timestamp": "2026-03-28T23:43:54.512Z",
"answer": 805
},
{
"i... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 1.22,
"mid": 3.76,
"hi": 5.73
} | ||
748479 | algebra_quadratic_discriminant_v1_865884756_645 | Let $m = 8125$. Let $T$ be the set of all positive integers $k$ such that $1 \leq k \leq m$ and $325$ divides $k$. Let $A$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = |T|$. Define $a$ to be the minimum value of $x + y$ over all such pairs. Compute the remainder when $44121 \cdot ((-1)^... | 63,091 | graphs = [
Graph(
let={
"_m": Const(8125),
"_n": Const(2),
"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")), CountOverSet(set=So... | ALG | NT | COMPUTE | sympy | B3 | [
"C2/B3"
] | 7c8509 | algebra_quadratic_discriminant_v1 | null | 5 | 0 | [
"B3",
"C2"
] | 2 | 0.02 | 2026-02-08T15:32:55.798390Z | {
"verified": true,
"answer": 63091,
"timestamp": "2026-02-08T15:32:55.818733Z"
} | 7d8910 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 167,
"completion_tokens": 853
},
"timestamp": "2026-02-16T07:47:14.535Z",
"answer": 63091
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V7",... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
fd3bf6 | modular_mod_compute_v1_784195855_3713 | Let $n = 68$. Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $x + y = n$. Let $a$ be the maximum value of $x \cdot y$ over all such pairs. Let $r = a \mod 47524$. Compute the remainder when $43351 \cdot r$ is divided by $90162$. | 73,846 | graphs = [
Graph(
let={
"_n": Const(68),
"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 | B1 | [
"B1"
] | 5b950e | modular_mod_compute_v1 | null | 4 | 0 | [
"B1"
] | 1 | 0.003 | 2026-02-08T06:35:32.767552Z | {
"verified": true,
"answer": 73846,
"timestamp": "2026-02-08T06:35:32.770260Z"
} | 98c32c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 130,
"completion_tokens": 858
},
"timestamp": "2026-02-13T02:40:48.951Z",
"answer": 73846
},
{... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
dc36ed | alg_poly_orbit_hensel_v1_601307018_877 | Let $f(a) = 3a^4 + 3a^2 - 3a - 1 \bmod 4489$. Define the sequence $N = f(a)$, $M = f(N)$, $R = f(M)$, $S = f(R)$. Let $Q$ be the number of non-negative integers $a$ with $0 \le a \le 6854702$ such that $S = a$, $N \ne a$, $M \ne a$, and $R \ne a$. Find $Q$. | 6,108 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Mul(Const(3), Pow(Var("a"), Const(4))), Mul(Const(3), Pow(Var("a"), Const(2))), Mul(Const(-3), Var("a")), Const(-1)), modulus=Const(4489)),
"p2": Mod(value=Sum(Mul(Const(3), Pow(Ref("p1"), Const(4))), Mul(Const(3), Pow(Ref("p1"), Const(2)))... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_orbit_hensel_v1 | null | 6 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.096 | 2026-03-10T01:29:38.500428Z | {
"verified": true,
"answer": 6108,
"timestamp": "2026-03-10T01:29:38.596695Z"
} | b15e4c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 229,
"completion_tokens": 25718
},
"timestamp": "2026-03-29T00:29:36.030Z",
"answer": 4
},
{
"... | 0 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 4.01,
"mid": 6.11,
"hi": 9.15
} | ||
70f49d | comb_count_partitions_v1_601307018_4294 | Let $n$ be the number of positive integers $t$ such that there exist integers $a$, $b$ with $1 \leq a \leq 3$, $1 \leq b \leq 19$, $t = 3a + 2b$, and $5 \leq t \leq 47$. Let $Q = p(n)$, where $p(n)$ denotes the number of partitions of $n$. Compute $Q$. | 44,583 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=3)), Geq(left=Var(name='b'), right=Const(value=1... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_count_partitions_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.004 | 2026-03-10T04:53:22.283725Z | {
"verified": true,
"answer": 44583,
"timestamp": "2026-03-10T04:53:22.287760Z"
} | 414ec8 | 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": 6306
},
"timestamp": "2026-03-29T11:44:08.952Z",
"answer": 44583
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": 3.34,
"mid": 5.77,
"hi": 8.89
} | ||
4c03e1 | nt_count_divisible_and_v1_48377204_1875 | Let $d_1 = \sum_{k=1}^{3} k$ and $d_2 = 8$. Compute the number of positive integers $n$ such that $1 \leq n \leq 94392$, $n$ is divisible by $d_1$, and $n$ is divisible by $d_2$. | 3,933 | graphs = [
Graph(
let={
"upper": Const(94392),
"d1": Summation(var="k", start=Const(1), end=Const(3), expr=Var("k")),
"d2": Const(8),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(M... | NT | null | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | nt_count_divisible_and_v1 | null | 3 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 3.693 | 2026-02-08T16:28:01.253576Z | {
"verified": true,
"answer": 3933,
"timestamp": "2026-02-08T16:28:04.946961Z"
} | f5f31e | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 132,
"completion_tokens": 301
},
"timestamp": "2026-02-16T07:26:43.787Z",
"answer": 3933
},
{
"id": 11,
... | 2 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": ... | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
ab6062 | antilemma_sum_equals_v1_124444284_3261 | Let $n = 20$. Consider the set of all ordered pairs $(i,j)$ of positive integers such that $i + j = n$ and $1 \leq i, j \leq 19$. Let $x$ be the number of such ordered pairs. Compute $$\sum_{k=1}^{x} \phi(k),$$ where $\phi$ denotes Euler's totient function. | 120 | graphs = [
Graph(
let={
"_n": Const(20),
"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(19)), right=IntegerRange(start=Const(1), end=Con... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 4 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.009 | 2026-02-08T05:20:07.871378Z | {
"verified": true,
"answer": 120,
"timestamp": "2026-02-08T05:20:07.880557Z"
} | 9f79b2 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 194,
"completion_tokens": 1241
},
"timestamp": "2026-02-24T03:12:44.144Z",
"answer": 120
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V8",
... | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
fbc782 | nt_count_divisible_v1_349078426_519 | Let $n$ be the number of elements in the Cartesian product $\{1,2\} \times \{1,2,3,4\}$. Evaluate the sum
$$
\sum_{k=0}^{4} (-1)^k \binom{c}{k},
$$
depending on $c$, where $c$ is the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = n$. Let $r$ be this sum. Determine the number of pos... | 8,580 | graphs = [
Graph(
let={
"_n": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(2)), right=IntegerRange(start=Const(1), end=Const(4)))),
"upper": Const(68644),
"divisor": Const(8),
"result": CountOverSet(set=SolutionsSet(var=Var("n"... | COMB | null | COUNT | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN/COMB1/BINOMIAL_ALTERNATING"
] | 365554 | nt_count_divisible_v1 | null | 6 | 0 | [
"BINOMIAL_ALTERNATING",
"COMB1",
"COUNT_CARTESIAN"
] | 3 | 3.783 | 2026-02-08T13:06:45.831344Z | {
"verified": true,
"answer": 8580,
"timestamp": "2026-02-08T13:06:49.614006Z"
} | 1a5c4a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 260,
"completion_tokens": 1190
},
"timestamp": "2026-02-24T17:09:58.514Z",
"answer": 8580
},
{
"i... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok_later"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
... | {
"lo": -5.97,
"mid": -3.97,
"hi": -1.93
} | ||
b704b6 | diophantine_product_count_v1_1520064083_8187 | Let $k = 1260$ and $\text{upper} = 339$. Consider the set of all positive integers $x$ such that $1 \leq x \leq \text{upper}$, $x$ divides $k$, and $\frac{k}{x} \leq \text{upper}$.
Compute the number of elements in this set. | 30 | graphs = [
Graph(
let={
"k": Const(1260),
"upper": Const(339),
"result": CountOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), Const(1)), Leq(Var("x"), Ref("upper")), Divides(divisor=Var("x"), dividend=Ref("k")), Leq(Div(Ref("k"), Var("x")), Ref("upper")... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM",
"B3"
] | 688dbe | diophantine_product_count_v1 | null | 4 | 0 | [
"B3",
"LIN_FORM"
] | 2 | 0.045 | 2026-02-08T10:03:30.159600Z | {
"verified": true,
"answer": 30,
"timestamp": "2026-02-08T10:03:30.204687Z"
} | 7cf8bd | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 120,
"completion_tokens": 1840
},
"timestamp": "2026-02-14T06:14:52.931Z",
"answer": 30
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
},
{
"le... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
89b817 | comb_binomial_compute_v1_1520064083_3509 | Let $n = 12$ and $k = 7$. Define $C = \binom{n}{k}$. Let $P$ be the largest prime number less than or equal to 3826. Compute the remainder when $P \cdot C$ is divided by 71574. | 21,708 | graphs = [
Graph(
let={
"_n": Const(3826),
"n": Const(12),
"k": Const(7),
"result": Binom(n=Ref("n"), k=Ref("k")),
"_c": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n")))))... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | 183c11 | comb_binomial_compute_v1 | affine_mod | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.001 | 2026-02-08T05:43:31.856411Z | {
"verified": true,
"answer": 21708,
"timestamp": "2026-02-08T05:43:31.857626Z"
} | 3ef3da | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 106,
"completion_tokens": 2438
},
"timestamp": "2026-02-12T12:53:01.824Z",
"answer": 21708
},
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
3073a5 | modular_sum_quadratic_residues_v1_1915831931_2906 | Let $p$ be the largest prime number less than or equal to 178. Compute the remainder when $\frac{p(p-1)}{4} \times 81127$ is divided by 99868. | 1,429 | graphs = [
Graph(
let={
"p": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(178)), IsPrime(Var("n"))))),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), Const(4)),
"_c": Const(81127),
"Q": Mod(value=M... | NT | null | SUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | modular_sum_quadratic_residues_v1 | null | 2 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.002 | 2026-02-08T17:14:14.001301Z | {
"verified": true,
"answer": 1429,
"timestamp": "2026-02-08T17:14:14.003263Z"
} | ed3990 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 90,
"completion_tokens": 1588
},
"timestamp": "2026-02-17T22:34:30.983Z",
"answer": 1429
},
{
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
117cf8 | modular_sum_quadratic_residues_v1_397696148_1081 | Let $p$ be the smallest prime divisor of $138693847$. Compute $\frac{p(p-1)}{4}$. | 64,643 | graphs = [
Graph(
let={
"_n": Const(2),
"p": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(138693847))))),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), Const(4)),
},
goal... | NT | null | SUM | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | modular_sum_quadratic_residues_v1 | null | 2 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.002 | 2026-02-08T12:20:27.777855Z | {
"verified": true,
"answer": 64643,
"timestamp": "2026-02-08T12:20:27.779753Z"
} | 2ee6f4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 72,
"completion_tokens": 5707
},
"timestamp": "2026-02-15T00:27:59.858Z",
"answer": 64643
},
{... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V5",
"status": ... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
935927 | nt_min_phi_inverse_v1_1918700295_2715 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = 20$. Let $P$ be the set of all values of $xy$ as $(x, y)$ ranges over $S$. Let $M$ be the maximum value in $P$. Let $T$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = M$. Let $U$ be the set of all val... | 7 | graphs = [
Graph(
let={
"upper": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), V... | NT | null | EXTREMUM | sympy | K2 | [
"B1/B3"
] | 80b49d | nt_min_phi_inverse_v1 | null | 6 | 0 | [
"B1",
"B3",
"K2"
] | 3 | 0.015 | 2026-02-08T08:10:41.225809Z | {
"verified": true,
"answer": 7,
"timestamp": "2026-02-08T08:10:41.240969Z"
} | f18ad9 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 246,
"completion_tokens": 2760
},
"timestamp": "2026-02-13T15:42:21.290Z",
"answer": 7
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "n... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
3ad422 | modular_modexp_compute_v1_1520064083_8280 | Let $n = 2$. Define $a$ to be the largest integer $k$ such that $2^k \leq 13508349759706$. Let $e = 2018$. Let $m$ be the maximum value of $xy$ over all ordered pairs $(x, y)$ of positive integers such that $x + y = 200$. Compute the remainder when $a^e$ is divided by $m$, and let $Q = 73984 - \text{that remainder}$. F... | 67,335 | graphs = [
Graph(
let={
"_n": Const(2),
"a": MaxOverSet(set=SolutionsSet(var=Var("k"), condition=Leq(Pow(Ref("_n"), Var("k")), Const(13508349759706)))),
"e": Const(2018),
"m": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]),... | NT | null | COMPUTE | sympy | MAX_VAL | [
"MAX_VAL",
"B1"
] | 978614 | modular_modexp_compute_v1 | null | 6 | 0 | [
"B1",
"MAX_VAL"
] | 2 | 0.002 | 2026-02-08T10:07:07.026508Z | {
"verified": true,
"answer": 67335,
"timestamp": "2026-02-08T10:07:07.028605Z"
} | fb3582 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 159,
"completion_tokens": 3702
},
"timestamp": "2026-02-14T06:27:56.931Z",
"answer": 67335
},
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "K16",
"status": "same_pattern_wrong"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "ok"
}... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
85a597 | nt_min_phi_inverse_v1_809748730_932 | Let $n = 24$. Define $\text{upper}$ to be the number of integers $t$ such that $9 \leq t \leq 70$ and there exist integers $a$ and $b$ with $1 \leq a \leq 5$, $1 \leq b \leq 10$, and $t = 4a + 5b$. Let $k = 12$. Let $\text{result}$ be the smallest positive integer $n$ such that $1 \leq n \leq \text{upper}$ and $\phi(n)... | 11 | graphs = [
Graph(
let={
"_n": Const(24),
"upper": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=5)), Geq(left=V... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_min_phi_inverse_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.052 | 2026-02-08T11:50:10.374464Z | {
"verified": true,
"answer": 11,
"timestamp": "2026-02-08T11:50:10.426823Z"
} | e00dc1 | 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": 1932
},
"timestamp": "2026-02-14T19:12:14.285Z",
"answer": 11
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
da3336 | nt_sum_gcd_range_mod_v1_1742523217_4058 | Let $D$ be the set of all positive integers $d$ such that $d \leq 8649$ and $d$ divides $75047373$. Let $N$ be the sum of $\phi(d)$ over all $d$ in $D$, where $\phi$ denotes Euler's totient function. Let $k = 60$. Define $\text{sum} = \sum_{n=1}^{N} \gcd(n, k)$. Find the remainder when $\text{sum}$ is divided by $11393... | 6,297 | graphs = [
Graph(
let={
"N": SumOverDivisors(n=MaxOverSet(set=SolutionsSet(var=Var(name='d'), condition=And(Geq(left=Var(name='d'), right=Const(value=1)), Leq(left=Var(name='d'), right=Const(value=8649)), Divides(divisor=Var(name='d'), dividend=Const(value=75047373))))), var='d', expr=EulerPhi(n... | NT | null | COMPUTE | sympy | MAX_DIVISOR | [
"MAX_DIVISOR/K3"
] | 97a225 | nt_sum_gcd_range_mod_v1 | null | 6 | 0 | [
"K3",
"MAX_DIVISOR"
] | 2 | 0.507 | 2026-02-08T06:12:45.993644Z | {
"verified": true,
"answer": 6297,
"timestamp": "2026-02-08T06:12:46.500543Z"
} | 0ea637 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 157,
"completion_tokens": 5507
},
"timestamp": "2026-02-13T06:40:10.663Z",
"answer": 6297
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K3",
"status": "ok_later"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
7146b8 | algebra_quadratic_discriminant_v1_168721529_918 | Let $a = 2$, $b = -12$, and $c = -32$. Consider the set of all positive integers $p$ for which there exists a positive integer $q$ such that $p < q$, $pq = 54$, and $\gcd(p, q) = 1$. Let $n$ be the number of such integers $p$.
Compute the value of
$$
(-12)^n - 4 \cdot 2 \cdot (-32).
$$ | 400 | graphs = [
Graph(
let={
"_n": Const(4),
"a": Const(2),
"b": Const(-12),
"c": Const(-32),
"result": Sub(Pow(Ref("b"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | algebra_quadratic_discriminant_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.003 | 2026-02-08T13:20:48.120043Z | {
"verified": true,
"answer": 400,
"timestamp": "2026-02-08T13:20:48.122652Z"
} | ec31df | 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": 763
},
"timestamp": "2026-02-09T10:42:13.787Z",
"answer": 400
},
{
"id"... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status":... | {
"lo": -6.97,
"mid": -4.58,
"hi": -1.65
} | ||
c0f1f0 | comb_catalan_compute_v1_784195855_8274 | Let $T$ be the set of all ordered pairs of positive odd integers $(x_1, x_2)$ such that $x_1 + x_2 = 26$. Let $\mathcal{N}$ be the number of elements in $T$. Let $S$ be the set of all ordered pairs $(i, j)$ with $1 \leq i \leq 11$ and $1 \leq j \leq 12$ such that $i + j = \mathcal{N}$. Let $C_n$ denote the $n$th Catala... | 5,722 | 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")), R... | COMB | null | COMPUTE | sympy | COMB1 | [
"COMB1/COUNT_SUM_EQUALS"
] | 4d9cac | comb_catalan_compute_v1 | null | 5 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS"
] | 2 | 0.011 | 2026-02-08T15:59:07.200007Z | {
"verified": true,
"answer": 5722,
"timestamp": "2026-02-08T15:59:07.211452Z"
} | 13eba9 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 258,
"completion_tokens": 2618
},
"timestamp": "2026-02-24T19:12:28.330Z",
"answer": 5722
},
{
"... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok_later"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"st... | {
"lo": -2.4,
"mid": 1.57,
"hi": 5.75
} | ||
ff3a13 | diophantine_fbi2_min_v1_1353956133_751 | Let $k$ be the number of positive integers $j$ with $1 \leq j \leq 72$ such that $j^2 \leq 5184$. Let $d$ be the smallest integer such that $4 \leq d \leq 82$, $d$ divides $k$, and $\frac{k}{d} \geq 6$. Compute the remainder when $44121 \cdot d$ is divided by $72638$. | 31,208 | graphs = [
Graph(
let={
"_n": Const(2),
"k": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(1)), Leq(Var("j"), Const(72)), Leq(Pow(Var("j"), Ref("_n")), Const(5184))), domain='positive_integers')),
"upper": Const(82),
"result": M... | NT | null | EXTREMUM | sympy | C3 | [
"C3"
] | 8a214c | diophantine_fbi2_min_v1 | null | 4 | 0 | [
"C3"
] | 1 | 0.008 | 2026-02-08T11:50:16.984596Z | {
"verified": true,
"answer": 31208,
"timestamp": "2026-02-08T11:50:16.992260Z"
} | 1f8647 | 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": 628
},
"timestamp": "2026-02-14T19:52:45.769Z",
"answer": 31208
},
{... | 1 | [
{
"lemma": "C3",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
bd7147 | comb_sum_binomial_row_v1_124444284_4274 | Let $n = 11221$. Let $j$ be a positive integer such that $1 \leq j \leq 13$ and $j^4 \leq 28561$. Let $c$ be the number of such integers $j$. Let $P = 2^c$. Find the remainder when $n \cdot P$ is divided by $92993$. | 45,348 | graphs = [
Graph(
let={
"_n": Const(11221),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(1)), Leq(Var("j"), Const(13)), Leq(Pow(Var("j"), Const(4)), Const(28561))), domain='positive_integers')),
"result": Pow(Const(2), Ref("n")),
... | NT | null | SUM | sympy | C3 | [
"C3"
] | 8a214c | comb_sum_binomial_row_v1 | null | 3 | 0 | [
"C3"
] | 1 | 0.001 | 2026-02-08T05:53:22.020100Z | {
"verified": true,
"answer": 45348,
"timestamp": "2026-02-08T05:53:22.021263Z"
} | dfa6ae | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 125,
"completion_tokens": 1419
},
"timestamp": "2026-02-12T16:33:29.288Z",
"answer": 45348
},
... | 1 | [
{
"lemma": "C3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
60dd72 | alg_qf_psd_min_v1_601307018_553 | Find the minimum value of $$4860a^2 - 1260cd + 2700bd + \left(\sum_{\substack{(a_1,b_1,c_1)\,:\, a_1^2+b_1^2+c_1^2 = a_1b_1+b_1c_1+c_1a_1 \\ 6a_1+3b_1+9c_1=540 \\ a_1,b_1,c_1 \ge 1}} a_1^2 + b_1^2 + c_1^2\right) \cdot ad - 1080bc - 900ab + 7380d^2 + 1260c^2 + 4140ac + 3690b^2$$ over all positive integers $a,b,c,d$ with... | 23,490 | graphs = [
Graph(
let={
"_n": Const(2),
"result": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b"), Var("c"), Var("d")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(15)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(15)), Geq(Var("c"),... | ALG | null | COMPUTE | sympy | SUM_SQUARES_IDENTITY | [
"SUM_SQUARES_IDENTITY"
] | 9879b8 | alg_qf_psd_min_v1 | null | 7 | 0 | [
"SUM_SQUARES_IDENTITY"
] | 1 | 0.211 | 2026-03-10T01:04:56.308133Z | {
"verified": true,
"answer": 23490,
"timestamp": "2026-03-10T01:04:56.518646Z"
} | 94e640 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 305,
"completion_tokens": 7417
},
"timestamp": "2026-03-28T23:21:03.226Z",
"answer": 23490
},
{
"... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_SQUARES_IDENTITY",
"status": "ok"
}
] | {
"lo": -0.92,
"mid": 2.07,
"hi": 4.68
} | ||
147757 | diophantine_sum_product_min_v1_124444284_7239 | Let $S = 75$ and $P = 1386$. Determine the value of $x$, where $1 \leq x \leq 74$, such that $x(S - x) = P$. Compute the smallest such $x$. | 33 | graphs = [
Graph(
let={
"S": Const(75),
"P": Const(1386),
"result": MinOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), Const(1)), Leq(Var("x"), Const(74)), Eq(Mul(Var("x"), Sub(Ref("S"), Var("x"))), Ref("P"))))),
},
goal=Ref("result"),
... | NT | null | EXTREMUM | sympy | B3 | [
"V8"
] | 86348e | diophantine_sum_product_min_v1 | null | 4 | 0 | [
"B3",
"V8"
] | 2 | 11.165 | 2026-02-08T08:57:48.888596Z | {
"verified": true,
"answer": 33,
"timestamp": "2026-02-08T08:58:00.053495Z"
} | 6e3e8e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 98,
"completion_tokens": 487
},
"timestamp": "2026-02-13T22:28:55.035Z",
"answer": 33
},
{
... | 1 | [
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
}
] | {
"lo": -9.14,
"mid": -6.05,
"hi": -3.73
} | ||
cc3e50 | nt_count_intersection_v1_458359167_1088 | Let $N$ be the number of positive integers $n$ such that $1 \le n \le 58328$, $8$ divides $n$, and $\gcd(n, 35) = 1$. Let $M$ be the number of positive integers $n$ such that $1 \le n \le N$, $9$ divides $n$, and $\gcd(n, 10) = 1$. Let $c$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive inte... | 80,993 | graphs = [
Graph(
let={
"_n": Const(8),
"N": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(58328)), Divides(divisor=Ref("_n"), dividend=Var("n")), Eq(GCD(a=Var("n"), b=Const(35)), Const(1))))),
"a": Const(9),
... | NT | null | COUNT | sympy | B3 | [
"B3",
"C5"
] | 0c0979 | nt_count_intersection_v1 | two_stage_modexp | 6 | 0 | [
"B3",
"C5"
] | 2 | 0.169 | 2026-02-08T04:16:44.356165Z | {
"verified": true,
"answer": 80993,
"timestamp": "2026-02-08T04:16:44.525249Z"
} | 3a4122 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 257,
"completion_tokens": 5606
},
"timestamp": "2026-02-10T16:26:55.863Z",
"answer": 80993
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C5",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V7... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
9ae49a | alg_qf_psd_orbit_v1_1218484723_6171 | Find the number of ordered triples $(a, b, c)$ of positive integers such that $1 \leq a \leq b$, $1 \leq b \leq c$, $1 \leq c \leq 62$, and $$510a^2 + 510b^2 + 510c^2 - 480ab - 480bc - 480ac = 67500.$$ | 7 | graphs = [
Graph(
let={
"_n": Const(510),
"result": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b"), Var("c")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a1"), Var("b1")]), condition=And(Geq(Var("... | ALG | null | COUNT | sympy | POLY4_COUNT | [
"POLY4_COUNT"
] | 861d91 | alg_qf_psd_orbit_v1 | null | 6 | 0 | [
"POLY4_COUNT"
] | 1 | 0.762 | 2026-02-25T07:46:44.862394Z | {
"verified": true,
"answer": 7,
"timestamp": "2026-02-25T07:46:45.624308Z"
} | 9266dd | 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": 20563
},
"timestamp": "2026-03-30T00:33:37.301Z",
"answer": 7
},
{
"id"... | 1 | [
{
"lemma": "POLY4_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -3.33,
"mid": 1.03,
"hi": 5.26
} | ||
579152 | nt_lcm_compute_v1_349078426_510 | Let $n = 63036$. Let $A$ be the set of all ordered pairs of positive integers $(x, y)$ such that $xy = 497025$, and define $a$ to be the minimum value of $x + y$ over all such pairs. Let $B$ be the set of all ordered pairs of positive integers $(x, y)$ such that $xy = 1638400$, and define $b$ to be the minimum value of... | 45,780 | graphs = [
Graph(
let={
"_n": Const(63036),
"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(497025)))), expr=Sum(Var("x"), Var("y"))... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_lcm_compute_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.003 | 2026-02-08T13:06:14.384353Z | {
"verified": true,
"answer": 45780,
"timestamp": "2026-02-08T13:06:14.387675Z"
} | 6e1e11 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 192,
"completion_tokens": 1944
},
"timestamp": "2026-02-15T09:28:05.776Z",
"answer": 45780
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
4d64ac | nt_count_coprime_and_v1_865884756_3910 | Let $S$ be the set of all prime numbers $n$ such that $2 \leq n \leq 31$. Let $k_1$ be the smallest divisor of $847$ that is at least $2$. Let $T$ be the set of all ordered pairs $(i, j)$ of integers such that $1 \leq i \leq 9$, $1 \leq j \leq 10$, and $i + j = |S|$. Let $k_2$ be the number of elements in $T$. Let $U$ ... | 9,880 | graphs = [
Graph(
let={
"_c": Const(847),
"_m": Const(2),
"_n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_m")), Leq(Var("n"), Const(31)), IsPrime(Var("n"))))),
"upper": Const(17288),
"k1": MinOverSet(set=Solution... | NT | null | COUNT | sympy | COUNT_PRIMES | [
"COUNT_PRIMES/COUNT_SUM_EQUALS",
"MIN_PRIME_FACTOR"
] | 4f137c | nt_count_coprime_and_v1 | null | 4 | 0 | [
"COUNT_PRIMES",
"COUNT_SUM_EQUALS",
"MIN_PRIME_FACTOR"
] | 3 | 1.974 | 2026-02-08T17:39:46.019378Z | {
"verified": true,
"answer": 9880,
"timestamp": "2026-02-08T17:39:47.993030Z"
} | e5a02b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 228,
"completion_tokens": 1418
},
"timestamp": "2026-02-18T05:35:25.722Z",
"answer": 9880
},
{... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok_later"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
477931 | antilemma_coprime_grid_v1_168721529_475 | Compute the number of ordered pairs $(i, j)$ of integers with $1 \leq i \leq 10$ and $1 \leq j \leq 143$ such that $\gcd(i, j) = \phi(2)$, where $\phi$ denotes Euler's totient function. | 895 | graphs = [
Graph(
let={
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(GCD(a=Var("i"), b=Var("j")), EulerPhi(n=Const(2))), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(10)), right=IntegerRange(start=Const(1), end=Const(143))))),
... | NT | COMB | COMPUTE | sympy | COUNT_COPRIME_GRID | [
"COUNT_COPRIME_GRID",
"ONE_PHI_2"
] | 98ffdc | antilemma_coprime_grid_v1 | null | 4 | 0 | [
"COUNT_COPRIME_GRID",
"ONE_PHI_2"
] | 2 | 0.001 | 2026-02-08T13:04:01.398934Z | {
"verified": true,
"answer": 895,
"timestamp": "2026-02-08T13:04:01.399749Z"
} | 2fb161 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 180,
"completion_tokens": 1593
},
"timestamp": "2026-02-09T05:25:33.038Z",
"answer": 895
},
{
"id... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "ONE_PHI_2",
"statu... | {
"lo": -6.69,
"mid": -2.4,
"hi": 1.77
} | ||
c53acd | alg_telescope_v1_601307018_260 | Let
$$R = \sum_{k=0}^{505} \bigl(3k^{2} + 3k + 1\bigr) \bmod \left|\{ t : \text{there exist integers } a, b \text{ with } 1 \le a \le 12,\ 1 \le b \le 1115 \text{ such that } t = 3a + 5b + 19,\ 27 \le t \le 5630 \}\right|.$$
Compute
$$\max\{ x y : (x, y),\ x > 0,\ y > 0,\ x + y = \min\{ x1 + y1 : (x1, y1),\ x1 > 0,\ y1... | 1,589 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(505),
"result": Mod(value=Summation(var="k", start=Const(0), end=Ref("_n"), expr=Sum(Mul(Const(3), Pow(Var("k"), Ref("_m"))), Mul(Const(3), Var("k")), Const(1))), modulus=CountOverSet(set=SolutionsSet(var=Var("t"), condi... | ALG | null | COMPUTE | sympy | B3 | [
"B3/B1",
"LIN_FORM"
] | e52246 | alg_telescope_v1 | negation_mod | 6 | 0 | [
"B1",
"B3",
"LIN_FORM"
] | 3 | 0.064 | 2026-03-10T00:49:31.472093Z | {
"verified": true,
"answer": 1589,
"timestamp": "2026-03-10T00:49:31.535941Z"
} | 948f64 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 297,
"completion_tokens": 4490
},
"timestamp": "2026-04-19T00:49:38.106Z",
"answer": 1589
},
{
"... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 1.67,
"mid": 4.44,
"hi": 6.77
} | ||
97ba6f | comb_catalan_compute_v1_1520064083_1559 | Let $n$ be the number of integers $t$ with $18 \leq t \leq 40$ for which there exist positive integers $a$ and $b$ such that $1 \leq a \leq 5$, $1 \leq b \leq 2$, and $t = 4a + 6b + 8$.
Compute the $n$-th Catalan number. | 16,796 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=5)), Geq(left=Var(name='b'), right=Const(value=1... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_catalan_compute_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.003 | 2026-02-08T04:06:30.518086Z | {
"verified": true,
"answer": 16796,
"timestamp": "2026-02-08T04:06:30.521565Z"
} | 58d8a2 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 201,
"completion_tokens": 1440
},
"timestamp": "2026-02-23T23:28:25.351Z",
"answer": 16796
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -4.92,
"mid": -2.9,
"hi": -0.7
} | ||
999826 | nt_count_divisors_in_range_v1_1742523217_791 | Let $a = 1$. Let $n$ be the number of positive integers $m \leq 37800$ such that $5$ divides the $m$-th Fibonacci number. Let $b$ be the number of positive integers $m \leq 39717$ such that $9$ divides $m$ and $\gcd(m, 14) = 1$. Determine the number of positive divisors $d$ of $n$ such that $a \leq d \leq b$. | 61 | graphs = [
Graph(
let={
"_m": Const(5),
"_n": Const(37800),
"n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_n")), Divides(divisor=Ref("_m"), dividend=Fibonacci(arg=Var(name='n')))))),
"a": Const(1),
... | NT | null | COUNT | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE",
"C5"
] | 97537d | nt_count_divisors_in_range_v1 | null | 7 | 0 | [
"C5",
"COUNT_FIB_DIVISIBLE"
] | 2 | 0.039 | 2026-02-08T03:14:48.845872Z | {
"verified": true,
"answer": 61,
"timestamp": "2026-02-08T03:14:48.885170Z"
} | 36df77 | 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": 2627
},
"timestamp": "2026-02-09T22:46:17.689Z",
"answer": 61
},
{
"id"... | 1 | [
{
"lemma": "C5",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
... | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
e2f82b | antilemma_sum_equals_v1_1520064083_2076 | Let $n = 12$. Define $x$ to be the number of ordered pairs $(i,j)$ of positive integers such that $i + j = 54$, $1 \le i \le 52$, and $1 \le j \le 53$. Let $y$ be the number of ordered pairs $(i,j)$ of positive integers such that $i + j = n$, $1 \le i \le 11$, and $1 \le j \le 11$. Compute the Bell number $B_r$, where ... | 4,140 | graphs = [
Graph(
let={
"_n": Const(12),
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(54)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(52)), right=IntegerRange(start=Const(1), end=Con... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | d4b992 | antilemma_sum_equals_v1 | bell_mod | 4 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.015 | 2026-02-08T04:30:29.615612Z | {
"verified": true,
"answer": 4140,
"timestamp": "2026-02-08T04:30:29.630778Z"
} | 4f3b05 | 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": 1193
},
"timestamp": "2026-02-24T00:51:11.585Z",
"answer": 4140
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"stat... | {
"lo": -5.97,
"mid": -3.96,
"hi": -1.93
} | ||
4512a6 | comb_sum_binomial_mod_v1_50713871_11 | Let $ p_{\text{max}} $ be the largest prime number at most $ 418 $. Define
$$
s = \sum_{k=124}^{388} \binom{p_{\text{max}}}{k}.
$$
Let $ r $ be the remainder when $ s $ is divided by $ 11311 $. Compute the remainder when $ 43 - r $ is divided by $ 75320 $. | 69,488 | graphs = [
Graph(
let={
"_n": Const(11311),
"sum": Summation(var="k", start=Const(124), end=Const(388), expr=Binom(n=MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(418)), IsPrime(Var("n"))))), k=Var("k"))),
"result": M... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | comb_sum_binomial_mod_v1 | null | 6 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.028 | 2026-02-08T02:42:40.538129Z | {
"verified": true,
"answer": 69488,
"timestamp": "2026-02-08T02:42:40.566605Z"
} | 454447 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 197,
"completion_tokens": 32768
},
"timestamp": "2026-02-23T15:46:13.878Z",
"answer": null
},
{
... | 0 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
... | {
"lo": 4.62,
"mid": 6.54,
"hi": 9.53
} | ||
ac63fa | comb_count_partitions_v1_1248542787_839 | Let $m = 1681$. Define $\mathcal{P}$ to be the set of all ordered pairs $(x,y)$ of positive integers such that $x \cdot y = m$. Let $s_{\text{min}}$ be the minimum value of $x + y$ over all such pairs. Let $n$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = s_{\text{min}}$. D... | 44,583 | graphs = [
Graph(
let={
"_m": Const(1681),
"_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")))),
... | COMB | null | COUNT | sympy | B3 | [
"B3/COMB1"
] | e26f7e | comb_count_partitions_v1 | null | 5 | 0 | [
"B3",
"COMB1"
] | 2 | 0.003 | 2026-02-08T03:27:34.975583Z | {
"verified": true,
"answer": 44583,
"timestamp": "2026-02-08T03:27:34.978893Z"
} | 207244 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 233,
"completion_tokens": 1210
},
"timestamp": "2026-02-09T08:57:17.253Z",
"answer": 44583
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COMB1",
"status": "ok_later"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V8",
"sta... | {
"lo": -0.05,
"mid": 2.89,
"hi": 5.27
} | ||
4a2c2b | comb_binomial_compute_v1_1353956133_752 | Let $n$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 80041500$, $\gcd(p, q) = 1$, and $p < q$. Let $k$ be the maximum value of $x \cdot y$ over all ordered pairs $(x, y)$ of positive integers such that $x + y = 6$. Compute $\binom{n}{k}$. | 11,440 | graphs = [
Graph(
let={
"_n": Const(6),
"n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=80041500)), Eq(left=GCD(a=Var(name='p'), b=Var(na... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS",
"B1"
] | aa8272 | comb_binomial_compute_v1 | null | 5 | 0 | [
"B1",
"COPRIME_PAIRS"
] | 2 | 0.002 | 2026-02-08T11:50:17.343941Z | {
"verified": true,
"answer": 11440,
"timestamp": "2026-02-08T11:50:17.346293Z"
} | 6b2060 | 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": 2167
},
"timestamp": "2026-02-14T19:53:57.873Z",
"answer": 11440
},
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
b69969 | modular_mod_compute_v1_971394319_1499 | Let $n$ be the minimum value of $x + y$ over all ordered pairs $(x,y)$ of positive integers such that $xy = 100$. Let $a$ be the maximum value of $xy$ over all ordered pairs $(x,y)$ of positive integers such that $x + y = n$. Compute the remainder when
$$
\sum_{k=1}^{2} \varphi(k) \left\lfloor \frac{2}{k} \right\rfloor... | 78,304 | graphs = [
Graph(
let={
"_c": Const(78401),
"_m": Const(2),
"_n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(100)))), ex... | NT | null | COMPUTE | sympy | K2 | [
"K2",
"B3/B1"
] | e5ce17 | modular_mod_compute_v1 | negation_mod | 6 | 0 | [
"B1",
"B3",
"K2"
] | 3 | 0.006 | 2026-02-08T13:42:48.781210Z | {
"verified": true,
"answer": 78304,
"timestamp": "2026-02-08T13:42:48.786976Z"
} | 8e5d4e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 156,
"completion_tokens": 714
},
"timestamp": "2026-02-15T20:18:03.550Z",
"answer": 78304
},
{... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3b",
... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
dae486 | nt_sum_totient_over_divisors_v1_1915831931_3070 | Let $m = 2$ and $n_0 = 64192$. Define $n$ to be the number of positive integers $n_1$ not exceeding $n_0$ such that the smallest divisor $d$ of 143143 satisfying $d \geq m$ divides the Fibonacci number $F_{n_1}$.
Compute the sum of $\phi(d_1)$ over all positive divisors $d_1$ of $n$, where $\phi$ denotes Euler's totie... | 8,024 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(64192),
"n": CountOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(1)), Leq(Var("n1"), Ref("_n")), Divides(divisor=MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_m")... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/COUNT_FIB_DIVISIBLE"
] | f5c873 | nt_sum_totient_over_divisors_v1 | null | 6 | 0 | [
"COUNT_FIB_DIVISIBLE",
"MIN_PRIME_FACTOR"
] | 2 | 0.005 | 2026-02-08T17:20:25.238172Z | {
"verified": true,
"answer": 8024,
"timestamp": "2026-02-08T17:20:25.243142Z"
} | 04aecb | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 151,
"completion_tokens": 2177
},
"timestamp": "2026-02-18T01:07:45.680Z",
"answer": 8024
},
{... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok_later"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
ea06a2 | alg_poly_preperiod_count_v1_1218484723_5481 | Let $N = (a^3 + 4a) \bmod 41$, $M = (N^3 + 4N) \bmod 41$, and $R = (M^3 + 4M) \bmod 41$. Find the number of non-negative integers $a$ with $0 \le a \le 58137$ such that $R = N$ and $M \neq N$. | 8,508 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Pow(Var("a"), Const(3)), Mul(Const(4), Var("a"))), modulus=Const(41)),
"p2": Mod(value=Sum(Pow(Ref("p1"), Const(3)), Mul(Const(4), Ref("p1"))), modulus=Const(41)),
"p3": Mod(value=Sum(Pow(Ref("p2"), Const(3)), Mul(Const(4), Ref(... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_preperiod_count_v1 | null | 6 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.013 | 2026-02-25T07:01:14.998237Z | {
"verified": true,
"answer": 8508,
"timestamp": "2026-02-25T07:01:15.010891Z"
} | 0efc21 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 202,
"completion_tokens": 18722
},
"timestamp": "2026-03-29T21:19:44.315Z",
"answer": 8508
},
{
"... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -3.33,
"mid": 1.03,
"hi": 5.26
} | ||
2701cc | lin_form_endings_v1_124444284_316 | Let $a = 28$ and $b = 21$. Let $L = \text{lcm}(a, b)$ and define $s = L + a + b$. Compute the remainder when $11947 \cdot s$ is divided by $59234$. | 48,867 | graphs = [
Graph(
let={
"a_coeff": Const(28),
"b_coeff": Const(21),
"k_val": Const(1),
"lcm_node": LCM(a=Ref("a_coeff"), b=Ref("b_coeff")),
"_inner_result": Sum(Mul(Ref("k_val"), Ref("lcm_node")), Ref("a_coeff"), Ref("b_coeff")),
"_scal... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 2 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T03:11:25.379754Z | {
"verified": true,
"answer": 48867,
"timestamp": "2026-02-08T03:11:25.380263Z"
} | 2d65a8 | 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": 692
},
"timestamp": "2026-02-09T16:01:29.986Z",
"answer": 48867
},
{
"i... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"st... | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
3746dc | nt_gcd_compute_v1_1439011603_758 | Let $a = 1153659$ and $b = 1863603$. Let $g = \gcd(a, b)$. Let $d$ be the number of decimal digits of $g$. Compute $$\sum_{i=0}^{d-1} \left( \text{the } i\text{th digit of } g \right) \cdot (i+1)^2 + 62001.$$ | 62,411 | graphs = [
Graph(
let={
"a": Const(1153659),
"b": Const(1863603),
"result": GCD(a=Ref("a"), b=Ref("b")),
"_c": Const(62001),
"Q": Sum(Summation(var="i", start=Summation(var="k", start=Const(0), end=Const(1), expr=Mul(Pow(Const(-1), Var("k")), Binom... | COMB | NT | COMPUTE | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING",
"ONE_BINOM_N"
] | 961fba | nt_gcd_compute_v1 | null | 5 | 0 | [
"BINOMIAL_ALTERNATING",
"ONE_BINOM_N"
] | 2 | 0.004 | 2026-02-08T15:42:23.028187Z | {
"verified": true,
"answer": 62411,
"timestamp": "2026-02-08T15:42:23.032191Z"
} | 8653a0 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 134,
"completion_tokens": 1299
},
"timestamp": "2026-02-16T11:09:45.535Z",
"answer": 62411
},
... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "ONE_BINOM_N",
"status": "ok"
},
{
"lemma": "V7",
"s... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
5bf901 | modular_mod_compute_v1_1874849503_1047 | Let $\binom{n}{k}$ denote the binomial coefficient and let $\phi(n)$ denote Euler's totient function. Define $m$ as the number of nonnegative integers $j$ with $0 \leq j \leq 64958$ such that $\binom{64958}{j} \equiv \phi(1) \pmod{2}$. Let $a = -30976$. Compute the remainder when $94964 \cdot (a \bmod m)$ is divided by... | 41,744 | graphs = [
Graph(
let={
"_n": Const(87879),
"a": Const(-30976),
"m": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(64958)), Eq(Mod(value=Binom(n=Const(64958), k=Var("j")), modulus=Const(2)), EulerPhi(n=Const(1)))), ... | NT | COMB | COMPUTE | sympy | ONE_PHI_1 | [
"ONE_PHI_1",
"V8"
] | 59ff2b | modular_mod_compute_v1 | null | 4 | 0 | [
"ONE_PHI_1",
"V8"
] | 2 | 0.003 | 2026-02-08T13:32:31.819458Z | {
"verified": true,
"answer": 41744,
"timestamp": "2026-02-08T13:32:31.822437Z"
} | 070307 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 223,
"completion_tokens": 2462
},
"timestamp": "2026-02-10T00:18:53.223Z",
"answer": 41744
},
{
"... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "ONE_PHI_1",
... | {
"lo": -6.5,
"mid": -0.2,
"hi": 6.11
} | ||
f7622b | antilemma_sum_equals_v1_1915831931_2911 | Compute the number of ordered pairs $(i, j)$ of positive integers such that $i + j = 86$, $1 \leq i \leq 84$, and $1 \leq j \leq 85$. | 84 | graphs = [
Graph(
let={
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(86)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(84)), right=IntegerRange(start=Const(1), end=Const(85))))),
},
... | COMB | GEOM | COMPUTE | sympy | LIN_FORM | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 2 | 0 | [
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 2 | 0.119 | 2026-02-08T17:14:15.555915Z | {
"verified": true,
"answer": 84,
"timestamp": "2026-02-08T17:14:15.674766Z"
} | 2c4665 | 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": 1225
},
"timestamp": "2026-02-24T22:22:41.700Z",
"answer": 84
},
{
... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status"... | {
"lo": -10,
"mid": -7.42,
"hi": -4.85
} | ||
b408a9 | nt_max_prime_below_v1_48377204_1660 | Let $S$ 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 $L$ be the number of elements in $S$. Find the largest prime number $n$ such that $L \leq n \leq 10559$. | 10,559 | graphs = [
Graph(
let={
"upper": Const(10559),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), V... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_max_prime_below_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.247 | 2026-02-08T16:17:59.107190Z | {
"verified": true,
"answer": 10559,
"timestamp": "2026-02-08T16:17:59.354161Z"
} | 61130f | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 144,
"completion_tokens": 560
},
"timestamp": "2026-02-16T07:16:20.487Z",
"answer": 109
},
{
"id": 11,
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
... | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
96d076 | nt_min_coprime_above_v1_1918700295_1000 | Let $s$ be the sum of the solutions to the equation $x^2 - 7744x - 319185 = 0$. Let $T$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 15077689$, and let $u$ be the minimum value of $x + y$ over all such pairs. Let $n$ be the smallest integer greater than $s$ and at most $u$ such that $\g... | 7,745 | graphs = [
Graph(
let={
"start": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Const(2)), Mul(Const(-7744), Var("x")), Const(-319185)), Const(0)))),
"upper": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(... | NT | null | EXTREMUM | sympy | VIETA_SUM | [
"VIETA_SUM",
"B3"
] | 018050 | nt_min_coprime_above_v1 | null | 6 | 0 | [
"B3",
"VIETA_SUM"
] | 2 | 0.006 | 2026-02-08T05:27:21.077576Z | {
"verified": true,
"answer": 7745,
"timestamp": "2026-02-08T05:27:21.083883Z"
} | ec7649 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 165,
"completion_tokens": 2548
},
"timestamp": "2026-02-12T10:01:59.854Z",
"answer": 7745
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma":... | {
"lo": -9.14,
"mid": -6.05,
"hi": -3.73
} | ||
def2c5 | algebra_poly_eval_v1_1125832087_682 | Let $m=8$, $n=2$, and $y=8$.
Let $C$ be the number of integers $t$ with $7\le t\le 1135$ for which there exist integers $a$ and $b$ satisfying $1\le a\le 3$, $1\le b\le 560$, and
$$t=5a+2b.$$
Let $N$ be the number of integers $k$ with $1\le k\le C$ such that $5$ divides the Fibonacci number $F_k$.
Let $S$ be the set... | 33,918 | graphs = [
Graph(
let={
"_m": Const(8),
"_n": Const(2),
"y": Const(8),
"result": Div(Sum(Mul(Ref("_m"), Pow(Ref("y"), Const(5))), Mul(Const(-22), Pow(Ref("y"), Const(4))), Mul(Const(-3), Pow(Ref("y"), Const(3))), Mul(Const(-16), Pow(Ref("y"), Ref("_n"))), Mul(... | ALG | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/COUNT_FIB_DIVISIBLE/B3"
] | cb7aba | algebra_poly_eval_v1 | null | 8 | 0 | [
"B3",
"COUNT_FIB_DIVISIBLE",
"LIN_FORM"
] | 3 | 0.016 | 2026-02-08T03:13:01.376965Z | {
"verified": true,
"answer": 33918,
"timestamp": "2026-02-08T03:13:01.392522Z"
} | 8f6226 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 351,
"completion_tokens": 4421
},
"timestamp": "2026-02-10T13:31:26.882Z",
"answer": 33918
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok_later"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 0.21,
"mid": 2.81,
"hi": 5.01
} | ||
484877 | comb_sum_binomial_row_v1_865884756_5828 | Let $n$ be the number of integers $t$ such that $32 \leq t \leq 77$ and $t = 15a + 6b + 11$ for some integers $a$ and $b$ with $1 \leq a \leq 2$ and $1 \leq b \leq 6$. Compute the remainder when $44121 \cdot 2^n$ is divided by $52805$. | 20,906 | graphs = [
Graph(
let={
"_n": Const(2),
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=2)), Geq(left=Var(na... | NT | null | SUM | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_sum_binomial_row_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T18:48:04.540359Z | {
"verified": true,
"answer": 20906,
"timestamp": "2026-02-08T18:48:04.542597Z"
} | 100c86 | 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": 1674
},
"timestamp": "2026-02-18T19:41:37.950Z",
"answer": 20906
},
... | 1 | [
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
32936c | sequence_fibonacci_compute_v1_1470522791_1784 | Let $m = 100$ and let $\mathcal{D}$ be the set of all positive integers $k$ with $1 \leq k \leq 10000$ such that $m$ divides $k$. Let $n$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy$ equals the number of elements in $\mathcal{D}$. Compute the $n$-th Fibonacci number. | 6,765 | graphs = [
Graph(
let={
"_m": Const(100),
"_n": CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(1)), Leq(Var("k"), Const(10000)), Divides(divisor=Ref("_m"), dividend=Var("k"))), domain='positive_integers')),
"n": MinOverSet(set=MapOverSet(set... | NT | null | COMPUTE | sympy | C2 | [
"C2/B3"
] | 7c8509 | sequence_fibonacci_compute_v1 | null | 6 | 0 | [
"B3",
"C2"
] | 2 | 0.003 | 2026-02-08T13:57:48.019387Z | {
"verified": true,
"answer": 6765,
"timestamp": "2026-02-08T13:57:48.022321Z"
} | 6a4cc3 | 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": 889
},
"timestamp": "2026-02-15T22:29:04.637Z",
"answer": 6765
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
79757e | geo_visible_lattice_v1_124444284_4984 | A lattice point $(x, y)$ in the first quadrant is said to be visible from the origin if $\gcd(x, y) = 1$. For $1 \leq x, y \leq 144$, compute the number of visible lattice points. Let this number be $R$. Compute the remainder when $44121 \times R$ is divided by 84800. | 34,939 | graphs = [
Graph(
let={
"n": Const(144),
"result": VisibleLatticePoints(n=Ref(name='n')),
"Q": Mod(value=Mul(Const(44121), Ref("result")), modulus=Const(84800)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 5 | 0 | null | null | 1.243 | 2026-02-08T06:19:41.611523Z | {
"verified": true,
"answer": 34939,
"timestamp": "2026-02-08T06:19:42.854317Z"
} | a67283 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 190,
"completion_tokens": 11687
},
"timestamp": "2026-02-24T06:03:43.797Z",
"answer": 28939
},
{
... | 1 | [] | {
"lo": 3.43,
"mid": 5.73,
"hi": 8.84
} | ||||
43b654 | nt_num_divisors_compute_v1_168721529_2001 | Let $n = 33856$. Define $d(n)$ to be the number of positive divisors of $n$. Compute $d(n)$. | 21 | graphs = [
Graph(
let={
"n": Const(33856),
"result": NumDivisors(n=Ref("n")),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | K14 | [
"K14"
] | a49bcb | nt_num_divisors_compute_v1 | null | 2 | 0 | [
"K14"
] | 1 | 0.01 | 2026-02-08T14:03:06.194064Z | {
"verified": true,
"answer": 21,
"timestamp": "2026-02-08T14:03:06.204455Z"
} | fb3a0a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 141,
"completion_tokens": 515
},
"timestamp": "2026-02-10T00:45:03.211Z",
"answer": 21
},
{
"id":... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
85da8b | comb_count_surjections_v1_1520064083_10087 | Let $k$ be the number of ordered triples $(x_1, x_2, x_3)$ of positive odd integers such that $x_1 + x_2 + x_3 = 5$. Let $n = 8$. Compute the value of $k! \cdot S(n, k)$, where $S(n, k)$ denotes the number of ways to partition a set of $n$ elements into $k$ nonempty subsets. Let this value be $R$. Find the remainder wh... | 7,846 | graphs = [
Graph(
let={
"_n": Const(5),
"n": Const(8),
"k": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2"), Var("x3")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsPositive(arg=Var(name='x3')), IsOdd(arg=Var(nam... | COMB | null | COUNT | sympy | COMB1 | [
"COMB1"
] | 567f58 | comb_count_surjections_v1 | null | 6 | 0 | [
"COMB1"
] | 1 | 0.002 | 2026-02-08T11:12:01.442045Z | {
"verified": true,
"answer": 7846,
"timestamp": "2026-02-08T11:12:01.444097Z"
} | 48f0bb | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 233,
"completion_tokens": 2539
},
"timestamp": "2026-02-24T12:54:51.965Z",
"answer": 7846
},
{
"i... | 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": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
ddd240 | comb_sum_binomial_row_v1_1520064083_4902 | Let $n$ be the number of integers $t$ with $5 \leq t \leq 18$ such that there exist positive integers $a$ and $b$ with $1 \leq a \leq 3$, $1 \leq b \leq 4$, and $t = 2a + 3b$. Compute the value of $2^n$. | 4,096 | graphs = [
Graph(
let={
"_n": Const(2),
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=3)), Geq(left=Var(na... | NT | null | SUM | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_sum_binomial_row_v1 | null | 3 | 0 | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T06:30:20.249695Z | {
"verified": true,
"answer": 4096,
"timestamp": "2026-02-08T06:30:20.250902Z"
} | c01411 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 136,
"completion_tokens": 827
},
"timestamp": "2026-02-15T17:31:51.232Z",
"answer": 8192
},
{
"id": 11,... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
8b2d94 | sequence_count_fib_divisible_v1_971394319_1860 | Let $u$ be the number of integers $t$ such that $8 \leq t \leq 667$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 5$, $1 \leq b \leq 214$, and $t = 5a + 3b$.
Determine the value of the number of positive integers $n$ such that $1 \leq n \leq u$ and $10$ divides the $n$-th Fibonacci number. | 43 | graphs = [
Graph(
let={
"upper": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=5)), Geq(left=Var(name='b'), right=Const(val... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | sequence_count_fib_divisible_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.059 | 2026-02-08T13:57:59.311790Z | {
"verified": true,
"answer": 43,
"timestamp": "2026-02-08T13:57:59.370430Z"
} | 89e60d | 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": 2288
},
"timestamp": "2026-02-15T22:37:02.115Z",
"answer": 43
},
{
... | 1 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
415214 | nt_sum_gcd_range_mod_v1_677425708_3859 | Let $N$ be the number of positive integers $n \leq 86700$ such that the $n$th Fibonacci number is divisible by 9. Let $k$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 2304$. Let $M = 11813$. Compute the remainder when $\sum_{n=1}^{N} \gcd(n, k)$ is divided by $M$. | 6,670 | graphs = [
Graph(
let={
"_n": Const(9),
"N": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(86700)), Divides(divisor=Ref("_n"), dividend=Fibonacci(arg=Var(name='n')))))),
"k": MinOverSet(set=MapOverSet(set=SolutionsS... | NT | null | COMPUTE | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE",
"B3"
] | a63611 | nt_sum_gcd_range_mod_v1 | null | 7 | 0 | [
"B3",
"COUNT_FIB_DIVISIBLE"
] | 2 | 0.623 | 2026-02-08T05:58:41.901493Z | {
"verified": true,
"answer": 6670,
"timestamp": "2026-02-08T05:58:42.524664Z"
} | 14c359 | 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": 2842
},
"timestamp": "2026-02-12T18:27:37.634Z",
"answer": 6670
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lem... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
2538f0 | modular_sum_quadratic_residues_v1_1915831931_2123 | Let $p$ be the largest prime number not exceeding $656$. Define $\text{result} = \frac{p(p-1)}{4}$. Let $Q$ be the remainder when $45159 \cdot \text{result}$ is divided by $70213$. Compute $Q$. | 37,247 | graphs = [
Graph(
let={
"_n": Const(70213),
"p": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(656)), IsPrime(Var("n"))))),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), Const(4)),
"_c": Const(4515... | NT | null | SUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | modular_sum_quadratic_residues_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.002 | 2026-02-08T16:37:42.782814Z | {
"verified": true,
"answer": 37247,
"timestamp": "2026-02-08T16:37:42.784815Z"
} | 0a6259 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 106,
"completion_tokens": 2697
},
"timestamp": "2026-02-17T07:44:59.334Z",
"answer": 37247
},
... | 1 | [
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V8_SUM",
"status"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
964c18 | diophantine_fbi2_min_v1_1125832087_1556 | Let $k$ be the number of ordered pairs $(a,b)$ where $a$ is an integer from 1 to 3, inclusive, and $b$ is an integer from 1 to 7, inclusive. Let $d$ be a divisor of $k$ such that $6 \leq d \leq 31$ and $\frac{k}{d} \geq 3$. Let $m$ be the smallest such $d$. Compute the value of
$$
\sum_{i=0}^{\mathrm{NumDigits}(m)-1} \... | 12,107 | graphs = [
Graph(
let={
"k": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(3)), right=IntegerRange(start=Const(1), end=Const(7)))),
"upper": Const(31),
"result": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(6)... | NT | null | EXTREMUM | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | diophantine_fbi2_min_v1 | null | 3 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.005 | 2026-02-08T03:47:36.373024Z | {
"verified": true,
"answer": 12107,
"timestamp": "2026-02-08T03:47:36.378243Z"
} | c09c5e | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 252,
"completion_tokens": 1180
},
"timestamp": "2026-02-10T15:43:03.536Z",
"answer": 12107
},
{
"... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_ADD",
"statu... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
1b86d4 | nt_max_prime_below_v1_1520064083_333 | Let $P$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 24$, $\gcd(p, q) = 1$, and $p < q$. Let $m$ be the number of elements in $P$. Define $S$ to be the set of all prime numbers $n$ such that $m \leq n \leq 45360$. Let $n_{\text{max}}$ be the largest element of $S... | 66,482 | graphs = [
Graph(
let={
"upper": Const(45360),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), V... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_max_prime_below_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 1.709 | 2026-02-08T03:15:39.827585Z | {
"verified": true,
"answer": 66482,
"timestamp": "2026-02-08T03:15:41.536234Z"
} | db2a54 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 249,
"completion_tokens": 4786
},
"timestamp": "2026-02-10T13:13:30.293Z",
"answer": 66482
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
5e1efb | comb_count_permutations_fixed_v1_1439011603_2633 | Let $k = \sum_{k_1=1}^{3} \phi(k_1) \left\lfloor \frac{3}{k_1} \right\rfloor$, where $\phi$ denotes Euler's totient function. Define $r = \binom{8}{k} \cdot ! (8 - k)$, where $!m$ denotes the number of derangements of $m$ elements. Compute the remainder when $82781 \cdot r$ is divided by 90493. | 55,543 | graphs = [
Graph(
let={
"n": Const(8),
"k": Summation(var="k1", start=Const(1), end=Const(3), expr=Mul(EulerPhi(n=Var("k1")), Floor(Div(Const(3), Var("k1"))))),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub(left=Ref(name='n'), right=Ref(name='k')))),
... | NT | COMB | COUNT | sympy | K2 | [
"K2"
] | 6897ab | comb_count_permutations_fixed_v1 | null | 5 | 0 | [
"K2"
] | 1 | 0.002 | 2026-02-08T16:53:31.243322Z | {
"verified": true,
"answer": 55543,
"timestamp": "2026-02-08T16:53:31.245464Z"
} | b46ff7 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 150,
"completion_tokens": 1315
},
"timestamp": "2026-02-17T14:20:36.478Z",
"answer": 55543
},
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
dbc8f8 | modular_min_linear_v1_458359167_1829 | Let $a$ be the largest prime number $n$ such that $2 \leq n \leq s$, where $s$ is the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers satisfying $xy = 9935104$. Let $b$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers satisfying $xy = 19722481$. Let $m =... | 81,843 | graphs = [
Graph(
let={
"_n": Const(2),
"a": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(ar... | NT | null | EXTREMUM | sympy | B3 | [
"B3/MAX_PRIME_BELOW"
] | f253c0 | modular_min_linear_v1 | null | 7 | 0 | [
"B3",
"MAX_PRIME_BELOW"
] | 2 | 0.842 | 2026-02-08T04:52:13.602718Z | {
"verified": true,
"answer": 81843,
"timestamp": "2026-02-08T04:52:14.444599Z"
} | 4c5f8e | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 269,
"completion_tokens": 7183
},
"timestamp": "2026-02-11T22:26:09.781Z",
"answer": 81843
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
9432d7 | comb_sum_binomial_row_v1_1218484723_2297 | Let $N = 0$, $M = 0$, $e = \sum_{k=0}^{M} (-1)^k \binom{M}{k}$, $u = \sum_{k=0}^{N} (-1)^k \binom{N}{k}$, $n = 14u$, $S = 3 + 1$, and $s = \sum_{k=0}^{S} (-1)^k \binom{S}{k}$. Compute $((2 + s) \cdot e)^n$. | 16,384 | graphs = [
Graph(
let={
"u1": Const(3),
"n3": Sum(Ref("u1"), Const(1)),
"s": Summation(var="k", start=Const(0), end=Ref("n3"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n3"), k=Var("k")))),
"n2": Const(0),
"e": Summation(var="k1", start=Const... | COMB | null | SUM | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING"
] | c21569 | comb_sum_binomial_row_v1 | null | 3 | 3 | [
"BINOMIAL_ALTERNATING"
] | 1 | 0.001 | 2026-02-25T04:08:14.714522Z | {
"verified": true,
"answer": 16384,
"timestamp": "2026-02-25T04:08:14.715997Z"
} | 3d7f02 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 229,
"completion_tokens": 606
},
"timestamp": "2026-03-29T03:57:33.199Z",
"answer": 16384
},
{
"i... | 2 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"sta... | {
"lo": -10,
"mid": -6.41,
"hi": -2.82
} | ||
3f1ac9 | modular_inverse_v1_655260480_4720 | Let $a = 180$ and $m = 251$. Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 15625$. Let $\text{upper}$ be the minimum value of $x + y$ over all pairs in $S$. Find the smallest positive integer $x_1$ such that $1 \le x_1 \le \text{upper}$ and $180x_1 \equiv 1 \pmod{251}$. | 152 | graphs = [
Graph(
let={
"a": Const(180),
"m": Const(251),
"upper": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(15625)))),... | NT | null | EXTREMUM | sympy | B3 | [
"B3"
] | 0cd20d | modular_inverse_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.016 | 2026-02-08T18:04:38.401627Z | {
"verified": true,
"answer": 152,
"timestamp": "2026-02-08T18:04:38.418038Z"
} | 32ba87 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 154,
"completion_tokens": 2263
},
"timestamp": "2026-02-18T12:51:31.428Z",
"answer": 152
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
6c48bd | lin_form_endings_v1_124444284_8134 | Let $a = 18$ and $b = 27$. Define $d = \gcd(a, b)$. Let $k = 144$ and let $g = \gcd(k, d)$. Define $m = \left\lfloor \frac{k}{g} \right\rfloor$. Let $x = (16397 \cdot m) \mod 69011$. Compute the value of $x$. | 55,319 | graphs = [
Graph(
let={
"a_coeff": Const(18),
"b_coeff": Const(27),
"k_val": Const(144),
"step": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"_inner_result": Floor(Div(Ref("k_val"), GCD(a=Ref("k_val"), b=Ref("step")))),
"_scale_k": Const(1... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 3 | null | [
"LIN_FORM"
] | 1 | 0 | 2026-02-08T09:34:34.099616Z | {
"verified": true,
"answer": 55319,
"timestamp": "2026-02-08T09:34:34.099971Z"
} | 0b740d | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 157,
"completion_tokens": 444
},
"timestamp": "2026-02-15T20:44:35.902Z",
"answer": 55319
},
{
"id": 11,
... | 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",
"status": "no"
}
] | {
"lo": -9.12,
"mid": -6.02,
"hi": -3.62
} | ||
3d4368 | comb_count_surjections_v1_124444284_1704 | 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 range $7 \leq t \leq 24$ for which there exist integers $a$ and $b$ with $1 \leq a \leq 4$, $1 \leq b \leq 3$, and $t = 3a + 4b$. Let $k = 3$. Compute $k! \cdot S(n, k)$, where $S(... | 540 | 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 | 2026-02-08T04:05:43.569393Z | {
"verified": true,
"answer": 540,
"timestamp": "2026-02-08T04:05:43.571305Z"
} | cd4caa | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 253,
"completion_tokens": 1063
},
"timestamp": "2026-02-23T23:24:20.584Z",
"answer": 540
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok_later"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM"... | {
"lo": -4.92,
"mid": -2.9,
"hi": -0.7
} | ||
2af916 | modular_modexp_compute_v1_124444284_1518 | Let $ a = \sum_{k=1}^{2} \phi(k) \left\lfloor \frac{2}{k} \right\rfloor $. Let $ S $ be the set of all ordered pairs $ (x,y) $ of positive integers such that $ xy = 153664 $. Let $ e $ be the minimum value of $ x + y $ over all such pairs. Compute the remainder when $ a^e $ is divided by 32768. | 13,121 | graphs = [
Graph(
let={
"a": Summation(var="k", start=Const(1), end=Const(2), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(2), Var("k"))))),
"e": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPosi... | NT | null | COMPUTE | sympy | B3 | [
"B3",
"K2"
] | f1ea07 | modular_modexp_compute_v1 | null | 6 | 0 | [
"B3",
"K2"
] | 2 | 0.003 | 2026-02-08T03:58:06.408752Z | {
"verified": true,
"answer": 13121,
"timestamp": "2026-02-08T03:58:06.411346Z"
} | bab7e7 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 209,
"completion_tokens": 3948
},
"timestamp": "2026-02-10T14:49:17.436Z",
"answer": 13121
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"le... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
fcd2a6 | modular_mod_compute_v1_655260480_2265 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = \sum_{k=1}^{16} \phi(k) \left\lfloor \frac{16}{k} \right\rfloor$. Let $P$ be the set of all products $xy$ where $(x, y) \in S$. Let $a$ be the maximum value in $P$. Compute the remainder when $75701$ times the remainder when $a$ is... | 13,802 | graphs = [
Graph(
let={
"_n": Const(54369),
"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")), Summation(var="k", start=Const(1), end=Const(1... | NT | null | COMPUTE | sympy | K2 | [
"K2/B1"
] | 995da8 | modular_mod_compute_v1 | null | 5 | 0 | [
"B1",
"K2"
] | 2 | 0.003 | 2026-02-08T16:39:19.090088Z | {
"verified": true,
"answer": 13802,
"timestamp": "2026-02-08T16:39:19.093447Z"
} | ec5499 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 166,
"completion_tokens": 1685
},
"timestamp": "2026-02-17T08:27:43.761Z",
"answer": 13802
},
... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
6a436e | diophantine_fbi2_count_v1_1742523217_3799 | Let $k = 720$. Define $r$ to be the number of positive integers $d$ such that $2 \leq d \leq 71$, $d$ divides $k$, and $2 \leq \frac{k}{d} \leq 71$. Let $Q = 4796 \cdot r$. Compute the value of $Q$. | 57,552 | graphs = [
Graph(
let={
"_n": Const(2),
"k": Const(720),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Leq(Var("d"), Const(71)), Divides(divisor=Var("d"), dividend=Ref("k")), Geq(Div(Ref("k"), Var("d")), Const(2)), Leq(Div(R... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | diophantine_fbi2_count_v1 | null | 3 | 0 | [
"B3"
] | 1 | 0.008 | 2026-02-08T06:06:18.142016Z | {
"verified": true,
"answer": 57552,
"timestamp": "2026-02-08T06:06:18.149593Z"
} | 2a9aba | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 121,
"completion_tokens": 2543
},
"timestamp": "2026-02-12T19:26:27.553Z",
"answer": 57552
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
73366c | nt_count_divisors_in_range_v1_898971024_541 | Let $n = 50400$. Let $a = 1$ and let $b$ be the number of positive integers $n_1$ such that $1 \le n_1 \le m$, where $m$ is the number of positive integers $n_2$ not exceeding 5929 that are relatively prime to 10, and such that $\gcd(n_1, 15) = 1$. Compute the number of positive divisors $d$ of $n$ such that $a \le d \... | 84 | graphs = [
Graph(
let={
"_n": Const(10),
"n": Const(50400),
"a": Const(1),
"b": CountOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(1)), Leq(Var("n1"), CountOverSet(set=SolutionsSet(var=Var("n2"), condition=And(Geq(Var("n2"), Const(... | NT | null | COUNT | sympy | LIN_FORM | [
"C4/C4"
] | c66105 | nt_count_divisors_in_range_v1 | null | 6 | 0 | [
"C4",
"LIN_FORM"
] | 2 | 0.387 | 2026-02-08T15:31:48.397038Z | {
"verified": true,
"answer": 84,
"timestamp": "2026-02-08T15:31:48.783948Z"
} | a4a85f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 159,
"completion_tokens": 2581
},
"timestamp": "2026-02-16T08:01:38.291Z",
"answer": 84
},
{
... | 1 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
934dea | lin_form_endings_v1_717093673_2450 | Let $a = 30$, $b = 45$, $A = 11$, and $B = 33$. Let $g$ be the greatest common divisor of $a$ and $b$. Define $n = \left\lfloor \frac{aA + bB - a - b}{g} \right\rfloor + 1$. Let $k = 13460$ and compute $s = k \cdot n$. Find the remainder when $s$ is divided by $79888$. | 56,948 | graphs = [
Graph(
let={
"a_coeff": Const(30),
"b_coeff": Const(45),
"A_val": Const(11),
"B_val": Const(33),
"g_step": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"numerator": Sub(Sum(Mul(Ref("a_coeff"), Ref("A_val")), Mul(Ref("b_coeff"), R... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 2 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T16:52:01.081298Z | {
"verified": true,
"answer": 56948,
"timestamp": "2026-02-08T16:52:01.082414Z"
} | 03ba63 | 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": 785
},
"timestamp": "2026-02-17T14:54:32.733Z",
"answer": 56948
},
{... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
12d6a4 | modular_sum_quadratic_residues_v1_898971024_1943 | Let $p = 661$. Define $\text{result} = \frac{p(p-1)}{4}$. Let $P$ be the set of all prime numbers $n$ such that $2 \le n \le 9012$. Compute the remainder when $\left(\max(P)\right) \cdot \text{result}$ is divided by 78671. | 26,583 | graphs = [
Graph(
let={
"_n": Const(4),
"p": Const(661),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), Ref("_n")),
"Q": Mod(value=Mul(MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(9012)), IsPrime(V... | NT | null | SUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | 183c11 | modular_sum_quadratic_residues_v1 | affine_mod | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.002 | 2026-02-08T16:26:11.510375Z | {
"verified": true,
"answer": 26583,
"timestamp": "2026-02-08T16:26:11.511894Z"
} | 86a0a0 | 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": 1413
},
"timestamp": "2026-02-17T04:18:13.098Z",
"answer": 26583
},
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
4c9b95_n | comb_count_surjections_v1_1218484723_1580 | A school has 3 students and wants to assign them to exactly 2 non-empty study groups, but first computes a number $n$ based on Euler's totient function and floor division: $n = \sum_{k=1}^{3} \varphi(k) \cdot \left\lfloor \frac{3}{k} \right\rfloor$. The number of ways to partition $n$ labeled objects into 2 non-empty u... | 62 | COMB | null | COUNT | sympy | K2 | [
"K2"
] | 6897ab | comb_count_surjections_v1 | null | 3 | null | [
"K2"
] | 1 | 0.002 | 2026-02-25T03:19:05.794806Z | null | 911fbb | 4c9b95 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 218,
"completion_tokens": 1106
},
"timestamp": "2026-03-30T17:03:51.276Z",
"answer": 62
},
{
"id"... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status":... | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | |
124146 | nt_count_with_divisor_count_v1_1520064083_10264 | Let $$
d = \sum_{k=1}^{4} \phi(k) \left\lfloor \frac{4}{k} \right\rfloor,
$$ where $\phi$ denotes Euler's totient function. Determine the number of positive integers $n$ such that $1 \leq n \leq 33489$ and the number of positive divisors of $n$ is equal to $d$. | 417 | graphs = [
Graph(
let={
"_n": Const(4),
"upper": Const(33489),
"div_count": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(4), Var("k"))))),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(G... | NT | null | COUNT | sympy | K2 | [
"K2"
] | 6897ab | nt_count_with_divisor_count_v1 | null | 6 | 0 | [
"K2"
] | 1 | 2.057 | 2026-02-08T11:18:46.700283Z | {
"verified": true,
"answer": 417,
"timestamp": "2026-02-08T11:18:48.757703Z"
} | 52ad60 | 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": 2814
},
"timestamp": "2026-02-14T12:02:31.260Z",
"answer": 417
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
bcde5e | antilemma_k3_v1_677425708_3362 | Let $x$ be the sum of $\phi(d)$ over all positive divisors $d$ of $69526$. Compute the remainder when $60645 \cdot x$ is divided by $74548$. | 43,938 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=69526), var='d', expr=EulerPhi(n=Var(name='d'))),
"_c": Const(60645),
"Q": Mod(value=Mul(Ref("_c"), Ref("x")), modulus=Const(74548)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T05:40:27.837520Z | {
"verified": true,
"answer": 43938,
"timestamp": "2026-02-08T05:40:27.838040Z"
} | 80f85b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 89,
"completion_tokens": 1009
},
"timestamp": "2026-02-12T12:20:25.106Z",
"answer": 43938
},
{... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
32ea57 | comb_count_partitions_v1_1978505735_6993 | Let $N = 44121$. Define $n$ to be the number of integers $t$ with $11 \le t \le 56$ such that there exist positive integers $a$ and $b$ with $1 \le a \le 16$, $1 \le b \le 6$, and $t = 2a + 3b + 6$. Let $p(n)$ denote the number of integer partitions of $n$. Compute the remainder when $N \cdot p(n)$ is divided by $79558... | 23,155 | graphs = [
Graph(
let={
"_n": Const(44121),
"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=16)), Geq(left=V... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_count_partitions_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T19:57:57.737017Z | {
"verified": true,
"answer": 23155,
"timestamp": "2026-02-08T19:57:57.738869Z"
} | 3c1d44 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 176,
"completion_tokens": 6276
},
"timestamp": "2026-02-18T23:47:56.411Z",
"answer": 23155
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.12,
"mid": 1.47,
"hi": 6.57
} | ||
a09d4c | geo_count_lattice_rect_v1_1440796553_1490 | Compute the number of lattice points $(x, y)$ such that $0 \leq x \leq 225$ and $0 \leq y \leq 288$. | 65,314 | graphs = [
Graph(
let={
"a": Const(225),
"b": Const(288),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.001 | 2026-02-08T14:01:57.201094Z | {
"verified": true,
"answer": 65314,
"timestamp": "2026-02-08T14:01:57.201692Z"
} | d7ad61 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 148,
"completion_tokens": 188
},
"timestamp": "2026-02-24T19:33:37.078Z",
"answer": 65314
},
{
"i... | 1 | [] | {
"lo": -5.09,
"mid": -2.97,
"hi": -0.71
} | ||||
994e61 | diophantine_product_count_v1_1520064083_4258 | Let $n = \sum_{k=1}^{5} k$. Define $k = \sum_{i=1}^{n} \phi(i) \cdot \left\lfloor \frac{15}{i} \right\rfloor$, where $\phi$ denotes Euler's totient function. Let $S$ be the set of all integers $x$ such that $1 \leq x \leq 60$, $x$ divides $k$, and $\frac{k}{x} \leq 60$. Compute the number of elements in $S$. | 14 | graphs = [
Graph(
let={
"_n": Summation(var="k", start=Const(1), end=Const(5), expr=Var("k")),
"k": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(15), Var("k"))))),
"upper": Const(60),
"result": CountOverSet(s... | NT | null | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC/K2"
] | 06cc86 | diophantine_product_count_v1 | null | 6 | 0 | [
"K2",
"SUM_ARITHMETIC"
] | 2 | 0.006 | 2026-02-08T06:10:37.653632Z | {
"verified": true,
"answer": 14,
"timestamp": "2026-02-08T06:10:37.659554Z"
} | c6869b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 160,
"completion_tokens": 991
},
"timestamp": "2026-02-12T21:15:51.048Z",
"answer": 14
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K2",
"status": "ok_later"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V1",
"sta... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
8ec31e_l | nt_max_prime_below_v1_1116507919_226 | Let $S$ be the set of all ordered pairs $(p, q)$ of positive integers such that $p \cdot q = 36$, $\gcd(p, q) = 1$, and $p < q$. Let $a = |S|$. Let $T$ be the set of all prime numbers $n$ such that $a \leq n \leq 18769$. Determine the value of the largest element in $T$. | 18,749 | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_max_prime_below_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.401 | 2026-02-08T02:29:18.698313Z | {
"verified": false,
"answer": 18757,
"timestamp": "2026-02-08T02:29:19.099184Z"
} | bcef0b | 8ec31e | legacy_text | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 210,
"completion_tokens": 3214
},
"timestamp": "2026-02-08T19:15:15.846Z",
"answer": 18757
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": 0.06,
"mid": 1.74,
"hi": 3.24
} | |
937532 | nt_count_divisors_in_range_v1_655260480_4152 | Let $m = 69216$. Define $n'$ to be the sum of all real solutions $x$ to the equation $x^2 - 1690x + m = 0$. Let $n = 10080$, $a = 15$, and $b$ be the sum of $\phi(d)$ over all positive divisors $d$ of $n'$. Compute the number of positive divisors $d_1$ of $n$ such that $a \leq d_1 \leq b$. | 55 | graphs = [
Graph(
let={
"_m": Const(69216),
"_n": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Const(2)), Mul(Const(-1690), Var("x")), Ref("_m")), Const(0)))),
"n": Const(10080),
"a": Const(15),
"b": SumOverDivisors(n=Re... | NT | null | COUNT | sympy | B3 | [
"VIETA_SUM/K3"
] | 9d9c7a | nt_count_divisors_in_range_v1 | null | 5 | 0 | [
"B3",
"K3",
"VIETA_SUM"
] | 3 | 0.039 | 2026-02-08T17:45:51.557167Z | {
"verified": true,
"answer": 55,
"timestamp": "2026-02-08T17:45:51.596348Z"
} | ca4bdb | 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": 2681
},
"timestamp": "2026-02-18T07:47:42.554Z",
"answer": 55
},
{
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K3",
"status": "ok_later"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
},
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
e959c7 | nt_count_intersection_v1_2051736721_2307 | Let $N = 100000$. Let $a$ be the largest positive integer $d$ such that $d \leq 11$ and $d$ divides 143. Let $b = 14$. Define $S$ as the set of all positive integers $n$ such that $1 \leq n \leq N$, $a$ divides $n$, and $\gcd(n, b) = 1$. Compute the number of elements in $S$. Let $c = 31567$. Find the remainder when $c... | 10,565 | graphs = [
Graph(
let={
"N": Const(100000),
"a": MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Leq(Var("d"), Const(11)), Divides(divisor=Var("d"), dividend=Const(143))))),
"b": Const(14),
"result": CountOverSet(set=SolutionsS... | NT | null | COUNT | sympy | MAX_DIVISOR | [
"MAX_DIVISOR"
] | 51757e | nt_count_intersection_v1 | null | 4 | 0 | [
"MAX_DIVISOR"
] | 1 | 4.494 | 2026-02-08T16:33:56.305384Z | {
"verified": true,
"answer": 10565,
"timestamp": "2026-02-08T16:34:00.799485Z"
} | ce4eda | 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": 1403
},
"timestamp": "2026-02-17T06:38:11.645Z",
"answer": 10565
},
... | 1 | [
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
5d33b4 | sequence_count_fib_divisible_v1_601307018_4897 | Let $F_n$ denote the $n$-th Fibonacci number. Find the number of positive integers $n$ with $1 \le n \le 466$ such that $3 \mid F_n$. | 116 | graphs = [
Graph(
let={
"upper": Const(466),
"d": Const(3),
"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 | SUM_GEOM | [
"SUM_GEOM/K13"
] | a934f5 | sequence_count_fib_divisible_v1 | null | 5 | 0 | [
"K13",
"SUM_GEOM"
] | 2 | 0.505 | 2026-03-10T05:36:59.690436Z | {
"verified": true,
"answer": 116,
"timestamp": "2026-03-10T05:37:00.195221Z"
} | d07985 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 154,
"completion_tokens": 1103
},
"timestamp": "2026-03-29T13:47:56.859Z",
"answer": 116
},
{
"id... | 1 | [
{
"lemma": "K13",
"status": "ok_later"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "SUM_GEOM",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemm... | {
"lo": -3.34,
"mid": 0.9,
"hi": 4.9
} | ||
11e9b7 | nt_sum_over_divisible_v1_784195855_1523 | Let $S$ be the set of all positive integers $n$ such that $n \leq 46360$ and $n$ is divisible by $136$. Let $r$ be the sum of all elements in $S$. Compute the remainder when $89451 \cdot r$ is divided by $62816$. | 37,456 | graphs = [
Graph(
let={
"upper": Const(46360),
"divisor": Const(136),
"result": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(value=Var("n"), modulus=Ref("divisor")), Const(0))))),
"_c": Co... | NT | null | SUM | sympy | C3 | [
"C3/B3"
] | 9118ce | nt_sum_over_divisible_v1 | null | 3 | 0 | [
"B3",
"C3"
] | 2 | 2.603 | 2026-02-08T05:06:13.809768Z | {
"verified": true,
"answer": 37456,
"timestamp": "2026-02-08T05:06:16.412726Z"
} | ecd860 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 178,
"completion_tokens": 2309
},
"timestamp": "2026-02-11T22:56:38.506Z",
"answer": 37456
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "C3",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemm... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
634c45 | antilemma_sum_factor_cartesian_v1_784195855_574 | Let $S$ be the set of all ordered pairs $(i, j)$ with $i$ an integer from $1$ to $17$ and $j$ an integer from $1$ to $6$. For each such pair, compute the product $i \cdot j$, and let $x$ be the sum of all these products. Let $k = |x| \bmod 11$. Compute the $k$-th Bell number, which is the number of partitions of a set ... | 1 | 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(6)))), expr=Mul(Var("i"), Var("j")))),
... | NT | COMB | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"SUM_FACTOR_CARTESIAN"
] | d9e436 | antilemma_sum_factor_cartesian_v1 | null | 3 | 0 | [
"MIN_PRIME_FACTOR",
"SUM_FACTOR_CARTESIAN"
] | 2 | 0.019 | 2026-02-08T04:28:37.218159Z | {
"verified": true,
"answer": 1,
"timestamp": "2026-02-08T04:28:37.237190Z"
} | 6264cd | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 202,
"completion_tokens": 649
},
"timestamp": "2026-02-18T11:40:53.894Z",
"answer": 137648
}
] | 0 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "SUM_FACTOR_CARTESIAN",... | {
"lo": -6.48,
"mid": 1.54,
"hi": 9.56
} | ||
0f9326 | algebra_poly_eval_v1_601307018_10759 | Let $b$ be the number of non-negative integers $j$ with $0 \le j \le 32842$ such that $\binom{32842}{j} \bmod 2 = 1$. Compute $8b^3 - 9b^2 + 9b + 7$. | 30,615 | graphs = [
Graph(
let={
"_n": Const(7),
"b": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(32842)), Eq(Mod(value=Binom(n=Const(32842), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')),
"re... | ALG | COMB | COMPUTE | sympy | POLY_ORBIT_LEGENDRE | [
"V8"
] | 86348e | algebra_poly_eval_v1 | null | 4 | 0 | [
"POLY_ORBIT_LEGENDRE",
"V8"
] | 2 | 0.006 | 2026-03-10T11:13:45.917390Z | {
"verified": true,
"answer": 30615,
"timestamp": "2026-03-10T11:13:45.923483Z"
} | 865865 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 176,
"completion_tokens": 808
},
"timestamp": "2026-04-19T14:38:39.306Z",
"answer": 30615
},
{
"... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V8",
"status": "ok... | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
f9daae | antilemma_k3_v1_48377204_2728 | Let $n = 92844$. Compute the sum of $\phi(d)$ over all positive divisors $d$ of $n$, where $\phi$ denotes Euler's totient function. | 92,844 | graphs = [
Graph(
let={
"_n": Const(92844),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T16:56:31.920341Z | {
"verified": true,
"answer": 92844,
"timestamp": "2026-02-08T16:56:31.921254Z"
} | d451e3 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 100,
"completion_tokens": 572
},
"timestamp": "2026-02-16T08:38:50.572Z",
"answer": 10896
},
{
"id": 11,... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
b5866f | diophantine_fbi2_count_v1_1125832087_2448 | Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 54$, $\gcd(p, q) = 1$, and $p < q$. Let $m$ be the number of elements in $S$. Let $D$ be the set of all positive divisors $d$ of $420$ such that $d \leq 78$, $\frac{420}{d} \geq 4$, and $\frac{420}{d} \leq 80$.... | 26 | graphs = [
Graph(
let={
"_n": Const(78),
"k": Const(420),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(... | NT | null | COUNT | sympy | MOBIUS_COPRIME | [
"COPRIME_PAIRS"
] | 2bb3aa | diophantine_fbi2_count_v1 | null | 6 | 0 | [
"COPRIME_PAIRS",
"MOBIUS_COPRIME"
] | 2 | 0.127 | 2026-02-08T04:37:23.275885Z | {
"verified": true,
"answer": 26,
"timestamp": "2026-02-08T04:37:23.402488Z"
} | 083c5d | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 292,
"completion_tokens": 2051
},
"timestamp": "2026-02-10T17:22:38.879Z",
"answer": 26
},
{
"id... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.33
} | ||
2de8bb | comb_count_surjections_v1_458359167_3493 | Let $n$ be the number of ordered pairs $(i,j)$ of positive integers such that $i + j = 8$, $1 \le i \le 7$, and $1 \le j \le 8$. Let $k = 4$. Compute $k! \cdot S(n, k)$, where $S(n, k)$ denotes the Stirling number of the second kind.
Find the value of this expression. | 8,400 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(8)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(7)), right=IntegerRange(start=Const(1), end=Const(8))))),
"k": Con... | COMB | null | COUNT | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | comb_count_surjections_v1 | null | 3 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.011 | 2026-02-08T08:23:29.484706Z | {
"verified": true,
"answer": 8400,
"timestamp": "2026-02-08T08:23:29.495881Z"
} | 90b38e | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 202,
"completion_tokens": 1549
},
"timestamp": "2026-02-24T09:27:39.147Z",
"answer": 8400
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V8",
... | {
"lo": -3.84,
"mid": -1.67,
"hi": 1.32
} | ||
6c9902 | lte_diff_endings_v1_124444284_705 | Let $a = 82$, $b = 1$, $p = 3$, and $n = 53083$. Define $d = a - b$, and let $v_p(d)$ be the largest integer $k$ such that $p^k$ divides $d$. Let $C = v_p(d)$. Compute the remainder when $n \cdot C + v_p(n!)$ is divided by $100000$, where $v_p(n!)$ is the largest integer $k$ such that $p^k$ divides $n!$. | 38,869 | graphs = [
Graph(
let={
"a_val": Const(82),
"b_val": Const(1),
"p_val": Const(3),
"n_val": Const(53083),
"ab_diff": Sub(Ref("a_val"), Ref("b_val")),
"vp_ab": MaxKDivides(target=Ref("ab_diff"), base=Ref("p_val")),
"n_times_C"... | NT | null | COMPUTE | sympy | LTE_DIFF | [
"LTE_DIFF"
] | cf8260 | lte_diff_endings_v1 | null | 5 | null | [
"LTE_DIFF"
] | 1 | 0.001 | 2026-02-08T03:27:36.551639Z | {
"verified": true,
"answer": 38869,
"timestamp": "2026-02-08T03:27:36.552304Z"
} | 764f3e | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 228,
"completion_tokens": 1604
},
"timestamp": "2026-02-09T20:50:53.646Z",
"answer": 38880
},
{
... | 1 | [
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": 1.69,
"mid": 5.03,
"hi": 8.38
} | ||
c9c00f | modular_sum_quadratic_residues_v1_798873815_357 | Let $n$ be the largest prime number not exceeding 18.
Let $p$ be the largest integer such that $n^p$ divides
$$
28351092476867700887730107366063041 \times 664922854477460304521274345132525020049169433616579424626190476175164425470051684475963537.
$$
Compute $\frac{p(p-1)}{4}$. | 2,525 | graphs = [
Graph(
let={
"_m": Const(4),
"_n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(18)), IsPrime(Var("n"))))),
"p": MaxKDivides(target=Mul(Const(28351092476867700887730107366063041), Const(6649228544774603045... | NT | null | SUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW/K13"
] | b92fdf | modular_sum_quadratic_residues_v1 | null | 5 | 0 | [
"K13",
"MAX_PRIME_BELOW"
] | 2 | 0.002 | 2026-02-08T02:36:46.230436Z | {
"verified": true,
"answer": 2525,
"timestamp": "2026-02-08T02:36:46.232558Z"
} | fd2ebb | CC BY 4.0 | [
{
"id": 4,
"model": "NousResearch/Hermes-4-405B",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 151,
"completion_tokens": 391
},
"timestamp": "2026-02-08T23:34:17.981Z",
"answer": 0
},
{... | 0 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K13",
"status": "ok_later"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"... | {
"lo": -1.65,
"mid": 3.89,
"hi": 9.61
} | ||
269b35 | diophantine_fbi2_min_v1_124444284_2303 | Let $n$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 82944$. Let $k$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = n$. Let $u$ be the number of positive integers $k$ between $1$ and $1682$ inclusive that are divisible by $29$... | 2 | graphs = [
Graph(
let={
"_c": Const(2),
"_m": Const(2),
"_n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(82944)))), expr... | NT | null | EXTREMUM | sympy | B3 | [
"B3/B3",
"C2"
] | a61a4e | diophantine_fbi2_min_v1 | null | 6 | 0 | [
"B3",
"C2"
] | 2 | 0.011 | 2026-02-08T04:35:36.921173Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-02-08T04:35:36.932374Z"
} | 6d7667 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 240,
"completion_tokens": 1299
},
"timestamp": "2026-02-10T17:15:08.839Z",
"answer": 2
},
{
"id"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V7",
... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
4a9f74 | sequence_fibonacci_compute_v1_1918700295_955 | Let $S$ be the set of all ordered pairs $(i,j)$ such that $i$ is an integer with $1 \leq i \leq 4$ and $j$ is an integer with $1 \leq j \leq 6$. Let $n$ be the number of elements in $S$. Compute the $n$-th Fibonacci number, where the Fibonacci sequence is defined by $F_1 = 1$, $F_2 = 1$, and $F_k = F_{k-1} + F_{k-2}$ f... | 46,368 | graphs = [
Graph(
let={
"n": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(4)), right=IntegerRange(start=Const(1), end=Const(6)))),
"result": Fibonacci(arg=Ref(name='n')),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | sequence_fibonacci_compute_v1 | null | 2 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0 | 2026-02-08T05:24:29.853306Z | {
"verified": true,
"answer": 46368,
"timestamp": "2026-02-08T05:24:29.853785Z"
} | 295ea6 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 178,
"completion_tokens": 764
},
"timestamp": "2026-02-12T07:56:35.582Z",
"answer": 46368
},
{... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
8f8403 | alg_poly_orbit_count_v1_601307018_1936 | For a non-negative integer $a$, define $N = a^3 \bmod 31$, $M = N^3 \bmod 31$, $R = M^3 \bmod 31$, and $S = R^3 \bmod 31$. Find the number of integers $a$ with $0 \le a \le 46995$ such that $S = a$, but $N \ne a$, $M \ne a$, and $R \ne a$. | 12,128 | graphs = [
Graph(
let={
"p1": Mod(value=Pow(Var("a"), Const(3)), modulus=Const(31)),
"p2": Mod(value=Pow(Ref("p1"), Const(3)), modulus=Const(31)),
"p3": Mod(value=Pow(Ref("p2"), Const(3)), modulus=Const(31)),
"p4": Mod(value=Pow(Ref("p3"), Const(3)), modulus=C... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_orbit_count_v1 | null | 5 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.014 | 2026-03-10T02:42:13.711605Z | {
"verified": true,
"answer": 12128,
"timestamp": "2026-03-10T02:42:13.725392Z"
} | 8d7539 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 215,
"completion_tokens": 6932
},
"timestamp": "2026-03-29T03:53:14.078Z",
"answer": 8
},
{
"i... | 0 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 3.99,
"mid": 6.11,
"hi": 9.15
} | ||
6aef6f | sequence_fibonacci_compute_v1_865884756_1103 | Let $n$ be the number of integers $t$ with $18 \leq t \leq 78$ such that there exist positive integers $a \leq 9$ and $b \leq 3$ satisfying $t = 4a + 14b$. Let $\text{result} = F_n$, the $n$-th Fibonacci number, where $F_1 = F_2 = 1$ and $F_{m} = F_{m-1} + F_{m-2}$ for $m > 2$. Let $Q$ be the remainder when $45179 \cdo... | 32,955 | graphs = [
Graph(
let={
"_n": Const(71885),
"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=9)), Geq(left=Va... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | sequence_fibonacci_compute_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.005 | 2026-02-08T15:47:34.556790Z | {
"verified": true,
"answer": 32955,
"timestamp": "2026-02-08T15:47:34.561671Z"
} | 9f4c89 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 190,
"completion_tokens": 2465
},
"timestamp": "2026-02-16T13:36:43.218Z",
"answer": 32955
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V8",
"status": "n... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
46b289 | nt_min_with_divisor_count_v1_717093673_2198 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 777924$. Define $A$ to be the minimum value of $x + y$ over all such pairs. Let $D$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq = 18$, $\gcd(p, q) = 1$, and $p < q$. Determine the... | 2 | graphs = [
Graph(
let={
"upper": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(777924)))), expr=Sum(Var("x"), Var("y")))),
"div_count":... | NT | null | EXTREMUM | sympy | MIN_PRIME_FACTOR | [
"COPRIME_PAIRS",
"B3"
] | 1999ea | nt_min_with_divisor_count_v1 | null | 5 | 0 | [
"B3",
"COPRIME_PAIRS",
"MIN_PRIME_FACTOR"
] | 3 | 5.341 | 2026-02-08T16:36:36.475026Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-02-08T16:36:41.816406Z"
} | a4a86c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 180,
"completion_tokens": 1405
},
"timestamp": "2026-02-17T08:18:01.383Z",
"answer": 2
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3c",
"status": ... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
3b3b81 | nt_min_coprime_above_v1_1125832087_146 | Let $m = 14$ and $n = 8$. Let $A$ be the number of positive integers $k$ such that $1 \leq k \leq 6831$ and $\gcd(k, m) = 1$. Let $B$ be the number of positive integers $j$ such that $1 \leq j \leq A$ and $n$ divides $F_j$, where $F_j$ is the $j$-th Fibonacci number. Let $S$ be the set of integers $x$ such that $44521 ... | 44,523 | graphs = [
Graph(
let={
"_m": Const(14),
"_n": Const(8),
"start": Const(44521),
"upper": Const(45019),
"modulus": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), CountOverSet(set=SolutionsSet(var=Var... | NT | null | EXTREMUM | sympy | C4 | [
"C4/COUNT_FIB_DIVISIBLE"
] | 9b27b7 | nt_min_coprime_above_v1 | null | 7 | 0 | [
"C4",
"COUNT_FIB_DIVISIBLE"
] | 2 | 0.043 | 2026-02-08T02:54:06.947723Z | {
"verified": true,
"answer": 44523,
"timestamp": "2026-02-08T02:54:06.990423Z"
} | 998690 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 260,
"completion_tokens": 1460
},
"timestamp": "2026-02-10T11:47:10.998Z",
"answer": 44523
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok_later"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"l... | {
"lo": -3.79,
"mid": -1.07,
"hi": 1.44
} | ||
29b6b5 | comb_sum_binomial_row_v1_1218484723_3314 | Compute the 15th power of the number of integers $a$ with $0 \le a \le 42$ such that
\[
3 \left( (3a^3 - 3a + 2) \bmod 43 \right)^3 - 3 \left( (3a^3 - 3a + 2) \bmod 43 \right) + 2 \equiv a \pmod{43}
\]
and $ (3a^3 - 3a + 2) \bmod 43 \ne a $. | 32,768 | graphs = [
Graph(
let={
"_n": Const(3),
"n": Const(15),
"result": Pow(CountOverSet(set=SolutionsSet(var=Var("a"), condition=And(Geq(Var("a"), Const(0)), Leq(Var("a"), Const(42)), Eq(Mod(value=Sum(Mul(Const(3), Pow(Mod(value=Sum(Mul(Ref("_n"), Pow(Var("a"), Const(3))), Mul... | COMB | null | SUM | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | comb_sum_binomial_row_v1 | null | 4 | 0 | [
"POLY_ORBIT_COUNT"
] | 1 | 0.001 | 2026-02-25T04:59:51.255144Z | {
"verified": true,
"answer": 32768,
"timestamp": "2026-02-25T04:59:51.256607Z"
} | e18243 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 232,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T09:35:32.324Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "... | {
"lo": 1.55,
"mid": 4.7,
"hi": 7.23
} | ||
02e1bb | sequence_count_fib_divisible_v1_124444284_7623 | Let $T$ be the set of all integers $t$ such that $7 \leq t \leq 339$ and there exist positive integers $a$, $b$ with $1 \leq a \leq 67$, $1 \leq b \leq 41$, and $t = 2a + 5b$. Let $\upper$ be the number of elements in $T$. Determine the number of positive integers $n$ such that $1 \leq n \leq \upper$ and the $n$-th Fib... | 82 | graphs = [
Graph(
let={
"upper": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=67)), Geq(left=Var(name='b'), right=Const(va... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | sequence_count_fib_divisible_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.016 | 2026-02-08T09:13:39.276534Z | {
"verified": true,
"answer": 82,
"timestamp": "2026-02-08T09:13:39.292601Z"
} | 6df859 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 164,
"completion_tokens": 2917
},
"timestamp": "2026-02-14T02:01:44.785Z",
"answer": 82
},
{
... | 1 | [
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
02ce68 | lin_form_endings_v1_1520064083_9779 | Let $a = 28$ and $b = 20$. Define $g = \gcd(a, b)$, $a' = \left\lfloor \frac{a}{g} \right\rfloor$, and $b' = \left\lfloor \frac{b}{g} \right\rfloor$. Let $A = 7$ and $B = 13$. Let $T$ be the set of all numbers of the form $ax + by$ where $1 \leq x \leq A$ and $1 \leq y \leq B$. The size of $T$ is given by $a'A + b'B - ... | 19,098 | graphs = [
Graph(
let={
"a_coeff": Const(28),
"b_coeff": Const(20),
"A_val": Const(7),
"B_val": Const(13),
"g_step": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"ap_node": Floor(Div(Ref("a_coeff"), Ref("g_step"))),
"bp_node": F... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 5 | null | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T11:00:21.625260Z | {
"verified": true,
"answer": 19098,
"timestamp": "2026-02-08T11:00:21.627031Z"
} | 4ce1df | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 260,
"completion_tokens": 1169
},
"timestamp": "2026-02-14T09:54:13.167Z",
"answer": 19098
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
3e9c05 | antilemma_sum_equals_v1_898971024_544 | Let $x$ be the number of ordered pairs $(i, j)$ of positive integers such that $i \le 52$, $j \le 53$, and $i + j = 53$. Let $c$ be the number of ordered pairs $(a, b)$ such that $1 \le a \le 64$ and $1 \le b \le 128$. Let $s = \sum_{i=0}^{t-1} d_i (i+1)^2$, where $d_i$ is the $i$-th decimal digit of $x$ (starting from... | 8,214 | graphs = [
Graph(
let={
"_n": Const(53),
"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(52)), right=IntegerRange(start=Const(1), end=Con... | COMB | GEOM | COMPUTE | sympy | COMB1 | [
"COUNT_CARTESIAN",
"COUNT_SUM_EQUALS"
] | f8b274 | antilemma_sum_equals_v1 | digits_weighted_mod | 5 | 0 | [
"COMB1",
"COUNT_CARTESIAN",
"COUNT_SUM_EQUALS"
] | 3 | 0.117 | 2026-02-08T15:32:05.548317Z | {
"verified": true,
"answer": 8214,
"timestamp": "2026-02-08T15:32:05.665476Z"
} | 4ea1af | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 265,
"completion_tokens": 755
},
"timestamp": "2026-02-24T17:57:14.594Z",
"answer": 8214
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "n... | {
"lo": -8.52,
"mid": -5.43,
"hi": -3.2
} | ||
bd877e | nt_count_divisible_and_v1_1915831931_2617 | Let $A$ be the set of all positive integers $n$ such that $1 \leq n \leq 102600$, $n$ is divisible by 8, and $n$ is divisible by 12. Let $k$ be the number of elements in $A$. Let $B$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x \cdot y = 1428025$. Let $s$ be the minimum value of $x + y$ ov... | 21,592 | graphs = [
Graph(
let={
"_n": Const(76087),
"upper": Const(102600),
"d1": Const(8),
"d2": Const(12),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(value=Var("n"), mo... | NT | null | COUNT | sympy | B3 | [
"B3"
] | e0298c | nt_count_divisible_and_v1 | affine_mod | 5 | 0 | [
"B3"
] | 1 | 3.515 | 2026-02-08T16:59:09.998127Z | {
"verified": true,
"answer": 21592,
"timestamp": "2026-02-08T16:59:13.513497Z"
} | 373592 | 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": 1340
},
"timestamp": "2026-02-17T17:12:01.464Z",
"answer": 21592
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
50ec9f | modular_sum_quadratic_residues_v1_809748730_793 | Let $p$ be the largest prime number $n$ such that $2 \leq n \leq d$, where $d$ is the smallest divisor of $272483$ that is at least $2$. Let $r = \frac{p(p-1)}{4}$. Compute the remainder when $44121 \cdot r$ is divided by $58048$. | 4,290 | graphs = [
Graph(
let={
"_n": Const(4),
"p": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(272483)))))), IsPrime(... | NT | null | SUM | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/MAX_PRIME_BELOW"
] | e4e16c | modular_sum_quadratic_residues_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW",
"MIN_PRIME_FACTOR"
] | 2 | 0.005 | 2026-02-08T11:45:36.565122Z | {
"verified": true,
"answer": 4290,
"timestamp": "2026-02-08T11:45:36.569930Z"
} | 9376c9 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 121,
"completion_tokens": 4242
},
"timestamp": "2026-02-14T18:31:06.609Z",
"answer": 4290
},
{... | 1 | [
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
9f1d05 | algebra_poly_eval_v1_48377204_1901 | Let $y = 12$. Define $c$ to be the number of positive integers $n$ such that $1 \leq n \leq 13908$ and $24$ divides the $n$-th Fibonacci number. Let $d$ be the minimum value of $x + y_1$ over all ordered pairs $(x, y_1)$ of positive integers such that $x y_1 = 6553600$. Compute the value of
$$
\frac{49 \cdot y^5 + 126 ... | 20,622 | graphs = [
Graph(
let={
"_m": Const(3),
"_n": Const(2),
"y": Const(12),
"result": Div(Sum(Mul(Const(49), Pow(Ref("y"), Const(5))), Mul(Const(126), Pow(Ref("y"), Const(4))), Mul(Const(-1026), Pow(Ref("y"), Ref("_m"))), Mul(CountOverSet(set=SolutionsSet(var=Var(... | NT | null | COMPUTE | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE",
"B3"
] | a63611 | algebra_poly_eval_v1 | null | 7 | 0 | [
"B3",
"COUNT_FIB_DIVISIBLE"
] | 2 | 0.012 | 2026-02-08T16:29:03.225567Z | {
"verified": true,
"answer": 20622,
"timestamp": "2026-02-08T16:29:03.238049Z"
} | bbea2f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 215,
"completion_tokens": 5564
},
"timestamp": "2026-02-17T04:39:16.785Z",
"answer": 20622
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
3d8196 | comb_catalan_compute_v1_677425708_3800 | Let $n$ be the number of ordered pairs $(i, j)$ of positive integers such that $1 \leq i \leq 11$, $1 \leq j \leq 12$, and $i + j = 12$. Compute the $n$-th Catalan number. | 58,786 | graphs = [
Graph(
let={
"_n": Const(12),
"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(11)), right=IntegerRange(start=Const(1), end=Con... | COMB | null | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | comb_catalan_compute_v1 | null | 5 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.011 | 2026-02-08T05:56:37.884426Z | {
"verified": true,
"answer": 58786,
"timestamp": "2026-02-08T05:56:37.895205Z"
} | a88793 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 174,
"completion_tokens": 13051
},
"timestamp": "2026-02-24T04:57:08.211Z",
"answer": 58786
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
... | {
"lo": -4.93,
"mid": -2.91,
"hi": -0.71
} | ||
bcc740 | nt_sum_divisors_range_v1_153355830_2170 | Let $n = 2$ and let $U = 5041$. Define $R$ to be the sum of the number of positive divisors of each integer $m$ such that $1 \leq m \leq U$. Let $C$ be the number of positive integers $m$ such that $1 \leq m \leq 9991$ and $\gcd(m, 15) = 1$. Compute the remainder when
$$
R^n + 32R + C
$$
is divided by $77399$. | 59,878 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": Const(5041),
"result": SumOverSet(set=MapOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")))), expr=NumDivisors(n=Var("n")))),
"Q": Mod(value=Sum(Pow(Ref("r... | NT | null | SUM | sympy | C4 | [
"C4"
] | 40da2d | nt_sum_divisors_range_v1 | quadratic_mod | 5 | 0 | [
"C4"
] | 1 | 0.178 | 2026-02-08T06:57:19.506755Z | {
"verified": true,
"answer": 59878,
"timestamp": "2026-02-08T06:57:19.684676Z"
} | 14c4dc | 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": 5150
},
"timestamp": "2026-02-13T06:44:55.526Z",
"answer": 59878
},
... | 1 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8",
"status": ... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} |
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