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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
c43695 | nt_count_divisors_in_range_v1_48377204_2598 | Let $n = 166320$. Consider the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 14318656$. Let $b$ be the minimum value of $x + y$ over all such pairs. Determine the number of positive divisors $d$ of $n$ such that $26 \leq d \leq b$.
Find the value of this number. | 122 | graphs = [
Graph(
let={
"n": Const(166320),
"a": Const(26),
"b": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(14318656))))... | NT | null | COUNT | sympy | LIN_FORM | [
"B3"
] | 0cd20d | nt_count_divisors_in_range_v1 | null | 4 | 0 | [
"B3",
"LIN_FORM"
] | 2 | 0.407 | 2026-02-08T16:50:06.549504Z | {
"verified": true,
"answer": 122,
"timestamp": "2026-02-08T16:50:06.956485Z"
} | f6e0e7 | 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": 3163
},
"timestamp": "2026-02-17T14:29:22.516Z",
"answer": 122
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
8c6eaa | geo_count_lattice_triangle_v1_1431428450_177 | Let $A$ be the absolute value of $360 \cdot 121 - 121 \cdot 196$. Let $a = |360|$ and $b = |196|$, let $c = |121 - 360|$ and $d = |121 - t_{\text{max}}|$, where $t_{\text{max}}$ is the number of integers $t$ such that there exist positive integers $a$ and $b$ with $1 \le a \le 39$, $1 \le b \le 12$, $9 \le t \le 216$, ... | 15 | graphs = [
Graph(
let={
"_m": Const(121),
"_n": Const(196),
"area_2x": Abs(arg=Sum(Mul(Const(value=360), Ref(name='_m')), Mul(Const(value=121), Sub(left=Const(value=0), right=Const(value=196))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=360)), b=Abs(arg=Ref(... | COMB | NT | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | geo_count_lattice_triangle_v1 | null | 7 | 0 | [
"LIN_FORM"
] | 1 | 0.011 | 2026-02-08T13:17:18.820404Z | {
"verified": true,
"answer": 15,
"timestamp": "2026-02-08T13:17:18.831018Z"
} | 38cb62 | 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": 4238
},
"timestamp": "2026-02-15T12:05:10.995Z",
"answer": 15
},
{
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"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": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
0923bb | antilemma_k3_v1_124444284_7397 | Let $n = 97193$. Compute the sum of $\phi(d)$ over all positive divisors $d$ of $n$, where $\phi$ denotes Euler's totient function. | 97,193 | graphs = [
Graph(
let={
"_n": Const(97193),
"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 | 2026-02-08T09:06:18.195115Z | {
"verified": true,
"answer": 97193,
"timestamp": "2026-02-08T09:06:18.195415Z"
} | 5845b1 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 84,
"completion_tokens": 891
},
"timestamp": "2026-02-14T00:29:37.668Z",
"answer": 97193
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
... | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
e0df72 | antilemma_sum_equals_v1_238844314_448 | Let $x$ be the number of ordered pairs $(i, j)$ of positive integers such that $i + j = 13$, $1 \leq i \leq 12$, and $1 \leq j \leq 12$.
Compute $361 - x$. | 349 | graphs = [
Graph(
let={
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(13)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(12)), right=IntegerRange(start=Const(1), end=Const(12))))),
"Q": ... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 2 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.021 | 2026-02-08T13:21:14.842355Z | {
"verified": true,
"answer": 349,
"timestamp": "2026-02-08T13:21:14.863152Z"
} | 1ff04c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 170,
"completion_tokens": 417
},
"timestamp": "2026-02-24T17:55:18.805Z",
"answer": 349
},
{
"id"... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status":... | {
"lo": -9.23,
"mid": -6.18,
"hi": -4.06
} | ||
1510d6 | algebra_quadratic_discriminant_v1_601307018_8492 | Let $D = 1^2 - 46 \cdot 6$. Compute $2 \cdot [D > 0] + [D = 0]$, where $[P]$ is the Iverson bracket (1 if $P$ is true, 0 otherwise). | 0 | graphs = [
Graph(
let={
"a": Const(6),
"b": Const(1),
"c": Const(6),
"D": Sub(Pow(Ref("b"), Const(2)), Mul(Const(4), Ref("a"), Ref("c"))),
"result": Sum(Mul(Const(2), Iverson(condition=Gt(Ref("D"), Const(0)))), Iverson(condition=Eq(Ref("D"), Const(... | ALG | null | COMPUTE | sympy | POLY3_COUNT | [
"POLY_ORBIT_HENSEL/POLY3_COUNT",
"QF_PSD_MIN/POLY3_COUNT"
] | 314675 | algebra_quadratic_discriminant_v1 | null | 2 | 0 | [
"POLY3_COUNT",
"POLY_ORBIT_HENSEL",
"QF_PSD_MIN"
] | 3 | 0.423 | 2026-03-10T08:58:50.411683Z | {
"verified": true,
"answer": 0,
"timestamp": "2026-03-10T08:58:50.834251Z"
} | 851e1a | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 171,
"completion_tokens": 199
},
"timestamp": "2026-04-19T09:09:43.597Z",
"answer": 0
},
{
"id":... | 2 | [
{
"lemma": "POLY3_COUNT",
"status": "ok_later"
},
{
"lemma": "POLY_ORBIT_HENSEL",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_MIN",
"status": "ok"
}
] | {
"lo": -10,
"mid": -5.89,
"hi": -1.79
} | ||
9882d8 | modular_modexp_compute_v1_601307018_4607 | Let $N$ be the largest divisor of $2488504$ that is at most $1576$. Let $e$ be the number of positive integers $n \leq N$ such that $\gcd(n, 15) = 1$. Compute $37^e \bmod 36481$. | 19,361 | graphs = [
Graph(
let={
"_n": MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Leq(Var("d"), Const(1576)), Divides(divisor=Var("d"), dividend=Const(2488504))))),
"a": Const(37),
"e": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And... | NT | null | COMPUTE | sympy | MAX_DIVISOR | [
"MAX_DIVISOR/C4"
] | ac1e32 | modular_modexp_compute_v1 | null | 5 | 0 | [
"C4",
"MAX_DIVISOR"
] | 2 | 0.005 | 2026-03-10T05:15:24.479001Z | {
"verified": true,
"answer": 19361,
"timestamp": "2026-03-10T05:15:24.483872Z"
} | 827776 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 175,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T12:52:26.833Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "C4",
"status": "ok_later"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"statu... | {
"lo": 3.34,
"mid": 5.77,
"hi": 8.89
} | ||
d38625 | modular_mod_compute_v1_677425708_116 | Let $m = 2$. Let $n$ be the sum of all real solutions $x$ to the equation $x^m - 8000x + 727536 = 0$. Let $a$ be the smallest divisor of $2021$ that is at least $2$. Define $m'$ as the sum of $\phi(d)$ over all positive divisors $d$ of $n$. Compute the remainder when $a$ is divided by $m'$. | 43 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Ref("_m")), Mul(Const(-8000), Var("x")), Const(727536)), Const(0)))),
"a": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)... | NT | null | COMPUTE | sympy | VIETA_SUM | [
"VIETA_SUM/K3",
"MIN_PRIME_FACTOR"
] | 01f272 | modular_mod_compute_v1 | null | 6 | 0 | [
"K3",
"MIN_PRIME_FACTOR",
"VIETA_SUM"
] | 3 | 0.003 | 2026-02-08T03:04:39.022371Z | {
"verified": true,
"answer": 43,
"timestamp": "2026-02-08T03:04:39.025125Z"
} | 74fa7a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 213,
"completion_tokens": 870
},
"timestamp": "2026-02-08T20:19:04.353Z",
"answer": 43
},
{
"id":... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K3",
"status": "ok_later"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "POL... | {
"lo": -5.91,
"mid": -3.14,
"hi": -0.3
} | ||
45c9fa | nt_count_intersection_v1_1439011603_319 | Let $N$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 25000000$. Let $b$ be the minimum value of $x_1 + y_1$ over all pairs of positive integers $(x_1, y_1)$ such that $x_1 y_1 = 81$. Compute the number of positive integers $n$ not exceeding $N$ such that $5$ divides $n$ a... | 667 | graphs = [
Graph(
let={
"N": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(25000000)))), expr=Sum(Var("x"), Var("y")))),
"a": Const(5),... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | nt_count_intersection_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.405 | 2026-02-08T15:24:48.949992Z | {
"verified": true,
"answer": 667,
"timestamp": "2026-02-08T15:24:49.354831Z"
} | b20474 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 162,
"completion_tokens": 1890
},
"timestamp": "2026-02-16T05:23:58.619Z",
"answer": 667
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
f1e1d0 | comb_count_derangements_v1_1439011603_1380 | Let $n$ be the number of positive integers $n_1$ such that $1 \leq n_1 \leq 23$ and
$$
n_1 \equiv \left\lfloor \frac{n_1}{2} \right\rfloor \pmod{3}.
$$
Define $!n$ to be the subfactorial of $n$, which counts the number of derangements of $n$ elements. Compute the remainder when $44121 \cdot (!n)$ is divided by 92768. | 71,726 | graphs = [
Graph(
let={
"_n": Const(23),
"n": CountOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(1)), Leq(Var("n1"), Ref("_n")), Congruent(a=Var(name='n1'), b=Floor(arg=Div(left=Var(name='n1'), right=Const(value=2))), modulus=Const(value=3))))),
... | NT | COMB | COUNT | sympy | L3C | [
"L3C"
] | 73f8b0 | comb_count_derangements_v1 | null | 6 | 0 | [
"L3C"
] | 1 | 0.002 | 2026-02-08T16:03:13.410550Z | {
"verified": true,
"answer": 71726,
"timestamp": "2026-02-08T16:03:13.412309Z"
} | e68970 | 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": 1735
},
"timestamp": "2026-02-16T19:23:02.506Z",
"answer": 71726
},
... | 1 | [
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
9a6a74 | modular_sum_quadratic_residues_v1_124444284_619 | Let $n = 2$. Define $p$ to be the smallest divisor of $746899234954679$ that is at least $n$. Compute $\frac{p(p-1)}{4}$. | 21,389 | 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(746899234954679))))),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), Const(4)),
},
... | NT | null | SUM | sympy | MAX_PRIME_BELOW | [
"MIN_PRIME_FACTOR"
] | bc3776 | modular_sum_quadratic_residues_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW",
"MIN_PRIME_FACTOR"
] | 2 | 0.004 | 2026-02-08T03:24:22.875257Z | {
"verified": true,
"answer": 21389,
"timestamp": "2026-02-08T03:24:22.878781Z"
} | ca507a | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 154,
"completion_tokens": 20207
},
"timestamp": "2026-02-23T19:07:50.139Z",
"answer": 21389
},
{
... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
0ddac2 | sequence_count_fib_divisible_v1_784195855_5659 | Compute the number of positive integers $n$ such that $1 \leq n \leq 854$ and the $n$-th Fibonacci number is divisible by $7$. | 106 | graphs = [
Graph(
let={
"upper": Const(854),
"d": Const(7),
"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 | MAX_VAL | [
"LIN_FORM"
] | 7b2633 | sequence_count_fib_divisible_v1 | null | 6 | 0 | [
"LIN_FORM",
"MAX_VAL"
] | 2 | 0.251 | 2026-02-08T08:01:51.122716Z | {
"verified": true,
"answer": 106,
"timestamp": "2026-02-08T08:01:51.373242Z"
} | 021431 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 82,
"completion_tokens": 2239
},
"timestamp": "2026-02-13T14:08:13.791Z",
"answer": 106
},
{
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
87422a | nt_sum_divisors_mod_v1_2051736721_3432 | Let $n$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 705600$. Let $\sigma$ be the sum of all positive divisors of $n$. Compute the remainder when $\sigma$ is divided by $11719$. | 5,952 | graphs = [
Graph(
let={
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(705600)))), expr=Sum(Var("x"), Var("y")))),
"M": Const(11719... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_divisors_mod_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.006 | 2026-02-08T17:18:08.940185Z | {
"verified": true,
"answer": 5952,
"timestamp": "2026-02-08T17:18:08.946024Z"
} | 345c90 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 110,
"completion_tokens": 1596
},
"timestamp": "2026-02-17T23:00:13.430Z",
"answer": 5952
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
904879 | comb_count_partitions_v1_1918700295_1093 | Let $n$ be the smallest integer greater than or equal to 2 that divides 1763. Compute the value of $14400 - p(n)$ modulo 68781, where $p(n)$ denotes the number of integer partitions of $n$. | 38,598 | graphs = [
Graph(
let={
"_n": Const(2),
"n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(1763))))),
"result": Partition(arg=Ref(name='n')),
"Q": Mod(value=Sub(Const(14400), Ref("res... | NT | COMB | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | comb_count_partitions_v1 | null | 4 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.002 | 2026-02-08T05:33:28.429641Z | {
"verified": true,
"answer": 38598,
"timestamp": "2026-02-08T05:33:28.431195Z"
} | a59015 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 99,
"completion_tokens": 964
},
"timestamp": "2026-02-12T11:00:10.937Z",
"answer": 38598
},
{
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
2c047d | comb_catalan_compute_v1_655260480_2539 | Let $T$ be the set of all positive integers $t$ such that $15 \leq t \leq 60$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 4$, $1 \leq b \leq 4$, and $t = 9a + 6b$. Let $n$ be the number of ordered pairs $(i, j)$ of positive integers such that $1 \leq i \leq 12$, $1 \leq j \leq 12$, and $i + j$ equ... | 58,786 | graphs = [
Graph(
let={
"_n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=4)), Geq(left=Var(name='b'), right=Const(value=... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/COUNT_SUM_EQUALS"
] | 8a3f7a | comb_catalan_compute_v1 | null | 4 | 0 | [
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 2 | 0.011 | 2026-02-08T16:49:38.641550Z | {
"verified": true,
"answer": 58786,
"timestamp": "2026-02-08T16:49:38.652842Z"
} | b922e8 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 182,
"completion_tokens": 1643
},
"timestamp": "2026-02-17T13:17:00.866Z",
"answer": 58786
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok_later"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
... | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||
82d264 | alg_poly4_sum_v1_601307018_6930 | Find the remainder when $$\sum_{\substack{a=1 \\ b=1}}^{21} \left| \left\{ (a_1, b_1) : 1 \le a_1, b_1 \le 40,\ 16a_1^2 - 8a_1b_1 + b_1^2 = 225 \right\} \right| \cdot a^3 b + 96 a^2 b^2 + 82 a^4 + \left| \left\{ v : 26 \le v \le 14114,\ \exists\, 1 \le a, b \le 17 \text{ such that } 4a^2 - 20ab + 50b^2 = v \right\} \ri... | 18,646 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(2),
"result": Mod(value=SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(21)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(2... | ALG | null | COMPUTE | sympy | QF_PSD_DISTINCT | [
"QF_PSD_DISTINCT",
"QF_PSD_COUNT"
] | 2a8bdf | alg_poly4_sum_v1 | null | 7 | 0 | [
"QF_PSD_COUNT",
"QF_PSD_DISTINCT"
] | 2 | 0.029 | 2026-03-10T07:35:41.418121Z | {
"verified": true,
"answer": 18646,
"timestamp": "2026-03-10T07:35:41.447612Z"
} | 092ac3 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 305,
"completion_tokens": 19469
},
"timestamp": "2026-04-19T05:40:02.160Z",
"answer": 18646
},
{
... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT",
"status": "ok"
},
{
"lemma": "QF_PSD_DISTINCT",
"status": "ok"
}
] | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
0efb0c | nt_min_with_divisor_count_v1_397696148_911 | Let $n$ be a positive integer such that $1 \leq n \leq 1681$ and $n$ has exactly 12 positive divisors. Compute the smallest possible value of $n$. | 60 | graphs = [
Graph(
let={
"upper": Const(1681),
"div_count": Const(12),
"result": MinOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(NumDivisors(n=Var("n")), Ref("div_count"))))),
},
goal=Ref("res... | NT | null | EXTREMUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW/MOBIUS_SQUAREFREE",
"COPRIME_PAIRS/OMEGA_ZERO"
] | 4fffd5 | nt_min_with_divisor_count_v1 | null | 4 | 0 | [
"COPRIME_PAIRS",
"MAX_PRIME_BELOW",
"MOBIUS_SQUAREFREE",
"OMEGA_ZERO"
] | 4 | 13.817 | 2026-02-08T11:56:43.557302Z | {
"verified": true,
"answer": 60,
"timestamp": "2026-02-08T11:56:57.374239Z"
} | b9210a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 88,
"completion_tokens": 1315
},
"timestamp": "2026-02-14T21:04:17.007Z",
"answer": 60
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOBIUS_SQUAREFREE",
"status": "ok_later"
},
{
"lemma": "MOD_MUL",
"sta... | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
344ac8 | diophantine_product_count_v1_677425708_4103 | Let $k = \sum_{i=1}^{15} i$. Let $S$ be the set of all positive integers $x$ such that $x \leq 78$, $x$ divides $k$, and $\frac{k}{x} \leq 78$. Let $c = 45749$. Compute the remainder when $c \cdot |S|$ is divided by $91317$. | 1,267 | graphs = [
Graph(
let={
"k": Summation(var="k", start=Const(1), end=Const(15), expr=Var("k")),
"upper": Const(78),
"result": CountOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), Const(1)), Leq(Var("x"), Ref("upper")), Divides(divisor=Var("x"), dividend=... | NT | null | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | diophantine_product_count_v1 | null | 4 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.023 | 2026-02-08T06:25:53.996851Z | {
"verified": true,
"answer": 1267,
"timestamp": "2026-02-08T06:25:54.020088Z"
} | 56a3eb | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 131,
"completion_tokens": 1402
},
"timestamp": "2026-02-12T23:53:31.555Z",
"answer": 1267
},
{... | 1 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
fb91a7 | comb_count_derangements_v1_1918700295_1871 | Let $n$ be the number of nonnegative integers $j$ such that $0 \le j \le 4360$ and $\binom{4360}{j}$ is odd. Compute the subfactorial of $n$. | 14,833 | graphs = [
Graph(
let={
"_n": Const(4360),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Ref("_n")), Eq(Mod(value=Binom(n=Const(4360), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')),
"res... | COMB | null | COUNT | sympy | V8 | [
"V8"
] | 86348e | comb_count_derangements_v1 | null | 7 | 0 | [
"V8"
] | 1 | 0.003 | 2026-02-08T06:08:06.507580Z | {
"verified": true,
"answer": 14833,
"timestamp": "2026-02-08T06:08:06.510116Z"
} | 17b3b7 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 159,
"completion_tokens": 1858
},
"timestamp": "2026-02-24T05:32:13.929Z",
"answer": 14833
},
{
"... | 1 | [
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status... | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
5a8775 | sequence_count_fib_divisible_v1_784195855_8767 | Let $U$ be the smallest value of $x+y$ over all ordered pairs $(x,y)$ of positive integers satisfying $xy=132496$. Let $d$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that
\[pq=60,\quad \gcd(p,q)=1,\quad p<q.
\]
Let $R$ be the number of integers $n$ with $1\le n\le U$ such ... | 1 | graphs = [
Graph(
let={
"_m": Const(12),
"_n": Const(2),
"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(132496)))),... | NT | COMB | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW",
"COPRIME_PAIRS",
"B3"
] | 145a42 | sequence_count_fib_divisible_v1 | bell_mod | 8 | 0 | [
"B3",
"COPRIME_PAIRS",
"MAX_PRIME_BELOW"
] | 3 | 0.036 | 2026-02-08T16:18:17.112524Z | {
"verified": true,
"answer": 1,
"timestamp": "2026-02-08T16:18:17.148916Z"
} | abc738 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 251,
"completion_tokens": 4111
},
"timestamp": "2026-02-17T01:10:36.954Z",
"answer": 1
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
a871bc | algebra_quadratic_discriminant_v1_124444284_529 | Let $n$ be the number of prime numbers between $2$ and $17551$, inclusive. Let $\Delta = b^2 - 4ac$ where $a = 1$, $b = -4$, and $c = -45$. Let $Q$ be the difference between the largest prime number at most $n$ and $\Delta$. Determine the value of $Q$. | 1,821 | graphs = [
Graph(
let={
"_m": Const(4),
"_n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(17551)), IsPrime(Var("n"))))),
"a": Const(1),
"b": Const(-4),
"c": Const(-45),
"result"... | NT | null | COMPUTE | sympy | COUNT_PRIMES | [
"COUNT_PRIMES/MAX_PRIME_BELOW"
] | aeba83 | algebra_quadratic_discriminant_v1 | negation_mod | 5 | 0 | [
"COUNT_PRIMES",
"MAX_PRIME_BELOW"
] | 2 | 0.005 | 2026-02-08T03:20:52.671500Z | {
"verified": true,
"answer": 1821,
"timestamp": "2026-02-08T03:20:52.676680Z"
} | 61daec | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 191,
"completion_tokens": 6815
},
"timestamp": "2026-02-23T18:02:58.884Z",
"answer": 1815
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status":... | {
"lo": 1.94,
"mid": 5.23,
"hi": 8.52
} | ||
0b7710 | comb_catalan_compute_v1_153355830_1863 | Let $ n = 11 $. Let $ c $ be the $ n $-th Catalan number. Let $ T $ be the set of all ordered pairs $ (i, j) $ such that $ 1 \leq i \leq 15 $ and $ 1 \leq j \leq 16 $. Compute the remainder when $ |T| - c $ is divided by $ 57232 $. | 55,918 | graphs = [
Graph(
let={
"_n": Const(57232),
"n": Const(11),
"result": Catalan(Ref("n")),
"Q": Mod(value=Sub(CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(15)), right=IntegerRange(start=Const(1), end=Const(16)))), Ref("result")),... | COMB | null | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 009729 | comb_catalan_compute_v1 | negation_mod | 4 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.002 | 2026-02-08T06:44:42.560458Z | {
"verified": true,
"answer": 55918,
"timestamp": "2026-02-08T06:44:42.562616Z"
} | 2e7f38 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 198,
"completion_tokens": 1525
},
"timestamp": "2026-02-24T07:01:52.450Z",
"answer": 55918
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no... | {
"lo": -4.93,
"mid": -2.91,
"hi": -0.71
} | ||
7028c5 | nt_min_phi_inverse_v1_124444284_2945 | Let $k$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 48$. Let $n$ be the smallest positive integer $n$ with $1 \leq n \leq 100$ such that $\phi(n) = k$. Compute $n$. | 35 | graphs = [
Graph(
let={
"_n": Const(48),
"upper": Const(100),
"k": 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')),... | NT | null | EXTREMUM | sympy | V5 | [
"COMB1"
] | 567f58 | nt_min_phi_inverse_v1 | null | 6 | 0 | [
"COMB1",
"V5"
] | 2 | 0.067 | 2026-02-08T05:05:18.616264Z | {
"verified": true,
"answer": 35,
"timestamp": "2026-02-08T05:05:18.683401Z"
} | fed5f5 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 185,
"completion_tokens": 1472
},
"timestamp": "2026-02-11T22:52:16.407Z",
"answer": 35
},
{
"id... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.33
} | ||
50ca10 | diophantine_sum_product_min_v1_717093673_1742 | Let $S = 140$ and let $P$ be the number of ordered pairs $(a,b)$ of integers such that $1 \leq a \leq 43$ and $1 \leq b \leq 97$. Determine the value of $x$, where $x$ is the smallest integer satisfying $1 \leq x \leq 139$ and $x(S - x) = P$. | 43 | graphs = [
Graph(
let={
"S": Const(140),
"P": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(43)), right=IntegerRange(start=Const(1), end=Const(97)))),
"result": MinOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), Const(1))... | NT | null | EXTREMUM | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | diophantine_sum_product_min_v1 | null | 5 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.013 | 2026-02-08T16:17:34.698942Z | {
"verified": true,
"answer": 43,
"timestamp": "2026-02-08T16:17:34.712134Z"
} | e8f8a5 | 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": 649
},
"timestamp": "2026-02-17T00:48:09.442Z",
"answer": 43
},
{
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8",
"status": "no... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
ebf6bb | comb_sum_binomial_row_v1_677425708_3997 | Let $n$ be the number of positive integers $k$ such that $1 \leq k \leq p$, where $p$ is the largest prime number less than or equal to $42$, and $\gcd(k, 6) = 1$. Compute $2^n$. | 16,384 | graphs = [
Graph(
let={
"_n": Const(2),
"n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(42)), IsPrime(Var("n")))))), Eq(GCD(a=Var... | NT | null | SUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW/C4"
] | a99ef8 | comb_sum_binomial_row_v1 | null | 4 | 0 | [
"C4",
"MAX_PRIME_BELOW"
] | 2 | 0.002 | 2026-02-08T06:07:39.789122Z | {
"verified": true,
"answer": 16384,
"timestamp": "2026-02-08T06:07:39.790836Z"
} | 03bbed | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 105,
"completion_tokens": 756
},
"timestamp": "2026-02-12T19:39:36.733Z",
"answer": 16384
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "C4",
"status": "ok_later"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status":... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
a9d9b2 | modular_count_residue_v1_124444284_2421 | Let $m = 20$. Let $r$ be the number of ordered pairs $(i,j)$ of positive integers such that $1 \leq i \leq 3$, $1 \leq j \leq 7$, and $\gcd(i,j) = 1$. Let $S$ be the set of all positive integers $n$ such that $1 \leq n \leq 30347$ and $n \equiv r \pmod{m}$. Compute the number of elements in $S$. | 1,517 | graphs = [
Graph(
let={
"upper": Const(30347),
"m": Const(20),
"r": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(GCD(a=Var("i"), b=Var("j")), Const(1)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(3)), right=... | NT | null | COUNT | sympy | B3 | [
"COUNT_COPRIME_GRID"
] | 20ec03 | modular_count_residue_v1 | null | 4 | 0 | [
"B3",
"COUNT_COPRIME_GRID"
] | 2 | 2.304 | 2026-02-08T04:39:13.166426Z | {
"verified": true,
"answer": 1517,
"timestamp": "2026-02-08T04:39:15.470128Z"
} | 3d53cc | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 169,
"completion_tokens": 651
},
"timestamp": "2026-02-11T21:39:46.230Z",
"answer": 1517
},
{
"id": 11,
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
dbdfe5 | nt_num_divisors_compute_v1_124444284_1660 | Let $m = 82944$. Consider the set of all ordered pairs $(x,y)$ of positive integers such that $xy = m$. For each such pair, compute $x + y$, and let $n_1$ be the minimum value of $x + y$ over all such pairs.
Now consider the set of all ordered pairs $(x,y)$ of positive integers such that $xy = n_1$. For each such pair... | 10 | graphs = [
Graph(
let={
"_m": Const(82944),
"_n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_m")))), expr=Sum(Var("x"), Var("y")))),... | NT | null | COMPUTE | sympy | COMB1 | [
"B3/B3"
] | 8ffef9 | nt_num_divisors_compute_v1 | null | 6 | 0 | [
"B3",
"COMB1"
] | 2 | 0.031 | 2026-02-08T04:04:42.026333Z | {
"verified": true,
"answer": 10,
"timestamp": "2026-02-08T04:04:42.057004Z"
} | 229a45 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 238,
"completion_tokens": 1178
},
"timestamp": "2026-02-10T15:21:38.136Z",
"answer": 10
},
{
"id... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
627362 | modular_modexp_compute_v1_601307018_3621 | Let $a$ be the minimum value of $|x - y|$ over all ordered pairs $(x, y)$ of positive integers with $xy = 684$. Let $e$ be the minimum value of $x_1 + y_1$ over all ordered pairs $(x_1, y_1)$ of positive integers with $x_1 y_1 = 49284$. Let $R = a^e \bmod 38809$. Find the remainder when $56209 \cdot R$ is divided by $8... | 74,561 | graphs = [
Graph(
let={
"_m": Const(56209),
"_n": Const(88699),
"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(684)))),... | NT | null | COMPUTE | sympy | B3_DIFF | [
"B3_DIFF",
"B3"
] | 69b567 | modular_modexp_compute_v1 | null | 5 | 0 | [
"B3",
"B3_DIFF"
] | 2 | 0.003 | 2026-03-10T04:14:52.518620Z | {
"verified": true,
"answer": 74561,
"timestamp": "2026-03-10T04:14:52.521953Z"
} | 360b92 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 225,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T09:22:15.858Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "B3_DIFF",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8"... | {
"lo": 1.23,
"mid": 4.27,
"hi": 6.7
} | ||
3c4d9a | modular_count_residue_v1_677425708_670 | Let $m = 13$. Consider the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 1521$. Let $n$ be the minimum value of $x + y$ over all such pairs. Let $S$ be the set of positive integers $k$ such that $1 \leq k \leq 65$ and $k$ is divisible by $m$. Define $m'$ as the largest integer $e$ such that $2^... | 20,932 | graphs = [
Graph(
let={
"_m": Const(13),
"_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(1521)))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | COUNT | sympy | B3 | [
"B3/SUM_DIVISIBLE/V7"
] | f62ecb | modular_count_residue_v1 | null | 6 | 0 | [
"B3",
"SUM_DIVISIBLE",
"V7"
] | 3 | 2.722 | 2026-02-08T03:40:23.565791Z | {
"verified": true,
"answer": 20932,
"timestamp": "2026-02-08T03:40:26.287985Z"
} | a234eb | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 295,
"completion_tokens": 2035
},
"timestamp": "2026-02-08T20:54:22.063Z",
"answer": 20932
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "SUM_DIVISIBLE",
"status": "ok_later"
},
... | {
"lo": -6.5,
"mid": -0.2,
"hi": 6.11
} | ||
f33fc0 | antilemma_k3_v1_2051736721_5042 | Let $n = 32354$. Compute the value of
$$
\sum_{d \mid n} \phi(d),
$$
where the sum is over all positive divisors $d$ of $n$, and $\phi(d)$ denotes Euler's totient function. Answer with this sum. | 32,354 | graphs = [
Graph(
let={
"_n": Const(32354),
"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 | 2026-02-08T18:21:06.738106Z | {
"verified": true,
"answer": 32354,
"timestamp": "2026-02-08T18:21:06.738507Z"
} | 6b7f39 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 125,
"completion_tokens": 631
},
"timestamp": "2026-02-16T12:17:45.429Z",
"answer": 670656
},
{
"id": 11... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
7a2010 | antilemma_k2_v1_1978505735_5226 | Let $n = 220$. Compute the value of
$$
\sum_{k=1}^{n} \phi(k) \left\lfloor \frac{220}{k} \right\rfloor.
$$ | 24,310 | graphs = [
Graph(
let={
"_n": Const(220),
"x": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(220), Var("k"))))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | antilemma_k2_v1 | null | 5 | 0 | [
"K2"
] | 1 | 0.001 | 2026-02-08T18:51:50.666043Z | {
"verified": true,
"answer": 24310,
"timestamp": "2026-02-08T18:51:50.667070Z"
} | 7f8448 | 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": 1580
},
"timestamp": "2026-02-18T19:51:54.662Z",
"answer": 24310
},
{... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
d92456 | comb_catalan_compute_v1_153355830_835 | Let $n$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 20$. Let $C_n$ denote the $n$-th Catalan number. Define $r = C_n \bmod{11}$, and let $B_r$ be the $r$-th Bell number. Compute the remainder when $B_r$ is divided by 87484. | 28,491 | graphs = [
Graph(
let={
"_n": Const(20),
"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")), Re... | COMB | null | COMPUTE | sympy | COMB1 | [
"COMB1"
] | 567f58 | comb_catalan_compute_v1 | null | 6 | 0 | [
"COMB1"
] | 1 | 0.001 | 2026-02-08T04:11:26.406110Z | {
"verified": true,
"answer": 28491,
"timestamp": "2026-02-08T04:11:26.407482Z"
} | 574c1f | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 207,
"completion_tokens": 958
},
"timestamp": "2026-02-23T23:40:44.260Z",
"answer": 28591
},
{
... | 1 | [
{
"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",
"status": "no"
},
{
"lemma": "V8... | {
"lo": 1.97,
"mid": 4.36,
"hi": 6.69
} | ||
e7d096 | nt_min_phi_inverse_v1_48377204_2078 | Let $ A $ be the set of all positive integers $ n $ such that $ n \leq 20 $ and $ n $ is divisible by 4. Let $ m $ be the sum of all elements in $ A $. Let $ B $ be the set of all positive integers $ n_1 $ such that $ 1 \leq n_1 \leq m $ and $ \phi(n_1) = 18 $. Let $ r $ be the smallest element in $ B $. Let $ D $ be t... | 22 | graphs = [
Graph(
let={
"_m": Const(2173),
"_n": Const(41),
"upper": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(20)), Eq(Mod(value=Var("n"), modulus=Const(4)), Const(0))))),
"k": Const(18),
... | NT | null | EXTREMUM | sympy | MAX_PRIME_BELOW | [
"MAX_DIVISOR",
"SUM_DIVISIBLE"
] | f7f205 | nt_min_phi_inverse_v1 | negation_mod | 5 | 0 | [
"MAX_DIVISOR",
"MAX_PRIME_BELOW",
"SUM_DIVISIBLE"
] | 3 | 0.179 | 2026-02-08T16:35:46.447449Z | {
"verified": true,
"answer": 22,
"timestamp": "2026-02-08T16:35:46.626859Z"
} | 0aba2f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 193,
"completion_tokens": 2063
},
"timestamp": "2026-02-17T07:22:41.941Z",
"answer": 22
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "SUM_DIVISIBLE",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
722091 | comb_sum_binomial_row_v1_53965629_33 | Let $n$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 34650$, $\gcd(p, q) = 1$, and $p < q$. Let $\text{result} = 2^n$. Compute the remainder when $92859 \cdot \text{result}$ is divided by $57656$. | 16,624 | graphs = [
Graph(
let={
"_n": Const(57656),
"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=34650)), Eq(left=GCD(a=Var(name='p'), b=Var(n... | NT | null | SUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_sum_binomial_row_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.003 | 2026-02-08T11:13:53.992541Z | {
"verified": true,
"answer": 16624,
"timestamp": "2026-02-08T11:13:53.995967Z"
} | 330d5f | 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": 2696
},
"timestamp": "2026-02-09T11:07:00.887Z",
"answer": 16624
},
{
"... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -5.15,
"mid": 0.01,
"hi": 5.44
} | ||
696d8a | comb_count_surjections_v1_1218484723_929 | Let $k = \sum_{k1=1}^{3} \varphi(k1) \cdot \left\lfloor \frac{3}{k1} \right\rfloor$. Compute $k! \cdot S(7, k)$, where $S(7, k)$ denotes the Stirling number of the second kind. | 15,120 | graphs = [
Graph(
let={
"_n": Const(3),
"n": Const(7),
"k": Summation(var="k1", start=Const(1), end=Const(3), expr=Mul(EulerPhi(n=Var("k1")), Floor(Div(Ref("_n"), Var("k1"))))),
"result": Mul(Factorial(Ref("k")), Stirling2(n=Ref(name='n'), k=Ref(name='k'))),
... | COMB | NT | COUNT | sympy | POLY_ORBIT_LEGENDRE | [
"K2"
] | 6897ab | comb_count_surjections_v1 | null | 4 | 0 | [
"K2",
"POLY_ORBIT_LEGENDRE"
] | 2 | 0.779 | 2026-02-25T02:37:43.793183Z | {
"verified": true,
"answer": 15120,
"timestamp": "2026-02-25T02:37:44.572217Z"
} | 77920f | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 184,
"completion_tokens": 605
},
"timestamp": "2026-03-10T02:57:41.301Z",
"answer": 15120
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "V8_SUM",
"statu... | {
"lo": -2.78,
"mid": -0.24,
"hi": 2.7
} | ||
dc6729 | comb_binomial_compute_v1_1520064083_2701 | Let $n = \sum_{d \mid 12} \phi(d)$, where $\phi$ denotes Euler's totient function. Compute $\binom{n}{6}$. | 924 | graphs = [
Graph(
let={
"_n": Const(12),
"n": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"k": Const(6),
"result": Binom(n=Ref("n"), k=Ref("k")),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | comb_binomial_compute_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0.003 | 2026-02-08T04:56:48.486291Z | {
"verified": true,
"answer": 924,
"timestamp": "2026-02-08T04:56:48.489570Z"
} | f9d58e | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 96,
"completion_tokens": 274
},
"timestamp": "2026-02-11T22:08:50.093Z",
"answer": 924
},
{
"id": 11,
... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status"... | {
"lo": -10,
"mid": -7.73,
"hi": -5.46
} | ||
a22b1b | geo_count_lattice_triangle_v1_1218484723_2356 | Let $M = \left|271 \cdot 120 + 225 \cdot (-64)\right|$ and let $R = \gcd(271, 64) + \gcd(|225 - 271|, |120 - 64|) + \gcd(225, 120)$. Compute $\frac{M + 2 - R}{2}$. | 9,052 | graphs = [
Graph(
let={
"_n": Const(271),
"area_2x": Abs(arg=Sum(Mul(Const(value=271), Const(value=120)), Mul(Const(value=225), Sub(left=Const(value=0), right=Const(value=64))))),
"boundary": Sum(GCD(a=Abs(arg=Ref(name='_n')), b=Abs(arg=Const(value=64))), GCD(a=Abs(arg=Su... | GEOM | NT | COUNT | sympy | QF_PSD_COUNT_LEQ | [
"QF_PSD_COUNT_LEQ"
] | 009d0f | geo_count_lattice_triangle_v1 | null | 3 | 0 | [
"QF_PSD_COUNT_LEQ"
] | 1 | 0.005 | 2026-02-25T04:09:49.462898Z | {
"verified": true,
"answer": 9052,
"timestamp": "2026-02-25T04:09:49.468252Z"
} | 121c63 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 192,
"completion_tokens": 835
},
"timestamp": "2026-03-29T04:17:22.879Z",
"answer": 9052
},
{
"id... | 1 | [
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
}
] | {
"lo": -4.26,
"mid": -1.8,
"hi": 1.26
} | ||
9c7f65 | algebra_quadratic_discriminant_v1_1520064083_5229 | Let $a = -1$, $b = 3$, and $c = 18$. Consider the quadratic equation
$$
x^2 - 4x - 1365 = 0.
$$
Let $r$ be the sum of the roots of this equation. Compute $b^2 - a \cdot r \cdot c$. Let $n$ be the absolute value of this result. Determine the value of
$$
\sum_{k=1}^{n} \phi(k),
$$
where $\phi(k)$ denotes Euler's totient ... | 2,020 | graphs = [
Graph(
let={
"a": Const(-1),
"b": Const(3),
"c": Const(18),
"result": Sub(Pow(Ref("b"), Const(2)), Mul(SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Const(2)), Mul(Const(-4), Var("x")), Const(-1365)), Const(0)))), Ref("a")... | NT | null | COMPUTE | sympy | ONE_PHI_1 | [
"VIETA_SUM"
] | b33a7a | algebra_quadratic_discriminant_v1 | null | 4 | 0 | [
"ONE_PHI_1",
"VIETA_SUM"
] | 2 | 0.016 | 2026-02-08T06:41:25.866942Z | {
"verified": true,
"answer": 2020,
"timestamp": "2026-02-08T06:41:25.882564Z"
} | 95cabb | 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": 1991
},
"timestamp": "2026-02-13T03:23:24.628Z",
"answer": 2020
},
{... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "VIETA_SUM",
"status": "ok"
}
... | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
2005a7 | comb_sum_binomial_row_v1_1218484723_6222 | Let $n$ be the number of non-negative integers $v \leq 405$ for which there exist integers $a, b$ with $1 \leq a, b \leq 5$ such that $5a^2 - 20ab + 20b^2 = v$. Compute $2^n$. | 1,024 | graphs = [
Graph(
let={
"_n": Const(2),
"n": CountOverSet(set=SolutionsSet(var=Var("v"), condition=And(Geq(Var("v"), Const(0)), Leq(Var("v"), Const(405)), Exists(var=Tuple(elements=[Var(name='a'), Var(name='b')]), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=... | COMB | null | SUM | sympy | LIN_FORM | [
"QF_PSD_DISTINCT"
] | a8f9cb | comb_sum_binomial_row_v1 | null | 4 | 0 | [
"LIN_FORM",
"QF_PSD_DISTINCT"
] | 2 | 0.299 | 2026-02-25T07:48:33.542242Z | {
"verified": true,
"answer": 1024,
"timestamp": "2026-02-25T07:48:33.841572Z"
} | 40f54f | 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": 1455
},
"timestamp": "2026-03-30T00:47:36.165Z",
"answer": 1024
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "QF_PSD_DISTINCT",
"status": "ok"
},
{
"lemma": "V8_SU... | {
"lo": -6.2,
"mid": -2.87,
"hi": 0.44
} | ||
4a4c14 | geo_count_lattice_triangle_v1_48377204_2714 | Let $A$ be the polygon with vertices at $(0,0)$, $(128,240)$, $(55,200)$, and $(0,0)$. The area of $A$ can be computed as $\frac{1}{2} \left| 128 \cdot 200 - 55 \cdot 240 \right|$. Let $B$ be the number of lattice points on the boundary of $A$, computed as the sum of the greatest common divisors of the differences in c... | 6,190 | graphs = [
Graph(
let={
"_m": Const(55),
"_n": SumOverDivisors(n=Const(value=200), var='d', expr=EulerPhi(n=Var(name='d'))),
"area_2x": Abs(arg=Sum(Mul(Const(value=128), Const(value=200)), Mul(Const(value=55), Sub(left=Const(value=0), right=Const(value=240))))),
... | NT | null | COUNT | sympy | K3 | [
"K3/COUNT_FIB_DIVISIBLE"
] | b1cab1 | geo_count_lattice_triangle_v1 | null | 7 | 0 | [
"COUNT_FIB_DIVISIBLE",
"K3"
] | 2 | 0.009 | 2026-02-08T16:56:30.847381Z | {
"verified": true,
"answer": 6190,
"timestamp": "2026-02-08T16:56:30.856325Z"
} | cdc5eb | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 286,
"completion_tokens": 1443
},
"timestamp": "2026-02-17T15:41:34.832Z",
"answer": 6190
},
{... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok_later"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"l... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
0e370d | nt_count_divisible_and_v1_397696148_2220 | Let $d_1 = 9$. Let $d_2$ be the number of integers $t$ in the range $14 \leq t \leq 44$ for which there exist integers $a$ and $b$ with $1 \leq a \leq 2$, $1 \leq b \leq 6$, such that $t = 10a + 4b$. Define $S$ to be the set of all positive integers $n \leq 45504$ such that $n$ is divisible by $d_1$ and the remainder w... | 1,264 | graphs = [
Graph(
let={
"upper": Const(45504),
"d1": Const(9),
"d2": 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'), ri... | COMB | null | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING",
"LIN_FORM"
] | 10f694 | nt_count_divisible_and_v1 | null | 6 | 0 | [
"BINOMIAL_ALTERNATING",
"LIN_FORM"
] | 2 | 1.54 | 2026-02-08T13:00:08.749123Z | {
"verified": true,
"answer": 1264,
"timestamp": "2026-02-08T13:00:10.289478Z"
} | c1af1a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 281,
"completion_tokens": 939
},
"timestamp": "2026-02-24T16:53:51.742Z",
"answer": 1264
},
{
"id... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "... | {
"lo": -5.97,
"mid": -3.97,
"hi": -1.93
} | ||
58a166 | antilemma_sum_equals_v1_48377204_633 | Let $m=84$. Let $n$ be the number of integers $t$ for which there exist integers $a$ and $b$ satisfying $1\le a\le 10$, $1\le b\le 5$, $7\le t\le 50$, and
$$t=3a+4b.$$
Let $x$ be the number of ordered pairs $(i,j)$ of integers with $1\le i\le 83$, $1\le j\le 84$, and
$$i+j=m.$$
Let $Q$ be the remainder when the follo... | 56,211 | graphs = [
Graph(
let={
"_m": Const(84),
"_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=10)), Geq(left=Var... | COMB | GEOM | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/COMB1",
"COUNT_SUM_EQUALS"
] | b9178b | antilemma_sum_equals_v1 | negation_mod | 4 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 3 | 0.009 | 2026-02-08T15:37:55.825577Z | {
"verified": true,
"answer": 56211,
"timestamp": "2026-02-08T15:37:55.834664Z"
} | 048a69 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 295,
"completion_tokens": 2926
},
"timestamp": "2026-02-24T18:05:52.356Z",
"answer": 56211
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok_later"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "LIN_FORM",
... | {
"lo": -2.4,
"mid": 1.57,
"hi": 5.75
} | ||
50e349 | nt_sum_divisors_mod_v1_397696148_2336 | Let $n$ be the smallest possible value of $x + y$ where $x$ and $y$ are positive integers such that $xy = 705600$. Let $\sigma$ denote the sum of all positive divisors of $n$. Find the remainder when $\sigma$ is divided by $11789$. | 5,952 | graphs = [
Graph(
let={
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(705600)))), expr=Sum(Var("x"), Var("y")))),
"M": Const(11789... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_divisors_mod_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.002 | 2026-02-08T13:07:04.497430Z | {
"verified": true,
"answer": 5952,
"timestamp": "2026-02-08T13:07:04.499542Z"
} | 8c4e17 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 111,
"completion_tokens": 1551
},
"timestamp": "2026-02-15T12:34:14.660Z",
"answer": 5952
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
56f5c7 | diophantine_fbi2_count_v1_784195855_8021 | Let $m$ be the number of positive integers $n \leq 209$ such that $n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{3}$. Let $k$ be the minimum value of $x + y$ over all ordered pairs of positive integers $(x, y)$ such that $xy = 129600$. Let $S$ be the set of positive integers $d$ satisfying $4 \leq d \leq \max\{... | 66,654 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(209)), Congruent(a=Var(name='n'), b=Floor(arg=Div(left=Var(name='n'), right=Const(value=2))), modulus=Const(value=3))))),
"... | NT | null | COUNT | sympy | L3C | [
"L3C/MAX_PRIME_BELOW",
"B3"
] | aaa463 | diophantine_fbi2_count_v1 | null | 7 | 0 | [
"B3",
"L3C",
"MAX_PRIME_BELOW"
] | 3 | 0.01 | 2026-02-08T09:40:41.254639Z | {
"verified": true,
"answer": 66654,
"timestamp": "2026-02-08T09:40:41.264671Z"
} | cf5ee6 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 208,
"completion_tokens": 2579
},
"timestamp": "2026-02-14T08:30:24.442Z",
"answer": 66654
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
c529c4 | geo_visible_lattice_v1_1248542787_100 | Let $n = 128$. A lattice point $(x, y)$ is called visible if $\gcd(x, y) = 1$. Define $V$ to be the number of visible lattice points $(x, y)$ with $1 \leq x, y \leq n$.
Compute $36856 - V$. | 26,813 | graphs = [
Graph(
let={
"n": Const(128),
"result": VisibleLatticePoints(n=Ref(name='n')),
"Q": Sub(Const(36856), Ref("result")),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 3 | 0 | null | null | 0.728 | 2026-02-08T02:57:13.046919Z | {
"verified": true,
"answer": 26813,
"timestamp": "2026-02-08T02:57:13.774496Z"
} | 86b8af | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 179,
"completion_tokens": 5992
},
"timestamp": "2026-02-23T18:54:56.136Z",
"answer": 26813
},
{
"... | 1 | [] | {
"lo": 4.14,
"mid": 5.36,
"hi": 6.65
} | ||||
f9a6a7 | nt_sum_divisors_mod_v1_2051736721_4319 | Let $n$ be the smallest possible value of $x + y$ where $x$ and $y$ are positive integers such that $xy = 8100$. Let $\sigma$ denote the sum of all positive divisors of $n$. Let $M = 11321$. Compute the value of $39204 - (\sigma \bmod M)$. | 38,658 | graphs = [
Graph(
let={
"_n": Const(8100),
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_n")))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_divisors_mod_v1 | null | 3 | 0 | [
"B3"
] | 1 | 0.003 | 2026-02-08T17:54:54.440456Z | {
"verified": true,
"answer": 38658,
"timestamp": "2026-02-08T17:54:54.443049Z"
} | 6b1594 | 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": 812
},
"timestamp": "2026-02-18T10:04:18.708Z",
"answer": 38658
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
cd0865 | comb_catalan_compute_v1_1520064083_5742 | Let $n$ be the number of integers $t$ such that $32 \leq t \leq 71$ and there exist integers $a$ and $b$ with $1 \leq a \leq 2$, $1 \leq b \leq 5$, and $t = 15a + 6b + 11$. 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=2)), Geq(left=Var(name='b'), right=Const(value=1... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_catalan_compute_v1 | null | 3 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T07:34:40.254101Z | {
"verified": true,
"answer": 16796,
"timestamp": "2026-02-08T07:34:40.255895Z"
} | da60fb | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 198,
"completion_tokens": 619
},
"timestamp": "2026-02-24T08:14:49.383Z",
"answer": 16796
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -3.84,
"mid": -1.67,
"hi": 1.32
} | ||
bb961a | comb_sum_binomial_mod_v1_349078426_1488 | Let $T$ be the set of all integers $t$ such that $5 \leq t \leq 86$ and there exist positive integers $a \leq 8$ and $b \leq 31$ for which $t = 3a + 2b$. Let $s$ be the number of elements in $T$. Compute the remainder when $$\sum_{k=14}^{s} \binom{103}{k}$$ is divided by $11927$. | 6,658 | graphs = [
Graph(
let={
"_n": Const(11927),
"sum": Summation(var="k", start=Const(14), end=CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(nam... | ALG | COMB | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_sum_binomial_mod_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.03 | 2026-02-08T13:40:46.101310Z | {
"verified": true,
"answer": 6658,
"timestamp": "2026-02-08T13:40:46.131343Z"
} | 048da2 | 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": 32768
},
"timestamp": "2026-02-24T18:51:23.991Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 3.25,
"mid": 5.68,
"hi": 8.81
} | ||
30ec0d | nt_max_prime_below_v1_1918700295_3960 | Let $S$ be the set of all positive integers $p$ such that there exists a positive integer $q$ with $p < q$, $\gcd(p, q) = 1$, and $pq = 36$. Let $m$ be the number of elements in $S$. Find the largest prime number $n$ such that $m \leq n \leq 50400$. | 50,387 | graphs = [
Graph(
let={
"upper": Const(50400),
"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 | 1.191 | 2026-02-08T09:03:48.550114Z | {
"verified": true,
"answer": 50387,
"timestamp": "2026-02-08T09:03:49.740642Z"
} | 50224c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 128,
"completion_tokens": 4129
},
"timestamp": "2026-02-14T00:01:12.051Z",
"answer": 50387
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
aa8182 | comb_bell_compute_v1_1978505735_6591 | Let $m=6$ and $n=8$. For each integer $t$, suppose there exist integers $a$ and $b$ such that $1\le a\le 2$, $1\le b\le 9$, $27\le t\le 96$, and
$$t=21a+6b.$$
Let $N$ be the number of integers $t$ for which such integers $a$ and $b$ exist. Define $n_2=0$ and
$$v=\sum_{k=\binom{N}{18}-1}^{n_2}(-1)^k\binom{n_2}{k}.$$
Let... | 4,140 | graphs = [
Graph(
let={
"_m": Const(6),
"_n": Const(8),
"n2": Const(0),
"v": Summation(var="k", start=Sub(Binom(n=CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(nam... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/ZERO_BINOM_N/BINOMIAL_ALTERNATING",
"COMB1/BINOMIAL_ALTERNATING"
] | 42ce04 | comb_bell_compute_v1 | null | 6 | 2 | [
"BINOMIAL_ALTERNATING",
"COMB1",
"LIN_FORM",
"ZERO_BINOM_N"
] | 4 | 0.006 | 2026-02-08T19:40:51.536314Z | {
"verified": true,
"answer": 4140,
"timestamp": "2026-02-08T19:40:51.542297Z"
} | 201bfd | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 326,
"completion_tokens": 1545
},
"timestamp": "2026-02-18T23:12:10.560Z",
"answer": 4140
},
{... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INT... | {
"lo": -3.12,
"mid": 1.47,
"hi": 6.57
} | ||
d68842 | comb_count_permutations_fixed_v1_458359167_5743 | Let $n$ be the largest prime number not exceeding 8. Compute the number of derangements of $n$ elements. | 1,854 | graphs = [
Graph(
let={
"_n": Const(2),
"n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Const(8)), IsPrime(Var("n"))))),
"k": Const(0),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub(left=... | NT | COMB | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | comb_count_permutations_fixed_v1 | null | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.002 | 2026-02-08T12:40:18.759354Z | {
"verified": true,
"answer": 1854,
"timestamp": "2026-02-08T12:40:18.760859Z"
} | 17b928 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 73,
"completion_tokens": 1191
},
"timestamp": "2026-02-15T03:53:31.524Z",
"answer": 1854
},
{
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": ... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
ebdf3d_l | antilemma_k2_v1_1116507919_14 | Let $n = 133$. Define
$$
S = \sum_{d \mid n} \phi(d),
$$
where $\phi$ denotes Euler's totient function. Let
$$
x = \sum_{k=1}^{S} \phi(k) \left\lfloor \frac{S}{k} \right\rfloor.
$$
Compute the value of
$$
11^{|x|} \bmod 99991 + 11664.
$$ | 11,664 | NT | COMB | COMPUTE | sympy | K13 | [
"K3/K2",
"K2"
] | c7f244 | antilemma_k2_v1 | null | 6 | 0 | [
"K13",
"K2",
"K3"
] | 3 | 0.004 | 2026-02-08T02:23:34.384898Z | {
"verified": false,
"answer": 64003,
"timestamp": "2026-02-08T02:23:34.388521Z"
} | d38c55 | ebdf3d | legacy_text | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 212,
"completion_tokens": 22811
},
"timestamp": "2026-02-23T15:10:41.771Z",
"answer": 69418
},
{
... | 1 | [
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8... | {
"lo": 2.56,
"mid": 3.97,
"hi": 5.36
} | |
daa1c3 | geo_count_lattice_triangle_v1_458359167_2168 | Let $A$ be the area of the triangle with vertices at $(0,0)$, $(144,77)$, and $(13,100)$, multiplied by 2. Let $B$ be the sum of the greatest common divisors of the absolute differences of the coordinates of the consecutive vertices of this triangle, where the third vertex is $(13, y_0)$ and $y_0$ is the smallest posit... | 7,014 | graphs = [
Graph(
let={
"_m": Const(144),
"_n": Const(2),
"area_2x": Abs(arg=Sum(Mul(Const(value=144), Const(value=100)), Mul(Const(value=13), Sub(left=Const(value=0), right=Const(value=77))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=144)), b=Abs(arg=Const(... | ALG | NT | COUNT | sympy | B3 | [
"B3/SUM_DIVISIBLE"
] | 138b1a | geo_count_lattice_triangle_v1 | null | 7 | 0 | [
"B3",
"SUM_DIVISIBLE"
] | 2 | 0.013 | 2026-02-08T05:09:53.861035Z | {
"verified": true,
"answer": 7014,
"timestamp": "2026-02-08T05:09:53.874174Z"
} | 5bdafc | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 393,
"completion_tokens": 3074
},
"timestamp": "2026-02-11T23:00:22.030Z",
"answer": 7014
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_DIVISIBLE",
"status": "ok_later"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
8304a8 | nt_count_coprime_v1_1742523217_2172 | Let $k$ be the number of positive integers $n$ such that $1 \leq n \leq 981$, $9$ divides $n$, and $\gcd(n, 14) = 1$. Let $S$ be the set of all positive integers $n$ such that $1 \leq n \leq 46225$ and $\gcd(n, k) = 1$. Compute the number of elements in $S$. Let this number be $r$. Find the remainder when $44121 \cdot ... | 3,408 | graphs = [
Graph(
let={
"_n": Const(14),
"upper": Const(46225),
"k": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(981)), Divides(divisor=Const(9), dividend=Var("n")), Eq(GCD(a=Var("n"), b=Ref("_n")), Const(1))))),
... | NT | null | COUNT | sympy | C5 | [
"C5"
] | 1d9668 | nt_count_coprime_v1 | null | 6 | 0 | [
"C5"
] | 1 | 7.049 | 2026-02-08T04:32:29.831215Z | {
"verified": true,
"answer": 3408,
"timestamp": "2026-02-08T04:32:36.880113Z"
} | 8ec148 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 233,
"completion_tokens": 2222
},
"timestamp": "2026-02-10T17:12:46.805Z",
"answer": 3408
},
{
"... | 1 | [
{
"lemma": "C5",
"status": "ok"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
733d0d | alg_telescope_v1_601307018_1660 | Find the remainder when $\sum_{k=0}^{178} (4k^3 + 6k^2 + 4k + 1)$ is divided by $\left|\{ (a, b) \mid 1 \le a, b \le 40,\ 41a^2 + 20b^2 - 12ab \le 61001 \}\right|$. | 1,054 | graphs = [
Graph(
let={
"_n": Const(6),
"result": Mod(value=Summation(var="k", start=Const(0), end=Const(178), expr=Sum(Mul(Const(4), Pow(Var("k"), Const(3))), Mul(Ref("_n"), Pow(Var("k"), Const(2))), Mul(Const(4), Var("k")), Const(1))), modulus=CountOverSet(set=SolutionsSet(var=Tupl... | ALG | null | COMPUTE | sympy | QF_PSD_COUNT_LEQ | [
"QF_PSD_COUNT_LEQ"
] | 009d0f | alg_telescope_v1 | null | 5 | 0 | [
"QF_PSD_COUNT_LEQ"
] | 1 | 0.026 | 2026-03-10T02:24:20.055586Z | {
"verified": true,
"answer": 1054,
"timestamp": "2026-03-10T02:24:20.081708Z"
} | d76f24 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 193,
"completion_tokens": 17137
},
"timestamp": "2026-03-29T03:04:12.212Z",
"answer": 1054
},
{
"... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
}
] | {
"lo": 2.78,
"mid": 4.94,
"hi": 7.11
} | ||
c5f486 | comb_count_partitions_v1_397696148_546 | Let $S$ be the set of all positive integers $p$ such that there exists a positive integer $q$ satisfying $p < q$, $\gcd(p, q) = 1$, and $pq = 54$. Let $n$ be the largest integer $k$ for which $|S|^k \leq 7387234676528$. Compute the number of integer partitions of $n$. | 53,174 | graphs = [
Graph(
let={
"_n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=54)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(value=1)), ... | NT | COMB | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/MAX_VAL"
] | aa93c6 | comb_count_partitions_v1 | null | 5 | 0 | [
"COPRIME_PAIRS",
"MAX_VAL"
] | 2 | 0.002 | 2026-02-08T11:33:39.281493Z | {
"verified": true,
"answer": 53174,
"timestamp": "2026-02-08T11:33:39.283722Z"
} | 26096d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 132,
"completion_tokens": 1510
},
"timestamp": "2026-02-14T16:24:55.813Z",
"answer": 53174
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
6d4650 | antilemma_cartesian_v1_865884756_6452 | Let $n = 16928$. Define $c$ to be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = n$. Let $x$ be the number of ordered pairs $(a,b)$ where $a$ is an integer from $1$ to $44$ and $b$ is an integer from $1$ to $50$. Compute $c - x$. | 6,264 | graphs = [
Graph(
let={
"_n": Const(16928),
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(44)), right=IntegerRange(start=Const(1), end=Const(50)))),
"_c": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condit... | COMB | GEOM | COMPUTE | sympy | COMB1 | [
"COMB1",
"COUNT_CARTESIAN"
] | 20f64e | antilemma_cartesian_v1 | negation_mod | 3 | 0 | [
"COMB1",
"COUNT_CARTESIAN"
] | 2 | 0.002 | 2026-02-08T19:12:21.672726Z | {
"verified": true,
"answer": 6264,
"timestamp": "2026-02-08T19:12:21.674422Z"
} | 07311d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 142,
"completion_tokens": 789
},
"timestamp": "2026-02-25T01:00:51.862Z",
"answer": 6264
},
{
... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7... | {
"lo": -8.48,
"mid": -5.37,
"hi": -3.03
} | ||
aa3a2b | geo_visible_lattice_v1_1218484723_3833 | Let $n = \sum_{k=0}^{2} 10^{k}$. Find the number of lattice points $(x,y)$ with $1 \leq x, y \leq n$ such that $\gcd(x,y) = 1$. | 7,575 | graphs = [
Graph(
let={
"_n": Const(2),
"n": Summation(var="k", start=Sub(Const(74), Const(74)), end=Ref("_n"), expr=Pow(Const(10), Var("k"))),
"result": VisibleLatticePoints(n=Ref(name='n')),
},
goal=Ref("result"),
)
] | GEOM | GEOM | COUNT | sympy | IDENTITY_SUB_SELF | [
"IDENTITY_SUB_SELF",
"SUM_GEOM"
] | 4c13b7 | geo_visible_lattice_v1 | null | 3 | 0 | [
"IDENTITY_SUB_SELF",
"SUM_GEOM"
] | 2 | 0.26 | 2026-02-25T05:28:37.574014Z | {
"verified": true,
"answer": 7575,
"timestamp": "2026-02-25T05:28:37.833902Z"
} | eac5ef | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 165,
"completion_tokens": 10762
},
"timestamp": "2026-03-29T12:30:44.427Z",
"answer": 7575
},
{
"... | 1 | [
{
"lemma": "IDENTITY_SUB_SELF",
"status": "ok"
},
{
"lemma": "SUM_GEOM",
"status": "ok"
}
] | {
"lo": -2.45,
"mid": 1.37,
"hi": 5.29
} | ||
6070ca | diophantine_sum_product_min_v1_798873815_284 | Let $S = 105$ and $P = 2054$. Find the smallest positive integer $x$ such that $1 \leq x \leq 104$ and
$$
x(S - x) = P.
$$ | 26 | graphs = [
Graph(
let={
"S": Const(105),
"P": Const(2054),
"result": MinOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), Const(1)), Leq(Var("x"), Const(104)), Eq(Mul(Var("x"), Sub(Ref("S"), Var("x"))), Ref("P"))))),
},
goal=Ref("result"),... | NT | null | EXTREMUM | sympy | MIN_PRIME_FACTOR | [
"SUM_DIVISIBLE"
] | 02dbe3 | diophantine_sum_product_min_v1 | null | 3 | 0 | [
"MIN_PRIME_FACTOR",
"SUM_DIVISIBLE"
] | 2 | 0.078 | 2026-02-08T02:32:17.073558Z | {
"verified": true,
"answer": 26,
"timestamp": "2026-02-08T02:32:17.151086Z"
} | 881b6e | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 164,
"completion_tokens": 408
},
"timestamp": "2026-02-08T19:19:53.998Z",
"answer": 26
},
{
"id":... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "SUM_DIVISIBLE",
"status": "ok"
},
{
"lemma": "V7",
"status": "n... | {
"lo": -7.1,
"mid": -5.34,
"hi": -3.62
} | ||
31c55b | sequence_count_fib_divisible_v1_458359167_2048 | Let $N = 59164$. Let $u$ be the number of positive integers $n$ such that $1 \leq n \leq 943$ and $\gcd(n, 6) = 1$. Let $d = 13$. Compute the number of positive integers $n$ such that $1 \leq n \leq u$ and $d$ divides the $n$-th Fibonacci number. Let this count be $c$. Find the remainder when $84589 \cdot c$ is divided... | 20,009 | graphs = [
Graph(
let={
"_n": Const(59164),
"upper": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(943)), Eq(GCD(a=Var("n"), b=Const(6)), Const(1))))),
"d": Const(13),
"result": CountOverSet(set=Solution... | NT | null | COUNT | sympy | C4 | [
"C4"
] | 08d162 | sequence_count_fib_divisible_v1 | null | 5 | 0 | [
"C4"
] | 1 | 0.016 | 2026-02-08T05:00:20.047957Z | {
"verified": true,
"answer": 20009,
"timestamp": "2026-02-08T05:00:20.063900Z"
} | 811b2d | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 226,
"completion_tokens": 2161
},
"timestamp": "2026-02-11T22:53:57.254Z",
"answer": 20009
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -3.49,
"mid": 1.84,
"hi": 7.55
} | ||
b78f4e | comb_count_derangements_v1_1520064083_7577 | Let $n$ be the number of positive integers $t$ with $15 \leq t \leq 42$ for which there exist positive integers $a$ and $b$ such that $1 \leq a \leq 4$, $1 \leq b \leq 2$, and $t = 6a + 9b$. Compute the number of derangements of $n$ elements, denoted $!n$. | 14,833 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=4)), Geq(left=Var(name='b'), right=Const(value=1... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_count_derangements_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T09:10:22.674486Z | {
"verified": true,
"answer": 14833,
"timestamp": "2026-02-08T09:10:22.676971Z"
} | 26a4ce | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 205,
"completion_tokens": 1238
},
"timestamp": "2026-02-24T10:44:35.396Z",
"answer": 14833
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8_SUM",
"st... | {
"lo": -4.92,
"mid": -2.91,
"hi": -0.68
} | ||
fdb24a | antilemma_k2_v1_2051736721_2812 | Let $n = 359$. Compute the value of
$$
\sum_{k=1}^{359} \phi(k) \left\lfloor \frac{\sum_{d \mid n} \phi(d)}{k} \right\rfloor.
$$ | 64,620 | graphs = [
Graph(
let={
"_n": Const(359),
"x": Summation(var="k", start=Const(1), end=Const(359), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))), Var("k"))))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3/K2",
"K2"
] | c7f244 | antilemma_k2_v1 | null | 5 | 0 | [
"K2",
"K3"
] | 2 | 0.001 | 2026-02-08T16:55:18.637807Z | {
"verified": true,
"answer": 64620,
"timestamp": "2026-02-08T16:55:18.638759Z"
} | aa2bfc | 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": 874
},
"timestamp": "2026-02-17T14:53:02.314Z",
"answer": 64620
},
{
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma":... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
820eef | sequence_lucas_compute_v1_48377204_1904 | Let $n = 23$. Compute the value of $L_n$, the $n$th Lucas number. Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $x + y = \sum_{d \mid 14} \phi(d)$. Let $M$ be the maximum value of $xy$ over all pairs $(x,y) \in S$. Find the remainder when $M - L_n$ is divided by $78676$. | 14,646 | graphs = [
Graph(
let={
"_n": Const(78676),
"n": Const(23),
"result": Lucas(arg=Ref(name='n')),
"Q": Mod(value=Sub(MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=... | NT | null | COMPUTE | sympy | K3 | [
"K3/B1"
] | fd7b28 | sequence_lucas_compute_v1 | negation_mod | 5 | 0 | [
"B1",
"K3"
] | 2 | 0.004 | 2026-02-08T16:29:04.078315Z | {
"verified": true,
"answer": 14646,
"timestamp": "2026-02-08T16:29:04.082734Z"
} | 9fe1ee | 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": 859
},
"timestamp": "2026-02-17T04:38:12.139Z",
"answer": 14646
},
{... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
9ca4a5 | comb_factorial_compute_v1_124444284_3757 | Let $n$ be the number of nonnegative integers $j$ with $0 \leq j \leq 65728$ such that $\binom{65728}{j}$ is odd. Compute $n!$. | 40,320 | graphs = [
Graph(
let={
"_n": Const(65728),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(65728)), Eq(Mod(value=Binom(n=Ref("_n"), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')),
"r... | ALG | COMB | COMPUTE | sympy | V8 | [
"V8"
] | 86348e | comb_factorial_compute_v1 | null | 7 | 0 | [
"V8"
] | 1 | 0.001 | 2026-02-08T05:35:16.292291Z | {
"verified": true,
"answer": 40320,
"timestamp": "2026-02-08T05:35:16.293250Z"
} | 1b0457 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 157,
"completion_tokens": 1114
},
"timestamp": "2026-02-24T04:04:57.634Z",
"answer": 40320
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
},
{
"lemma": "VAL_SUM_EQ",
"sta... | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
e0ddce | nt_lcm_compute_v1_124444284_3794 | Compute the least common multiple of $522$ and $1122$. | 97,614 | graphs = [
Graph(
let={
"a": Const(522),
"b": Const(1122),
"result": LCM(a=Ref("a"), b=Ref("b")),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | VIETA_SUM | [
"MIN_PRIME_FACTOR"
] | bc3776 | nt_lcm_compute_v1 | null | 2 | 0 | [
"MIN_PRIME_FACTOR",
"VIETA_SUM"
] | 2 | 0.008 | 2026-02-08T05:37:08.019176Z | {
"verified": true,
"answer": 97614,
"timestamp": "2026-02-08T05:37:08.026905Z"
} | 387418 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 61,
"completion_tokens": 865
},
"timestamp": "2026-02-12T11:22:34.017Z",
"answer": 97614
},
{
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
5326aa | modular_mod_compute_v1_1520064083_431 | Let $a = -53824$. Let $m$ be the minimum value of $x + y$ over all ordered pairs of positive integers $(x, y)$ such that $x \cdot y = 262144$. Find the remainder when $a$ is divided by $m$. | 448 | graphs = [
Graph(
let={
"a": Const(-53824),
"m": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(262144)))), expr=Sum(Var("x"), Var("y"))... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | modular_mod_compute_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.001 | 2026-02-08T03:21:28.672815Z | {
"verified": true,
"answer": 448,
"timestamp": "2026-02-08T03:21:28.674137Z"
} | 00b1f7 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 170,
"completion_tokens": 815
},
"timestamp": "2026-02-10T14:23:26.128Z",
"answer": 448
},
{
"id"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
}
] | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
f3502e | comb_binomial_compute_v1_1218484723_773 | Let $M = \binom{15}{7}$. Find the remainder when $\left|\{ j : j \geq 1, j \leq 7885, j^2 \leq 62173225 \}\right| \cdot M$ is divided by $63698$. | 36,367 | graphs = [
Graph(
let={
"_n": Const(7885),
"n": Const(15),
"k": Const(7),
"result": Binom(n=Ref("n"), k=Ref("k")),
"Q": Mod(value=Mul(CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(1)), Leq(Var("j"), Ref("_n")), Leq(P... | COMB | null | COMPUTE | sympy | C3 | [
"C3"
] | 887000 | comb_binomial_compute_v1 | affine_mod | 3 | 0 | [
"C3"
] | 1 | 0.002 | 2026-02-25T02:30:46.236280Z | {
"verified": true,
"answer": 36367,
"timestamp": "2026-02-25T02:30:46.238216Z"
} | 79d7df | 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": 1964
},
"timestamp": "2026-03-10T01:31:59.820Z",
"answer": 36367
},
{
"... | 1 | [
{
"lemma": "C3",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V8",
... | {
"lo": -0.93,
"mid": 2.04,
"hi": 4.6
} | ||
b3d0b1 | algebra_poly_eval_v1_1742523217_2533 | Let $m = 12$. Compute $4m^4 + 3m^3 - 5m^2 + 4m + 7$. | 87,463 | graphs = [
Graph(
let={
"m": Const(12),
"result": Sum(Mul(Const(4), Pow(Ref("m"), Const(4))), Mul(Const(3), Pow(Ref("m"), Const(3))), Mul(Const(-5), Pow(Ref("m"), Const(2))), Mul(Const(4), Ref("m")), Const(7)),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/V1",
"LTE_DIFF/V1"
] | 6fe4fb | algebra_poly_eval_v1 | null | 2 | 0 | [
"LTE_DIFF",
"MIN_PRIME_FACTOR",
"V1"
] | 3 | 0.011 | 2026-02-08T04:50:06.000393Z | {
"verified": true,
"answer": 87463,
"timestamp": "2026-02-08T04:50:06.011893Z"
} | 94e0b4 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 89,
"completion_tokens": 338
},
"timestamp": "2026-02-11T21:53:11.161Z",
"answer": 87463
},
{
"id": 11,
... | 2 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "... | {
"lo": -9.14,
"mid": -6.05,
"hi": -3.73
} | ||
fead20 | nt_num_divisors_compute_v1_784195855_1082 | Let $n$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 3360$. Define $Q$ to be the remainder when the number of positive divisors of $n$ is divided by $99234$. Find the value of $Q$. | 40 | graphs = [
Graph(
let={
"_n": Const(3360),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2")), ... | NT | null | COMPUTE | sympy | COMB1 | [
"COMB1"
] | 567f58 | nt_num_divisors_compute_v1 | null | 4 | 0 | [
"COMB1"
] | 1 | 0.004 | 2026-02-08T04:50:29.927904Z | {
"verified": true,
"answer": 40,
"timestamp": "2026-02-08T04:50:29.931953Z"
} | 198e03 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 181,
"completion_tokens": 711
},
"timestamp": "2026-02-11T22:15:09.992Z",
"answer": 40
},
{
"id"... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.33
} | ||
3830e7 | comb_sum_binomial_row_v1_1742523217_3108 | Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 216$, $\gcd(p, q) = 1$, and $p < q$.
Let $N$ be the number of elements in $S$. Compute $N^{12}$. | 4,096 | graphs = [
Graph(
let={
"n": Const(12),
"result": Pow(CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=216)), Eq(left=GCD(a=Var(name='p'), b=Va... | NT | null | SUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_sum_binomial_row_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.001 | 2026-02-08T05:39:32.145721Z | {
"verified": true,
"answer": 4096,
"timestamp": "2026-02-08T05:39:32.147057Z"
} | 1efed1 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 114,
"completion_tokens": 863
},
"timestamp": "2026-02-12T12:25:57.378Z",
"answer": 4096
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V5",
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
98434e | alg_poly3_sum_v1_601307018_6012 | Find the remainder when $$\sum_{\substack{1 \le a \le 36\\1 \le b \le \sum_{k=1}^{8} k\\1 \le c \le \min\{ x + y \mid x>0, y>0, xy=324, x \le y \}}} \left( -150 a^2 b + \min\{ |x_1 - y_1| \mid x_1>0, y_1>0, x_1 y_1 = 12166 \} \cdot a^2 c -125 a^3 -60a b^2 -124 c^3 -363 b^2 c -8 b^3 -381b c^2 + 60a b c -15a c^2 \right)$... | 71,463 | graphs = [
Graph(
let={
"_c": Const(8),
"_m": Const(2),
"_n": Const(3),
"result": Mod(value=SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b"), Var("c")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(36)), Geq(Var(... | ALG | null | COMPUTE | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC",
"B3_DIFF",
"B3"
] | d678b6 | alg_poly3_sum_v1 | null | 7 | 0 | [
"B3",
"B3_DIFF",
"SUM_ARITHMETIC"
] | 3 | 0.965 | 2026-03-10T06:36:35.065287Z | {
"verified": true,
"answer": 71463,
"timestamp": "2026-03-10T06:36:36.030229Z"
} | d953f7 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 293,
"completion_tokens": 8429
},
"timestamp": "2026-04-19T03:22:29.017Z",
"answer": 71463
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "B3_DIFF",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
}
] | {
"lo": 2.1,
"mid": 5.36,
"hi": 8.63
} | ||
910ab3 | modular_inverse_v1_1742523217_4736 | Let $m$ be the number of positive integers $n$ not exceeding $6196$ such that $n$ is divisible by $4$ and $\gcd(n, 15) = 1$. Let $r$ be the smallest positive integer $x$ not exceeding $826$ such that $592x \equiv 1 \pmod{m}$. Compute the remainder when $53746 \cdot r$ is divided by $77023$. | 29,097 | graphs = [
Graph(
let={
"_n": Const(15),
"a": Const(592),
"m": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(6196)), Divides(divisor=Const(4), dividend=Var("n")), Eq(GCD(a=Var("n"), b=Ref("_n")), Const(1))))),
... | NT | null | EXTREMUM | sympy | C5 | [
"C5"
] | 1d9668 | modular_inverse_v1 | null | 6 | 0 | [
"C5"
] | 1 | 0.035 | 2026-02-08T09:06:16.442649Z | {
"verified": true,
"answer": 29097,
"timestamp": "2026-02-08T09:06:16.477434Z"
} | 25e8cb | 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": 2146
},
"timestamp": "2026-02-14T00:22:33.372Z",
"answer": 29097
},
... | 1 | [
{
"lemma": "C5",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
948d0a | comb_count_permutations_fixed_v1_458359167_1242 | Let $n = 7$ and $m = 2$. Define $k$ as
$$
k = \sum_{i=1}^{m} i.
$$
Let $Q = \binom{n}{k} \cdot !{(n - k)}$, where $!r$ denotes the number of derangements of $r$ elements. Compute the remainder when $44121 \cdot Q$ is divided by $87487$. | 75,169 | graphs = [
Graph(
let={
"_n": Const(2),
"n": Const(7),
"k": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Var("k")),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub(left=Ref(name='n'), right=Ref(name='k')))),
"Q": Mod(val... | COMB | null | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | comb_count_permutations_fixed_v1 | null | 3 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.001 | 2026-02-08T04:30:45.782607Z | {
"verified": true,
"answer": 75169,
"timestamp": "2026-02-08T04:30:45.783805Z"
} | 9b3605 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 206,
"completion_tokens": 1546
},
"timestamp": "2026-02-24T00:50:33.840Z",
"answer": 75169
},
{
"... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"... | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
0d928a | algebra_poly_eval_v1_784195855_3441 | Let $b = 19$. Define $$ r = b^{\sum_{k=1}^{2} \phi(k) \left\lfloor \frac{2}{k} \right\rfloor} - b^2 - 10b - 10. $$ Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x y = 1827904$. Let $m$ be the minimum value of $x + y$ over all $(x, y) \in S$. Compute the remainder when $r^2 + 4r + m$ i... | 20,386 | graphs = [
Graph(
let={
"_m": Const(58861),
"_n": Const(2),
"b": Const(19),
"result": Sum(Pow(Ref("b"), Summation(var="k", start=Const(1), end=Const(2), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(2), Var("k")))))), Mul(Const(-1), Pow(Ref("b"), Ref("_n"))),... | NT | null | COMPUTE | sympy | B3 | [
"B3",
"K2"
] | 37bca4 | algebra_poly_eval_v1 | quadratic_mod | 5 | 0 | [
"B3",
"K2"
] | 2 | 0.003 | 2026-02-08T06:26:00.491939Z | {
"verified": true,
"answer": 20386,
"timestamp": "2026-02-08T06:26:00.494900Z"
} | ba0a45 | 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": 1741
},
"timestamp": "2026-02-13T00:02:30.963Z",
"answer": 20386
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
472dd6 | nt_count_divisors_in_range_v1_1742523217_128 | Let $n = 20160$. Let $k_0$ be the smallest positive integer $n$ such that $3^{40}$ divides $n!$. Define $b$ to be the number of positive integers $k$ with $1 \leq k \leq 47385$ that are divisible by $k_0$. Define $a = 1$. Let $S$ be the set of all positive divisors $d$ of $n$ such that $a \leq d \leq b$. Compute the va... | 1,228 | graphs = [
Graph(
let={
"n": Const(20160),
"a": Const(1),
"b": CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(1)), Leq(Var("k"), Const(47385)), Divides(divisor=MinOverSet(set=SolutionsSet(var=Var("n"), condition=Geq(MaxKDivides(target=Factor... | NT | null | COUNT | sympy | V5 | [
"V5/C2"
] | 0b0b64 | nt_count_divisors_in_range_v1 | null | 7 | 0 | [
"C2",
"V5"
] | 2 | 0.01 | 2026-02-08T02:53:17.851090Z | {
"verified": true,
"answer": 1228,
"timestamp": "2026-02-08T02:53:17.861548Z"
} | 65f5dd | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 256,
"completion_tokens": 4470
},
"timestamp": "2026-02-09T13:57:38.477Z",
"answer": 1228
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "ok_later"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V5",
"status": "ok"
},
{
... | {
"lo": -6.51,
"mid": -0.31,
"hi": 5.43
} | ||
663122 | alg_sum_powers_v1_601307018_5755 | Let $M$ be the largest prime number $n$ such that $2 \le n \le 4$. Let $R = \sum_{k=1}^{1716} k^M \bmod d$, where $d$ is the largest positive divisor of $72232997$ such that $d^2 \le 72232997$. Compute $|R|$. | 7,649 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_m")), Leq(Var("n"), Const(4)), IsPrime(Var("n"))))),
"result": Mod(value=Summation(var="k", start=Const(1), end=Const(1716), expr=Pow(Var("k"), Ref("_... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW/B3_CLOSEST"
] | 271776 | alg_sum_powers_v1 | null | 4 | 0 | [
"B3_CLOSEST",
"MAX_PRIME_BELOW"
] | 2 | 0.073 | 2026-03-10T06:19:01.840873Z | {
"verified": true,
"answer": 7649,
"timestamp": "2026-03-10T06:19:01.914009Z"
} | 7866fb | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 190,
"completion_tokens": 21420
},
"timestamp": "2026-04-19T02:52:21.377Z",
"answer": 22
},
{
... | 0 | [
{
"lemma": "B3_CLOSEST",
"status": "ok_later"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
... | {
"lo": 2.1,
"mid": 5.36,
"hi": 8.63
} | ||
847677 | geo_count_lattice_triangle_v1_48377204_2961 | Let $A$ be twice the area of the triangle with vertices at $(0,0)$, $(100,128)$, and $(100,256)$. Let $B$ be the number of lattice points on the boundary of this triangle, including the vertices. These are computed as follows:
- $A = |100 \cdot 128 + 100 \cdot (0 - 256)| = |12800 - 25600| = 12800$,
- $B = \gcd(100, 25... | 35,047 | graphs = [
Graph(
let={
"area_2x": Abs(arg=Sum(Mul(Const(value=100), Const(value=128)), Mul(Const(value=100), Sub(left=Const(value=0), right=Const(value=256))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=100)), b=Abs(arg=Const(value=256))), GCD(a=Abs(arg=Sub(left=Const(value=100), r... | ALG | NT | COUNT | sympy | [] | geo_count_lattice_triangle_v1 | null | 4 | 0 | null | null | 0.004 | 2026-02-08T17:05:55.654927Z | {
"verified": true,
"answer": 35047,
"timestamp": "2026-02-08T17:05:55.658494Z"
} | f09cf3 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 290,
"completion_tokens": 2727
},
"timestamp": "2026-02-17T18:54:52.695Z",
"answer": 35047
},
... | 1 | [] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||||
3325ae | algebra_poly_eval_v1_397696148_698 | Let $m = 7$ and $n = 8$. Define $S$ as the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 216$, $\gcd(p, q) = 1$, and $p < q$. Compute $$ m \cdot n^4 + 8 \cdot n^3 + 5 \cdot n^{|S|} - 6n + \sum_{k=1}^{2} k. $$ | 33,043 | graphs = [
Graph(
let={
"_m": Const(7),
"_n": Const(3),
"n": Const(8),
"result": Sum(Mul(Ref("_m"), Pow(Ref("n"), Const(4))), Mul(Const(8), Pow(Ref("n"), Ref("_n"))), Mul(Const(5), Pow(Ref("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPosit... | NT | null | COMPUTE | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC",
"COPRIME_PAIRS"
] | ac053f | algebra_poly_eval_v1 | null | 6 | 0 | [
"COPRIME_PAIRS",
"SUM_ARITHMETIC"
] | 2 | 0.009 | 2026-02-08T11:42:24.163956Z | {
"verified": true,
"answer": 33043,
"timestamp": "2026-02-08T11:42:24.172592Z"
} | 2c9693 | 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": 1124
},
"timestamp": "2026-02-14T17:21:17.070Z",
"answer": 33043
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V5",
"status": "n... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
ecdbca | geo_visible_lattice_v1_238844314_629 | Let $n = 50$. Define $S$ to be the set of all ordered pairs $(x, y)$ of positive integers such that $1 \leq x, y \leq n$ and $\gcd(x, y) = 1$. Let $r$ be the number of elements in $S$. Compute $3721 - r$. | 2,174 | graphs = [
Graph(
let={
"n": Const(50),
"result": VisibleLatticePoints(n=Ref(name='n')),
"Q": Sub(Const(3721), Ref("result")),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 5 | 0 | null | null | 2.947 | 2026-02-08T13:27:25.143524Z | {
"verified": true,
"answer": 2174,
"timestamp": "2026-02-08T13:27:28.090895Z"
} | d8387b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 184,
"completion_tokens": 3776
},
"timestamp": "2026-02-24T18:15:05.272Z",
"answer": 2174
},
{
"i... | 1 | [] | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||||
55bb24_l | comb_count_permutations_fixed_v1_151522320_26 | Let $n$ be the smallest divisor of $20449$ that is at least $2$. Compute $\binom{n}{6} \cdot !(n - 6)$, where $!k$ denotes the number of derangements of $k$ elements. Then compute the sum of $\phi(k)$ for $k$ from $1$ to the absolute value of this result, and find the remainder when this sum is divided by $59245$. | 0 | NT | COMB | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | comb_count_permutations_fixed_v1 | null | 7 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 1.09 | 2026-02-08T02:55:37.939351Z | {
"verified": false,
"answer": 9864,
"timestamp": "2026-02-08T02:55:39.029257Z"
} | a8f95f | 55bb24 | legacy_text | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 205,
"completion_tokens": 32768
},
"timestamp": "2026-02-23T20:02:09.026Z",
"answer": null
},
{
... | 0 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": 4.63,
"mid": 6.54,
"hi": 9.53
} | |
5d8c72 | modular_mod_compute_v1_124444284_6316 | Let $a$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 8450$. Compute the remainder when $a$ is divided by $54756$. | 4,225 | graphs = [
Graph(
let={
"a": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2")), Const(8450))))),
"m... | NT | null | COMPUTE | sympy | COMB1 | [
"COMB1"
] | 567f58 | modular_mod_compute_v1 | null | 3 | 0 | [
"COMB1"
] | 1 | 0.001 | 2026-02-08T08:17:15.902204Z | {
"verified": true,
"answer": 4225,
"timestamp": "2026-02-08T08:17:15.903045Z"
} | 9599f4 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 113,
"completion_tokens": 421
},
"timestamp": "2026-02-15T19:46:56.632Z",
"answer": 4223
},
{
"id": 11,... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
5fc9f6 | comb_count_derangements_v1_1978505735_1287 | Let $S$ be the set of all positive integers $p$ for which there exists an integer $q$ such that $p q = 10290$, $\gcd(p, q) = 1$, and $p < q$. Let $n$ be the number of elements in $S$. Let $r = !n$ denote the subfactorial of $n$. Compute the remainder when $75916 \cdot r$ is divided by 55409. | 40,330 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=10290)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(value=1))... | NT | COMB | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_count_derangements_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.002 | 2026-02-08T16:00:19.068969Z | {
"verified": true,
"answer": 40330,
"timestamp": "2026-02-08T16:00:19.071406Z"
} | 82d878 | 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": 2870
},
"timestamp": "2026-02-16T18:07:52.621Z",
"answer": 40330
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
4a7792 | antilemma_sum_factor_cartesian_v1_1248542787_475 | Let $S$ be the set of all ordered pairs $(i,j)$ of positive integers with $1 \leq i \leq 25$ and $1 \leq j \leq 7$. For each such pair, compute $i \cdot j$. Let $x$ be the sum of all these products. Find the value of $x$. | 9,100 | graphs = [
Graph(
let={
"x": SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=EulerPhi(n=Const(2)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(25)), right=IntegerRange(start=Const(1), end=Const(7)))), expr=Mul(Var("i"), Var("... | NT | null | COMPUTE | sympy | SUM_FACTOR_CARTESIAN | [
"SUM_FACTOR_CARTESIAN",
"ONE_PHI_2"
] | 09bd3b | antilemma_sum_factor_cartesian_v1 | null | 3 | 0 | [
"ONE_PHI_2",
"SUM_FACTOR_CARTESIAN"
] | 2 | 0.001 | 2026-02-08T03:10:09.233559Z | {
"verified": true,
"answer": 9100,
"timestamp": "2026-02-08T03:10:09.234537Z"
} | d3c6ed | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 190,
"completion_tokens": 339
},
"timestamp": "2026-02-09T04:31:59.585Z",
"answer": 9100
},
{
"id... | 2 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "ONE_PHI_2",
"status": "ok"
},
{
"lemma": "SUM_FACTOR_CARTESIAN",
"status": "ok"
},
{
"lemma": "V1",
"status"... | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
75e995 | geo_count_lattice_rect_v1_784195855_2221 | Let $ a = 25 $ and $ b = 37 $. Compute the number of lattice points $ (x, y) $ contained in the rectangle defined by $ 0 \leq x \leq a $ and $ 0 \leq y \leq b $, including the boundary.
Find the value of this number. | 988 | graphs = [
Graph(
let={
"a": Const(25),
"b": Const(37),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 2 | 0 | null | null | 0.002 | 2026-02-08T05:37:00.347814Z | {
"verified": true,
"answer": 988,
"timestamp": "2026-02-08T05:37:00.350087Z"
} | e3ae5e | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 179,
"completion_tokens": 251
},
"timestamp": "2026-02-24T03:57:49.332Z",
"answer": 988
},
{
"id"... | 2 | [] | {
"lo": -9.23,
"mid": -6.18,
"hi": -4.06
} | ||||
0a30e8 | comb_sum_binomial_mod_v1_601307018_3051 | Let $A = \left|\{ (a, b) : a, b \in \mathbb{Z}^+,\ 1 \le a, b \le 40,\ 41a^2 + 20b^2 - 12ab \le 7684 \}\right|$. Compute the remainder when $\sum_{k=13}^{210} \binom{A}{k}$ is divided by $11437$. | 10,825 | graphs = [
Graph(
let={
"_n": Const(20),
"sum": Summation(var="k", start=Const(13), end=Const(210), expr=Binom(n=CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(40)), Geq(Var("b"), Const(1)), Leq(Var("... | COMB | null | COMPUTE | sympy | QF_PSD_COUNT_LEQ | [
"QF_PSD_COUNT_LEQ"
] | 009d0f | comb_sum_binomial_mod_v1 | null | 6 | 0 | [
"QF_PSD_COUNT_LEQ"
] | 1 | 0.018 | 2026-03-10T03:39:21.142824Z | {
"verified": true,
"answer": 10825,
"timestamp": "2026-03-10T03:39:21.161136Z"
} | 2c922d | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 203,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T07:21:21.274Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
},
{
"lemma": "V8",
... | {
"lo": 3.34,
"mid": 5.77,
"hi": 8.89
} | ||
564d48 | nt_max_prime_below_v1_1978505735_1092 | Let $S$ be the set of all positive integers $p$ such that there exists a positive integer $q$ with $p < q$, $pq = 72$, and $\gcd(p, q) = 1$. Let $k$ be the number of elements in $S$. Determine the largest prime number $n$ such that $k \leq n \leq 73984$. | 73,973 | graphs = [
Graph(
let={
"upper": Const(73984),
"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 | 3 | 0 | [
"COPRIME_PAIRS"
] | 1 | 2.259 | 2026-02-08T15:49:25.801773Z | {
"verified": true,
"answer": 73973,
"timestamp": "2026-02-08T15:49:28.060841Z"
} | 860f5a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 128,
"completion_tokens": 4353
},
"timestamp": "2026-02-16T14:44:58.746Z",
"answer": 73973
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
e6fd45 | antilemma_k3_v1_655260480_3575 | Let $n = 74980$ and $m = 2$. Define $x = \sum_{d \mid n} \phi(d)$, where the sum is over all positive divisors $d$ of $n$ and $\phi$ denotes Euler's totient function. Let $r$ be the sum of the solutions to the quadratic equation $t^2 - 840t + 39500 = 0$. Compute the remainder when $x^m + 19x + r$ is divided by $88046$. | 15,886 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(74980),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Mod(value=Sum(Pow(Ref("x"), Ref("_m")), Mul(Const(19), Ref("x")), SumOverSet(set=SolutionsSet(var=Var("x1"), condi... | NT | COMB | COMPUTE | sympy | VIETA_SUM | [
"VIETA_SUM",
"K3"
] | 74525f | antilemma_k3_v1 | quadratic_mod | 4 | 0 | [
"K3",
"VIETA_SUM"
] | 2 | 0.001 | 2026-02-08T17:27:11.263695Z | {
"verified": true,
"answer": 15886,
"timestamp": "2026-02-08T17:27:11.265029Z"
} | 2b7506 | 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": 2739
},
"timestamp": "2026-02-18T02:30:01.118Z",
"answer": 15886
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
e29aec | comb_binomial_compute_v1_168721529_8 | Let $n$ be the sum of all integers $x$ such that
$$
x^2 - 12x - 5589 = \sum_{d \mid \gcd(45,5)} \mu(d),
$$
where $\mu$ denotes the M\"obius function. Let $k = 6$. Define $Q$ to be the remainder when $44121 \cdot \binom{n}{k}$ is divided by $65227$. Compute $Q$. | 929 | graphs = [
Graph(
let={
"_n": Const(44121),
"n": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Const(2)), Mul(Const(-12), Var("x")), Const(-5589)), SumOverDivisors(n=GCD(a=Const(value=45), b=Const(value=5)), var='d', expr=MoebiusMu(n=Var(name='d')))))),
... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MOBIUS_COPRIME",
"VIETA_SUM"
] | 7389ac | comb_binomial_compute_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW",
"MOBIUS_COPRIME",
"VIETA_SUM"
] | 3 | 0.013 | 2026-02-08T12:46:03.425326Z | {
"verified": true,
"answer": 929,
"timestamp": "2026-02-08T12:46:03.438650Z"
} | 5bd29c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 217,
"completion_tokens": 1598
},
"timestamp": "2026-02-08T20:53:24.900Z",
"answer": 929
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok"
},
{
"le... | {
"lo": -2.06,
"mid": 1.85,
"hi": 5.2
} | ||
e2d9d7 | modular_sum_quadratic_residues_v1_48377204_1979 | Let $S$ be the set of positive integers $n$ such that $1 \leq n \leq 88$ and $n$ is divisible by the number of ordered pairs $(i, j)$ where $1 \leq i \leq 8$ and $1 \leq j \leq 11$. Let $s$ be the sum of all elements in $S$. Let $p$ be the number of positive integers $k$ such that $1 \leq k \leq 57464$ and $s$ divides ... | 64,703 | graphs = [
Graph(
let={
"_m": Const(4),
"_n": Const(86272),
"p": CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(1)), Leq(Var("k"), Const(57464)), Divides(divisor=SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1))... | NT | null | SUM | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN/SUM_DIVISIBLE/C2"
] | 76e1ff | modular_sum_quadratic_residues_v1 | null | 5 | 0 | [
"C2",
"COUNT_CARTESIAN",
"SUM_DIVISIBLE"
] | 3 | 0.006 | 2026-02-08T16:32:07.504959Z | {
"verified": true,
"answer": 64703,
"timestamp": "2026-02-08T16:32:07.511002Z"
} | 982076 | 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": 1468
},
"timestamp": "2026-02-17T06:22:07.042Z",
"answer": 64703
},
... | 1 | [
{
"lemma": "C2",
"status": "ok_later"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
140b69 | nt_count_with_divisor_count_v1_458359167_2549 | Compute the number of positive integers $n \leq 6765$ such that the number of positive divisors of $n$ is equal to $\sum_{d \mid 10} \phi(d)$, where $\phi$ denotes Euler's totient function. | 108 | graphs = [
Graph(
let={
"upper": Const(6765),
"div_count": SumOverDivisors(n=Const(value=10), var='d', expr=EulerPhi(n=Var(name='d'))),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(NumDivisors... | NT | null | COUNT | sympy | K3 | [
"K3"
] | 54c41e | nt_count_with_divisor_count_v1 | null | 4 | 0 | [
"K3"
] | 1 | 0.556 | 2026-02-08T06:19:39.718779Z | {
"verified": true,
"answer": 108,
"timestamp": "2026-02-08T06:19:40.275236Z"
} | 5d8ac0 | 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": 1663
},
"timestamp": "2026-02-12T22:48:36.509Z",
"answer": 108
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
b25ffa | antilemma_sum_equals_v1_1520064083_3617 | Let $n$ be the number of integers $t$ such that $27 \leq t \leq 150$ and there exist integers $a$ and $b$ with $1 \leq a \leq 4$, $1 \leq b \leq 11$, and $t = 21a + 6b$.
Let $x$ be the number of ordered pairs $(i, j)$ of positive integers such that $i \leq 34$, $j \leq 35$, and $i + j = n$.
Compute $$\sum_{k=1}^{|x|}... | 127 | graphs = [
Graph(
let={
"_n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=4)), Geq(left=Var(name='b'), right=Const(value=... | COMB | GEOM | COMPUTE | sympy | COMB1 | [
"LIN_FORM/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | ada383 | antilemma_sum_equals_v1 | null | 6 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 3 | 0.046 | 2026-02-08T05:46:51.132396Z | {
"verified": true,
"answer": 127,
"timestamp": "2026-02-08T05:46:51.178419Z"
} | 894605 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 264,
"completion_tokens": 3911
},
"timestamp": "2026-02-24T04:32:43.334Z",
"answer": 127
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"st... | {
"lo": -0.06,
"mid": 2.89,
"hi": 5.27
} | ||
f85c48 | diophantine_fbi2_min_v1_1742523217_1373 | Let $k = 120$. Find the smallest positive integer $d$ such that $6 \leq d \leq 130$, $d$ divides $k$, and $\frac{k}{d} \geq 7$. | 6 | graphs = [
Graph(
let={
"k": Const(120),
"a": Const(5),
"b": Const(6),
"upper": Const(130),
"result": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(6)), Leq(Var("d"), Ref("upper")), Divides(divisor=Var("d"), dividend=R... | NT | null | EXTREMUM | sympy | ONE_PHI_1 | [
"ONE_PHI_1"
] | f6b5a5 | diophantine_fbi2_min_v1 | null | 3 | 0 | [
"ONE_PHI_1"
] | 1 | 0.022 | 2026-02-08T03:41:58.244091Z | {
"verified": true,
"answer": 6,
"timestamp": "2026-02-08T03:41:58.266481Z"
} | cd3235 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 159,
"completion_tokens": 513
},
"timestamp": "2026-02-10T15:21:12.976Z",
"answer": 6
},
{
"id": ... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "ONE_PHI_1",
"status": "ok"
},
{
"lemma": "V1",
"status": "n... | {
"lo": -9.14,
"mid": -6.05,
"hi": -3.74
} | ||
fa75ea | nt_count_gcd_equals_v1_784195855_753 | Let $k$ be the largest prime number less than or equal to 102. Determine the number of positive integers $n$ not exceeding 16384 such that $\gcd(n, k) = 101$. Let $r$ be the remainder when that number is taken modulo 11. Compute the $r$-th Bell number. | 4,140 | graphs = [
Graph(
let={
"_n": Const(102),
"upper": Const(16384),
"k": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))),
"d": Const(101),
"result": CountOverSet(set=Solut... | NT | COMB | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | nt_count_gcd_equals_v1 | null | 6 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 1.291 | 2026-02-08T04:34:32.333078Z | {
"verified": true,
"answer": 4140,
"timestamp": "2026-02-08T04:34:33.624159Z"
} | 881f43 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 180,
"completion_tokens": 621
},
"timestamp": "2026-02-10T17:25:10.409Z",
"answer": 4140
},
{
"i... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.33
} | ||
ed08f9 | nt_count_divisible_v1_1918700295_2142 | Let $d$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 225$. Let $S$ be the set of all positive integers $n \leq 50176$ such that $d$ divides $n$. Let $r$ be the number of elements in $S$. Compute the remainder when $512 - r$ is divided by $82109$. | 80,949 | graphs = [
Graph(
let={
"_n": Const(512),
"upper": Const(50176),
"divisor": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(2... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | nt_count_divisible_v1 | null | 3 | 0 | [
"B3"
] | 1 | 2.207 | 2026-02-08T07:42:56.912695Z | {
"verified": true,
"answer": 80949,
"timestamp": "2026-02-08T07:42:59.119494Z"
} | 99ccaf | 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": 674
},
"timestamp": "2026-02-13T11:56:29.626Z",
"answer": 80949
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
57d44d | algebra_vieta_sum_v1_1978505735_1382 | Let $P(x)=x^{3}+3x^{2}-46x-168$. Let $S$ be the set of all integers $x$ such that $P(x)=0$. Let $N$ be the product of all elements of $S$. Compute $N$. | 168 | graphs = [
Graph(
let={
"result": ProductOverSet(set=SolutionsSet(var=Var(name='x'), condition=Eq(left=Sum(Pow(base=Var(name='x'), exp=Const(value=3)), Mul(Const(value=3), Pow(base=Var(name='x'), exp=Const(value=2))), Mul(Const(value=-46), Var(name='x')), Const(value=-168)), right=Const(value=0)... | NT | null | COMPUTE | sympy | BINOMIAL_ALTERNATING | [
"MIN_PRIME_FACTOR/K13/COPRIME_PAIRS",
"MAX_PRIME_BELOW/K13/COPRIME_PAIRS"
] | 919583 | algebra_vieta_sum_v1 | null | 3 | 0 | [
"BINOMIAL_ALTERNATING",
"COPRIME_PAIRS",
"K13",
"MAX_PRIME_BELOW",
"MIN_PRIME_FACTOR"
] | 5 | 0.173 | 2026-02-08T16:06:27.569286Z | {
"verified": true,
"answer": 168,
"timestamp": "2026-02-08T16:06:27.742775Z"
} | 785cda | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 105,
"completion_tokens": 885
},
"timestamp": "2026-02-16T20:57:32.432Z",
"answer": 168
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok_later"
},
{
"lemma": "K13",
"status": "ok_later"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MIN_PRIME_FACTOR",
"st... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
97c6e1 | comb_catalan_compute_v1_784195855_3032 | Let $n$ be the number of elements in the Cartesian product of the sets $\{1, 2\}$ and $\{1, 2, 3, 4, 5\}$. Compute the $n$-th Catalan number, denoted $C_n$. Let $m = 17809$. Find the remainder when $m \cdot C_n$ is divided by $86494$. | 23,712 | graphs = [
Graph(
let={
"_n": Const(17809),
"n": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(2)), right=IntegerRange(start=Const(1), end=Const(5)))),
"result": Catalan(Ref("n")),
"Q": Mod(value=Mul(Ref("_n"), Ref("result")), m... | COMB | null | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | comb_catalan_compute_v1 | null | 3 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.001 | 2026-02-08T06:11:46.104286Z | {
"verified": true,
"answer": 23712,
"timestamp": "2026-02-08T06:11:46.105422Z"
} | cd12ba | 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": 2859
},
"timestamp": "2026-02-24T05:35:33.908Z",
"answer": 23712
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
... | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
eb0990 | comb_count_derangements_v1_1456120455_64 | Let $m = 65560$. Let $p$ be a positive integer such that there exists a positive integer $q$ satisfying $pq = 216$, $\gcd(p, q) = 1$, and $p < q$. Let $n$ be the number of nonnegative integers $j$ with $0 \leq j \leq 65560$ such that $\binom{65560}{j} \equiv \varphi(2) \pmod{k}$, where $k$ is the number of such integer... | 76,523 | graphs = [
Graph(
let={
"_m": Const(65560),
"_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=216)), Eq(left=GCD(a=Var(name='p'), b=Var(na... | NT | COMB | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/V8",
"ONE_PHI_2"
] | fdd057 | comb_count_derangements_v1 | null | 7 | 0 | [
"COPRIME_PAIRS",
"ONE_PHI_2",
"V8"
] | 3 | 0.003 | 2026-02-08T02:52:29.057169Z | {
"verified": true,
"answer": 76523,
"timestamp": "2026-02-08T02:52:29.059687Z"
} | 7c18a7 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 273,
"completion_tokens": 3397
},
"timestamp": "2026-02-08T19:57:41.709Z",
"answer": 76523
},
{
"... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "ONE_PHI_2",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
},
{
"le... | {
"lo": -6.51,
"mid": -0.53,
"hi": 4.75
} | ||
b10160 | comb_count_surjections_v1_809748730_428 | Let $n = 4$ and $k = 2$. Define
$$
R = k! \cdot S(n, k),
$$
where $S(n, k)$ denotes the Stirling number of the second kind. Compute the value of
$$
R + \phi\left(|R| + \binom{16}{0}\right) + \tau\left(|R| + \binom{7}{0}\right),
$$
where $\phi$ denotes Euler's totient function and $\tau(m)$ denotes the number of positiv... | 26 | graphs = [
Graph(
let={
"n": Const(4),
"k": Const(2),
"result": Mul(Factorial(Ref("k")), Stirling2(n=Ref(name='n'), k=Ref(name='k'))),
"Q": Sum(Ref("result"), EulerPhi(n=Sum(Abs(arg=Ref(name='result')), Binom(n=Const(16), k=Const(0)))), NumDivisors(n=Sum(Abs(a... | COMB | NT | COUNT | sympy | ONE_BINOM_0 | [
"ONE_BINOM_0"
] | d74bad | comb_count_surjections_v1 | null | 4 | 0 | [
"ONE_BINOM_0"
] | 1 | 0.004 | 2026-02-08T11:30:52.068492Z | {
"verified": true,
"answer": 26,
"timestamp": "2026-02-08T11:30:52.072332Z"
} | 3695c7 | 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": 580
},
"timestamp": "2026-02-24T14:13:15.134Z",
"answer": 26
},
{
"id":... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "ONE_BINOM_0",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": ... | {
"lo": -5.97,
"mid": -3.97,
"hi": -1.93
} | ||
1ffd0d | algebra_quadratic_discriminant_v1_1248542787_791 | Let $a = 10$, $b = -9$, and $c = -7$. Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $p < q$, $pq = 216$, and $\gcd(p, q) = 1$. Compute the value of $27225 - \left(b^{|S|} - 4ac\right)$. | 26,864 | graphs = [
Graph(
let={
"_n": Const(27225),
"a": Const(10),
"b": Const(-9),
"c": Const(-7),
"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... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | algebra_quadratic_discriminant_v1 | null | 6 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.002 | 2026-02-08T03:25:20.052363Z | {
"verified": true,
"answer": 26864,
"timestamp": "2026-02-08T03:25:20.054683Z"
} | 5a09e9 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 207,
"completion_tokens": 878
},
"timestamp": "2026-02-09T08:19:34.837Z",
"answer": 26864
},
{
"i... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -3.46,
"mid": 0.96,
"hi": 5.17
} | ||
5e945d | nt_min_coprime_above_v1_124444284_413 | Let $S$ be the set of all integers $t$ with $13 \leq t \leq 501$ for which there exist positive integers $a$ and $b$, with $1 \leq a \leq 50$ and $1 \leq b \leq 79$, such that $t = 2a + 5b + 6$. Let $m$ be the number of elements in $S$. Find the smallest integer $n$ such that $51984 < n \leq 52479$ and $\gcd(n, m) = 1$... | 25,180 | graphs = [
Graph(
let={
"_n": Const(15066),
"start": Const(51984),
"upper": Const(52479),
"modulus": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_min_coprime_above_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.157 | 2026-02-08T03:15:56.472587Z | {
"verified": true,
"answer": 25180,
"timestamp": "2026-02-08T03:15:56.630076Z"
} | 6f78ab | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 256,
"completion_tokens": 4460
},
"timestamp": "2026-02-09T17:24:30.702Z",
"answer": 10114
},
{
... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": 1.71,
"mid": 5.04,
"hi": 8.38
} | ||
a4a89c | nt_count_with_divisor_count_v1_397696148_1185 | Let $T$ be the set of all integers $t$ with $35 \le t \le 65$ such that $t = 6a + 9b + 20$ for some integers $a,b$ with $1 \le a \le 3$ and $1 \le b \le 3$. Let $d$ be the number of elements in $T$. Let $R$ be the number of positive integers $n \le 21609$ such that the number of positive divisors of $n$ is exactly $d$.... | 9,259 | graphs = [
Graph(
let={
"_n": Const(62389),
"upper": Const(21609),
"div_count": 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(na... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_count_with_divisor_count_v1 | null | 3 | 0 | [
"LIN_FORM"
] | 1 | 1.002 | 2026-02-08T12:24:30.611958Z | {
"verified": true,
"answer": 9259,
"timestamp": "2026-02-08T12:24:31.613889Z"
} | 8537d0 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 181,
"completion_tokens": 2161
},
"timestamp": "2026-02-15T01:01:20.063Z",
"answer": 9259
},
{... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} |
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