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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
885ca2 | algebra_poly_eval_v1_898971024_1782 | Let $b$ be the number of positive integers $n$ such that $1 \le n \le 11$ and $\gcd(n, 21) = 1$. Compute $3b^4 - 8b^3 + 3b^2 - b - 3$. | 4,596 | graphs = [
Graph(
let={
"_n": Const(2),
"b": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(11)), Eq(GCD(a=Var("n"), b=Const(21)), Const(1))))),
"result": Sum(Mul(Const(3), Pow(Ref("b"), Const(4))), Mul(Const(-8), Po... | NT | null | COMPUTE | sympy | C4 | [
"C4"
] | 08d162 | algebra_poly_eval_v1 | null | 3 | 0 | [
"C4"
] | 1 | 0.004 | 2026-02-08T16:21:23.185444Z | {
"verified": true,
"answer": 4596,
"timestamp": "2026-02-08T16:21:23.189187Z"
} | 57477e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 108,
"completion_tokens": 564
},
"timestamp": "2026-02-17T01:22:29.798Z",
"answer": 4596
},
{
... | 1 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
ccec67 | geo_count_lattice_triangle_v1_655260480_993 | Let the vertices of a triangle be located at $ (0, 0) $, $ (120, 25) $, and $ (40, 0) $. The quantity $ 2A $, where $ A $ is twice the area of the triangle, is given by $ |120 \cdot 120 + 40 \cdot (-25)| $. Let $ B $ be the sum of the greatest common divisors of the absolute differences in coordinates along each side: ... | 69,747 | graphs = [
Graph(
let={
"_n": Const(120),
"area_2x": Abs(arg=Sum(Mul(Const(value=120), Const(value=120)), Mul(Const(value=40), Sub(left=Const(value=0), right=Const(value=25))))),
"boundary": Sum(GCD(a=Abs(arg=Summation(expr=Var(name='k'), var='k', start=Const(value=1), en... | NT | null | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | geo_count_lattice_triangle_v1 | null | 4 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.009 | 2026-02-08T15:51:33.566825Z | {
"verified": true,
"answer": 69747,
"timestamp": "2026-02-08T15:51:33.575865Z"
} | e778c2 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 237,
"completion_tokens": 2042
},
"timestamp": "2026-02-16T15:04:37.247Z",
"answer": 69747
},
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
103a8e | modular_sum_quadratic_residues_v1_784195855_9564 | Let $p$ be the number of positive integers $j \leq 509$ such that $j^2 \leq 259081$. Compute $\frac{p(p - 1)}{4}$. | 64,643 | graphs = [
Graph(
let={
"_n": Const(4),
"p": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(1)), Leq(Var("j"), Const(509)), Leq(Pow(Var("j"), Const(2)), Const(259081))), domain='positive_integers')),
"result": Div(Mul(Ref("p"), Sub(Ref("p"),... | NT | null | SUM | sympy | C3 | [
"C3"
] | 8a214c | modular_sum_quadratic_residues_v1 | null | 3 | 0 | [
"C3"
] | 1 | 0.001 | 2026-02-08T16:53:34.151567Z | {
"verified": true,
"answer": 64643,
"timestamp": "2026-02-08T16:53:34.152876Z"
} | 7f53dc | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 87,
"completion_tokens": 482
},
"timestamp": "2026-02-17T15:28:52.812Z",
"answer": 64643
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "C3",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
e98321 | nt_count_coprime_v1_1431428450_214 | Let $k$ be the number of integers $t$ with $21 \leq t \leq 96$ for which there exist integers $a$ and $b$ such that $1 \leq a \leq 4$, $1 \leq b \leq 6$, and $t = 15a + 6b$. Determine the number of positive integers $n$ with $1 \leq n \leq 59536$ such that $\gcd(n, k) = 1$. | 27,062 | graphs = [
Graph(
let={
"upper": Const(59536),
"k": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=4)), Geq(left... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_count_coprime_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 13.768 | 2026-02-08T13:18:06.937347Z | {
"verified": true,
"answer": 27062,
"timestamp": "2026-02-08T13:18:20.705309Z"
} | 3cd0ac | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 149,
"completion_tokens": 1922
},
"timestamp": "2026-02-15T13:52:20.335Z",
"answer": 27062
},
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
c001e8 | sequence_count_fib_divisible_v1_124444284_397 | Let $S$ be the set of all positive integers $n$ such that $1 \leq n \leq 655$ and $\gcd(n, 14) = 1$. Let $T$ be the set of all prime numbers $n$ such that $2 \leq n \leq |S|$. Define $k$ to be the largest integer such that $41^k$ divides $41^m$, where $m = \max T$. Determine the value of the number of positive integers... | 11 | graphs = [
Graph(
let={
"_n": Const(41),
"upper": MaxKDivides(target=Pow(Ref("_n"), MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(65... | NT | null | COUNT | sympy | COUNT_COPRIME_GRID | [
"C4/MAX_PRIME_BELOW/K14"
] | dcb2b7 | sequence_count_fib_divisible_v1 | null | 7 | 0 | [
"C4",
"COUNT_COPRIME_GRID",
"K14",
"MAX_PRIME_BELOW"
] | 4 | 0.05 | 2026-02-08T03:14:56.365379Z | {
"verified": true,
"answer": 11,
"timestamp": "2026-02-08T03:14:56.415329Z"
} | 355ac5 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 258,
"completion_tokens": 2062
},
"timestamp": "2026-02-09T17:08:34.627Z",
"answer": 6
},
{
"id... | 1 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "ok_later"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MOD_SUB",
"status": "no"... | {
"lo": 1.69,
"mid": 5.03,
"hi": 8.38
} | ||
e9723a | lin_form_endings_v1_48377204_2707 | Let $a = 27$ and $b = 36$. Define $k = 675$. Let $d = \gcd(a, b)$, and let $m = \gcd(k, d)$. Compute $\left\lfloor \frac{k}{m} \right\rfloor$, then multiply this value by $7809$. Find the remainder when this product is divided by $96456$. Determine the value of this remainder. | 6,939 | graphs = [
Graph(
let={
"a_coeff": Const(27),
"b_coeff": Const(36),
"k_val": Const(675),
"step": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"_inner_result": Floor(Div(Ref("k_val"), GCD(a=Ref("k_val"), b=Ref("step")))),
"_scale_k": Const(7... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 4 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T16:55:56.783537Z | {
"verified": true,
"answer": 6939,
"timestamp": "2026-02-08T16:55:56.784849Z"
} | 2d7e20 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 134,
"completion_tokens": 544
},
"timestamp": "2026-02-17T15:39:11.447Z",
"answer": 6939
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
69ef13 | comb_catalan_compute_v1_601307018_2220 | Let $C_n$ denote the $n$-th Catalan number. For each non-negative integer $a$ with $0 \le a \le 120$, define \[
R = (a^3 + 5a) \bmod 121,\quad S = (R^3 + 5R) \bmod 121,\quad T = (S^3 + 5S) \bmod 121,\quad K = (T^3 + 5T) \bmod \sum_{k=0}^{4} 3^k,\quad L = (K^3 + 5K) \bmod 121.
\] Let $n$ be the number of such $a$ for wh... | 16,796 | graphs = [
Graph(
let={
"_m": Const(4),
"_n": Const(121),
"n": CountOverSet(set=SolutionsSet(var=Var("a"), condition=And(Geq(Var("a"), Const(0)), Leq(Var("a"), Const(120)), Eq(Ref("_po_p5"), Var("a")), Neq(Ref("_po_p1"), Var("a")), Neq(Ref("_po_p2"), Var("a")), Neq(Ref("_... | COMB | null | COMPUTE | sympy | SUM_GEOM | [
"SUM_GEOM/POLY_ORBIT_HENSEL"
] | c77562 | comb_catalan_compute_v1 | null | 6 | 0 | [
"POLY_ORBIT_HENSEL",
"SUM_GEOM"
] | 2 | 0.009 | 2026-03-10T02:53:53.231094Z | {
"verified": true,
"answer": 16796,
"timestamp": "2026-03-10T02:53:53.240007Z"
} | e6f2d9 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 299,
"completion_tokens": 4154
},
"timestamp": "2026-03-29T04:46:19.713Z",
"answer": 16796
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "POLY_ORBIT_HENSEL",
"status": "ok_later"
},
{
"lemma": "... | {
"lo": 1.23,
"mid": 4.27,
"hi": 6.7
} | ||
06ccdb | sequence_count_fib_divisible_v1_677425708_2611 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 3560769$. Define $\_n$ to be the minimum value of $x + y$ as $(x, y)$ ranges over $S$. Let $\text{upper}$ be the number of positive integers $k$ such that $1 \le k \le \_n$ and $37$ divides $k$. Let $d = 2$. Define $\text{result}$ to ... | 33,455 | 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(3560769)))), expr=Sum(Var("x"), Var("y")))),
"upper": Count... | NT | null | COUNT | sympy | B3 | [
"B3/C2"
] | dcbe93 | sequence_count_fib_divisible_v1 | null | 7 | 0 | [
"B3",
"C2"
] | 2 | 0.08 | 2026-02-08T05:09:25.420911Z | {
"verified": true,
"answer": 33455,
"timestamp": "2026-02-08T05:09:25.500495Z"
} | 1a9d46 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 288,
"completion_tokens": 869
},
"timestamp": "2026-02-11T22:58:16.824Z",
"answer": 33455
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "ok_later"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
61ec8f | comb_count_partitions_v1_1978505735_4668 | Let $n$ be the smallest divisor of $94987$ that is greater than or equal to $2$. Let $p(n)$ denote the number of integer partitions of $n$. Compute the remainder when $44121 \cdot p(n)$ is divided by $52936$. | 35,045 | graphs = [
Graph(
let={
"_n": Const(44121),
"n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(94987))))),
"result": Partition(arg=Ref(name='n')),
"Q": Mod(value=Mul(Ref("_n"), Ref("re... | NT | COMB | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | comb_count_partitions_v1 | null | 4 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.001 | 2026-02-08T18:25:55.660534Z | {
"verified": true,
"answer": 35045,
"timestamp": "2026-02-08T18:25:55.662000Z"
} | 0146dd | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 104,
"completion_tokens": 2387
},
"timestamp": "2026-02-18T17:02:42.906Z",
"answer": 35045
},
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
fbde97 | geo_count_lattice_triangle_v1_124444284_7608 | Let $A$ be twice the area of the triangle with vertices at $(0,0)$, $(128,1)$, and $(29,128)$. Let $B$ be the sum of the greatest common divisors of the absolute values of the differences in coordinates along each side of the triangle:
\begin{align*}
B = &\gcd(|128 - 0|, |1 - 0|) + \gcd(|29 - 128|, |128 - 1|) + \gcd(|0... | 40,479 | graphs = [
Graph(
let={
"area_2x": Abs(arg=Sum(Mul(Const(value=128), Const(value=128)), Mul(Const(value=29), Sub(left=Const(value=0), right=Const(value=1))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=128)), b=Abs(arg=Const(value=1))), GCD(a=Abs(arg=Sub(left=Const(value=29), right=C... | ALG | NT | COUNT | sympy | [] | geo_count_lattice_triangle_v1 | null | 5 | 0 | null | null | 0.004 | 2026-02-08T09:13:20.714601Z | {
"verified": true,
"answer": 40479,
"timestamp": "2026-02-08T09:13:20.718825Z"
} | d921ae | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 204,
"completion_tokens": 1098
},
"timestamp": "2026-02-14T02:00:52.570Z",
"answer": 40479
},
... | 1 | [] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||||
3718d9 | nt_sum_gcd_range_mod_v1_458359167_232 | Let $N$ be the maximum value of $xy$ over all ordered pairs $(x, y)$ of positive integers such that $x + y = 136$. Let $k = 84$ and $M = 11731$. Define
$$
\text{sum} = \sum_{n=1}^{N} \gcd(n, k).
$$
Let $c = 93636$ and let $\text{result}$ be the remainder when $\text{sum}$ is divided by $M$. Compute $c - \text{result}$. | 88,488 | graphs = [
Graph(
let={
"N": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Const(136)))), expr=Mul(Var("x"), Var("y")))),
"k": Const(84),
... | NT | null | COMPUTE | sympy | B1 | [
"B1"
] | 5b950e | nt_sum_gcd_range_mod_v1 | null | 6 | 0 | [
"B1"
] | 1 | 0.209 | 2026-02-08T03:05:26.106505Z | {
"verified": true,
"answer": 88488,
"timestamp": "2026-02-08T03:05:26.315562Z"
} | 1fac72 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 227,
"completion_tokens": 5011
},
"timestamp": "2026-02-10T13:18:33.316Z",
"answer": 88488
},
{
"... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
59ecc5 | comb_count_partitions_v1_898971024_2226 | Let $n$ be the number of integers $t$ such that $8 \leq t \leq 58$ and there exist positive integers $a \leq 8$, $b \leq 6$ satisfying $t = 5a + 3b$. Determine the value of the number of integer partitions of $n$. | 63,261 | 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=8)), Geq(left=Var(name='b'), right=Const(value=1... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_count_partitions_v1 | null | 3 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T16:36:42.257639Z | {
"verified": true,
"answer": 63261,
"timestamp": "2026-02-08T16:36:42.259464Z"
} | ca479e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 115,
"completion_tokens": 3502
},
"timestamp": "2026-02-17T07:51:18.684Z",
"answer": 63261
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"st... | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||
2c1997 | comb_binomial_compute_v1_1742523217_1895 | Let $n = 15$ and $k = 8$. Define $r = \binom{n}{k}$.
Let $T$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x \cdot y = 256$. Let $s$ be the minimum value of $x + y$ as $(x, y)$ ranges over $T$.
Consider the set of all prime numbers $n$ such that $n \geq 2$ and $n \leq s$. Let $M$ be the max... | 89,217 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(95621),
"n": Const(15),
"k": Const(8),
"result": Binom(n=Ref("n"), k=Ref("k")),
"Q": Mod(value=Sub(MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_m")), Leq... | NT | null | COMPUTE | sympy | B3 | [
"B3/MAX_PRIME_BELOW"
] | 511ec9 | comb_binomial_compute_v1 | negation_mod | 6 | 0 | [
"B3",
"MAX_PRIME_BELOW"
] | 2 | 0.003 | 2026-02-08T04:19:21.116802Z | {
"verified": true,
"answer": 89217,
"timestamp": "2026-02-08T04:19:21.119643Z"
} | 7b74ba | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 250,
"completion_tokens": 627
},
"timestamp": "2026-02-10T16:10:44.680Z",
"answer": 89217
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "V1",
"status": "no"
},
{
"l... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
489bcc | alg_poly4_count_v1_601307018_711 | Find the number of ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 387$ such that $$162a^4 - 648a^3b + (27 \cdot 36)a^2b^2 - 648ab^3 + 162b^4 = 546491214882.$$. | 292 | graphs = [
Graph(
let={
"_n": Const(4),
"result": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(387)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(387)), Eq(Sum(Mul(Const(-648), Var("a"), Pow(Var("b... | ALG | null | COUNT | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | alg_poly4_count_v1 | null | 5 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 1.281 | 2026-03-10T01:21:51.615128Z | {
"verified": true,
"answer": 292,
"timestamp": "2026-03-10T01:21:52.895782Z"
} | d18d26 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 185,
"completion_tokens": 1649
},
"timestamp": "2026-03-28T23:54:16.004Z",
"answer": 292
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8_S... | {
"lo": -0.92,
"mid": 2.07,
"hi": 4.68
} | ||
3e7192 | nt_count_intersection_v1_655260480_3950 | Let $N$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 6250000$. Let $a = 5$. Let $b$ be the number of integers $t$ with $7 \leq t \leq 34$ for which there exist integers $a$ and $b$ such that $1 \leq a \leq 6$, $1 \leq b \leq 4$, and $t = 3a + 4b$. Compute the numb... | 33,427 | graphs = [
Graph(
let={
"N": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(6250000)))), expr=Sum(Var("x"), Var("y")))),
"a": Const(5),
... | NT | null | COUNT | sympy | LTE_DIFF | [
"LIN_FORM",
"B3"
] | 688dbe | nt_count_intersection_v1 | null | 6 | 0 | [
"B3",
"LIN_FORM",
"LTE_DIFF"
] | 3 | 3.769 | 2026-02-08T17:38:20.842175Z | {
"verified": true,
"answer": 33427,
"timestamp": "2026-02-08T17:38:24.610686Z"
} | 07ec9d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 220,
"completion_tokens": 2576
},
"timestamp": "2026-02-18T05:11:32.483Z",
"answer": 33427
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"le... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
50b18f | nt_count_digit_sum_v1_677425708_1645 | Let $T$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 100$. Let $s$ be the minimum value of $x + y$ over all such pairs. Let $A$ be the number of positive integers $n$ with $1 \leq n \leq 99999$ such that the sum of the digits of $n$ is $s$. Let $B$ be the number of integers $t$ with $15... | 82,280 | graphs = [
Graph(
let={
"_n": Const(87686),
"upper": Const(99999),
"target_sum": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Co... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM",
"B3"
] | ad075d | nt_count_digit_sum_v1 | negation_mod | 6 | 0 | [
"B3",
"LIN_FORM"
] | 2 | 7.353 | 2026-02-08T04:21:14.942985Z | {
"verified": true,
"answer": 82280,
"timestamp": "2026-02-08T04:21:22.296137Z"
} | 06b993 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 274,
"completion_tokens": 5185
},
"timestamp": "2026-02-10T16:16:19.404Z",
"answer": 82280
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma":... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
3f2748 | comb_binomial_compute_v1_168721529_2096 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 196$. Define $n$ to be the minimum value of $x + y$ over all such pairs. Let $N$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = n$. Compute the remainder when $20563 \cdot \binom{N}{6}$ is ... | 69,177 | graphs = [
Graph(
let={
"_m": Const(97752),
"_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(196)))), expr=Sum(Var("x"), Var("y"))))... | ALG | COMB | COMPUTE | sympy | B3 | [
"B3/COMB1"
] | e26f7e | comb_binomial_compute_v1 | null | 5 | 0 | [
"B3",
"COMB1"
] | 2 | 0.003 | 2026-02-08T14:07:03.588509Z | {
"verified": true,
"answer": 69177,
"timestamp": "2026-02-08T14:07:03.591986Z"
} | baf94f | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 218,
"completion_tokens": 6335
},
"timestamp": "2026-02-10T02:07:34.758Z",
"answer": 69177
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COMB1",
"status": "ok_later"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -2.43,
"mid": 1.2,
"hi": 4.84
} | ||
20b61e | antilemma_k3_v1_1742523217_3982 | Let $n = 86760$. Define $x$ to be the sum of Euler's totient function $\phi(d)$ over all positive divisors $d$ of $n$. Compute $x$. | 86,760 | graphs = [
Graph(
let={
"_n": Const(86760),
"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 | 2026-02-08T06:10:15.948692Z | {
"verified": true,
"answer": 86760,
"timestamp": "2026-02-08T06:10:15.949002Z"
} | b5890b | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 103,
"completion_tokens": 606
},
"timestamp": "2026-02-15T18:47:19.064Z",
"answer": 12400
},
{
"id": 11,... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.34
} | ||
0c9d07 | comb_binomial_compute_v1_1470522791_1397 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 900$. Let $m$ be the minimum value of $x + y$ over all pairs in $S$. Define $n$ to be the number of positive integers $k \leq m$ such that $k \equiv \left\lfloor \frac{k}{2} \right\rfloor \pmod{5}$. Compute the remainder when $44121 \... | 20,258 | graphs = [
Graph(
let={
"_n": Const(50909),
"n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositi... | NT | null | COMPUTE | sympy | B3 | [
"B3/L3C"
] | 345f3b | comb_binomial_compute_v1 | null | 6 | 0 | [
"B3",
"L3C"
] | 2 | 0.002 | 2026-02-08T13:36:41.496078Z | {
"verified": true,
"answer": 20258,
"timestamp": "2026-02-08T13:36:41.498502Z"
} | fd0781 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 160,
"completion_tokens": 1142
},
"timestamp": "2026-02-15T19:14:34.481Z",
"answer": 20258
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok_later"
},
{
"lemma": "MOD_FACTORIAL",
"status": ... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
82d330 | comb_binomial_compute_v1_397696148_19 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 49$. For each such pair, compute $x + y$. Let $n$ be the minimum value of $x + y$ over all such pairs. Let $T$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 9$. For each such pair, compute $x + y$. Let ... | 53,217 | graphs = [
Graph(
let={
"_n": Const(49),
"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")))),
... | ALG | COMB | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | comb_binomial_compute_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.003 | 2026-02-08T11:14:53.714326Z | {
"verified": true,
"answer": 53217,
"timestamp": "2026-02-08T11:14:53.717255Z"
} | fa1846 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 259,
"completion_tokens": 2563
},
"timestamp": "2026-02-24T13:07:01.999Z",
"answer": 53217
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
1ba57e | comb_bell_compute_v1_1915831931_3076 | Let $n = 9$ and let $\text{result} = B_n$, where $B_n$ denotes the $n$th Bell number, the number of partitions of a set of size $n$. Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = 20$. Let $c$ be the maximum value of $xy$ over all such pairs. Let $Q$ be the remainder when $c - ... | 61,384 | graphs = [
Graph(
let={
"n": Const(9),
"result": Bell(Ref("n")),
"_c": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Const(20))))... | COMB | null | COMPUTE | sympy | B1 | [
"B1"
] | d2b6e1 | comb_bell_compute_v1 | negation_mod | 6 | 0 | [
"B1"
] | 1 | 0.002 | 2026-02-08T17:21:02.525275Z | {
"verified": true,
"answer": 61384,
"timestamp": "2026-02-08T17:21:02.527254Z"
} | f176c3 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 164,
"completion_tokens": 1023
},
"timestamp": "2026-02-18T01:07:44.760Z",
"answer": 61384
},
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -4.1,
"mid": -1.76,
"hi": 1.32
} | ||
e880ec | nt_min_coprime_above_v1_798873815_454 | Let $ p_1 = 19 $. Define $ m $ as the remainder when $ (p_1 - 1)! + 1 $ is divided by $ p_1 $. Let $ p = 2 $, and define $ c $ as the remainder when $ (p - 1)! + 1 + m $ is divided by $ p $. Let $ m' = 50 + c $. Determine the smallest integer $ n $ such that $ 1296 < n \leq 1356 $ and $ \gcd(n, m') = 1 $. Compute the v... | 1,297 | graphs = [
Graph(
let={
"p1": Const(19),
"m": Mod(value=Sum(Factorial(Sub(Ref("p1"), Const(1))), Const(1)), modulus=Ref("p1")),
"p": Const(2),
"c": Mod(value=Sum(Factorial(Sub(Ref("p"), Const(1))), Sum(Const(1), Ref("m"))), modulus=Ref("p")),
"star... | NT | null | EXTREMUM | sympy | WILSON | [
"WILSON"
] | 963bac | nt_min_coprime_above_v1 | null | 5 | 2 | [
"WILSON"
] | 1 | 0.007 | 2026-02-08T02:38:50.197826Z | {
"verified": true,
"answer": 1297,
"timestamp": "2026-02-08T02:38:50.205115Z"
} | 4e1601 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 239,
"completion_tokens": 860
},
"timestamp": "2026-02-08T19:33:02.773Z",
"answer": 1297
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "WILSON",
"status": "ok"
}
] | {
"lo": -4.84,
"mid": -1.65,
"hi": 1.93
} | ||
930b83 | comb_count_permutations_fixed_v1_784195855_9590 | Let $n$ be the number of integers $t$ with $10 \leq t \leq 30$ for which there exist integers $a$ and $b$, each between 1 and 3 inclusive, such that $t = 6a + 4b$. Let $k = 4$. Compute the value of $\binom{n}{k} \cdot !(n - k)$, where $!m$ denotes the number of derangements of $m$ elements. | 5,544 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=3)), Geq(left=Var(name='b'), right=Const(value=1... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_count_permutations_fixed_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.003 | 2026-02-08T16:54:11.991499Z | {
"verified": true,
"answer": 5544,
"timestamp": "2026-02-08T16:54:11.994332Z"
} | 562118 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 146,
"completion_tokens": 1036
},
"timestamp": "2026-02-17T15:31:25.109Z",
"answer": 5544
},
{... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -8,
"mid": -4.75,
"hi": -2.28
} | ||
8dd68f | alg_poly_orbit_hensel_v1_601307018_7133 | Let $N = (3a^3 - 3a^2 - 4a - 4) \bmod 1369$ and $M = (3N^3 - 3N^2 - 4N - 4) \bmod 1369$. Find the number of non-negative integers $a$ with $0 \le a \le 2570981$ such that $M = a$ and $N \ne a$. | 3,756 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Mul(Const(3), Pow(Var("a"), Const(3))), Mul(Const(-3), Pow(Var("a"), Const(2))), Mul(Const(-4), Var("a")), Const(-4)), modulus=Const(1369)),
"p2": Mod(value=Sum(Mul(Const(3), Pow(Ref("p1"), Const(3))), Mul(Const(-3), Pow(Ref("p1"), Const(2)... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_orbit_hensel_v1 | null | 6 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.044 | 2026-03-10T07:45:20.469171Z | {
"verified": true,
"answer": 3756,
"timestamp": "2026-03-10T07:45:20.513166Z"
} | d4d749 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 207,
"completion_tokens": 10110
},
"timestamp": "2026-04-19T06:03:45.823Z",
"answer": 3756
},
{
... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
3a3ad4 | comb_count_derangements_v1_865884756_160 | Let $ n $ be the largest integer such that $ 3^n $ divides $ 2^{2187} + 1 $. Compute the number of derangements of $ n $ elements. Find the value of this number. | 14,833 | graphs = [
Graph(
let={
"_n": Const(3),
"n": MaxKDivides(target=Sum(Pow(Const(2), Const(2187)), Const(1)), base=Ref("_n")),
"result": Subfactorial(arg=Ref(name='n')),
},
goal=Ref("result"),
)
] | NT | COMB | COUNT | sympy | COUNT_PRIMES | [
"COUNT_PRIMES/LTE_SUM"
] | 35192d | comb_count_derangements_v1 | null | 5 | 0 | [
"COUNT_PRIMES",
"LTE_SUM"
] | 2 | 0.007 | 2026-02-08T15:12:56.560407Z | {
"verified": true,
"answer": 14833,
"timestamp": "2026-02-08T15:12:56.567344Z"
} | ed724a | 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": 1002
},
"timestamp": "2026-02-10T04:57:24.239Z",
"answer": 14833
}
] | 2 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "ok_later"
},
{
"lemma": "MAX_PRIME_BELOW",
"st... | {
"lo": -10,
"mid": -1.96,
"hi": 6.09
} | ||
62f4b9 | antilemma_k2_v1_784195855_6763 | Let $x = \sum_{k=1}^{51} \phi(k) \left\lfloor \frac{51}{k} \right\rfloor$. Compute the remainder when $13363 \cdot x$ is divided by $56985$. | 53,988 | graphs = [
Graph(
let={
"x": Summation(var="k", start=Div(Const(91), Const(91)), end=Const(51), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(51), Var("k"))))),
"_c": Const(13363),
"Q": Mod(value=Mul(Ref("_c"), Ref("x")), modulus=Const(56985)),
},
goal=Re... | NT | COMB | COMPUTE | sympy | IDENTITY_DIV_SELF | [
"IDENTITY_DIV_SELF",
"K2"
] | 39e678 | antilemma_k2_v1 | null | 4 | 0 | [
"IDENTITY_DIV_SELF",
"K2"
] | 2 | 0.001 | 2026-02-08T08:51:27.022082Z | {
"verified": true,
"answer": 53988,
"timestamp": "2026-02-08T08:51:27.022823Z"
} | 1bc2f6 | 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": 2322
},
"timestamp": "2026-02-13T22:14:16.531Z",
"answer": 53988
},
{... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "IDENTITY_DIV_SELF",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3c",
"status": "n... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
21d4cf | algebra_quadratic_discriminant_v1_124444284_2281 | Let $a = -5$, $b = -8$, and $n = 2$. Consider the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 90$, $\gcd(p, q) = 1$, and $p < q$. Let $k$ be the number of such integers $p$. Compute $b^n - a \cdot 3 \cdot k$. | 124 | graphs = [
Graph(
let={
"_n": Const(2),
"a": Const(-5),
"b": Const(-8),
"c": Const(3),
"result": Sub(Pow(Ref("b"), Ref("_n")), Mul(CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), co... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | algebra_quadratic_discriminant_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.001 | 2026-02-08T04:34:07.240666Z | {
"verified": true,
"answer": 124,
"timestamp": "2026-02-08T04:34:07.241888Z"
} | dbeed2 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 205,
"completion_tokens": 1173
},
"timestamp": "2026-02-10T17:14:35.639Z",
"answer": 124
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.33
} | ||
fa9cba | comb_sum_binomial_row_v1_798873815_407 | Let $n = 15$ and $N = 5698$. Compute $2^n$ and denote it by $r$. Let $c = \sum_{d \mid N} \phi(d)$, where $\phi$ denotes Euler's totient function. Find the remainder when $c \cdot r$ is divided by $73707$. | 12,233 | graphs = [
Graph(
let={
"_n": Const(5698),
"n": Const(15),
"result": Pow(Const(2), Ref("n")),
"_c": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Mod(value=Mul(Ref("_c"), Ref("result")), modulus=Const(73707)),
... | NT | null | SUM | sympy | K3 | [
"K3"
] | fd5c4e | comb_sum_binomial_row_v1 | affine_mod | 3 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T02:38:05.027049Z | {
"verified": true,
"answer": 12233,
"timestamp": "2026-02-08T02:38:05.027927Z"
} | 4260f1 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 188,
"completion_tokens": 1725
},
"timestamp": "2026-02-08T19:28:58.452Z",
"answer": 12233
},
{
"... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -0.84,
"mid": 1,
"hi": 2.63
} | ||
a45245_n | modular_mod_compute_v1_601307018_2271 | A security system uses a code derived from the number $4028033$. Let $N$ be the largest divisor of this number no greater than its square root. A secondary value $S$ is defined as $-71824 \bmod 41209$. A grid of $25 \times 25$ sensor positions $(a, b)$ activates if the inequality $2b^2 - 2ab + 13a^2 \leq 2425$ holds; l... | 52,553 | NT | null | COMPUTE | sympy | QF_PSD_COUNT_LEQ | [
"QF_PSD_COUNT_LEQ",
"B3_CLOSEST"
] | ea8e86 | modular_mod_compute_v1 | two_moduli | 6 | null | [
"B3_CLOSEST",
"QF_PSD_COUNT_LEQ"
] | 2 | 0.01 | 2026-03-10T02:56:10.063413Z | null | a1e6ce | a45245 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 258,
"completion_tokens": 7675
},
"timestamp": "2026-03-29T16:00:38.525Z",
"answer": 49640
},
{
... | 1 | [
{
"lemma": "B3_CLOSEST",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status... | {
"lo": 1.7,
"mid": 5.03,
"hi": 8.38
} | |
619ee4_l | comb_count_surjections_v1_1918700295_1506 | Let $T$ be the set of all integers $t$ such that $5 \leq t \leq 16$ and there exist integers $a$ and $b$ with $1 \leq a \leq 2$, $1 \leq b \leq 5$, and $t = 3a + 2b$. Let $n$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = |T|$. Define $k = 5$. Let $r = k! \cdot S(n, k)$, whe... | 0 | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/COMB1"
] | 268a62 | comb_count_surjections_v1 | null | 7 | 0 | [
"COMB1",
"LIN_FORM"
] | 2 | 0.002 | 2026-02-08T05:52:03.821355Z | {
"verified": false,
"answer": 41436,
"timestamp": "2026-02-08T05:52:03.823460Z"
} | 1df44d | 619ee4 | legacy_text | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 281,
"completion_tokens": 2025
},
"timestamp": "2026-02-24T04:42:38.645Z",
"answer": 41436
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok_later"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "... | {
"lo": -3.84,
"mid": -1.69,
"hi": 1.09
} | |
53d42c | comb_count_derangements_v1_1978505735_141 | Let $s$ be the smallest possible value of $x + y$ where $x$ and $y$ are positive integers such that $xy = 16941456$. Define $n$ to be the number of nonnegative integers $j$ such that $0 \leq j \leq 8232$ and $\binom{s}{j}$ is odd. Compute the subfactorial of $n$. | 14,833 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(16941456)))), expr=Sum(Var("x"), Var("y")))... | COMB | null | COUNT | sympy | B3 | [
"B3/V8"
] | 4fad5b | comb_count_derangements_v1 | null | 6 | 0 | [
"B3",
"V8"
] | 2 | 0.003 | 2026-02-08T15:12:28.060730Z | {
"verified": true,
"answer": 14833,
"timestamp": "2026-02-08T15:12:28.063283Z"
} | 34e6c9 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 196,
"completion_tokens": 12050
},
"timestamp": "2026-02-24T20:06:41.132Z",
"answer": 14833
},
{
... | 1 | [
{
"lemma": "B3",
"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": -4.1,
"mid": -1.76,
"hi": 1.26
} | ||
6c9f8b | comb_binomial_compute_v1_784195855_10106 | Let $k$ be the number of integers $t$ with $10 \leq t \leq 28$ for which there exist positive integers $a$ and $b$ such that $1 \leq a \leq 2$, $1 \leq b \leq 4$, and $t = 6a + 4b$. Compute $\binom{15}{k}$. | 6,435 | graphs = [
Graph(
let={
"n": Const(15),
"k": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=2)), Geq(left=Var(na... | ALG | COMB | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_binomial_compute_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T17:25:52.361559Z | {
"verified": true,
"answer": 6435,
"timestamp": "2026-02-08T17:25:52.362887Z"
} | a30e30 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 125,
"completion_tokens": 1735
},
"timestamp": "2026-02-18T01:47:56.003Z",
"answer": 6435
},
{... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.64,
"mid": -3.17,
"hi": -0.81
} | ||
d13ff9 | alg_poly4_count_v1_1218484723_1479 | Let $C = \left|\{ (a_1, b_1) : 1 \leq a_1, b_1 \leq 35,\ 13a_1^2 - 2a_1b_1 + 2b_1^2 \leq 1602 \}\right|$. Find the number of ordered pairs $(a, b)$ of positive integers with $1 \leq a \leq C$ and $1 \leq b \leq 266$ such that
$$
32a^4 - 64a^3b + 48a^2b^2 - 16ab^3 + 2b^4 = 184473632.
$$ | 217 | graphs = [
Graph(
let={
"_n": Const(2),
"result": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a1"), Var("b1")]), condition=And(Geq(Var("a1"), Const(... | ALG | null | COUNT | sympy | QF_PSD_COUNT_LEQ | [
"QF_PSD_COUNT_LEQ"
] | 009d0f | alg_poly4_count_v1 | null | 5 | 0 | [
"QF_PSD_COUNT_LEQ"
] | 1 | 1.112 | 2026-02-25T03:10:55.168244Z | {
"verified": true,
"answer": 217,
"timestamp": "2026-02-25T03:10:56.280154Z"
} | c32435 | 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": 5885
},
"timestamp": "2026-03-10T04:01:37.009Z",
"answer": 217
},
{
"id... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
}
] | {
"lo": -2.47,
"mid": 1.2,
"hi": 4.81
} | ||
eba5eb | nt_count_with_divisor_count_v1_655260480_3127 | Let $j$ be a positive integer such that $1 \leq j \leq 125$ and $j^2 \leq 15625$. Let $m$ be the number of such integers $j$. Define $u = \sum_{k=1}^{m} k$.
A positive integer $n$ is called special if it has exactly $13$ positive divisors and $1 \leq n \leq u$.
Determine the number of special positive integers. | 1 | graphs = [
Graph(
let={
"upper": Summation(var="k", start=Const(1), end=CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(1)), Leq(Var("j"), Const(125)), Leq(Pow(Var("j"), Const(2)), Const(15625))), domain='positive_integers')), expr=Var("k")),
"div_count"... | NT | null | COUNT | sympy | C3 | [
"C3/SUM_ARITHMETIC"
] | dda0ec | nt_count_with_divisor_count_v1 | null | 5 | 0 | [
"C3",
"SUM_ARITHMETIC"
] | 2 | 0.327 | 2026-02-08T17:12:07.298506Z | {
"verified": true,
"answer": 1,
"timestamp": "2026-02-08T17:12:07.625880Z"
} | 782cf9 | 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": 787
},
"timestamp": "2026-02-17T21:06:04.943Z",
"answer": 1
},
{
... | 1 | [
{
"lemma": "C3",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok_la... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
380a1a | antilemma_k2_v1_1440796553_36 | Let $n = 189$. Compute $$
\sum_{k=1}^{n} \varphi(k) \left\lfloor \frac{1}{k} \sum_{d \mid 189} \varphi(d) \right\rfloor.
$$ | 17,955 | graphs = [
Graph(
let={
"_n": Const(189),
"x": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(SumOverDivisors(n=Const(value=189), 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 | 7 | 0 | [
"K2",
"K3"
] | 2 | 0.001 | 2026-02-08T11:12:54.213845Z | {
"verified": true,
"answer": 17955,
"timestamp": "2026-02-08T11:12:54.214758Z"
} | c88254 | 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": 881
},
"timestamp": "2026-02-14T15:45:33.289Z",
"answer": 17955
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
d4f80a | diophantine_fbi2_count_v1_124444284_10273 | Let $k = 60$. Determine the number of integers $d$ such that $3 \leq d \leq 57$, $d$ divides $k$, and $4 \leq \frac{k}{d} \leq 58$. Compute the value of this count. | 7 | graphs = [
Graph(
let={
"k": Const(60),
"a": Const(2),
"b": Const(3),
"upper": Const(55),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(3)), Leq(Var("d"), Const(57)), Divides(divisor=Var("d"), dividend=Ref(... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"B3",
"K2",
"C5"
] | 2564e6 | diophantine_fbi2_count_v1 | null | 3 | 0 | [
"B3",
"C5",
"K2",
"MAX_PRIME_BELOW"
] | 4 | 0.088 | 2026-02-08T12:56:07.311334Z | {
"verified": true,
"answer": 7,
"timestamp": "2026-02-08T12:56:07.399827Z"
} | 8470c0 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 104,
"completion_tokens": 1191
},
"timestamp": "2026-02-15T07:49:59.364Z",
"answer": 7
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C5",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
dfb926_l | antilemma_sum_equals_v1_1918700295_135 | Let $x$ be the number of ordered pairs $(i, j)$ of positive integers with $1 \leq i \leq 40$, $1 \leq j \leq 40$, and $i + j = 41$. Let $c$ be the number of integers $t$ with $7 \leq t \leq 7933$ such that there exist positive integers $a \leq 1171$ and $b \leq 1105$ satisfying $t = 3a + 4b$. Compute $x^2 + 31x + c$. | 10,767 | COMB | GEOM | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM",
"COUNT_SUM_EQUALS"
] | a464cd | antilemma_sum_equals_v1 | quadratic_mod | 4 | 0 | [
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 2 | 0.009 | 2026-02-08T03:01:02.338183Z | {
"verified": false,
"answer": 10761,
"timestamp": "2026-02-08T03:01:02.346732Z"
} | 81dc71 | dfb926 | 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": 237,
"completion_tokens": 32768
},
"timestamp": "2026-02-23T21:33:10.527Z",
"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": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "LIN_F... | {
"lo": 3.43,
"mid": 5.73,
"hi": 8.84
} | |
13071f | comb_binomial_compute_v1_655260480_6051 | Let $m = 72$. Define $n'$ to be the number of positive integers $n_1$ with $1 \leq n_1 \leq 72$ such that the sum of the decimal digits of $n_1$ is even. Let $n$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = n'$. Let $k = 5$. Compute $\binom{n}{k}$. Find the remain... | 16,896 | graphs = [
Graph(
let={
"_m": Const(72),
"_n": CountOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(1)), Leq(Var("n1"), Ref("_m")), Eq(Mod(value=DigitSum(Var("n1")), modulus=Const(2)), Const(0))))),
"n": MinOverSet(set=MapOverSet(set=SolutionsSe... | ALG | COMB | COMPUTE | sympy | L3B | [
"L3B/B3"
] | f2ec8b | comb_binomial_compute_v1 | null | 6 | 0 | [
"B3",
"L3B"
] | 2 | 0.002 | 2026-02-08T18:47:36.223832Z | {
"verified": true,
"answer": 16896,
"timestamp": "2026-02-08T18:47:36.225705Z"
} | e9bb5d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 168,
"completion_tokens": 2888
},
"timestamp": "2026-02-18T19:32:51.041Z",
"answer": 16896
},
... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "L3B",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -3.12,
"mid": 1.47,
"hi": 6.57
} | ||
53748d | modular_sum_quadratic_residues_v1_48377204_2525 | Let $A$ be the set of all positive integers $p_1$ for which there exists a positive integer $q$ such that $p_1 \cdot q = 2700$, $\gcd(p_1, q) = 1$, and $p_1 < q$. Let $n$ be the number of elements in $A$. Let $B$ be the set of all positive integers $p_2$ for which there exists a positive integer $q$ such that $p_2 \cdo... | 40,100 | graphs = [
Graph(
let={
"_n": CountOverSet(set=SolutionsSet(var=Var("p1"), condition=And(IsPositive(arg=Var(name='p1')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p1'), Var(name='q')), right=Const(value=2700)), Eq(left=GCD(a=Var(name='p1'), b=Var(name='q')), right=Const(value... | NT | null | SUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/MIN_PRIME_FACTOR"
] | 52cee2 | modular_sum_quadratic_residues_v1 | null | 7 | 0 | [
"COPRIME_PAIRS",
"MIN_PRIME_FACTOR"
] | 2 | 0.007 | 2026-02-08T16:48:28.231376Z | {
"verified": true,
"answer": 40100,
"timestamp": "2026-02-08T16:48:28.238122Z"
} | 923790 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 222,
"completion_tokens": 2316
},
"timestamp": "2026-02-17T12:09:34.971Z",
"answer": 40100
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"st... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
9c9755 | comb_count_derangements_v1_1978505735_1398 | Let $n$ be the number of integers $j$ with $0 \leq j \leq 16389$ such that $\binom{16389}{j}$ is odd. Compute the subfactorial of $n$, denoted $!n$. Find the value of $!n$. | 14,833 | graphs = [
Graph(
let={
"_n": Const(2),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(16389)), Eq(Mod(value=Binom(n=Const(16389), k=Var("j")), modulus=Ref("_n")), Const(1))), domain='nonnegative_integers')),
"r... | COMB | null | COUNT | sympy | V8 | [
"V8"
] | 86348e | comb_count_derangements_v1 | null | 5 | 0 | [
"V8"
] | 1 | 0.003 | 2026-02-08T16:06:56.983997Z | {
"verified": true,
"answer": 14833,
"timestamp": "2026-02-08T16:06:56.986760Z"
} | 89f865 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 173,
"completion_tokens": 936
},
"timestamp": "2026-02-24T20:01:54.666Z",
"answer": 14833
},
{
"... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
}
... | {
"lo": -2.4,
"mid": 1.57,
"hi": 5.75
} | ||
2cdc18 | diophantine_fbi2_min_v1_1820931509_695 | Let $S$ be the set of all ordered pairs $(i, j)$ of integers such that $1 \leq i \leq 9$ and $1 \leq j \leq 18$. Let $k = 96$ and let $N$ be the number of pairs in $S$ for which $\gcd(i, j) = 1$. Let $D$ be the set of all integers $d$ such that $7 \leq d \leq N$, $d$ divides $k$, and $\frac{k}{d} \geq 5$. Let $m$ be th... | 50,168 | graphs = [
Graph(
let={
"k": Const(96),
"upper": 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(9)), right=IntegerRange(start=Const(1), en... | NT | null | EXTREMUM | sympy | COUNT_COPRIME_GRID | [
"COUNT_COPRIME_GRID"
] | 20ec03 | diophantine_fbi2_min_v1 | null | 5 | 0 | [
"COUNT_COPRIME_GRID"
] | 1 | 0.007 | 2026-02-08T11:49:35.215898Z | {
"verified": true,
"answer": 50168,
"timestamp": "2026-02-08T11:49:35.222656Z"
} | 75238b | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 202,
"completion_tokens": 1302
},
"timestamp": "2026-02-16T03:24:21.713Z",
"answer": 50164
},
{
"id": 1... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"... | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
bb28c0 | modular_min_modexp_v1_1918700295_3112 | Let $m = 106$. Let $n$ be the maximum value of $xy$ over all pairs of positive integers $(x, y)$ such that $x + y = m$. Let $b$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = n$. Let $k$ be the number of positive integers $n \leq 1156$ that are relatively prime to 21. Find ... | 11 | graphs = [
Graph(
let={
"_m": Const(106),
"_n": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Ref("_m")))), expr=Mul(Var("x"), Var("y")))),
... | NT | null | EXTREMUM | sympy | B1 | [
"B1/B3",
"C4"
] | 113e02 | modular_min_modexp_v1 | null | 7 | 0 | [
"B1",
"B3",
"C4"
] | 3 | 0.067 | 2026-02-08T08:23:23.934109Z | {
"verified": true,
"answer": 11,
"timestamp": "2026-02-08T08:23:24.000684Z"
} | 6f2d99 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 169,
"completion_tokens": 1327
},
"timestamp": "2026-02-13T18:28:38.259Z",
"answer": 11
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
ffc704_l | comb_count_permutations_fixed_v1_1918700295_217 | Let $a$ be the number of nonnegative integers $j$ such that $0 \leq j \leq 520$ and $\binom{520}{j}$ is odd. Let $n = 8$. Let $T$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = a$. Let $k$ be the minimum value of $x + y$ over all pairs in $T$. Compute $\binom{n}{k} \cdot !(n - k)$, where ... | 0 | COMB | null | COUNT | sympy | V8 | [
"V8/B3"
] | b4fc86 | comb_count_permutations_fixed_v1 | null | 6 | 0 | [
"B3",
"V8"
] | 2 | 0.005 | 2026-02-08T03:06:16.146371Z | {
"verified": false,
"answer": 630,
"timestamp": "2026-02-08T03:06:16.151200Z"
} | 0e4776 | ffc704 | legacy_text | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 239,
"completion_tokens": 1181
},
"timestamp": "2026-02-10T13:09:07.649Z",
"answer": 630
},
{
"id... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"l... | {
"lo": -3.83,
"mid": -1.68,
"hi": 1.09
} | |
cde879 | comb_binomial_compute_v1_1520064083_4377 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 36$. For each pair, compute $x + y$, and let $n$ be the smallest such sum. Let $k = 7$. Compute the binomial coefficient $\binom{n}{k}$, then multiply this value by $44121$. Find the remainder when this product is divided by $97778$. ... | 37,086 | graphs = [
Graph(
let={
"_n": Const(97778),
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(36)))), expr=Sum(Var("x"), Var("y")))),
... | ALG | COMB | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | comb_binomial_compute_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.001 | 2026-02-08T06:14:56.405188Z | {
"verified": true,
"answer": 37086,
"timestamp": "2026-02-08T06:14:56.406375Z"
} | 1f9d2f | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 208,
"completion_tokens": 1759
},
"timestamp": "2026-02-24T05:46:28.568Z",
"answer": 37086
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
bd9a3e | modular_count_residue_v1_1431428450_1207 | Let $r = \sum_{k=0}^{5} (-1)^k \binom{5}{k}$ and let $m = 4$. Compute the number of positive integers $n$ such that $1 \leq n \leq 56616$ and $n \equiv r \pmod{m}$. Let this count be $C$. Find the remainder when $93113 \cdot C$ is divided by $99135$. | 20,712 | graphs = [
Graph(
let={
"upper": Const(56616),
"m": Const(4),
"r": Summation(var="k", start=Const(0), end=Const(5), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Const(5), k=Var("k")))),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var(... | COMB | null | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING"
] | c21569 | modular_count_residue_v1 | null | 4 | 0 | [
"BINOMIAL_ALTERNATING"
] | 1 | 1.872 | 2026-02-08T13:57:46.393545Z | {
"verified": true,
"answer": 20712,
"timestamp": "2026-02-08T13:57:48.265052Z"
} | 767c1f | 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": 3264
},
"timestamp": "2026-02-24T19:25:21.302Z",
"answer": 20712
},
{
"... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"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"
},
{
... | {
"lo": -2.37,
"mid": 1.22,
"hi": 4.84
} | ||
4d52c4 | nt_count_divisors_in_range_v1_124444284_743 | Let $n = 15120$. Let $a$ be the maximum value of $xy$ over all ordered pairs $(x, y)$ of positive integers such that $x + y = 10$. Let $b$ be the number of integers $t$ with $10 \leq t \leq 1282$ for which there exist positive integers $a$ and $b$ such that $a \leq 110$, $b \leq 136$, and $t = 3a + 7b$. Compute the num... | 20,950 | graphs = [
Graph(
let={
"n": Const(15120),
"a": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Const(10)))), expr=Mul(Var("x"), Var("y")))),
... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM",
"B1"
] | 2f9b70 | nt_count_divisors_in_range_v1 | null | 6 | 0 | [
"B1",
"LIN_FORM"
] | 2 | 0.015 | 2026-02-08T03:29:21.147341Z | {
"verified": true,
"answer": 20950,
"timestamp": "2026-02-08T03:29:21.162561Z"
} | 5523e0 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 274,
"completion_tokens": 6847
},
"timestamp": "2026-02-09T05:27:12.768Z",
"answer": 20950
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
62bcf5 | comb_binomial_compute_v1_655260480_4294 | Let $t = \sum_{k_1=0}^{0} (-1)^{k_1} \binom{0}{k_1}$ and $f = \sum_{k_2=0}^{0} (-1)^{k_2} \binom{0}{k_2}$. Let $r = \binom{13}{7}$. Compute the remainder when $20 \cdot t \cdot f - r$ is divided by 75334. | 73,638 | graphs = [
Graph(
let={
"n2": Const(0),
"t": Summation(var="k1", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k1")), Binom(n=Ref("n2"), k=Var("k1")))),
"n1": Const(0),
"f": Summation(var="k2", start=Sub(Binom(n=Const(15), k=Const(15)), Const(1))... | COMB | null | COMPUTE | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING",
"ZERO_BINOM_N"
] | ba7829 | comb_binomial_compute_v1 | null | 3 | 2 | [
"BINOMIAL_ALTERNATING",
"ZERO_BINOM_N"
] | 2 | 0.003 | 2026-02-08T17:52:25.254968Z | {
"verified": true,
"answer": 73638,
"timestamp": "2026-02-08T17:52:25.257517Z"
} | 748a1d | 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": 1199
},
"timestamp": "2026-02-24T23:07:54.427Z",
"answer": 73638
},
... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status... | {
"lo": -8.52,
"mid": -5.43,
"hi": -3.2
} | ||
3cd03d | nt_count_divisible_and_v1_1125832087_1736 | Let $m = 38$. Let $T$ be the set of all ordered pairs $(i, j)$ of positive integers such that $i + j = 38$, $1 \leq i \leq 36$, and $1 \leq j \leq 37$. Let $n$ be the number of elements in $T$. Let $D$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = n$. Define $d_1$ to be the minimum value... | 504 | graphs = [
Graph(
let={
"_m": Const(38),
"_n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref("_m")), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(36)), right=IntegerRange(start=Const(1), end=Co... | COMB | null | COUNT | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS/B3",
"BINOMIAL_ALTERNATING",
"ONE_BINOM_N"
] | 8c8633 | nt_count_divisible_and_v1 | null | 6 | 0 | [
"B3",
"BINOMIAL_ALTERNATING",
"COUNT_SUM_EQUALS",
"ONE_BINOM_N"
] | 4 | 0.624 | 2026-02-08T03:54:29.675384Z | {
"verified": true,
"answer": 504,
"timestamp": "2026-02-08T03:54:30.299460Z"
} | 21d499 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 342,
"completion_tokens": 1374
},
"timestamp": "2026-02-10T16:08:12.630Z",
"answer": 504
},
{
"id... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "ONE_BINOM_... | {
"lo": -4.92,
"mid": -2.9,
"hi": -0.7
} | ||
e04ac3 | nt_euler_phi_compute_v1_153355830_87 | Let $n = 31477$. Compute $\phi(n)$, Euler's totient function at $n$, and denote this value by $T$. Let $P$ be the maximum value of $xy$ over all pairs of positive integers $(x, y)$ such that $x + y = 34$. Compute $T^2 + 44T + P$, and let $Q$ be the remainder when this value is divided by 75833.
Find the value of $Q$. | 670 | graphs = [
Graph(
let={
"n": Const(31477),
"result": EulerPhi(n=Ref("n")),
"_c": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Co... | NT | null | COMPUTE | sympy | B1 | [
"B1"
] | bf138c | nt_euler_phi_compute_v1 | quadratic_mod | 4 | 0 | [
"B1"
] | 1 | 0.002 | 2026-02-08T02:53:00.851235Z | {
"verified": true,
"answer": 670,
"timestamp": "2026-02-08T02:53:00.853604Z"
} | dcb225 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 211,
"completion_tokens": 21307
},
"timestamp": "2026-02-23T17:34:28.489Z",
"answer": 670
},
{
"i... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
}
] | {
"lo": 1.12,
"mid": 2.83,
"hi": 4.45
} | ||
1f5714 | comb_count_derangements_v1_898971024_1297 | Let $n$ be the largest prime number less than or equal to 10. Compute the number of derangements of a set of $n$ elements. | 1,854 | graphs = [
Graph(
let={
"_n": Const(10),
"n": MaxOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(2)), Leq(Var("n1"), Ref("_n")), IsPrime(Var("n1"))))),
"result": Subfactorial(arg=Ref(name='n')),
},
goal=Ref("result"),
)
] | NT | COMB | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | comb_count_derangements_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.002 | 2026-02-08T16:01:48.378671Z | {
"verified": true,
"answer": 1854,
"timestamp": "2026-02-08T16:01:48.380235Z"
} | 388b80 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 79,
"completion_tokens": 1389
},
"timestamp": "2026-02-16T20:09:22.863Z",
"answer": 1854
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
a47213 | sequence_fibonacci_compute_v1_1915831931_3486 | Let $n$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2$ equals the number of integers $t$ with $21 \leq t \leq 174$ for which there exist integers $a$ and $b$ satisfying $1 \leq a \leq 14$, $1 \leq b \leq 4$, and $t = 9a + 12b$. Let $Q$ be the remainder when $44121$ times the ... | 74,387 | graphs = [
Graph(
let={
"_n": Const(44121),
"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 | LIN_FORM | [
"LIN_FORM/COMB1"
] | 268a62 | sequence_fibonacci_compute_v1 | null | 6 | 0 | [
"COMB1",
"LIN_FORM"
] | 2 | 0.003 | 2026-02-08T17:41:48.912644Z | {
"verified": true,
"answer": 74387,
"timestamp": "2026-02-08T17:41:48.916013Z"
} | a9c56b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 176,
"completion_tokens": 3393
},
"timestamp": "2026-02-18T07:01:40.541Z",
"answer": 74387
},
... | 1 | [
{
"lemma": "COMB1",
"status": "ok_later"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
568721 | algebra_quadratic_discriminant_v1_1218484723_1537 | Let $b$ be the number of ordered pairs $(a_1, b_1)$ of positive integers with $1 \le a_1 \le b_1 \le 40$ such that $5a_1^2 - 8a_1b_1 + 5b_1^2 = 1845$. Compute $Q = b^2 - 16$. | 0 | graphs = [
Graph(
let={
"_n": Const(2),
"a": Const(-1),
"b": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a1"), Var("b1")]), condition=And(Geq(Var("a1"), Const(1)), Leq(Var("a1"), Const(40)), Geq(Var("b1"), Const(1)), Leq(Var("b1"), Const(40)), Leq(Var("a1"), Va... | ALG | null | COMPUTE | sympy | POLY_ORBIT_HENSEL | [
"QF_PSD_ORBIT"
] | 1d37f3 | algebra_quadratic_discriminant_v1 | null | 4 | 0 | [
"POLY_ORBIT_HENSEL",
"QF_PSD_ORBIT"
] | 2 | 1.693 | 2026-02-25T03:16:28.029231Z | {
"verified": true,
"answer": 0,
"timestamp": "2026-02-25T03:16:29.721790Z"
} | 2823cd | 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": 2484
},
"timestamp": "2026-03-10T04:38:11.672Z",
"answer": 0
},
{
"id":... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_ORBIT",
"status": "ok"
}
] | {
"lo": 1.14,
"mid": 4.13,
"hi": 6.32
} | ||
24502a | alg_qf_psd_min_v1_601307018_10154 | Let $S$ be the set of all ordered quadruples $(a, b, c, d)$ of positive integers such that $1 \le a \le 8$, $1 \le b \le 8$, $1 \le d \le 8$, and $1 \le c \le \min\{x + y : x > 0, y > 0, xy = 16, x \le y\}$. Find the minimum value of the expression
\[
13230bc + 17010ac + 14490c^2 + 11970a^2 + 12285d^2 - 3150cd - 10080a... | 90,090 | graphs = [
Graph(
let={
"_n": Const(8),
"result": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b"), Var("c"), Var("d")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(8)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(8)), Geq(Var("c"), C... | ALG | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | alg_qf_psd_min_v1 | null | 7 | 0 | [
"B3"
] | 1 | 0.042 | 2026-03-10T10:39:54.351882Z | {
"verified": true,
"answer": 90090,
"timestamp": "2026-03-10T10:39:54.393754Z"
} | 7df923 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 290,
"completion_tokens": 5681
},
"timestamp": "2026-04-19T13:06:25.967Z",
"answer": 90090
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
3dae9d | antilemma_k2_v1_124444284_3237 | Let $r$ be the sum of all real solutions to the equation $x^2 - 225x - 454 = 0$. Compute the value of
$$
\sum_{k=1}^{r} \phi(k) \left\lfloor \frac{225}{k} \right\rfloor,
$$
where $\phi(k)$ denotes Euler's totient function. | 25,425 | graphs = [
Graph(
let={
"_n": Const(225),
"x": Summation(var="k", start=Const(1), end=SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Const(2)), Mul(Const(-225), Var("x")), Const(-454)), Const(0)))), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Ref("_n"), Var("k"... | NT | COMB | COMPUTE | sympy | VIETA_SUM | [
"VIETA_SUM/K2",
"K2"
] | 6be084 | antilemma_k2_v1 | null | 6 | 0 | [
"K2",
"VIETA_SUM"
] | 2 | 0.001 | 2026-02-08T05:17:38.553692Z | {
"verified": true,
"answer": 25425,
"timestamp": "2026-02-08T05:17:38.555061Z"
} | 7c4a7f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 122,
"completion_tokens": 707
},
"timestamp": "2026-02-12T06:36:47.225Z",
"answer": 25425
},
{... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
... | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
f26ce4 | comb_sum_binomial_row_v1_124444284_9522 | Let $a = 1$. Let $b$ be the number of ordered triples $(x_1, x_2, x_3)$ of positive odd integers such that $x_1 + x_2 + x_3 = 5$. Define $n_2 = a + b$. Compute
$$
t = \sum_{k=0}^{n_2} (-1)^k \binom{n_2}{k}.
$$
Let $u = 5$ and $n_1 = u + 1$. Compute
$$
f = \sum_{k=0}^{n_1} (-1)^k \binom{n_1}{k}.
$$
Let $n = 16 + t + f$.... | 65,536 | graphs = [
Graph(
let={
"a": Const(1),
"b": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2"), Var("x3")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsPositive(arg=Var(name='x3')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name... | COMB | null | SUM | sympy | COMB1 | [
"COMB1/BINOMIAL_ALTERNATING"
] | e72f96 | comb_sum_binomial_row_v1 | null | 7 | 2 | [
"BINOMIAL_ALTERNATING",
"COMB1"
] | 2 | 0.002 | 2026-02-08T12:33:17.226114Z | {
"verified": true,
"answer": 65536,
"timestamp": "2026-02-08T12:33:17.228048Z"
} | 35f592 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 276,
"completion_tokens": 1112
},
"timestamp": "2026-02-24T15:52:59.265Z",
"answer": 65536
},
{
"... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
... | {
"lo": -9.23,
"mid": -6.18,
"hi": -4.06
} | ||
7d10f7 | antilemma_k3_v1_717093673_2361 | Let $m = 307$ and $n = 99740$. Let $x = \sum_{d \mid n} \phi(d)$, where $\phi$ denotes Euler's totient function. Let $c = \sum_{d \mid 3001} \phi(d)$.
Compute the remainder when $\left( x \bmod m \right) + c \cdot \left( x \bmod 317 \right)$ is divided by $72817$. | 23,938 | graphs = [
Graph(
let={
"_m": Const(307),
"_n": Const(99740),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"_c": SumOverDivisors(n=Const(value=3001), var='d1', expr=EulerPhi(n=Var(name='d1'))),
"Q": Mod(value=Sum... | NT | COMB | COMPUTE | sympy | K3 | [
"K3",
"K3"
] | d06fb8 | antilemma_k3_v1 | two_moduli | 4 | 0 | [
"K3"
] | 1 | 0.002 | 2026-02-08T16:46:40.356676Z | {
"verified": true,
"answer": 23938,
"timestamp": "2026-02-08T16:46:40.358490Z"
} | 953754 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 145,
"completion_tokens": 693
},
"timestamp": "2026-02-17T12:22:52.012Z",
"answer": 23938
},
{... | 1 | [
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
946b13 | antilemma_sum_equals_v1_458359167_2057 | Let $x$ be the number of ordered pairs $(i, j)$ of integers such that $1 \leq i \leq 77$, $1 \leq j \leq 77$, and $i + j = 78$. Determine the value of $\sum_{n=\binom{8}{8}}^{|x|} \phi(n)$, where $\phi(n)$ denotes Euler's totient function. | 1,832 | graphs = [
Graph(
let={
"_n": Const(78),
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref("_n")), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(77)), right=IntegerRange(start=Const(1), end=Con... | COMB | GEOM | COMPUTE | sympy | LIN_FORM | [
"COUNT_SUM_EQUALS",
"ONE_BINOM_N"
] | eb8b36 | antilemma_sum_equals_v1 | null | 4 | 0 | [
"COUNT_SUM_EQUALS",
"LIN_FORM",
"ONE_BINOM_N"
] | 3 | 0.024 | 2026-02-08T05:06:00.346351Z | {
"verified": true,
"answer": 1832,
"timestamp": "2026-02-08T05:06:00.370333Z"
} | b03981 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 200,
"completion_tokens": 5843
},
"timestamp": "2026-02-24T02:41:38.388Z",
"answer": 1832
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "ONE_B... | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
f613e3 | comb_count_partitions_v1_1520064083_9953 | Let $n$ be the number of integers $t$ with $10 \leq t \leq 64$ for which there exist positive integers $a$ and $b$ such that $1 \leq a \leq 4$, $1 \leq b \leq 12$, and $t = 7a + 3b$. Let $p$ be the number of integer partitions of $n$. Compute the sum of $d_i \cdot (i+1)^2$ over all digits $d_i$ of $p$, where the sum ra... | 21,850 | graphs = [
Graph(
let={
"_n": Const(7),
"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(na... | COMB | null | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING",
"LIN_FORM"
] | 10f694 | comb_count_partitions_v1 | null | 7 | 0 | [
"BINOMIAL_ALTERNATING",
"LIN_FORM"
] | 2 | 0.003 | 2026-02-08T11:03:38.766600Z | {
"verified": true,
"answer": 21850,
"timestamp": "2026-02-08T11:03:38.769639Z"
} | 56c93f | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 297,
"completion_tokens": 3177
},
"timestamp": "2026-02-24T12:50:32.170Z",
"answer": 21850
},
{
"... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemm... | {
"lo": 1.15,
"mid": 4.18,
"hi": 6.61
} | ||
c5fbd6 | nt_count_divisors_in_range_v1_798873815_115 | Let $n = 10080$. Let $a$ be the largest integer $k$ such that $2^k$ divides $5^{2048} - 3^{2048}$. Let $b = 10080$. Define $S$ as the set of all positive divisors $d$ of $n$ such that $a \leq d \leq b$. Let $r$ be the number of elements in $S$. Compute the value of $11^{|r|} \mod 99991 + 35721$. | 47,966 | graphs = [
Graph(
let={
"n": Const(10080),
"a": MaxKDivides(target=Sub(Pow(Const(5), Const(2048)), Pow(Const(3), Const(2048))), base=Const(2)),
"b": Const(10080),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Divides(divisor=Var("d"), div... | NT | null | COUNT | sympy | LTE_DIFF_P2 | [
"LTE_DIFF_P2"
] | 6d866c | nt_count_divisors_in_range_v1 | null | 6 | 0 | [
"LTE_DIFF_P2"
] | 1 | 0.084 | 2026-02-08T02:26:14.299987Z | {
"verified": true,
"answer": 47966,
"timestamp": "2026-02-08T02:26:14.383961Z"
} | 72a7cb | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 225,
"completion_tokens": 7208
},
"timestamp": "2026-02-09T13:39:48.939Z",
"answer": 47966
},
{
... | 1 | [
{
"lemma": "LTE_DIFF_P2",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"... | {
"lo": 2.41,
"mid": 5.29,
"hi": 8.55
} | ||
6922e8 | geo_count_lattice_rect_v1_1978505735_4190 | Compute the number of lattice points $(x, y)$ such that $0 \leq x \leq 222$ and $0 \leq y \leq 81$. | 18,286 | graphs = [
Graph(
let={
"a": Const(222),
"b": Const(81),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.003 | 2026-02-08T18:04:31.675952Z | {
"verified": true,
"answer": 18286,
"timestamp": "2026-02-08T18:04:31.678495Z"
} | 9d975d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 81,
"completion_tokens": 475
},
"timestamp": "2026-02-24T23:28:55.259Z",
"answer": 18286
},
{
... | 1 | [] | {
"lo": -6.4,
"mid": -4.13,
"hi": -2.01
} | ||||
c958ef | comb_catalan_compute_v1_1918700295_2818 | Let $m = 22$. Define $a$ to be the number of ordered pairs of positive odd integers $(x_1, x_2)$ such that $x_1 + x_2 = m$. Define $b$ to be the number of ordered pairs $(i, j)$ with $1 \leq i, j \leq 11$ such that $i + j = a$. Let $c = 22113$ and let $C_b$ denote the $b$-th Catalan number. Find the remainder when $c \... | 66,063 | graphs = [
Graph(
let={
"_m": Const(22),
"_n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2")), R... | COMB | null | COMPUTE | sympy | COMB1 | [
"COMB1/COUNT_SUM_EQUALS"
] | 4d9cac | comb_catalan_compute_v1 | null | 6 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS"
] | 2 | 0.16 | 2026-02-08T08:14:29.405145Z | {
"verified": true,
"answer": 66063,
"timestamp": "2026-02-08T08:14:29.564820Z"
} | 8f8f0a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 238,
"completion_tokens": 1987
},
"timestamp": "2026-02-24T09:11:11.090Z",
"answer": 66063
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
496d90 | antilemma_k3_v1_2051736721_6243 | Let $n = 95858$. Compute the sum of $\phi(d)$ over all positive divisors $d$ of $n$, where $\phi$ denotes Euler's totient function. | 95,858 | graphs = [
Graph(
let={
"_n": Const(95858),
"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 | 2026-02-08T19:03:58.798717Z | {
"verified": true,
"answer": 95858,
"timestamp": "2026-02-08T19:03:58.799023Z"
} | 40c9cb | 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": 620
},
"timestamp": "2026-02-18T21:05:43.878Z",
"answer": 95858
},
{
... | 1 | [
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
b6d9cd | comb_bell_compute_v1_601307018_585 | Let $n$ be the number of integers $t$ such that $t = 6a + 9b + 19$ for some integers $a, b$ with $1 \leq a, b \leq 3$, and $34 \leq t \leq 64$. Let $R = B_n$, where $B_n$ denotes the $n$-th Bell number. Find the remainder when $14891 \cdot R$ is divided by $87676$. | 55,461 | graphs = [
Graph(
let={
"_n": Const(87676),
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=3)), Geq(left=Va... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_bell_compute_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.003 | 2026-03-10T01:06:44.120153Z | {
"verified": true,
"answer": 55461,
"timestamp": "2026-03-10T01:06:44.122939Z"
} | ce197a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 215,
"completion_tokens": 1707
},
"timestamp": "2026-03-28T23:30:38.869Z",
"answer": 55461
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": 1.27,
"mid": 3.84,
"hi": 5.91
} | ||
e9733c | antilemma_coprime_grid_v1_1248542787_505 | Let $x$ be the number of ordered pairs $(i, j)$ of positive integers such that $1 \leq i \leq 36$, $1 \leq j \leq 171$, and $\gcd(i, j) = 1$. Compute $75025 - x$. | 71,263 | graphs = [
Graph(
let={
"x": 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(36)), right=IntegerRange(start=Const(1), end=Const(171))))),
"... | NT | COMB | COMPUTE | sympy | COUNT_COPRIME_GRID | [
"COUNT_COPRIME_GRID"
] | 20ec03 | antilemma_coprime_grid_v1 | null | 6 | 0 | [
"COUNT_COPRIME_GRID"
] | 1 | 0.001 | 2026-02-08T03:10:54.487500Z | {
"verified": true,
"answer": 71263,
"timestamp": "2026-02-08T03:10:54.488010Z"
} | 4c517b | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 173,
"completion_tokens": 2673
},
"timestamp": "2026-02-09T17:35:43.077Z",
"answer": 71263
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}... | {
"lo": -6.49,
"mid": 0.51,
"hi": 7.52
} | ||
1dd140 | modular_mod_compute_v1_48377204_2817 | Let $a = -4356$ and $m = 76729$. Define $r$ to be the remainder when $a$ is divided by $m$, so that $0 \le r < m$ and $r \equiv a \pmod{m}$. Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 6250000$. Let $c$ be the minimum value of $x + y$ over all such pairs in $S$. Compute the rem... | 55,301 | graphs = [
Graph(
let={
"a": Const(-4356),
"m": Const(76729),
"result": Mod(value=Ref("a"), modulus=Ref("m")),
"_c": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(ar... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | fc629c | modular_mod_compute_v1 | negation_mod | 4 | 0 | [
"B3"
] | 1 | 0.003 | 2026-02-08T16:59:55.535023Z | {
"verified": true,
"answer": 55301,
"timestamp": "2026-02-08T16:59:55.538050Z"
} | a46e2e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 169,
"completion_tokens": 1598
},
"timestamp": "2026-02-17T17:54:09.040Z",
"answer": 55301
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
bc816e | nt_count_divisible_v1_1918700295_56 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x \cdot y = 196$. Define $\text{divisor}$ to be the minimum value of $x + y$ as $(x, y)$ ranges over $S$. Compute the number of positive integers $n$ such that $1 \leq n \leq 30000$ and $n$ is divisible by $\text{divisor}$. | 1,071 | graphs = [
Graph(
let={
"upper": Const(30000),
"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(196)))), expr=Sum(Var("x"), Var... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | nt_count_divisible_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.934 | 2026-02-08T02:57:57.364342Z | {
"verified": true,
"answer": 1071,
"timestamp": "2026-02-08T02:57:58.298332Z"
} | c54f32 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 208,
"completion_tokens": 641
},
"timestamp": "2026-02-10T12:03:53.779Z",
"answer": 1071
},
{
"id... | 2 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -9.14,
"mid": -6.05,
"hi": -3.74
} | ||
7eb63b | sequence_count_fib_divisible_v1_655260480_155 | Let $S$ be the set of all positive integers $n$ such that $1 \le n \le 585$ and the sum of the decimal digits of $n$ is even. Let $\text{upper}$ be the number of elements in $S$.
Determine the number of positive integers $n_1$ such that $1 \le n_1 \le \text{upper}$ and $12$ divides the $n_1$-th Fibonacci number. | 24 | graphs = [
Graph(
let={
"_n": Const(585),
"upper": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_n")), Eq(Mod(value=DigitSum(Var("n")), modulus=Const(2)), Const(0))))),
"d": Const(12),
"result": CountOve... | NT | null | COUNT | sympy | L3B | [
"L3B"
] | cc148f | sequence_count_fib_divisible_v1 | null | 6 | 0 | [
"L3B"
] | 1 | 0.029 | 2026-02-08T15:14:21.760311Z | {
"verified": true,
"answer": 24,
"timestamp": "2026-02-08T15:14:21.789618Z"
} | 33b191 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 145,
"completion_tokens": 2250
},
"timestamp": "2026-02-16T02:50:19.089Z",
"answer": 24
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3B",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
06fc65 | geo_count_lattice_triangle_v1_1520064083_8505 | Let $A$ be the area of a triangle with vertices at $(0,0)$, $(120, 11)$, and $(144, 120)$, multiplied by 2. Compute $A$.
Let $B$ be the sum of the greatest common divisors of the absolute differences of the coordinates of the consecutive vertices of this triangle, including the edge from $(144, 120)$ back to $(0, 0)$,... | 89,174 | graphs = [
Graph(
let={
"_n": Const(144),
"area_2x": Abs(arg=Sum(Mul(Const(value=120), Const(value=120)), Mul(Ref(name='_n'), Sub(left=Const(value=0), right=Const(value=11))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=120)), b=Abs(arg=Const(value=11))), GCD(a=Abs(arg=Su... | NT | null | COUNT | sympy | K2 | [
"K2"
] | 6897ab | geo_count_lattice_triangle_v1 | null | 7 | 0 | [
"K2"
] | 1 | 0.006 | 2026-02-08T10:13:56.612271Z | {
"verified": true,
"answer": 89174,
"timestamp": "2026-02-08T10:13:56.617861Z"
} | 4b71b0 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 216,
"completion_tokens": 1463
},
"timestamp": "2026-02-14T06:46:05.713Z",
"answer": 89174
},
... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
478538 | nt_euler_phi_compute_v1_1116507919_441 | Let $n = 68121$. Compute $\varphi(n)$, the number of positive integers less than or equal to $n$ that are relatively prime to $n$. Let $Q$ be the remainder when $\sum_{k=1}^{\varphi(n)} \tau(k)$ is divided by $96833$, where $\tau(k)$ is the number of positive divisors of $k$. Find the value of $Q$. | 88,139 | graphs = [
Graph(
let={
"n": Const(68121),
"result": EulerPhi(n=Ref("n")),
"Q": Mod(value=Summation(var="n", start=EulerPhi(n=Const(2)), end=Abs(arg=Ref(name='result')), expr=NumDivisors(n=Var("n"))), modulus=Const(96833)),
},
goal=Ref("Q"),
)
] | NT | null | COMPUTE | sympy | ONE_PHI_2 | [
"ONE_PHI_2"
] | e19278 | nt_euler_phi_compute_v1 | null | 4 | 0 | [
"ONE_PHI_2"
] | 1 | 0.001 | 2026-02-08T02:34:18.861028Z | {
"verified": true,
"answer": 88139,
"timestamp": "2026-02-08T02:34:18.862487Z"
} | 9558e3 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 132,
"completion_tokens": 4523
},
"timestamp": "2026-02-09T21:23:46.450Z",
"answer": 0
},
{... | 0 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "ONE_PHI_2",
"status": "ok"
}
] | {
"lo": 2.52,
"mid": 6.26,
"hi": 10
} | ||
d00d09 | nt_min_coprime_above_v1_1918700295_2894 | Let $s$ be the sum of $\phi(d)$ over all positive divisors $d$ of $6765$. Let $k_{\text{max}}$ be the number of positive integers $k$ at most $625770$ that are divisible by $90$. Let $u$ be the number of positive integers $j$ such that $j^2 \leq 48344209$ and $j \leq k_{\text{max}}$. Let $r$ be the smallest integer $n$... | 6,767 | graphs = [
Graph(
let={
"start": SumOverDivisors(n=Const(value=6765), var='d', expr=EulerPhi(n=Var(name='d'))),
"upper": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(1)), Leq(Var("j"), CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var(... | NT | null | EXTREMUM | sympy | C2 | [
"C2/C3",
"K3"
] | 59f91d | nt_min_coprime_above_v1 | null | 6 | 0 | [
"C2",
"C3",
"K3"
] | 3 | 0.03 | 2026-02-08T08:18:21.632185Z | {
"verified": true,
"answer": 6767,
"timestamp": "2026-02-08T08:18:21.662261Z"
} | 8d6147 | 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": 1125
},
"timestamp": "2026-02-13T17:11:46.070Z",
"answer": 6767
},
{... | 1 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "C3",
"status": "ok_later"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
6a6b7f | lte_diff_endings_v1_784195855_4437 | Let $a = 14$ and $b = 8$. Let $p = 3$ and $T = 11$. Let $v$ be the largest integer $k$ such that $p^k$ divides $a - b$. Compute $p^{T - v}$. | 59,049 | graphs = [
Graph(
let={
"a_val": Const(14),
"b_val": Const(8),
"p_val": Const(3),
"T_val": Const(11),
"diff": Sub(Ref("a_val"), Ref("b_val")),
"vp_diff": MaxKDivides(target=Ref("diff"), base=Ref("p_val")),
"exp": Sub(Ref("T_... | NT | null | COMPUTE | sympy | LTE_DIFF | [
"LTE_DIFF"
] | cf8260 | lte_diff_endings_v1 | null | 3 | null | [
"LTE_DIFF"
] | 1 | 0 | 2026-02-08T07:06:05.326454Z | {
"verified": true,
"answer": 59049,
"timestamp": "2026-02-08T07:06:05.326885Z"
} | 77aa58 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 155,
"completion_tokens": 318
},
"timestamp": "2026-02-19T23:24:17.428Z",
"answer": 59049
}
] | 2 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
}
] | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
2e5a17 | diophantine_product_count_v1_784195855_5184 | Let $d_{\max}$ be the largest positive divisor of $9421740$ that is at most $3060$. Let $k = 480$. Let $C$ be the number of positive integers $n$ such that $1 \leq n \leq d_{\max}$ and the $n$-th Fibonacci number is divisible by $12$. Let $D$ be the number of positive integers $x$ such that $1 \leq x \leq C$, $x$ divid... | 87,932 | graphs = [
Graph(
let={
"_m": Const(88273),
"_n": MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Leq(Var("d"), Const(3060)), Divides(divisor=Var("d"), dividend=Const(9421740))))),
"k": Const(480),
"upper": CountOverSet(set=Sol... | NT | null | COUNT | sympy | MAX_DIVISOR | [
"MAX_DIVISOR/COUNT_FIB_DIVISIBLE"
] | bc4d0c | diophantine_product_count_v1 | null | 7 | 0 | [
"COUNT_FIB_DIVISIBLE",
"MAX_DIVISOR"
] | 2 | 0.011 | 2026-02-08T07:42:59.790396Z | {
"verified": true,
"answer": 87932,
"timestamp": "2026-02-08T07:42:59.801873Z"
} | f3d188 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 183,
"completion_tokens": 2238
},
"timestamp": "2026-02-13T12:24:24.865Z",
"answer": 87932
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok_later"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
"lemma": "MAX_VAL",
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
aa5257 | sequence_lucas_compute_v1_601307018_6870 | Let $S = \min\{ x + y : x, y > 0,\ xy = 36864 \}$. Find the number $n$ of ordered pairs $(a, b)$ of positive integers with $1 \leq a, b \leq 40$ such that $S \cdot a^2 b + 128a^3 + 384a b^2 + 128b^3 = 27648000$. Let $Q = L_n$, where $L_n$ denotes the $n$-th Lucas number. Compute $Q$. | 24,476 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(2),
"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("b"), Const(40)), Eq(Sum(Mul(MinOverSet(s... | ALG | null | COMPUTE | sympy | B3 | [
"B3/POLY3_COUNT"
] | f5b896 | sequence_lucas_compute_v1 | null | 7 | 0 | [
"B3",
"POLY3_COUNT"
] | 2 | 0.006 | 2026-03-10T07:30:59.789204Z | {
"verified": true,
"answer": 24476,
"timestamp": "2026-03-10T07:30:59.794705Z"
} | 1e41ad | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 231,
"completion_tokens": 1827
},
"timestamp": "2026-04-19T05:29:55.474Z",
"answer": 24476
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY3_COUNT",
"status": "ok_later"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
651f41 | nt_num_divisors_compute_v1_1918700295_4541 | Let $S$ be the set of all positive integers $x$ such that $x^2 - 198x + 5957 = 0$.
Let $n$ be the maximum value of $xy$ over all pairs of positive integers $(x, y)$ such that $x + y$ equals the sum of the elements in $S$.
Let $Q$ be the remainder when $60594$ multiplied by the number of positive divisors of $n$ is di... | 63,495 | graphs = [
Graph(
let={
"_m": Const(5957),
"_n": Const(60594),
"n": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), SumOverSet(set=... | NT | null | COMPUTE | sympy | VIETA_SUM | [
"VIETA_SUM/B1"
] | 80af64 | nt_num_divisors_compute_v1 | null | 6 | 0 | [
"B1",
"VIETA_SUM"
] | 2 | 0.002 | 2026-02-08T09:25:45.149643Z | {
"verified": true,
"answer": 63495,
"timestamp": "2026-02-08T09:25:45.152003Z"
} | 0bd5d3 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 156,
"completion_tokens": 934
},
"timestamp": "2026-02-14T04:06:55.737Z",
"answer": 63495
},
{... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "VIETA_SU... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
84c3c1 | nt_max_prime_below_v1_1520064083_6898 | Let $n$ be an integer. Define $\alpha$ to be the largest prime number less than or equal to 84681. Let $\beta$ be the sum of all real solutions $x$ to the equation $x^2 - 8614x - 372251 = 0$. Compute the remainder when $\alpha \cdot \beta$ is divided by 79203. | 71,998 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": Const(84681),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("upper")), IsPrime(Var("n"))))),
"_c": SumOverSet(set=SolutionsSet(var=Var("x"), conditi... | NT | null | EXTREMUM | sympy | VIETA_SUM | [
"VIETA_SUM"
] | e2aa68 | nt_max_prime_below_v1 | affine_mod | 6 | 0 | [
"VIETA_SUM"
] | 1 | 1.949 | 2026-02-08T08:24:46.274615Z | {
"verified": true,
"answer": 71998,
"timestamp": "2026-02-08T08:24:48.223937Z"
} | c69a04 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 126,
"completion_tokens": 4301
},
"timestamp": "2026-02-13T18:11:08.580Z",
"answer": 71998
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "VIETA_SUM",
"status": "ok"
}
] | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
841f32 | antilemma_k3_v1_1520064083_2397 | Let $n = 29963$. Compute
$$
\sum_{d \mid n} \phi(d),
$$
where $\phi$ denotes Euler's totient function and the sum is taken over all positive divisors $d$ of $n$. Find the value of this sum. | 29,963 | graphs = [
Graph(
let={
"_n": Const(29963),
"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 | 4 | 0 | [
"K3"
] | 1 | 0 | 2026-02-08T04:42:07.043638Z | {
"verified": true,
"answer": 29963,
"timestamp": "2026-02-08T04:42:07.044027Z"
} | 0c7342 | 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": 762
},
"timestamp": "2026-02-11T21:50:00.405Z",
"answer": 29963
},
{
"i... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.02,
"hi": 0.32
} | ||
44d208 | comb_catalan_compute_v1_1470522791_1526 | Let $ n_1 = 0 $ and $ n_2 = 0 $. Define $ c = \sum_{k=0}^{n_2} (-1)^k \binom{n_2}{k} $ and $ m = \sum_{k=0}^{n_1} (-1)^k \binom{n_1}{k} $. Let $ n = 10 \cdot m $. Determine the value of the $ n $-th Catalan number. | 16,796 | graphs = [
Graph(
let={
"n2": Const(0),
"c": Summation(var="k", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n2"), k=Var("k")))),
"n1": Const(0),
"m": Summation(var="k", start=Const(0), end=Ref("n1"), expr=Mul(Pow(Const(-1), V... | COMB | null | COMPUTE | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING"
] | c21569 | comb_catalan_compute_v1 | null | 3 | 2 | [
"BINOMIAL_ALTERNATING"
] | 1 | 0.002 | 2026-02-08T13:43:50.754291Z | {
"verified": true,
"answer": 16796,
"timestamp": "2026-02-08T13:43:50.756749Z"
} | 13788b | 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": 497
},
"timestamp": "2026-02-24T19:00:18.727Z",
"answer": 16796
},
{
"i... | 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
} | ||
704e5a | algebra_quadratic_discriminant_v1_1742523217_407 | Let $a = -2$ and $b = 2$. Let $c$ be the number of integers $t$ such that $14 \leq t \leq 48$ and there exist integers $a'$ and $b'$ with $1 \leq a' \leq 3$, $1 \leq b' \leq 4$, and $t = 8a' + 6b'$. Compute $b^k - 4ac$, where $k$ is the number of positive integers $p$ for which there exists a positive integer $q$ such ... | 100 | graphs = [
Graph(
let={
"a": Const(-2),
"b": Const(2),
"c": 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... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS",
"LIN_FORM"
] | 67610e | algebra_quadratic_discriminant_v1 | null | 4 | 0 | [
"COPRIME_PAIRS",
"LIN_FORM"
] | 2 | 0.003 | 2026-02-08T03:01:49.406586Z | {
"verified": true,
"answer": 100,
"timestamp": "2026-02-08T03:01:49.409346Z"
} | 6c8f0d | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 287,
"completion_tokens": 1213
},
"timestamp": "2026-02-09T17:34:12.710Z",
"answer": 100
},
{
"id... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{... | {
"lo": -3.47,
"mid": 0.81,
"hi": 4.81
} | ||
f019c3 | algebra_quadratic_discriminant_v1_677425708_697 | Let $a = -2$, $b = \sum_{k=1}^{4} k$, and $c = 48$. Define $\Delta = b^2 - 4ac$. Compute the remainder when $80075 \cdot \Delta$ is divided by $81488$. | 49,500 | graphs = [
Graph(
let={
"_n": Const(81488),
"a": Const(-2),
"b": Summation(var="k", start=Const(1), end=Const(4), expr=Var("k")),
"c": Const(48),
"result": Sub(Pow(Ref("b"), Const(2)), Mul(Const(4), Ref("a"), Ref("c"))),
"Q": Mod(value=... | NT | null | COMPUTE | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | algebra_quadratic_discriminant_v1 | null | 2 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.001 | 2026-02-08T03:41:24.440097Z | {
"verified": true,
"answer": 49500,
"timestamp": "2026-02-08T03:41:24.441357Z"
} | 9c20d1 | 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": 1762
},
"timestamp": "2026-02-08T20:56:43.951Z",
"answer": 49500
},
{
"... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
}
] | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
71ec4b | sequence_fibonacci_compute_v1_1978505735_2610 | Let $n = \sum_{k=1}^{6} \phi(k) \left\lfloor \frac{6}{k} \right\rfloor$. Let $F_n$ denote the $n$th Fibonacci number, where $F_1 = F_2 = 1$ and $F_{k} = F_{k-1} + F_{k-2}$ for $k \geq 3$. Compute the remainder when $25567 \cdot F_n$ is divided by $61071$. | 29,060 | graphs = [
Graph(
let={
"_n": Const(25567),
"n": Summation(var="k", start=Const(1), end=Const(6), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(6), Var("k"))))),
"result": Fibonacci(arg=Ref(name='n')),
"Q": Mod(value=Mul(Ref("_n"), Ref("result")), modulus=Con... | NT | null | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | sequence_fibonacci_compute_v1 | null | 4 | 0 | [
"K2"
] | 1 | 0.002 | 2026-02-08T17:01:57.180562Z | {
"verified": true,
"answer": 29060,
"timestamp": "2026-02-08T17:01:57.182391Z"
} | 4373c7 | 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": 4942
},
"timestamp": "2026-02-17T18:33:20.797Z",
"answer": 29060
},
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
668c9b | diophantine_fbi2_min_v1_151522320_201 | Let $d$ be an integer such that $d \geq 2$, $d \leq 43$, $d$ divides $33$, and $\frac{33}{d} \geq 4$. Determine the smallest such integer $d$. | 3 | graphs = [
Graph(
let={
"k": Const(33),
"a": Const(1),
"b": Const(3),
"upper": Const(43),
"result": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Leq(Var("d"), Ref("upper")), Divides(divisor=Var("d"), dividend=Ref... | NT | null | EXTREMUM | sympy | V8 | [
"LIN_FORM"
] | 7b2633 | diophantine_fbi2_min_v1 | null | 3 | 0 | [
"LIN_FORM",
"V8"
] | 2 | 0.053 | 2026-02-08T03:02:19.008544Z | {
"verified": true,
"answer": 3,
"timestamp": "2026-02-08T03:02:19.061065Z"
} | 81bbcb | 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": 500
},
"timestamp": "2026-02-10T12:30:17.033Z",
"answer": 3
},
{
"id": ... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
9330cd | algebra_quadratic_discriminant_v1_124444284_7821 | Let $a = 3$ and $b = 4$. Let $c$ be the number of nonnegative integers $j$ such that $0 \le j \le 16512$ and
$$
\binom{16512}{j} \equiv 1 \pmod{m},
$$
where $m$ is the number of ordered pairs $(p,q)$ of positive integers satisfying $pq = 18$, $\gcd(p,q) = 1$, and $p < q$. Define $D = b^2 - 4ac$. Compute the value of
$$... | 0 | graphs = [
Graph(
let={
"a": Const(3),
"b": Const(4),
"c": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(16512)), Eq(Mod(value=Binom(n=Const(16512), k=Var("j")), modulus=CountOverSet(set=SolutionsSet(var=Var("p"), c... | NT | null | COMPUTE | sympy | B1 | [
"COPRIME_PAIRS/V8"
] | 93b9b8 | algebra_quadratic_discriminant_v1 | null | 6 | 0 | [
"B1",
"COPRIME_PAIRS",
"V8"
] | 3 | 0.009 | 2026-02-08T09:23:02.825525Z | {
"verified": true,
"answer": 0,
"timestamp": "2026-02-08T09:23:02.834787Z"
} | 985b5a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 210,
"completion_tokens": 1718
},
"timestamp": "2026-02-14T03:39:08.126Z",
"answer": 0
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8",
"status": "ok_later"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma... | {
"lo": -9.12,
"mid": -6.02,
"hi": -3.62
} | ||
e76873 | alg_poly_orbit_hensel_v1_1218484723_419 | Define a function $f(a) = 3a^5 + 3a^3 + 5a^2 + 1 \bmod 2197$. Let $N = f(a)$, $M = f(N)$, $R = f(M)$. Find the number of non-negative integers $a$ with $0 \leq a \leq 2476018$ such that $R = a$, $N \neq a$, and $M \neq a$. | 3,381 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Mul(Const(3), Pow(Var("a"), Const(5))), Mul(Const(3), Pow(Var("a"), Const(3))), Mul(Const(5), Pow(Var("a"), Const(2))), Const(1)), modulus=Const(2197)),
"p2": Mod(value=Sum(Mul(Const(3), Pow(Ref("p1"), Const(5))), Mul(Const(3), Pow(Ref("p1"... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_orbit_hensel_v1 | null | 5 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.051 | 2026-02-25T02:07:18.378841Z | {
"verified": true,
"answer": 3381,
"timestamp": "2026-02-25T02:07:18.429592Z"
} | 92fc8c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 212,
"completion_tokens": 9969
},
"timestamp": "2026-03-28T22:37:04.268Z",
"answer": 3381
},
{
"i... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 1.22,
"mid": 3.76,
"hi": 5.73
} | ||
d7e6a1 | diophantine_fbi2_count_v1_2051736721_4077 | Let $k = 180$. Compute the number of integers $d$ such that $5 \le d \le 81$, $d$ divides $k$, and
$$
3 \le \frac{k}{d} \le 79.
$$ | 12 | graphs = [
Graph(
let={
"k": Const(180),
"a": Const(4),
"b": Const(2),
"upper": Const(77),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(5)), Leq(Var("d"), Const(81)), Divides(divisor=Var("d"), dividend=Ref... | NT | null | COUNT | sympy | B1 | [
"B1/COUNT_CARTESIAN"
] | a89ad7 | diophantine_fbi2_count_v1 | null | 3 | 0 | [
"B1",
"COUNT_CARTESIAN"
] | 2 | 0.04 | 2026-02-08T17:42:55.172875Z | {
"verified": true,
"answer": 12,
"timestamp": "2026-02-08T17:42:55.213074Z"
} | d56acf | 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": 832
},
"timestamp": "2026-02-18T07:50:06.131Z",
"answer": 12
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok_later"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
d739ea_n | geo_visible_lattice_v1_1218484723_1229 | A city grid spans from $(1,1)$ to $(99,99)$, with a building at each lattice point. Two buildings at $(x_1, y_1)$ and $(x_2, y_2)$ can see each other clearly if the line segment between them doesn't pass through any other building. A building at $(x, y)$ has an unobstructed view to the origin if $\gcd(x, y) = 1$. How m... | 10,653 | GEOM | GEOM | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 3 | null | null | null | 0.196 | 2026-02-25T02:59:43.177935Z | null | 6e915b | d739ea | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 231,
"completion_tokens": 32768
},
"timestamp": "2026-03-30T16:36:57.671Z",
"answer": null
},
{
... | 1 | [] | {
"lo": 1.5,
"mid": 4.69,
"hi": 7.23
} | |||
d1b3b7 | nt_count_divisible_and_v1_124444284_1129 | Let $d_1 = \sum_{d \mid 6} \phi(d)$ and let $d_2$ be the maximum value of $xy$ over all pairs of positive integers $(x, y)$ such that $x + y = 6$. Compute the number of positive integers $n \leq 71064$ such that $n$ is divisible by both $d_1$ and $d_2$. | 3,948 | graphs = [
Graph(
let={
"upper": Const(71064),
"d1": SumOverDivisors(n=Const(value=6), var='d', expr=EulerPhi(n=Var(name='d'))),
"d2": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPosit... | NT | null | COUNT | sympy | K3 | [
"K3",
"B1"
] | 9ff3cb | nt_count_divisible_and_v1 | null | 4 | 0 | [
"B1",
"K3"
] | 2 | 6.144 | 2026-02-08T03:42:10.547575Z | {
"verified": true,
"answer": 3948,
"timestamp": "2026-02-08T03:42:16.691764Z"
} | 100819 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 200,
"completion_tokens": 750
},
"timestamp": "2026-02-10T03:09:36.567Z",
"answer": 3948
},
{
"id... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"st... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
1e5c23 | antilemma_sum_factor_cartesian_v1_168721529_1515 | Let
$$x = \sum_{i=1}^{5} \sum_{j=1}^{6} ij.$$
Let $p$ be the number of positive integers $u$ for which there exist positive integers $v$ such that
$$uv = 108, \quad \gcd(u,v)=1, \quad u<v.$$
Let $n_0 = 26741$, and let $d_0$ be the smallest integer $d$ such that $d\ge p$ and $d$ divides $n_0$.
Define
$$Q = B_{\,|x| \... | 877 | graphs = [
Graph(
let={
"_n": Const(26741),
"x": SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Const(1), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(5)), right=IntegerRange(start=Const(1), end=Const(6)))), expr=... | NT | COMB | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/MIN_PRIME_FACTOR",
"SUM_FACTOR_CARTESIAN"
] | d57b21 | antilemma_sum_factor_cartesian_v1 | bell_mod | 5 | 0 | [
"COPRIME_PAIRS",
"MIN_PRIME_FACTOR",
"SUM_FACTOR_CARTESIAN"
] | 3 | 0.003 | 2026-02-08T13:44:40.932007Z | {
"verified": true,
"answer": 877,
"timestamp": "2026-02-08T13:44:40.935493Z"
} | f39b5e | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 297,
"completion_tokens": 1815
},
"timestamp": "2026-02-09T18:26:44.173Z",
"answer": 877
},
{
"id... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok_l... | {
"lo": -6.5,
"mid": -0.2,
"hi": 6.11
} | ||
252f13 | antilemma_sum_equals_v1_2051736721_4972 | Let $x$ be the number of ordered pairs $(i, j)$ of positive integers such that $i + j = 38$, $1 \le i \le 37$, and $1 \le j \le 38$. Compute the remainder when $48061 \cdot x$ is divided by $71703$. | 57,385 | graphs = [
Graph(
let={
"_n": Const(38),
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref("_n")), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(37)), right=IntegerRange(start=Const(1), end=Con... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 3 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.008 | 2026-02-08T18:17:09.000312Z | {
"verified": true,
"answer": 57385,
"timestamp": "2026-02-08T18:17:09.008560Z"
} | e906c4 | 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": 840
},
"timestamp": "2026-02-18T15:57:28.346Z",
"answer": 57385
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V8_SU... | {
"lo": -5.39,
"mid": -2.64,
"hi": 0.63
} | ||
3e40ce | nt_max_prime_below_v1_1431428450_658 | Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q > p$ such that $pq = 18$ and $\gcd(p, q) = 1$. Let $m$ be the number of elements in $S$. Let $n$ be the largest prime number $p$ such that $m \leq p \leq 46656$. Compute the remainder when $65656 \cdot n$ is divided by $76665$. | 19,994 | graphs = [
Graph(
let={
"_n": Const(76665),
"upper": Const(46656),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_max_prime_below_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 1.114 | 2026-02-08T13:36:39.080428Z | {
"verified": true,
"answer": 19994,
"timestamp": "2026-02-08T13:36:40.194299Z"
} | 47ad16 | 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": 3402
},
"timestamp": "2026-02-15T18:58:49.365Z",
"answer": 19994
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
1632f2 | nt_count_with_divisor_count_v1_124444284_9303 | Let $T$ be the number of integers $t$ for which there exist integers $a$ and $b$ satisfying
\[
1 \le a \le 1211, \quad 1 \le b \le 476, \quad 5 \le t \le 3850, \quad \text{and} \quad t = 2a + 3b.
\]
Let $D$ be the largest prime among the integers $n$ with $2 \le n \le 7$.
Let $R$ be the number of integers $n$ with $1... | 3,841 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=1211)), Geq(left=Va... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/MAX_DIVISOR",
"MAX_PRIME_BELOW"
] | 17f5a5 | nt_count_with_divisor_count_v1 | negation_mod | 7 | 0 | [
"LIN_FORM",
"MAX_DIVISOR",
"MAX_PRIME_BELOW"
] | 3 | 3.027 | 2026-02-08T12:21:52.554433Z | {
"verified": true,
"answer": 3841,
"timestamp": "2026-02-08T12:21:55.581078Z"
} | b6efc9 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 241,
"completion_tokens": 4488
},
"timestamp": "2026-02-15T00:44:45.628Z",
"answer": 3841
},
{... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok_later"
},
{
"lemma": "MAX_PRIME_BELOW",
"st... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
8ebb25 | diophantine_fbi2_min_v1_655260480_4607 | Let $ c = 64 $. Let $ S $ be the set of all ordered pairs $ (x, y) $ of positive integers such that $ xy = c $. Let $ T $ be the set of all values $ x + y $ where $ (x, y) \in S $. Let $ k $ be the minimum value in $ T $.
Let $ U $ be the set of all positive integers $ t $ such that $ 9 \leq t \leq 183 $ and there ex... | 2 | graphs = [
Graph(
let={
"_c": Const(64),
"_m": Const(2),
"_n": Const(2),
"k": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var(... | NT | null | EXTREMUM | sympy | B1 | [
"LIN_FORM/B3"
] | 05313e | diophantine_fbi2_min_v1 | null | 6 | 0 | [
"B1",
"B3",
"LIN_FORM"
] | 3 | 0.063 | 2026-02-08T18:00:44.305134Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-02-08T18:00:44.367752Z"
} | 1c76ec | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 350,
"completion_tokens": 2413
},
"timestamp": "2026-02-18T11:45:51.933Z",
"answer": 2
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V5",
"status": ... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
acba12 | comb_factorial_compute_v1_1353956133_435 | Let $m = 16$. Define $n_0$ to be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 16$. Let $n$ be the sum of all positive integers $k$ with $1 \leq k \leq s$ such that $k$ is divisible by $n_0$, where $s$ is the number of positive integers $p$ for which there exists a po... | 40,320 | graphs = [
Graph(
let={
"_m": Const(16),
"_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 | COPRIME_PAIRS | [
"COPRIME_PAIRS/SUM_DIVISIBLE",
"B3/SUM_DIVISIBLE"
] | 974b16 | comb_factorial_compute_v1 | null | 6 | 0 | [
"B3",
"COPRIME_PAIRS",
"SUM_DIVISIBLE"
] | 3 | 0.004 | 2026-02-08T11:27:01.668887Z | {
"verified": true,
"answer": 40320,
"timestamp": "2026-02-08T11:27:01.672435Z"
} | 8e04bc | 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": 1463
},
"timestamp": "2026-02-14T14:44:33.660Z",
"answer": 40320
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
643df0 | comb_count_surjections_v1_124444284_7884 | Let $n = 7$. Consider the set of all ordered pairs $(i,j)$ of integers such that $1 \leq i \leq 6$, $1 \leq j \leq 7$, and $i + j = 7$. Let $k$ be the number of elements in this set. Define $\text{result} = k! \cdot S(n, k)$, where $S(n, k)$ denotes the Stirling number of the second kind. Let $Q$ be the remainder when ... | 67,424 | graphs = [
Graph(
let={
"n": Const(7),
"k": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(7)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(6)), right=IntegerRange(start=Const(1), end=Const(7... | COMB | null | COUNT | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | comb_count_surjections_v1 | null | 4 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.012 | 2026-02-08T09:24:47.033279Z | {
"verified": true,
"answer": 67424,
"timestamp": "2026-02-08T09:24:47.045250Z"
} | ae84f9 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 243,
"completion_tokens": 8432
},
"timestamp": "2026-02-24T11:19:36.011Z",
"answer": 67424
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V8_SU... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
e566ca | nt_euler_phi_compute_v1_1520064083_802 | Let $n = 31684$. Let $\varphi(n)$ denote Euler's totient function. Define $r = \varphi(n)$. Let $s = \sum_{d \mid 4181} \varphi(d)$. Compute the remainder when $r^2 + 22r + s$ is divided by 78402. | 76,219 | graphs = [
Graph(
let={
"n": Const(31684),
"result": EulerPhi(n=Ref("n")),
"Q": Mod(value=Sum(Pow(Ref("result"), Const(2)), Mul(Const(22), Ref("result")), SumOverDivisors(n=Const(value=4181), var='d', expr=EulerPhi(n=Var(name='d')))), modulus=Const(78402)),
},
... | NT | null | COMPUTE | sympy | K3 | [
"K3"
] | 373090 | nt_euler_phi_compute_v1 | quadratic_mod | 4 | 0 | [
"K3"
] | 1 | 0.002 | 2026-02-08T03:36:07.681575Z | {
"verified": true,
"answer": 76219,
"timestamp": "2026-02-08T03:36:07.684069Z"
} | b7e137 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 183,
"completion_tokens": 2833
},
"timestamp": "2026-02-10T15:06:35.630Z",
"answer": 76219
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
6df5ac | algebra_poly_eval_v1_677425708_3597 | Let $b = 25$. Define $$R = \frac{9b^3 - 94b^2 - 45b - 110}{14}.$$ Let $S$ be the set of all prime numbers $n$ such that $2 \leq n \leq 49$. Let $M$ be the maximum element of $S$. Compute $M - R$, then determine the remainder when this value is divided by $57539$. | 51,826 | graphs = [
Graph(
let={
"_n": Const(57539),
"b": Const(25),
"result": Div(Sum(Mul(Const(9), Pow(Ref("b"), Const(3))), Mul(Const(-94), Pow(Ref("b"), Const(2))), Mul(Const(-45), Ref("b")), Const(-110)), Const(14)),
"Q": Mod(value=Sub(MaxOverSet(set=SolutionsSet(... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | 2ed1de | algebra_poly_eval_v1 | negation_mod | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.002 | 2026-02-08T05:51:19.485632Z | {
"verified": true,
"answer": 51826,
"timestamp": "2026-02-08T05:51:19.487265Z"
} | 27f510 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 140,
"completion_tokens": 588
},
"timestamp": "2026-02-12T15:14:53.316Z",
"answer": 51826
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
0afaef | algebra_poly_eval_v1_1419126231_1175 | Let $m = 23$. Let $M = \frac{45m^3 + 89m^2 + 7m - 42}{\max\{xy : x > 0, y > 0, x + y = 22\}}$. Compute $|M|$. | 4,915 | graphs = [
Graph(
let={
"_n": Const(2),
"m": Const(23),
"result": Div(Sum(Mul(Const(45), Pow(Ref("m"), Const(3))), Mul(Const(89), Pow(Ref("m"), Ref("_n"))), Mul(Const(7), Ref("m")), Const(-42)), MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var(... | ALG | null | COMPUTE | sympy | B1 | [
"B1"
] | 5b950e | algebra_poly_eval_v1 | null | 4 | 0 | [
"B1"
] | 1 | 0.003 | 2026-02-25T10:39:25.053440Z | {
"verified": true,
"answer": 4915,
"timestamp": "2026-02-25T10:39:25.056477Z"
} | 76353c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 173,
"completion_tokens": 728
},
"timestamp": "2026-03-30T11:36:57.647Z",
"answer": 4915
},
{
"id... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | ||
030c71 | modular_mod_compute_v1_1874849503_615 | Let $a = 2209$ and $m = 7000$. Define $r$ to be the remainder when $a$ is divided by $m$. Let $k$ be the largest integer such that $2^k \leq 3795386610711$. Compute the remainder when $k - r$ is divided by $78794$. | 76,626 | graphs = [
Graph(
let={
"a": Const(2209),
"m": Const(7000),
"result": Mod(value=Ref("a"), modulus=Ref("m")),
"_c": MaxOverSet(set=SolutionsSet(var=Var("k"), condition=Leq(Pow(Const(2), Var("k")), Const(3795386610711)))),
"Q": Mod(value=Sub(Ref("_c"... | NT | null | COMPUTE | sympy | MAX_VAL | [
"MAX_VAL"
] | b9f7ee | modular_mod_compute_v1 | negation_mod | 4 | 0 | [
"MAX_VAL"
] | 1 | 0.002 | 2026-02-08T13:13:18.787744Z | {
"verified": true,
"answer": 76626,
"timestamp": "2026-02-08T13:13:18.789799Z"
} | a67d7e | 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": 742
},
"timestamp": "2026-02-09T19:04:18.445Z",
"answer": 76626
},
{
"i... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "same_pattern_wrong"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_VAL",
... | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
97ac96 | diophantine_product_count_v1_1439011603_2701 | Let $k$ be the number of positive integers $n$ with $1 \le n \le 1800$ such that $n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{5}$. Let $S$ be the set of all positive integers $x$ such that $1 \le x \le 333$, $x$ divides $k$, and $\frac{k}{x} \le 333$. Compute the remainder when $35318 \cdot |S|$ is divided by... | 30,754 | graphs = [
Graph(
let={
"_n": Const(35318),
"k": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(1800)), Congruent(a=Var(name='n'), b=Floor(arg=Div(left=Var(name='n'), right=Const(value=2))), modulus=Const(value=5))))),
... | NT | null | COUNT | sympy | L3C | [
"L3C"
] | 73f8b0 | diophantine_product_count_v1 | null | 6 | 0 | [
"L3C"
] | 1 | 0.033 | 2026-02-08T16:55:08.214921Z | {
"verified": true,
"answer": 30754,
"timestamp": "2026-02-08T16:55:08.247962Z"
} | 6dfbbf | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 163,
"completion_tokens": 1665
},
"timestamp": "2026-02-17T16:21:18.189Z",
"answer": 30754
},
... | 1 | [
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
c08fe6 | geo_visible_lattice_v1_1978505735_7340 | Let $n = 200$. Define a visible lattice point as an ordered pair $(x, y)$ of positive integers such that $1 \leq x, y \leq n$ and $\gcd(x, y) = 1$. Let $R$ be the number of visible lattice points. Let $c = 841$. Compute the remainder when $c - R$ is divided by $84552$. | 60,930 | graphs = [
Graph(
let={
"n": Const(200),
"result": VisibleLatticePoints(n=Ref(name='n')),
"_c": Const(841),
"Q": Mod(value=Sub(Ref("_c"), Ref("result")), modulus=Const(84552)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 3 | 0 | null | null | 0.797 | 2026-02-08T20:12:47.739417Z | {
"verified": true,
"answer": 60930,
"timestamp": "2026-02-08T20:12:48.536539Z"
} | c39c53 | 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": 5731
},
"timestamp": "2026-02-25T01:54:00.596Z",
"answer": 60930
},
... | 1 | [] | {
"lo": -3.12,
"mid": 1.47,
"hi": 6.57
} | ||||
7e87a2 | modular_sum_quadratic_residues_v1_124444284_3899 | Let $p$ be the number of integers $t$ such that $14 \le t \le 586$ and there exist positive integers $a$ and $b$ with $1 \le a \le 71$, $1 \le b \le 20$, and $t = 6a + 8b$. Compute $\frac{p(p-1)}{4}$. | 19,670 | graphs = [
Graph(
let={
"_n": Const(4),
"p": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=71)), Geq(left=Var(n... | NT | null | SUM | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | modular_sum_quadratic_residues_v1 | null | 3 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T05:39:47.762052Z | {
"verified": true,
"answer": 19670,
"timestamp": "2026-02-08T05:39:47.763624Z"
} | d7dcd7 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 126,
"completion_tokens": 3603
},
"timestamp": "2026-02-12T12:01:11.719Z",
"answer": 19670
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status":... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} |
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