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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
51cb10_n | comb_count_surjections_v1_1218484723_711 | A teacher wants to assign 3 different tasks to groups of students, where each task must be done by at least one student and every student is assigned exactly one task. The number of students $n$ is determined by the formula $n = \sum_{d=1}^{3} \varphi(d) \left\lfloor \frac{3}{d} \right\rfloor$. How many ways can the st... | 540 | COMB | null | COUNT | sympy | K2 | [
"K2"
] | 6897ab | comb_count_surjections_v1 | null | 3 | null | [
"K2"
] | 1 | 0.001 | 2026-02-25T02:27:18.598402Z | null | abf134 | 51cb10 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 221,
"completion_tokens": 775
},
"timestamp": "2026-03-30T15:47:52.512Z",
"answer": 540
},
{
"id"... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -10,
"mid": -5.89,
"hi": -1.79
} | |
5166ad | alg_poly4_count_v1_1218484723_4547 | Let $R$ be the largest prime number $n$ with $2 \le n \le 282$. Let $Q$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \le a \le 281$ and $1 \le b \le R$ such that $$
128b^4 - 64a^3b + \left|\{ t : t = 2a' + 3b'\ \text{for integers}\ a', b'\ \text{with}\ 1 \le a' \le 6,\ 1 \le b' \le 62,\ 5 \le t ... | 275 | graphs = [
Graph(
let={
"_c": Const(281),
"_m": Const(2),
"_n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(282)), IsPrime(Var("n"))))),
"result": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a... | NT | null | COUNT | sympy | POLY3_COUNT | [
"MAX_PRIME_BELOW/MAX_PRIME_BELOW",
"LIN_FORM"
] | d03071 | alg_poly4_count_v1 | null | 5 | 0 | [
"LIN_FORM",
"MAX_PRIME_BELOW",
"POLY3_COUNT"
] | 3 | 1.822 | 2026-02-25T06:13:04.254032Z | {
"verified": true,
"answer": 275,
"timestamp": "2026-02-25T06:13:06.076174Z"
} | f94cbd | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 286,
"completion_tokens": 7090
},
"timestamp": "2026-03-29T16:12:41.286Z",
"answer": 275
},
{
"id... | 1 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
... | {
"lo": -3.33,
"mid": 1.03,
"hi": 5.26
} | ||
c98a26 | nt_count_divisors_in_range_v1_1820931509_586 | Let $n = 1680$ and let $a = \sum_{k=1}^5 k$. Define $S$ as the set of all positive divisors $d$ of $n$ such that $a \le d \le 217$. Compute the number of elements in $S$, and subtract this value from $32041$. | 32,019 | graphs = [
Graph(
let={
"_n": Const(32041),
"n": Const(1680),
"a": Summation(var="k", start=Const(1), end=Const(5), expr=Var("k")),
"b": Const(217),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Divides(divisor=Var("d"), divid... | NT | null | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | nt_count_divisors_in_range_v1 | null | 3 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.005 | 2026-02-08T11:46:42.422051Z | {
"verified": true,
"answer": 32019,
"timestamp": "2026-02-08T11:46:42.427066Z"
} | bd100a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 118,
"completion_tokens": 1499
},
"timestamp": "2026-02-14T18:43:42.529Z",
"answer": 32019
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
96ef81 | diophantine_fbi2_min_v1_124444284_3319 | Let $k$ be the minimum value of $x + y$ over all ordered pairs of positive integers $(x, y)$ such that $xy = 32400$. Let $r$ be the smallest integer $d$ with $2 \leq d \leq 370$ such that $d$ divides $k$ and $\frac{k}{d} \geq 3$. Compute the number of ordered pairs $(i, j)$ with $1 \leq i \leq 86$ and $1 \leq j \leq 11... | 6,082 | graphs = [
Graph(
let={
"_n": Const(3),
"k": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(32400)))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | EXTREMUM | sympy | COUNT_COPRIME_GRID | [
"COUNT_COPRIME_GRID",
"B3"
] | 968810 | diophantine_fbi2_min_v1 | negation_mod | 6 | 0 | [
"B3",
"COUNT_COPRIME_GRID"
] | 2 | 0.029 | 2026-02-08T05:21:36.533718Z | {
"verified": true,
"answer": 6082,
"timestamp": "2026-02-08T05:21:36.562538Z"
} | 95dd28 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 174,
"completion_tokens": 5156
},
"timestamp": "2026-02-12T06:49:14.394Z",
"answer": 6082
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no... | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
cb75e5 | alg_sym_quad_system_v1_601307018_2983 | Let $S$ be the set of all ordered triples $(a, b, c)$ of positive integers satisfying $a^2 + b^2 + c^2 = ab + bc + ca$ and $2a + 4b + 6c = 4416$. Let $d = \min \{ |x - y| : x > 0, y > 0, xy = 11503205 \}$. Define $R = \left( \sum_{(a,b,c) \in S} a^4 + b^4 + c^4 \right) \bmod d$. Find the remainder when $84655 \cdot R$ ... | 28,221 | graphs = [
Graph(
let={
"_n": Const(98817),
"result": Mod(value=SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b"), Var("c")]), condition=And(Eq(Sum(Pow(Var("a"), Const(2)), Pow(Var("b"), Const(2)), Pow(Var("c"), Const(2))), Sum(Mul(Var("a"), Var("b")),... | ALG | null | COMPUTE | sympy | B3_DIFF | [
"B3_DIFF"
] | b47ea7 | alg_sym_quad_system_v1 | null | 8 | 0 | [
"B3_DIFF"
] | 1 | 0.018 | 2026-03-10T03:36:29.089318Z | {
"verified": true,
"answer": 28221,
"timestamp": "2026-03-10T03:36:29.107716Z"
} | 8a105e | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 258,
"completion_tokens": 4667
},
"timestamp": "2026-04-18T23:09:51.621Z",
"answer": 28221
},
{
... | 1 | [
{
"lemma": "B3_DIFF",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -3.31,
"mid": 1.32,
"hi": 5.87
} | ||
caa253 | comb_count_permutations_fixed_v1_717093673_3431 | Let $n$ be the smallest divisor of $1859$ that is at least $2$. Let $k = 8$. Define $r = \binom{n}{k} \cdot !(n - k)$, where $!m$ denotes the number of derangements of $m$ elements. Compute $44521 - r$. | 44,191 | graphs = [
Graph(
let={
"n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(1859))))),
"k": Const(8),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub(left=Ref(name='n'), right=Ref... | NT | COMB | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | comb_count_permutations_fixed_v1 | null | 4 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.003 | 2026-02-08T17:37:05.529839Z | {
"verified": true,
"answer": 44191,
"timestamp": "2026-02-08T17:37:05.533304Z"
} | 9e3229 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 116,
"completion_tokens": 736
},
"timestamp": "2026-02-18T05:13:43.352Z",
"answer": 44191
},
{... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"stat... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
6f3dfb | sequence_count_fib_divisible_v1_784195855_2747 | Let $d$ be the number of integers $t$ such that $14 \leq t \leq 45$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 4$, $1 \leq b \leq 5$, and $t = 5a + 4b + 5$. Let $S$ be the set of positive integers $n$ such that $1 \leq n \leq 900$ and $d$ divides the $n$th Fibonacci number. Compute the remainder ... | 44,532 | graphs = [
Graph(
let={
"upper": Const(900),
"d": 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=V... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | sequence_count_fib_divisible_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.04 | 2026-02-08T05:57:35.478031Z | {
"verified": true,
"answer": 44532,
"timestamp": "2026-02-08T05:57:35.517915Z"
} | d6b63c | 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": 1552
},
"timestamp": "2026-02-12T17:09:55.489Z",
"answer": 44532
},
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
167fb6 | antilemma_coprime_grid_v1_1874849503_830 | Compute the number of ordered pairs $(i, j)$ of positive integers such that $1 \leq i \leq 18$, $1 \leq j \leq 72$, and $\gcd(i, j) = 1$. Determine the value of this number. | 803 | 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(18)), right=IntegerRange(start=Const(1), end=Const(72))))),
},
... | NT | COMB | COMPUTE | sympy | COUNT_COPRIME_GRID | [
"COUNT_COPRIME_GRID"
] | 20ec03 | antilemma_coprime_grid_v1 | null | 6 | 0 | [
"COUNT_COPRIME_GRID"
] | 1 | 0.001 | 2026-02-08T13:19:44.885814Z | {
"verified": true,
"answer": 803,
"timestamp": "2026-02-08T13:19:44.886435Z"
} | 50aab8 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 169,
"completion_tokens": 1774
},
"timestamp": "2026-02-09T21:27:22.639Z",
"answer": 803
},
{
"id... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "... | {
"lo": -6.5,
"mid": -0.2,
"hi": 6.11
} | ||
b31e70 | alg_linear_system_2x2_v1_1218484723_6564 | Let $V$ be the number of integers $v$ with $41 \le v \le 11849$ such that $v = 41b^2$ for some integer $b$ with $1 \le b \le 17$. Let
$$
det = \min_{\substack{1 \le a \le 8 \\ 1 \le b \le 8}} \left( V \cdot a^2 - 4ab + 5b^2 \right) + 60.
$$
Let $R = 1685730 + 5631840$ and $S = 5068656 - 5057190$. Compute $\frac{R + S}{... | 93,962 | graphs = [
Graph(
let={
"_m": Const(41),
"_n": Const(18),
"num_x": Sub(Const(1685730), Mul(Const(281592), Const(-20))),
"num_y": Sub(Mul(Ref("_n"), Const(281592)), Mul(Const(3), Const(1685730))),
"det": Sub(MinOverSet(set=MapOverSet(set=SolutionsSe... | ALG | null | COMPUTE | sympy | QF_PSD_DISTINCT | [
"QF_PSD_DISTINCT/QF_PSD_MIN"
] | c847e8 | alg_linear_system_2x2_v1 | null | 4 | 0 | [
"QF_PSD_DISTINCT",
"QF_PSD_MIN"
] | 2 | 0.006 | 2026-02-25T08:06:52.704392Z | {
"verified": true,
"answer": 93962,
"timestamp": "2026-02-25T08:06:52.710398Z"
} | bba02d | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 261,
"completion_tokens": 1999
},
"timestamp": "2026-03-30T02:14:19.395Z",
"answer": 93962
},
{
"... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_DISTINCT",
"status": "ok"
},
{
"lemma": "QF_PSD_MIN",
"status": "ok_later"
}
] | {
"lo": -3.33,
"mid": 1.03,
"hi": 5.26
} | ||
ef87d8 | comb_binomial_compute_v1_601307018_10989 | Let $k$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 40$ such that $$
\min\{ 4a_1^2 + 20a_1b_1 + 26b_1^2 : a_1, b_1 \in \mathbb{Z}^+,\, 1 \le a_1, b_1 \le 8 \} \cdot b^2 + 50a^2 = 62500.
$$ Let $S = \binom{12}{k}$. Find the remainder when $50393S$ is divided by $91391$. | 64,780 | graphs = [
Graph(
let={
"_m": Const(91391),
"_n": Const(2),
"n": Const(12),
"k": 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"), Con... | COMB | null | COMPUTE | sympy | POLY_ORBIT_HENSEL | [
"QF_PSD_MIN/QF_PSD_COUNT"
] | 8acf65 | comb_binomial_compute_v1 | null | 7 | 0 | [
"POLY_ORBIT_HENSEL",
"QF_PSD_COUNT",
"QF_PSD_MIN"
] | 3 | 0.053 | 2026-03-10T11:25:27.284341Z | {
"verified": true,
"answer": 64780,
"timestamp": "2026-03-10T11:25:27.337428Z"
} | 1c20d8 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 256,
"completion_tokens": 2157
},
"timestamp": "2026-04-19T15:15:11.493Z",
"answer": 64780
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT",
"status": "ok_later"
},
{
"lemma": "QF_PSD_MIN",
"status": "ok"
},
{
"lemma": "V7",
"... | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
f238de | nt_count_intersection_v1_1978505735_2858 | Let $N = 100000$. Let $a$ be the smallest divisor of $3823963$ that is at least $2$. Let $b = 6$. Compute the number of positive integers $n$ with $1 \leq n \leq N$ such that $a$ divides $n$ and $\gcd(n, b) = 1$. | 3,030 | graphs = [
Graph(
let={
"N": Const(100000),
"a": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(3823963))))),
"b": Const(6),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condit... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | nt_count_intersection_v1 | null | 4 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 4.794 | 2026-02-08T17:13:20.680779Z | {
"verified": true,
"answer": 3030,
"timestamp": "2026-02-08T17:13:25.474501Z"
} | 7b5e77 | 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": 1054
},
"timestamp": "2026-02-17T21:36:13.518Z",
"answer": 3030
},
{... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
7f2e49 | algebra_quadratic_discriminant_v1_238844314_521 | Compute the value of $(-11)^2 - 4(-1)(-30)$. | 1 | graphs = [
Graph(
let={
"a": Const(-1),
"b": Const(-11),
"c": Const(-30),
"result": Sub(Pow(Ref("b"), Const(2)), Mul(Const(4), Ref("a"), Ref("c"))),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"MIN_PRIME_FACTOR"
] | bc3776 | algebra_quadratic_discriminant_v1 | null | 2 | 0 | [
"COPRIME_PAIRS",
"MIN_PRIME_FACTOR"
] | 2 | 0.013 | 2026-02-08T13:23:12.780038Z | {
"verified": true,
"answer": 1,
"timestamp": "2026-02-08T13:23:12.792882Z"
} | 9e999c | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 75,
"completion_tokens": 108
},
"timestamp": "2026-02-16T04:32:21.467Z",
"answer": 1
},
{
"id": 11,
"m... | 2 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
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"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V8_SUM",
"status":... | {
"lo": -9.12,
"mid": -6.02,
"hi": -3.62
} | ||
f240b4 | geo_count_lattice_rect_v1_349078426_1002 | Compute the number of lattice points $(x, y)$ with integer coordinates that lie in the rectangle defined by $0 \le x \le 169$ and $0 \le y \le 291$, inclusive. | 49,640 | graphs = [
Graph(
let={
"a": Const(169),
"b": Const(291),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"Q": Abs(arg=Ref(name='result')),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.002 | 2026-02-08T13:21:55.731946Z | {
"verified": true,
"answer": 49640,
"timestamp": "2026-02-08T13:21:55.733690Z"
} | 6a2b4f | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 154,
"completion_tokens": 292
},
"timestamp": "2026-02-24T18:04:32.880Z",
"answer": 49640
},
{
"i... | 1 | [] | {
"lo": -7.18,
"mid": -5,
"hi": -3.01
} | ||||
9ec8d0 | diophantine_product_count_v1_1520064083_817 | Let $m = 57600$ and $n = 216$. Define $k$ to be the minimum value of $x + y$ over all ordered pairs of positive integers $(x, y)$ such that $xy = m$. Let $u$ be the number of ordered pairs of positive odd integers $(x_1, x_2)$ such that $x_1 + x_2 = n$. Compute the number of positive integers $x$ such that $1 \le x \le... | 16 | graphs = [
Graph(
let={
"_m": Const(57600),
"_n": Const(216),
"k": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_m")))), ex... | NT | null | COUNT | sympy | LIN_FORM | [
"COMB1",
"B3"
] | 44bb30 | diophantine_product_count_v1 | null | 7 | 0 | [
"B3",
"COMB1",
"LIN_FORM"
] | 3 | 0.16 | 2026-02-08T03:37:14.734513Z | {
"verified": true,
"answer": 16,
"timestamp": "2026-02-08T03:37:14.894787Z"
} | cd919a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 233,
"completion_tokens": 2182
},
"timestamp": "2026-02-10T15:06:58.124Z",
"answer": 16
},
{
"id"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},... | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
f02532 | antilemma_sum_equals_v1_865884756_2317 | Let $n = 75$. Consider the set of all ordered pairs $(i, j)$ of positive integers such that $1 \leq i \leq 74$, $1 \leq j \leq 75$, and $i + j = n$. Let $x$ be the number of such pairs. Let $s$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 22$. Define $Q$ to be the Bell num... | 4,140 | graphs = [
Graph(
let={
"_n": Const(75),
"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(74)), right=IntegerRange(start=Const(1), end=Con... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COMB1",
"COUNT_SUM_EQUALS"
] | 8e32ac | antilemma_sum_equals_v1 | bell_mod | 3 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS"
] | 2 | 0.016 | 2026-02-08T16:41:26.026769Z | {
"verified": true,
"answer": 4140,
"timestamp": "2026-02-08T16:41:26.043177Z"
} | 1c313a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 173,
"completion_tokens": 718
},
"timestamp": "2026-02-17T09:52:10.281Z",
"answer": 4140
},
{
... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7... | {
"lo": -8,
"mid": -4.75,
"hi": -2.28
} | ||
88336f | nt_count_divisors_in_range_v1_784195855_4383 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = 34$. Let $P$ be the maximum value of $xy$ over all such pairs. Let $T$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = P$. Define $a$ to be the minimum value of $x + y$ over all such pairs in $T$. Let ... | 64,893 | graphs = [
Graph(
let={
"n": Const(166320),
"a": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), MaxOverSet(set=MapOverSet(set=SolutionsSet(var... | NT | null | COUNT | sympy | B1 | [
"B1/B3"
] | 80b49d | nt_count_divisors_in_range_v1 | null | 6 | 0 | [
"B1",
"B3"
] | 2 | 0.282 | 2026-02-08T07:04:35.562918Z | {
"verified": true,
"answer": 64893,
"timestamp": "2026-02-08T07:04:35.844470Z"
} | bf2295 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 194,
"completion_tokens": 2596
},
"timestamp": "2026-02-13T07:33:34.094Z",
"answer": 64893
},
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
9e1098_l | comb_binomial_compute_v1_809748730_117 | Let $n = 16$. Define $k$ to be the number of nonnegative integers $j$ such that $0 \le j \le 10304$ and $\binom{10304}{j}$ is odd. Compute $\binom{n}{k}$. | 0 | ALG | COMB | COMPUTE | sympy | V8 | [
"V8"
] | 86348e | comb_binomial_compute_v1 | null | 6 | 0 | [
"V8"
] | 1 | 0.002 | 2026-02-08T11:19:45.019499Z | {
"verified": false,
"answer": 12870,
"timestamp": "2026-02-08T11:19:45.021072Z"
} | c7e70d | 9e1098 | 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": 168,
"completion_tokens": 975
},
"timestamp": "2026-02-24T13:31:09.938Z",
"answer": 12870
},
{
"i... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
},
{
"lemma": "VAL_SUM_EQ",
"status": "n... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | |
1ec0b9 | sequence_fibonacci_compute_v1_1918700295_2416 | Let $m = 20$. Let $\mathcal{P}$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = m$, and let $\mathcal{S}$ be the set of all products $xy$ as $(x, y)$ ranges over $\mathcal{P}$. Let $n$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy$ eq... | 26,060 | graphs = [
Graph(
let={
"_m": Const(20),
"_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 | COMPUTE | sympy | B1 | [
"B1/B3"
] | 80b49d | sequence_fibonacci_compute_v1 | null | 5 | 0 | [
"B1",
"B3"
] | 2 | 0.004 | 2026-02-08T07:52:36.371749Z | {
"verified": true,
"answer": 26060,
"timestamp": "2026-02-08T07:52:36.375684Z"
} | 656603 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 197,
"completion_tokens": 1365
},
"timestamp": "2026-02-13T13:07:04.025Z",
"answer": 26060
},
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
b658a9 | algebra_vieta_sum_v1_1742523217_248 | Let $f(x) = -x^3 + 5x^2 + a x - 240$, where $a$ is the number of positive integers $n$ at most $128$ that are relatively prime to $21$. Compute the sum of all integer roots of the equation $f(x) = 0$. Multiply this sum by $44121$, and find the remainder when the result is divided by $57331$. | 48,612 | graphs = [
Graph(
let={
"_n": Const(21),
"result": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Mul(Const(-1), Pow(Var("x"), Const(3))), Mul(Const(5), Pow(Var("x"), Const(2))), Mul(CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Va... | NT | null | COMPUTE | sympy | C4 | [
"C4"
] | 08d162 | algebra_vieta_sum_v1 | null | 6 | 0 | [
"C4"
] | 1 | 0.014 | 2026-02-08T02:56:46.738239Z | {
"verified": true,
"answer": 48612,
"timestamp": "2026-02-08T02:56:46.752260Z"
} | bc4bb6 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 199,
"completion_tokens": 1232
},
"timestamp": "2026-02-09T15:27:31.918Z",
"answer": 48612
},
{
"... | 1 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
}
] | {
"lo": -5.54,
"mid": -3.04,
"hi": -0.38
} | ||
37e59d | comb_binomial_compute_v1_458359167_2898 | Let $ n $ be the largest prime number such that $ 2 \leq n \leq 13 $. Let $ k $ be the largest prime number such that $ 2 \leq k \leq 6 $. Compute $ \binom{n}{k} $. Find the value of this binomial coefficient. | 1,287 | graphs = [
Graph(
let={
"_n": Const(6),
"n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(13)), IsPrime(Var("n"))))),
"k": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n")... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | comb_binomial_compute_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.002 | 2026-02-08T06:49:37.730746Z | {
"verified": true,
"answer": 1287,
"timestamp": "2026-02-08T06:49:37.732376Z"
} | 2fcc26 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 121,
"completion_tokens": 845
},
"timestamp": "2026-02-15T17:47:58.580Z",
"answer": 1287
},
{
"id": 11,
... | 2 | [
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -9.14,
"mid": -6.05,
"hi": -3.73
} | ||
0f3446 | diophantine_fbi2_min_v1_1520064083_7644 | Let $k = 77$ and let $u$ be the number of positive integers $n \leq 175$ for which the sum of the decimal digits of $n$ is even. Compute the smallest divisor $d$ of $k$ such that $4 \leq d \leq u$ and $\frac{k}{d} \geq 2$. | 7 | graphs = [
Graph(
let={
"k": Const(77),
"upper": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(175)), Eq(Mod(value=DigitSum(Var("n")), modulus=Const(2)), Const(0))))),
"result": MinOverSet(set=SolutionsSet(var=Var("... | NT | null | EXTREMUM | sympy | L3B | [
"L3B"
] | cc148f | diophantine_fbi2_min_v1 | null | 4 | 0 | [
"L3B"
] | 1 | 0.006 | 2026-02-08T09:13:50.266116Z | {
"verified": true,
"answer": 7,
"timestamp": "2026-02-08T09:13:50.271711Z"
} | 780b9d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 121,
"completion_tokens": 2003
},
"timestamp": "2026-02-14T01:38:26.485Z",
"answer": 7
},
{
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3B",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
f4fdc3_l | antilemma_sum_equals_v1_2051736721_2025 | Let $c = 65$. Define $m$ to be the number of ordered pairs $(i, j)$ of positive integers such that $i + j = c$, $1 \le i \le 64$, and $1 \le j \le 65$. Define $n$ to be the number of ordered pairs $(i_1, j_1)$ of positive integers such that $i_1 + j_1 = m$, $1 \le i_1 \le 63$, and $1 \le j_1 \le 63$. Let $x$ be the num... | 61 | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | ae9919 | antilemma_sum_equals_v1 | null | 4 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.024 | 2026-02-08T16:25:09.852351Z | {
"verified": false,
"answer": 60,
"timestamp": "2026-02-08T16:25:09.876489Z"
} | 767dc7 | f4fdc3 | legacy_text | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 291,
"completion_tokens": 1016
},
"timestamp": "2026-02-24T21:07:06.802Z",
"answer": 60
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"stat... | {
"lo": -2.4,
"mid": 1.57,
"hi": 5.75
} | |
e97158 | diophantine_fbi2_min_v1_1520064083_8970 | Let $m = 57165$ and $n = \sum_{k=1}^{2} k$. Let $d$ be an integer satisfying the following conditions:
- $d \geq \sum_{k=1}^{n} \phi(k) \left\lfloor \frac{3}{k} \right\rfloor$,
- $d \leq 70$,
- $d$ divides $60$,
- $\frac{60}{d} \geq 6$.
Let $r$ be the smallest such integer $d$. Define $Q = m \cdot r \mod 91346$, the r... | 68,952 | graphs = [
Graph(
let={
"_m": Const(57165),
"_n": Summation(var="k", start=Const(1), end=Const(2), expr=Var("k")),
"k": Const(60),
"upper": Const(70),
"result": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Summation(var="k"... | NT | null | EXTREMUM | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC/K2"
] | 06cc86 | diophantine_fbi2_min_v1 | null | 5 | 0 | [
"K2",
"SUM_ARITHMETIC"
] | 2 | 0.007 | 2026-02-08T10:27:23.834147Z | {
"verified": true,
"answer": 68952,
"timestamp": "2026-02-08T10:27:23.840723Z"
} | bafc0c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 197,
"completion_tokens": 949
},
"timestamp": "2026-02-14T07:30:02.090Z",
"answer": 68952
},
{... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K2",
"status": "ok_later"
},
{
"lemma": "LTE_DIFF_P2",
... | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
f221e3 | modular_modexp_compute_v1_1456120455_106 | Let $a = 47$. Let $e$ be the number of integers $t$ such that $36 \leq t \leq 1692$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 54$, $1 \leq b \leq 42$, and $t = 15a + 21b$. Let $m = 58564$. Compute the remainder when $a^e$ is divided by $m$. | 51,363 | graphs = [
Graph(
let={
"a": Const(47),
"e": 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=54)), Geq(left=Var(n... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | modular_modexp_compute_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T02:53:45.559274Z | {
"verified": true,
"answer": 51363,
"timestamp": "2026-02-08T02:53:45.560247Z"
} | 9a9b69 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 216,
"completion_tokens": 32768
},
"timestamp": "2026-02-23T17:55:12.122Z",
"answer": null
},
{
... | 0 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
}
] | {
"lo": 4.62,
"mid": 6.54,
"hi": 9.53
} | ||
6c9d5c | nt_max_prime_below_v1_865884756_4940 | Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 36$, $\gcd(p, q) = 1$, and $p < q$. Let $L$ be the number of elements in $S$. Let $T$ be the set of all prime numbers $n$ such that $L \leq n \leq 10609$. Let $M$ be the maximum element of $T$. Compute the rema... | 21,096 | graphs = [
Graph(
let={
"_n": Const(44121),
"upper": Const(10609),
"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 | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.232 | 2026-02-08T18:17:19.906241Z | {
"verified": true,
"answer": 21096,
"timestamp": "2026-02-08T18:17:20.138445Z"
} | 83b5c3 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 165,
"completion_tokens": 3223
},
"timestamp": "2026-02-18T15:53:25.261Z",
"answer": 21096
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
355bbe | comb_count_derangements_v1_1218484723_5038 | Let $D_n$ denote the number of derangements of $n$ elements, and let $n = \sum_{k=\binom{10}{0} - 1}^{2} 2^{k}$. Compute the remainder when $88523 \cdot D_n$ is divided by $62460$. | 39,222 | graphs = [
Graph(
let={
"_n": Const(62460),
"n": Summation(var="k", start=Sub(Binom(n=Const(10), k=Const(0)), Const(1)), end=Const(2), expr=Pow(Const(2), Var("k"))),
"result": Subfactorial(arg=Ref(name='n')),
"Q": Mod(value=Mul(Const(88523), Ref("result")), mo... | COMB | null | COUNT | sympy | SUM_GEOM | [
"SUM_GEOM",
"ZERO_BINOM_0"
] | 71c45c | comb_count_derangements_v1 | null | 3 | 0 | [
"SUM_GEOM",
"ZERO_BINOM_0"
] | 2 | 0.002 | 2026-02-25T06:39:56.326908Z | {
"verified": true,
"answer": 39222,
"timestamp": "2026-02-25T06:39:56.328639Z"
} | 79125b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 176,
"completion_tokens": 1675
},
"timestamp": "2026-03-29T19:08:27.876Z",
"answer": 39222
},
{
"... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "SUM_GEOM",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"st... | {
"lo": -3.33,
"mid": 1.03,
"hi": 5.26
} | ||
71a18b | antilemma_sum_equals_v1_1915831931_1384 | Let $c = 56805$. Let $m$ be the number of ordered pairs $(i, j)$ of integers such that $1 \leq i \leq 55$, $1 \leq j \leq 55$, and $i + j = 55$. Let $n$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = m$. Let $x$ be the number of ordered pairs $(i_1, j_1)$ of integers such th... | 35,255 | graphs = [
Graph(
let={
"_c": Const(56805),
"_m": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(55)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(55)), right=IntegerRange(start=Const(1), end... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS/COMB1/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | 24903c | antilemma_sum_equals_v1 | null | 5 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS"
] | 2 | 0.021 | 2026-02-08T16:03:44.016864Z | {
"verified": true,
"answer": 35255,
"timestamp": "2026-02-08T16:03:44.037869Z"
} | d50be2 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 287,
"completion_tokens": 1346
},
"timestamp": "2026-02-24T19:42:35.371Z",
"answer": 35255
},
{
... | 1 | [
{
"lemma": "COMB1",
"status": "ok_later"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"sta... | {
"lo": -2.4,
"mid": 1.57,
"hi": 5.75
} | ||
d2be13 | sequence_count_fib_divisible_v1_168721529_43 | Let $S$ be the set of all even integers $n$ such that $1 \leq n \leq 44$. Let $T$ be the set of all positive integers $n \leq \sum S$ for which the Fibonacci number $F_n$ is divisible by $2$. Let $r$ be the number of elements in $T$. Compute the value of $\sum_{i=0}^{d-1} d_i (i+1)^2 + 13689$, where $d_i$ is the $i$-th... | 13,730 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(44)), Eq(Mod(value=Var("n"), modulus=Const(2)), Const(0))))),
"d": Const(2),
"result": CountOverSet(set=Soluti... | NT | null | COUNT | sympy | SUM_DIVISIBLE | [
"SUM_DIVISIBLE"
] | 02dbe3 | sequence_count_fib_divisible_v1 | null | 4 | 0 | [
"SUM_DIVISIBLE"
] | 1 | 0.028 | 2026-02-08T12:46:43.316691Z | {
"verified": true,
"answer": 13730,
"timestamp": "2026-02-08T12:46:43.345038Z"
} | 29b22f | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 262,
"completion_tokens": 854
},
"timestamp": "2026-02-08T20:57:40.334Z",
"answer": 13730
},
{
"i... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "SUM_DIVISIBLE",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -5.3,
"mid": -2.04,
"hi": 1.84
} | ||
016fe1 | comb_catalan_compute_v1_898971024_1461 | Let $n_2 = \binom{16}{16} - 1$. Define $w = \sum_{k=0}^{n_2} (-1)^k \binom{n_2}{k}$. Let $u = 5$ and $n_1 = u + w$. Define $h = \sum_{k_1=0}^{n_1} (-1)^{k_1} \binom{n_1}{k_1}$. Let $m$ be the number of ordered triples $(x_1, x_2, x_3)$ of positive odd integers such that $x_1 + x_2 + x_3 = 9$. Define $n = m + h$. Let $\... | 228 | graphs = [
Graph(
let={
"n2": Sub(Binom(n=Const(16), k=Const(16)), Const(1)),
"w": Summation(var="k", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n2"), k=Var("k")))),
"u": Const(5),
"n1": Sum(Ref("u"), Ref("w")),
... | COMB | NT | COMPUTE | sympy | COMB1 | [
"COMB1/BINOMIAL_ALTERNATING",
"ZERO_BINOM_N"
] | fcdf3f | comb_catalan_compute_v1 | null | 6 | 2 | [
"BINOMIAL_ALTERNATING",
"COMB1",
"ZERO_BINOM_N"
] | 3 | 0.008 | 2026-02-08T16:08:57.779296Z | {
"verified": true,
"answer": 228,
"timestamp": "2026-02-08T16:08:57.787443Z"
} | 9e932b | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 323,
"completion_tokens": 6212
},
"timestamp": "2026-02-24T19:58:24.604Z",
"answer": 228
},
{
"i... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok_later"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"... | {
"lo": 1.98,
"mid": 5.23,
"hi": 8.52
} | ||
5b1175 | diophantine_fbi2_count_v1_168721529_229 | Let $k = 1260$. Determine the number of positive integers $d$ such that $6 \leq d \leq 110$, $d$ divides $k$, and $2 \leq \frac{k}{d} \leq 106$. Denote this count by $m$. Compute the value of
$$
\sum_{n=1}^{m} \phi(n),
$$
where $\phi(n)$ denotes Euler's totient function. | 102 | graphs = [
Graph(
let={
"k": Const(1260),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(6)), Leq(Var("d"), Const(110)), Divides(divisor=Var("d"), dividend=Ref("k")), Geq(Div(Ref("k"), Var("d")), Const(2)), Leq(Div(Ref("k"), Var("d")), Const(1... | NT | null | COUNT | sympy | ONE_PHI_2 | [
"SUM_ARITHMETIC"
] | eb34f0 | diophantine_fbi2_count_v1 | null | 5 | 0 | [
"ONE_PHI_2",
"SUM_ARITHMETIC"
] | 2 | 0.04 | 2026-02-08T12:54:22.538487Z | {
"verified": true,
"answer": 102,
"timestamp": "2026-02-08T12:54:22.578570Z"
} | 20b00a | CC BY 4.0 | [
{
"id": 4,
"model": "NousResearch/Hermes-4-405B",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 156,
"completion_tokens": 778
},
"timestamp": "2026-02-09T14:37:12.250Z",
"answer": 396
},
... | 1 | [
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "... | {
"lo": -1.9,
"mid": 2.34,
"hi": 6.68
} | ||
fb4c8a | antilemma_sum_equals_v1_1915831931_316 | Let $T$ be the set of all integers $t$ such that there exist positive integers $a$ and $b$ with $1 \leq a \leq 29$, $1 \leq b \leq 5$, $7 \leq t \leq 83$, and $t = 2a + 5b$. Let $n$ be the number of elements in $T$. Determine the number of ordered pairs $(i, j)$ of positive integers with $1 \leq i \leq 71$, $1 \leq j \... | 71 | 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=29)), Geq(left=Var(name='b'), right=Const(value... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"LIN_FORM/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | ada383 | antilemma_sum_equals_v1 | null | 5 | 0 | [
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 2 | 0.036 | 2026-02-08T15:21:45.276818Z | {
"verified": true,
"answer": 71,
"timestamp": "2026-02-08T15:21:45.313056Z"
} | 6e1d14 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 245,
"completion_tokens": 5333
},
"timestamp": "2026-02-24T20:32:43.707Z",
"answer": 71
},
{
"id"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"statu... | {
"lo": -4.1,
"mid": -1.76,
"hi": 1.26
} | ||
722614 | comb_count_derangements_v1_717093673_1519 | Let $d$ be a positive divisor of $41503$. Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $p < q$, $pq = 6$, and $\gcd(p, q) = 1$. Determine the number of elements in $S$, and let $n$ be the smallest such divisor $d$ satisfying $d \geq |S|$. Compute the subfactori... | 1,854 | graphs = [
Graph(
let={
"_n": Const(41503),
"n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name=... | NT | COMB | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/MIN_PRIME_FACTOR"
] | 52cee2 | comb_count_derangements_v1 | null | 4 | 0 | [
"COPRIME_PAIRS",
"MIN_PRIME_FACTOR"
] | 2 | 0.003 | 2026-02-08T16:08:05.275272Z | {
"verified": true,
"answer": 1854,
"timestamp": "2026-02-08T16:08:05.277977Z"
} | a6234a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 153,
"completion_tokens": 1806
},
"timestamp": "2026-02-16T21:59:54.936Z",
"answer": 1854
},
{... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok_later"
},
{
"lemma": "MOD_SUB",
"status":... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
a49d40 | sequence_count_fib_divisible_v1_458359167_4288 | Let $n = 289$. Let $T$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = n$. For each such pair, compute $x + y$, and let $s$ be the minimum value of $x + y$ over all such pairs. Now, let $U$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = s$. For each such p... | 72 | graphs = [
Graph(
let={
"_n": Const(289),
"upper": 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")), MinOverSet(set=MapOverSet(set=SolutionsSet(v... | NT | null | COUNT | sympy | V1 | [
"B3/B1"
] | 7f76f7 | sequence_count_fib_divisible_v1 | null | 6 | 0 | [
"B1",
"B3",
"V1"
] | 3 | 0.032 | 2026-02-08T11:40:41.628724Z | {
"verified": true,
"answer": 72,
"timestamp": "2026-02-08T11:40:41.661065Z"
} | 22b113 | 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": 1636
},
"timestamp": "2026-02-14T17:07:28.255Z",
"answer": 72
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemm... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
c36ac2 | algebra_quadratic_discriminant_v1_1520064083_6797 | Let $a = \sum_{k=1}^{4} \phi(k) \left\lfloor \frac{4}{k} \right\rfloor$, $b = 3$, and $c = 10$. Define $D = b^2 - 4ac$. Let $x = 2 \cdot [D > 0] + [D = 0]$, where $[P]$ is $1$ if $P$ is true and $0$ otherwise. Find the value of $x$. | 0 | graphs = [
Graph(
let={
"_n": Const(2),
"a": Summation(var="k", start=Const(1), end=Const(4), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(4), Var("k"))))),
"b": Const(3),
"c": Const(10),
"D": Sub(Pow(Ref("b"), Const(2)), Mul(Const(4), Ref("a"), ... | NT | null | COMPUTE | sympy | V8 | [
"K2"
] | 6897ab | algebra_quadratic_discriminant_v1 | null | 4 | 0 | [
"K2",
"V8"
] | 2 | 0.056 | 2026-02-08T08:20:41.915009Z | {
"verified": true,
"answer": 0,
"timestamp": "2026-02-08T08:20:41.970592Z"
} | 3f648a | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 165,
"completion_tokens": 434
},
"timestamp": "2026-02-15T20:11:34.380Z",
"answer": 0
},
{
"id": 11,
"... | 2 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
... | {
"lo": -10,
"mid": -7.73,
"hi": -5.46
} | ||
007c61 | comb_sum_binomial_row_v1_655260480_804 | Let $n$ be the number of ordered triples $(x_1, x_2, x_3)$ of positive odd integers such that $x_1 + x_2 + x_3 = 9$. Compute $2^n$. | 1,024 | graphs = [
Graph(
let={
"_n": Const(2),
"n": 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(nam... | NT | null | SUM | sympy | COMB1 | [
"COMB1"
] | 567f58 | comb_sum_binomial_row_v1 | null | 3 | 0 | [
"COMB1"
] | 1 | 0.002 | 2026-02-08T15:37:32.421511Z | {
"verified": true,
"answer": 1024,
"timestamp": "2026-02-08T15:37:32.423582Z"
} | 320e1f | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 108,
"completion_tokens": 429
},
"timestamp": "2026-02-16T06:12:40.666Z",
"answer": 32768
},
{
"id": 11... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
4b3d20 | sequence_fibonacci_compute_v1_2051736721_5860 | Let $n$ be the smallest divisor of $640987$ that is at least $2$. Let $F_n$ denote the $n$th Fibonacci number, with $F_1 = F_2 = 1$ and $F_{k} = F_{k-1} + F_{k-2}$ for $k \geq 3$. Compute the remainder when $50141 \cdot F_n$ is divided by $96430$. | 83,637 | graphs = [
Graph(
let={
"_n": Const(2),
"n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(640987))))),
"result": Fibonacci(arg=Ref(name='n')),
"Q": Mod(value=Mul(Const(50141), Ref("r... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | sequence_fibonacci_compute_v1 | null | 2 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.002 | 2026-02-08T18:50:18.833663Z | {
"verified": true,
"answer": 83637,
"timestamp": "2026-02-08T18:50:18.835256Z"
} | cc641f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 141,
"completion_tokens": 2105
},
"timestamp": "2026-02-18T19:54:50.198Z",
"answer": 83637
},
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": ... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
9126ed | nt_max_prime_below_v1_898971024_2256 | Let $P$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 54$, $\gcd(p, q) = 1$, and $p < q$. Let $L$ be the number of elements in $P$. Define $S$ to be the set of all prime numbers $n$ such that $L \leq n \leq 46225$. Compute the largest element of $S$. | 46,219 | graphs = [
Graph(
let={
"upper": Const(46225),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), V... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_max_prime_below_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 1.157 | 2026-02-08T16:38:01.114596Z | {
"verified": true,
"answer": 46219,
"timestamp": "2026-02-08T16:38:02.271731Z"
} | c59d7c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 144,
"completion_tokens": 2680
},
"timestamp": "2026-02-17T07:55:18.143Z",
"answer": 46219
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
718cce | comb_count_permutations_fixed_v1_1915831931_142 | Let $k$ be the largest prime number $n_1$ such that $2 \le n_1 \le 6$. Define $\text{result} = \binom{7}{k} \cdot ! (7 - k)$, where $!m$ denotes the number of derangements of $m$ elements. Compute the value of $\text{result}$. | 21 | graphs = [
Graph(
let={
"_n": Const(2),
"n": Const(7),
"k": MaxOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Ref("_n")), Leq(Var("n1"), Const(6)), IsPrime(Var("n1"))))),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub(l... | NT | COMB | COUNT | sympy | COPRIME_PAIRS | [
"MAX_PRIME_BELOW"
] | dc3ad3 | comb_count_permutations_fixed_v1 | null | 4 | 0 | [
"COPRIME_PAIRS",
"MAX_PRIME_BELOW"
] | 2 | 0.106 | 2026-02-08T15:12:20.594054Z | {
"verified": true,
"answer": 21,
"timestamp": "2026-02-08T15:12:20.699634Z"
} | 321155 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 123,
"completion_tokens": 486
},
"timestamp": "2026-02-16T01:51:58.734Z",
"answer": 21
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_MUL",... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
aceebe | alg_sym_quad_system_v1_1218484723_2571 | Let $T$ be the number of integers $t$ with $20 \le t \le 17560$ that can be written as $t = 6a + 14b$ for some integers $a, b$ satisfying $1 \le a \le 269$, $1 \le b \le 1139$. Let $M$ be the sum of $a^5 + b^5 + c^5$ modulo $2233$ over all positive integers $a, b, c$ such that $a^2 + b^2 + c^2 = ab + bc + ca$ and $7a +... | 10,176 | graphs = [
Graph(
let={
"_n": Const(2233),
"result": Mod(value=SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b"), Var("c")]), condition=And(Eq(Sum(Pow(Var("a"), Const(2)), Pow(Var("b"), Const(2)), Pow(Var("c"), Const(2))), Sum(Mul(Var("a"), Var("b")), ... | ALG | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | alg_sym_quad_system_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.016 | 2026-02-25T04:18:49.627897Z | {
"verified": true,
"answer": 10176,
"timestamp": "2026-02-25T04:18:49.643484Z"
} | 50eadf | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 260,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T05:30:29.096Z",
"answer": 10176
},
{
... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 1.55,
"mid": 4.7,
"hi": 7.23
} | ||
a8c4a9 | nt_sum_divisors_mod_v1_151522320_1722 | Let $n_1 = 1$, $n_2 = 1$, and $n = 180$. Define $f = \omega(n_2)$, where $\omega(n)$ denotes the number of distinct prime factors of $n$. Let $m = \sum_{d \mid n_1} \mu(d)$, where $\mu$ is the M\"obius function. Define $M = (10733 + f) \cdot m$ and $\sigma = \sum_{d \mid n} d$. Compute the remainder when $\sigma$ is di... | 546 | graphs = [
Graph(
let={
"n2": Const(1),
"f": SmallOmega(n=Ref(name='n2')),
"n1": Const(1),
"m": SumOverDivisors(n=Ref(name='n1'), var='d', expr=MoebiusMu(n=Var(name='d'))),
"n": Const(180),
"M": Mul(Sum(Const(10733), Ref("f")), Ref("m")... | NT | null | COMPUTE | sympy | MOBIUS_SUM | [
"MOBIUS_SUM",
"OMEGA_ZERO"
] | ef9fb4 | nt_sum_divisors_mod_v1 | null | 4 | 2 | [
"MOBIUS_SUM",
"OMEGA_ZERO"
] | 2 | 0.004 | 2026-02-08T04:12:58.898561Z | {
"verified": true,
"answer": 546,
"timestamp": "2026-02-08T04:12:58.902447Z"
} | 15d528 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 221,
"completion_tokens": 396
},
"timestamp": "2026-02-18T10:50:50.183Z",
"answer": 546
}
] | 2 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOBIUS_SUM",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},... | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
029bc8 | comb_catalan_compute_v1_655260480_447 | Let $S$ be the set of all ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = N$, where $N$ is the number of integers $t$ with $7 \le t \le 32$ for which there exist integers $a$ and $b$ satisfying $1 \le a \le 4$, $1 \le b \le 5$, and $t = 3a + 4b$. Let $n$ be the number of elements in $S$. Let ... | 42,557 | graphs = [
Graph(
let={
"_n": Const(57305),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2")),... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM",
"LIN_FORM/COMB1"
] | 336462 | comb_catalan_compute_v1 | negation_mod | 6 | 0 | [
"COMB1",
"LIN_FORM"
] | 2 | 0.01 | 2026-02-08T15:23:40.492081Z | {
"verified": true,
"answer": 42557,
"timestamp": "2026-02-08T15:23:40.502374Z"
} | 8457dc | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 338,
"completion_tokens": 18854
},
"timestamp": "2026-02-24T20:48:17.174Z",
"answer": 42557
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok_later"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
... | {
"lo": -2.43,
"mid": 1.2,
"hi": 4.84
} | ||
351bfa | nt_count_divisible_and_v1_1874849503_19 | Let $d_1$ be the number of integers $t$ such that $14 \leq t \leq 44$ and there exist integers $a$, $b$ with $1 \leq a \leq 6$, $1 \leq b \leq 2$, and $t = 4a + 10b$. Let $d_2 = 18$. Define $N$ to be the number of positive integers $n$ such that $n \leq 73260$, $n$ is divisible by $d_1$, and $n$ is divisible by $d_2$. ... | 15,823 | graphs = [
Graph(
let={
"upper": Const(73260),
"d1": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=6)), Geq(lef... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_count_divisible_and_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 2.384 | 2026-02-08T12:45:55.365081Z | {
"verified": true,
"answer": 15823,
"timestamp": "2026-02-08T12:45:57.749276Z"
} | 6deb56 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 278,
"completion_tokens": 4156
},
"timestamp": "2026-02-09T12:55:29.464Z",
"answer": 15823
},
{
"... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -5.15,
"mid": 0.01,
"hi": 5.44
} | ||
52e47a | comb_sum_binomial_row_v1_458359167_5184 | Let $m = 14$ and $n_0 = 2$. Define $n$ to be the largest prime number satisfying $2 \leq n \leq 14$. Let $r = 2^n$. Let $p$ be the largest prime number satisfying $2 \leq p \leq 11$. Compute the Bell number $B_{r \bmod p}$.
Find the value of this Bell number. | 4,140 | graphs = [
Graph(
let={
"_m": Const(14),
"_n": Const(2),
"n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Ref("_m")), IsPrime(Var("n"))))),
"result": Pow(Const(2), Ref("n")),
"Q": Bell(Mod(value=A... | NT | COMB | SUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | 88ea9c | comb_sum_binomial_row_v1 | bell_mod | 5 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.002 | 2026-02-08T12:20:24.544103Z | {
"verified": true,
"answer": 4140,
"timestamp": "2026-02-08T12:20:24.546405Z"
} | cb471b | 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": 503
},
"timestamp": "2026-02-15T00:02:32.716Z",
"answer": 4140
},
{
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V8",
"status": "no"... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
8e1b2f | comb_count_permutations_fixed_v1_458359167_3162 | Let $n = 9$ and $d_0 = 2$. Let $k$ be the smallest divisor of $13013$ that is at least $d_0$. Define
$$
\text{result} = \binom{n}{k} \cdot !(n - k),
$$
where $!m$ denotes the number of derangements of $m$ elements. Let $c = 18127$. Compute the remainder when $c \cdot \text{result}$ is divided by $89030$. Determine th... | 29,362 | graphs = [
Graph(
let={
"_n": Const(2),
"n": Const(9),
"k": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(13013))))),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub... | NT | COMB | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | comb_count_permutations_fixed_v1 | null | 5 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.001 | 2026-02-08T07:00:20.681507Z | {
"verified": true,
"answer": 29362,
"timestamp": "2026-02-08T07:00:20.682949Z"
} | b8cddf | 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": 1305
},
"timestamp": "2026-02-13T07:03:17.940Z",
"answer": 29362
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
7687d0 | sequence_lucas_compute_v1_1248542787_691 | Let $n$ be the number of integers $t$ such that $27 \leq t \leq 120$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 5$, $1 \leq b \leq 4$, and $t = 12a + 15b$. Compute the $n$-th Lucas number. | 15,127 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=5)), Geq(left=Var(name='b'), right=Const(value=1... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | sequence_lucas_compute_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T03:19:59.325477Z | {
"verified": true,
"answer": 15127,
"timestamp": "2026-02-08T03:19:59.326262Z"
} | 760889 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 199,
"completion_tokens": 1330
},
"timestamp": "2026-02-09T07:01:56.293Z",
"answer": 15127
},
{
"... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.53,
"mid": 1.02,
"hi": 5.49
} | ||
6ddca3 | nt_sum_gcd_range_mod_v1_865884756_3842 | Let $N$ be the number of nonnegative integers $j$ such that $0 \leq j \leq 89595$ and $\binom{89595}{j}$ is odd. Let $k = 96$ and $M = 10267$. Define $\text{sum} = \sum_{n=1}^{N} \gcd(n, k)$. Let $r$ be the remainder when $\text{sum}$ is divided by $M$. Compute the remainder when $19479r$ is divided by $58300$. | 14,010 | graphs = [
Graph(
let={
"N": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(89595)), Eq(Mod(value=Binom(n=Const(89595), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')),
"k": Const(96),
"M"... | NT | null | COMPUTE | sympy | V8 | [
"V8"
] | 86348e | nt_sum_gcd_range_mod_v1 | null | 6 | 0 | [
"V8"
] | 1 | 0.599 | 2026-02-08T17:35:28.483460Z | {
"verified": true,
"answer": 14010,
"timestamp": "2026-02-08T17:35:29.082267Z"
} | f4c125 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 158,
"completion_tokens": 2895
},
"timestamp": "2026-02-18T05:27:23.630Z",
"answer": 14010
},
... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
9173ba | comb_sum_binomial_row_v1_1520064083_3300 | Let $n = \sum_{k=1}^{5} k$. Let $r = 2^n$. Let $d_0$ be the smallest divisor of $537251$ that is at least $2$. Compute the remainder when the Bell number $B_{|r| \bmod d_0}$ is divided by $82472$. | 33,503 | graphs = [
Graph(
let={
"_n": Const(2),
"n": Summation(var="k", start=Const(1), end=Const(5), expr=Var("k")),
"result": Pow(Ref("_n"), Ref("n")),
"Q": Mod(value=Bell(Mod(value=Abs(arg=Ref(name='result')), modulus=MinOverSet(set=SolutionsSet(var=Var("d"), condi... | NT | COMB | SUM | sympy | K13 | [
"MIN_PRIME_FACTOR",
"SUM_ARITHMETIC"
] | 82dc2c | comb_sum_binomial_row_v1 | bell_mod | 6 | 0 | [
"K13",
"MIN_PRIME_FACTOR",
"SUM_ARITHMETIC"
] | 3 | 0.218 | 2026-02-08T05:34:04.046897Z | {
"verified": true,
"answer": 33503,
"timestamp": "2026-02-08T05:34:04.264621Z"
} | 900fb2 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 119,
"completion_tokens": 853
},
"timestamp": "2026-02-12T10:46:07.325Z",
"answer": 33503
},
{... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "POLY_PADIC... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
bbf1f2 | comb_binomial_compute_v1_1918700295_1876 | Let $n$ be the number of integers $t$ such that $14 \leq t \leq 54$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 3$, $1 \leq b \leq 5$, and $t = 8a + 6b$. Compute the value of $48841 - \binom{n}{6}$. | 43,836 | 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... | ALG | COMB | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_binomial_compute_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T06:08:18.518201Z | {
"verified": true,
"answer": 43836,
"timestamp": "2026-02-08T06:08:18.520220Z"
} | c71532 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 202,
"completion_tokens": 951
},
"timestamp": "2026-02-24T05:32:08.499Z",
"answer": 43836
},
{
"i... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -4.93,
"mid": -2.91,
"hi": -0.71
} | ||
d64fe1 | antilemma_k2_v1_971394319_1451 | For each integer $k$ from $1$ to $404$, define $s_k$ to be the sum of all real solutions to the equation $x^2 - 404x - 25245 = 0$, divided by $k$, and then rounded down to the nearest integer. Let $x = \sum_{k=1}^{404} \phi(k) \cdot s_k$, where $\phi$ denotes Euler's totient function. Compute $x$. | 81,810 | graphs = [
Graph(
let={
"_n": Const(404),
"x": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Const(2)), Mul(Const(-404), Var("x")), Const(-25245)), Const(0)))), Var("... | NT | COMB | COMPUTE | sympy | VIETA_SUM | [
"VIETA_SUM/K2",
"K2"
] | 6be084 | antilemma_k2_v1 | null | 7 | 0 | [
"K2",
"VIETA_SUM"
] | 2 | 0.001 | 2026-02-08T13:41:58.276038Z | {
"verified": true,
"answer": 81810,
"timestamp": "2026-02-08T13:41:58.277112Z"
} | deefda | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 143,
"completion_tokens": 2543
},
"timestamp": "2026-02-15T19:38:57.114Z",
"answer": 81810
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemm... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
dcca47 | comb_catalan_compute_v1_124444284_2575 | Let $m$ be the number of ordered pairs $(i, j)$ with $1 \le i \le 4$ and $1 \le j \le 7$. Let $S$ be the set of all ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = m$. Define $n$ to be the number of ordered pairs $(i, j)$ with $1 \le i, j \le 12$ such that $i + j$ equals the number of element... | 840 | graphs = [
Graph(
let={
"_m": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(4)), right=IntegerRange(start=Const(1), end=Const(7)))),
"_n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='... | COMB | NT | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN/COMB1/COUNT_SUM_EQUALS"
] | 2d9173 | comb_catalan_compute_v1 | null | 5 | 0 | [
"COMB1",
"COUNT_CARTESIAN",
"COUNT_SUM_EQUALS"
] | 3 | 0.012 | 2026-02-08T04:46:18.664112Z | {
"verified": true,
"answer": 840,
"timestamp": "2026-02-08T04:46:18.676385Z"
} | 270dab | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 275,
"completion_tokens": 8786
},
"timestamp": "2026-02-24T01:55:38.952Z",
"answer": 840
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok_later"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_... | {
"lo": -0.05,
"mid": 2.89,
"hi": 5.27
} | ||
3082f9 | geo_visible_lattice_v1_1742523217_2779 | Let $n = 100$. Define a visible lattice point as an ordered pair $(x, y)$ of positive integers with $1 \leq x, y \leq n$ such that $\gcd(x, y) = 1$. Let $r$ be the number of visible lattice points. Compute the remainder when $44121 \cdot r$ is divided by 62870. | 46,757 | graphs = [
Graph(
let={
"n": Const(100),
"result": VisibleLatticePoints(n=Ref(name='n')),
"Q": Mod(value=Mul(Const(44121), Ref("result")), modulus=Const(62870)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 6 | 0 | null | null | 1.164 | 2026-02-08T05:21:12.426769Z | {
"verified": true,
"answer": 46757,
"timestamp": "2026-02-08T05:21:13.590352Z"
} | f76780 | 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": 5380
},
"timestamp": "2026-02-24T03:30:39.560Z",
"answer": 46757
},
{
"... | 1 | [] | {
"lo": -0.06,
"mid": 2.89,
"hi": 5.27
} | ||||
01ce15 | sequence_lucas_compute_v1_397696148_400 | Let $n$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $x \cdot y = 100$. Let $L_n$ denote the $n$-th Lucas number, defined by $L_1 = 1$, $L_2 = 3$, and $L_k = L_{k-1} + L_{k-2}$ for $k \geq 3$. Find the remainder when $75433 \cdot L_n$ is divided by $83687$. | 2,746 | graphs = [
Graph(
let={
"_n": Const(100),
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_n")))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | sequence_lucas_compute_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.001 | 2026-02-08T11:28:05.802545Z | {
"verified": true,
"answer": 2746,
"timestamp": "2026-02-08T11:28:05.803451Z"
} | 064d87 | 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": 1295
},
"timestamp": "2026-02-14T14:19:24.979Z",
"answer": 2746
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
b49a69 | nt_max_prime_below_v1_2051736721_2260 | Let $S$ be the set of all positive integers $p$ such that there exists a positive integer $q$ with $pq = 12$, $\gcd(p, q) = 1$, and $p < q$. Let $L$ be the number of elements in $S$. Let $n$ be a prime number satisfying $L \leq n \leq 26244$. Determine the maximum possible value of such $n$. | 26,237 | graphs = [
Graph(
let={
"upper": Const(26244),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), V... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_max_prime_below_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.635 | 2026-02-08T16:33:08.833888Z | {
"verified": true,
"answer": 26237,
"timestamp": "2026-02-08T16:33:09.468500Z"
} | 14db40 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 137,
"completion_tokens": 4211
},
"timestamp": "2026-02-17T06:35:09.376Z",
"answer": 26237
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
ead1e7 | geo_count_lattice_rect_v1_784195855_7777 | Compute the number of lattice points $(x, y)$ such that $0 \leq x \leq 40$ and $0 \leq y \leq 155$. This includes all points with integer coordinates in the closed rectangle from $(0,0)$ to $(40,155)$. | 6,396 | graphs = [
Graph(
let={
"a": Const(40),
"b": Const(155),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.001 | 2026-02-08T09:31:15.110753Z | {
"verified": true,
"answer": 6396,
"timestamp": "2026-02-08T09:31:15.111460Z"
} | d050f9 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 172,
"completion_tokens": 279
},
"timestamp": "2026-02-24T11:30:07.769Z",
"answer": 6396
},
{
"id... | 1 | [] | {
"lo": -5.97,
"mid": -3.97,
"hi": -1.93
} | ||||
52b2e0 | nt_sum_divisors_mod_v1_784195855_3496 | Let $n$ be the number of positive integers $k$ with $1 \leq k \leq 5400$ such that $20$ divides the $k$-th Fibonacci number. Compute the remainder when the sum of all positive divisors of $n$ is divided by $10267$. | 546 | graphs = [
Graph(
let={
"_n": Const(20),
"n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(5400)), Divides(divisor=Ref("_n"), dividend=Fibonacci(arg=Var(name='n')))))),
"M": Const(10267),
"sigma": SumDi... | NT | null | COMPUTE | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE"
] | 66de3c | nt_sum_divisors_mod_v1 | null | 6 | 0 | [
"COUNT_FIB_DIVISIBLE"
] | 1 | 0.006 | 2026-02-08T06:27:42.307661Z | {
"verified": true,
"answer": 546,
"timestamp": "2026-02-08T06:27:42.313826Z"
} | be4469 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 107,
"completion_tokens": 1385
},
"timestamp": "2026-02-13T00:35:12.361Z",
"answer": 546
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
15ae8a | nt_min_coprime_above_v1_784195855_2746 | Let $N$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 688900$. Let $m$ be the number of positive integers $n \leq N$ such that $n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{5}$.
Compute the smallest positive integer $r$ such that $20449 < r \leq 20791$ a... | 31,716 | 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(688900)))), expr=Sum(Var("x"), Var("y")))),
"start": Const(... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM",
"B3/L3C"
] | fccd01 | nt_min_coprime_above_v1 | negation_mod | 7 | 0 | [
"B3",
"L3C",
"LIN_FORM"
] | 3 | 0.055 | 2026-02-08T05:57:35.367854Z | {
"verified": true,
"answer": 31716,
"timestamp": "2026-02-08T05:57:35.423265Z"
} | d92310 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 231,
"completion_tokens": 3345
},
"timestamp": "2026-02-12T17:11:12.407Z",
"answer": 31716
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok_later"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": ... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
25551b | nt_min_coprime_above_v1_1520064083_8931 | Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 42849$. Let $m$ be the minimum value of $x + y$ as $(x,y)$ ranges over $S$. Determine the value of the smallest integer $n$ such that $67600 < n \leq 68024$ and $\gcd(n, m) = 1$. | 67,601 | graphs = [
Graph(
let={
"start": Const(67600),
"upper": Const(68024),
"modulus": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Co... | NT | null | EXTREMUM | sympy | B3 | [
"B3"
] | 0cd20d | nt_min_coprime_above_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.056 | 2026-02-08T10:26:39.598539Z | {
"verified": true,
"answer": 67601,
"timestamp": "2026-02-08T10:26:39.654605Z"
} | b8b4cb | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 132,
"completion_tokens": 1250
},
"timestamp": "2026-02-14T07:25:53.629Z",
"answer": 67601
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
dd40ac | nt_count_gcd_equals_v1_1742523217_1710 | Let $k$ be the sum of all positive integers $n$ such that $1 \leq n \leq 256$ and $n$ is divisible by $128$. Let $N$ be the number of positive integers $n$ such that $1 \leq n \leq 35344$ and $\gcd(n, k) = 12$. Find the value of $N$. | 1,473 | graphs = [
Graph(
let={
"upper": Const(35344),
"k": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(256)), Eq(Mod(value=Var("n"), modulus=Const(128)), Const(0))))),
"d": Const(12),
"result": CountOverSet(set... | NT | null | COUNT | sympy | SUM_DIVISIBLE | [
"SUM_DIVISIBLE"
] | 02dbe3 | nt_count_gcd_equals_v1 | null | 4 | 0 | [
"SUM_DIVISIBLE"
] | 1 | 3.134 | 2026-02-08T04:06:43.047207Z | {
"verified": true,
"answer": 1473,
"timestamp": "2026-02-08T04:06:46.181260Z"
} | c071d7 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 195,
"completion_tokens": 1403
},
"timestamp": "2026-02-10T15:50:12.076Z",
"answer": 1473
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_DIVISIBLE",
"status... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
8afb02 | nt_num_divisors_compute_v1_1742523217_315 | Let $n$ be the smallest integer greater than or equal to 2 that divides 107113. Define $\text{result}$ to be the number of positive divisors of $n$. Compute the remainder when $74083 \times \text{result}$ is divided by 62172.
Find the value of $Q$, where $Q$ is this remainder. | 23,822 | graphs = [
Graph(
let={
"_n": Const(62172),
"n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(107113))))),
"result": NumDivisors(n=Ref("n")),
"_c": Const(74083),
"Q": Mod(... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | nt_num_divisors_compute_v1 | null | 4 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.002 | 2026-02-08T02:58:08.719140Z | {
"verified": true,
"answer": 23822,
"timestamp": "2026-02-08T02:58:08.721001Z"
} | 904669 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 189,
"completion_tokens": 928
},
"timestamp": "2026-02-09T01:44:01.782Z",
"answer": 23822
},
{
"... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
... | {
"lo": -3.45,
"mid": 1.18,
"hi": 5.72
} | ||
6bbfc3 | geo_count_lattice_triangle_v1_898971024_1721 | Let $A$ be the value of
\[
|128 \cdot 111 + 34 \cdot (0 - 30)|.
\]
Let $B$ be the sum of the following three greatest common divisors:
- $\gcd(d, 30)$, where $d$ is the largest positive divisor of $17536$ that is at most $128$,
- $\gcd(|34 - 128|, |S - 30|)$, where $S$ is the number of ordered pairs $(i,j)$ with $1 \le... | 6,593 | graphs = [
Graph(
let={
"_m": Const(34),
"_n": Const(2),
"area_2x": Abs(arg=Sum(Mul(Const(value=128), Const(value=111)), Mul(Const(value=34), Sub(left=Const(value=0), right=Const(value=30))))),
"boundary": Sum(GCD(a=Abs(arg=MaxOverSet(set=SolutionsSet(var=Var(... | NT | null | COUNT | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN",
"MAX_DIVISOR"
] | 203b2d | geo_count_lattice_triangle_v1 | null | 6 | 0 | [
"COUNT_CARTESIAN",
"MAX_DIVISOR"
] | 2 | 0.014 | 2026-02-08T16:16:18.969374Z | {
"verified": true,
"answer": 6593,
"timestamp": "2026-02-08T16:16:18.983764Z"
} | dbe16b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 202,
"completion_tokens": 893
},
"timestamp": "2026-02-16T23:43:50.809Z",
"answer": 6593
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
b65e75 | antilemma_sum_equals_v1_2051736721_6032 | Let $x$ be the number of ordered pairs $(i, j)$ of positive integers such that $i + j = 86$, $1 \leq i \leq 84$, and $1 \leq j \leq 84$. Find the remainder when $38705x$ is divided by $58558$. | 50,383 | graphs = [
Graph(
let={
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(86)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(84)), right=IntegerRange(start=Const(1), end=Const(84))))),
"Q": ... | COMB | GEOM | COMPUTE | sympy | COMB1 | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 2 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS"
] | 2 | 0.024 | 2026-02-08T18:54:40.243506Z | {
"verified": true,
"answer": 50383,
"timestamp": "2026-02-08T18:54:40.267942Z"
} | 1d2377 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 112,
"completion_tokens": 1267
},
"timestamp": "2026-02-18T20:21:42.818Z",
"answer": 50383
},
... | 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": -3.12,
"mid": 1.47,
"hi": 6.57
} | ||
5c859a | nt_max_prime_below_v1_153355830_2652 | Let $S$ be the set of all ordered pairs of positive integers $(p, q)$ such that $pq = 18$, $\gcd(p, q) = 1$, and $p < q$. Let $m$ be the number of elements in $S$. Find the largest prime number $n$ such that $m \leq n \leq 13689$. | 13,687 | graphs = [
Graph(
let={
"upper": Const(13689),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), V... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_max_prime_below_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.316 | 2026-02-08T07:15:27.626958Z | {
"verified": true,
"answer": 13687,
"timestamp": "2026-02-08T07:15:27.942902Z"
} | 8589a7 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 124,
"completion_tokens": 2253
},
"timestamp": "2026-02-13T09:22:13.450Z",
"answer": 13687
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -8.32,
"mid": -5.11,
"hi": -2.37
} | ||
f1f089 | geo_count_lattice_rect_v1_798873815_205 | Let $ a = 484 $ and $ b = 162 $. Define $ R $ to be the set of all lattice points $ (x, y) $ such that $ 0 \leq x \leq a $ and $ 0 \leq y \leq b $. Let $ c = 14425 $. Compute the remainder when $ c $ times the number of points in $ R $ is divided by $ 58424 $. | 48,743 | graphs = [
Graph(
let={
"a": Const(484),
"b": Const(162),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"_c": Const(14425),
"Q": Mod(value=Mul(Ref("_c"), Ref("result")), modulus=Const(58424)),
},
goal=Ref("Q"),
... | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.151 | 2026-02-08T02:31:08.362854Z | {
"verified": true,
"answer": 48743,
"timestamp": "2026-02-08T02:31:08.513485Z"
} | d4ae92 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 206,
"completion_tokens": 3138
},
"timestamp": "2026-02-08T19:11:01.271Z",
"answer": 48743
},
{
"... | 1 | [] | {
"lo": -1.86,
"mid": 0.04,
"hi": 1.71
} | ||||
087de1 | lin_form_endings_v1_168721529_1154 | Let $a = 28$ and $b = 98$. Let $A = 30$ and $B = 3$. Define $g$ to be the greatest common divisor of $a$ and $b$. Let $a' = \left\lfloor \frac{a}{g} \right\rfloor$ and $b' = \left\lfloor \frac{b}{g} \right\rfloor$. Define the size of $T$ as
$$
|T| = a'A + b'B - a'b'.
$$
Let
$$
total = aA + bB - (a + b) + 1.
$$
Let $\te... | 9,496 | graphs = [
Graph(
let={
"a_coeff": Const(28),
"b_coeff": Const(98),
"A_val": Const(30),
"B_val": Const(3),
"g_step": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"ap_node": Floor(Div(Ref("a_coeff"), Ref("g_step"))),
"bp_node": F... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 5 | null | [
"LIN_FORM"
] | 1 | 0.003 | 2026-02-08T13:30:25.459575Z | {
"verified": true,
"answer": 9496,
"timestamp": "2026-02-08T13:30:25.462452Z"
} | 5e7516 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 312,
"completion_tokens": 1152
},
"timestamp": "2026-02-09T14:10:21.635Z",
"answer": 9496
},
{
"i... | 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": -1.95,
"mid": 2.14,
"hi": 6.33
} | ||
c63b00 | sequence_fibonacci_compute_v1_677425708_1598 | Let $n$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 48$. Compute the $n$-th Fibonacci number, then let $Q$ be the remainder when $72945$ times this number is divided by $63503$. Find $Q$. | 16,974 | graphs = [
Graph(
let={
"_n": Const(48),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2")), Re... | NT | null | COMPUTE | sympy | COMB1 | [
"COMB1"
] | 567f58 | sequence_fibonacci_compute_v1 | null | 4 | 0 | [
"COMB1"
] | 1 | 0.001 | 2026-02-08T04:18:43.558797Z | {
"verified": true,
"answer": 16974,
"timestamp": "2026-02-08T04:18:43.559638Z"
} | b21ff2 | 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": 3784
},
"timestamp": "2026-02-09T22:11:16.208Z",
"answer": 16974
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
}
] | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
6219d8 | comb_count_permutations_fixed_v1_784195855_9407 | Let $\phi(k)$ denote Euler's totient function. Define $N = \sum_{k=1}^{4} \phi(k) \left\lfloor \frac{4}{k} \right\rfloor$. Let $n$ be the number of positive integers $j$ such that $1 \leq j \leq N$ and $j^5 \leq 100000$. Compute the value of $\binom{n}{5} \cdot !(n-5)$, where $!m$ denotes the number of derangements of ... | 11,088 | graphs = [
Graph(
let={
"_n": Summation(var="k", start=Const(1), end=Const(4), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(4), Var("k"))))),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(1)), Leq(Var("j"), Ref("_n")), Leq(Pow(Var("j"), Const(5)... | NT | COMB | COUNT | sympy | K2 | [
"K2/C3"
] | 2f11e4 | comb_count_permutations_fixed_v1 | null | 6 | 0 | [
"C3",
"K2"
] | 2 | 0.003 | 2026-02-08T16:47:30.881507Z | {
"verified": true,
"answer": 11088,
"timestamp": "2026-02-08T16:47:30.884688Z"
} | 514565 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 161,
"completion_tokens": 1188
},
"timestamp": "2026-02-17T11:34:54.440Z",
"answer": 11088
},
... | 1 | [
{
"lemma": "C3",
"status": "ok_later"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
a501eb | nt_count_coprime_and_v1_260342960_153 | Let $A$ be the set of all integers $n$ such that $\phi(1) \leq n \leq 13874$, $\gcd(n, 3) = 1$, and $\gcd(n, 11) = 1$. Let $r$ be the number of elements in $A$. Compute the remainder when $44121 \cdot r$ is divided by $62059$. | 24,787 | graphs = [
Graph(
let={
"upper": Const(13874),
"k1": Const(3),
"k2": Const(11),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), EulerPhi(n=Const(1))), Leq(Var("n"), Ref("upper")), Eq(GCD(a=Var("n"), b=Ref("k1")), Const(1)), Eq... | NT | null | COUNT | sympy | ONE_PHI_1 | [
"ONE_PHI_1"
] | f6b5a5 | nt_count_coprime_and_v1 | null | 4 | 0 | [
"ONE_PHI_1"
] | 1 | 1.428 | 2026-02-08T11:16:41.534157Z | {
"verified": true,
"answer": 24787,
"timestamp": "2026-02-08T11:16:42.961904Z"
} | 7c7d34 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 202,
"completion_tokens": 2179
},
"timestamp": "2026-02-08T20:32:29.787Z",
"answer": 24787
},
{
"... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "ONE_PHI_1",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -2.08,
"mid": 1.77,
"hi": 4.93
} | ||
5da070 | nt_count_divisible_and_v1_2051736721_407 | Let $d_1$ be the number of ordered pairs $(i,j)$ of positive integers such that $i + j = 8$, $1 \leq i \leq 6$, and $1 \leq j \leq 7$. Let $d_2 = 9$ and $N = 13986$. Determine the number of positive integers $n \leq N$ such that $$n \equiv \sum_{k=0}^{5} (-1)^k \binom{5}{k} \pmod{d_1}$$ and $n \equiv 0 \pmod{d_2}$. | 777 | graphs = [
Graph(
let={
"_n": Const(5),
"upper": Const(13986),
"d1": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(8)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(6)), right=Int... | COMB | null | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING",
"COUNT_SUM_EQUALS"
] | b9499e | nt_count_divisible_and_v1 | null | 5 | 0 | [
"BINOMIAL_ALTERNATING",
"COUNT_SUM_EQUALS"
] | 2 | 0.636 | 2026-02-08T15:23:24.442344Z | {
"verified": true,
"answer": 777,
"timestamp": "2026-02-08T15:23:25.078407Z"
} | cc14b5 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 248,
"completion_tokens": 845
},
"timestamp": "2026-02-24T20:40:31.461Z",
"answer": 777
},
{
"id"... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",... | {
"lo": -8.52,
"mid": -5.43,
"hi": -3.2
} | ||
81d5fa | comb_catalan_compute_v1_717093673_1823 | Let $n$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 22$. Define $r = C_n$, the $n$-th Catalan number. Find the remainder when $60875 \cdot r$ is divided by 66902. Compute this remainder. | 9,770 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2")), Const(22))))),
"res... | COMB | null | COMPUTE | sympy | COMB1 | [
"COMB1"
] | 567f58 | comb_catalan_compute_v1 | null | 3 | 0 | [
"COMB1"
] | 1 | 0.003 | 2026-02-08T16:21:56.394320Z | {
"verified": true,
"answer": 9770,
"timestamp": "2026-02-08T16:21:56.397665Z"
} | 3fe418 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 187,
"completion_tokens": 2146
},
"timestamp": "2026-02-24T20:41:55.719Z",
"answer": 9770
},
{
"... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"stat... | {
"lo": -2.4,
"mid": 1.57,
"hi": 5.75
} | ||
3dd2a8 | nt_count_gcd_equals_v1_677425708_1503 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 54289$. Let $k$ be the minimum value of $x + y$ as $(x, y)$ ranges over $S$. Let $N$ be the number of positive integers $n$ such that $1 \leq n \leq 30625$ and $\gcd(n, k) = 1$. Compute $N$. | 15,247 | graphs = [
Graph(
let={
"upper": Const(30625),
"k": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(54289)))), expr=Sum(Var("x"), Var("y"... | NT | null | COUNT | sympy | ONE_PHI_2 | [
"ONE_PHI_2",
"B3"
] | 0519c9 | nt_count_gcd_equals_v1 | null | 5 | 0 | [
"B3",
"ONE_PHI_2"
] | 2 | 6.639 | 2026-02-08T04:13:50.761473Z | {
"verified": true,
"answer": 15247,
"timestamp": "2026-02-08T04:13:57.400017Z"
} | c76e52 | 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": 2094
},
"timestamp": "2026-02-09T20:47:32.587Z",
"answer": 15247
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "ONE_PHI_2",
"status": "ok"
},
{
"le... | {
"lo": -6.5,
"mid": -0.2,
"hi": 6.11
} | ||
93a9ad | alg_poly4_count_v1_601307018_1597 | Find the number of ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 458$ such that $$16b^4 + 256a^4 - 128ab^3 + 384a^2b^2 - 512a^3b = 126247696.$$ | 431 | graphs = [
Graph(
let={
"result": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(458)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(458)), Eq(Sum(Mul(Const(16), Pow(Var("b"), Const(4))), Mul(Const(256), Pow(Var(... | ALG | null | COUNT | sympy | B1 | [
"B1/POLY_ORBIT_HENSEL",
"MOBIUS_COPRIME"
] | 1f94d4 | alg_poly4_count_v1 | null | 5 | null | [
"B1",
"MOBIUS_COPRIME",
"POLY_ORBIT_HENSEL"
] | 3 | 6.331 | 2026-03-10T02:20:33.601916Z | {
"verified": true,
"answer": 431,
"timestamp": "2026-03-10T02:20:39.932535Z"
} | 449324 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 178,
"completion_tokens": 4301
},
"timestamp": "2026-03-29T02:48:06.276Z",
"answer": 405
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok"
},
{
"lemma": "POLY_ORBIT_HENSEL",
"status": "ok_later"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 0.86,
"mid": 3.78,
"hi": 5.89
} | ||
fd5f81 | antilemma_sum_equals_v1_124444284_4896 | Let $T$ be the set of all integers $t$ such that $7 \leq t \leq 87$ and there exist positive integers $a$, $b$ with $1 \leq a \leq 6$, $1 \leq b \leq 15$, and $t = 2a + 5b$. Let $n$ be the number of elements in $T$.
Now consider the number of ordered pairs $(i, j)$ such that $1 \leq i \leq 76$, $1 \leq j \leq 77$, and... | 76 | graphs = [
Graph(
let={
"_n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=6)), Geq(left=Var(name='b'), right=Const(value=... | COMB | GEOM | COMPUTE | sympy | COMB1 | [
"LIN_FORM/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | ada383 | antilemma_sum_equals_v1 | null | 6 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 3 | 0.041 | 2026-02-08T06:16:56.629183Z | {
"verified": true,
"answer": 76,
"timestamp": "2026-02-08T06:16:56.670304Z"
} | 9c7bb8 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 249,
"completion_tokens": 13810
},
"timestamp": "2026-02-24T05:53:21.958Z",
"answer": 76
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"st... | {
"lo": -3.84,
"mid": -1.69,
"hi": 1.09
} | ||
58d0e0 | nt_min_coprime_above_v1_1742523217_1530 | Let $S$ be the set of all integers $d \geq 2$ that divide $97543451$. Let $m$ be the smallest element of $S$. Determine the smallest integer $n$ such that $40804 < n \leq 41271$ and $\gcd(n, m) = 1$. | 40,805 | graphs = [
Graph(
let={
"start": Const(40804),
"upper": Const(41271),
"modulus": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(97543451))))),
"result": MinOverSet(set=SolutionsSet(var=... | NT | null | EXTREMUM | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | nt_min_coprime_above_v1 | null | 5 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.072 | 2026-02-08T04:02:27.892211Z | {
"verified": true,
"answer": 40805,
"timestamp": "2026-02-08T04:02:27.963876Z"
} | eb21ee | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 136,
"completion_tokens": 684
},
"timestamp": "2026-02-13T05:06:46.936Z",
"answer": 40805
},
{
"id": 11,
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
}... | {
"lo": -9.14,
"mid": -6.05,
"hi": -3.73
} | ||
85c3ba | nt_max_prime_below_v1_1125832087_202 | Let $s$ be the number of positive integers $p$ such that there exists a positive integer $q > p$ with $pq = 6$ and $\gcd(p, q) = 1$. Determine the value of the largest prime number $n$ such that $s \leq n \leq 42025$. | 42,023 | graphs = [
Graph(
let={
"upper": Const(42025),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), V... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_max_prime_below_v1 | null | 3 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.928 | 2026-02-08T02:56:24.290641Z | {
"verified": true,
"answer": 42023,
"timestamp": "2026-02-08T02:56:25.218975Z"
} | d88f15 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 180,
"completion_tokens": 8161
},
"timestamp": "2026-02-10T11:48:43.447Z",
"answer": 42023
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V8_SUM",
"statu... | {
"lo": -7.01,
"mid": -4.67,
"hi": -2.19
} | ||
ff7c8f_l | comb_count_permutations_fixed_v1_397696148_531 | Let $u = 5$, and define $n_2 = u + 1$. Let
$$
m = \sum_{k=0}^{n_2} (-1)^k \binom{n_2}{k}.
$$
Let $n_1 = 0$, and define
$$
f = \sum_{k=0}^{n_1} (-1)^k \binom{n_1}{k}.
$$
Let $n = 11 \cdot f$. Let $k$ be $m$ multiplied by the number of ordered pairs $(i, j)$ of integers such that $1 \leq i \leq 6$, $1 \leq j \leq 7$, and... | 14,684,570 | COMB | null | COUNT | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS/BINOMIAL_ALTERNATING"
] | ab0fe8 | comb_count_permutations_fixed_v1 | null | 4 | 2 | [
"BINOMIAL_ALTERNATING",
"COUNT_SUM_EQUALS"
] | 2 | 0.013 | 2026-02-08T11:33:00.187840Z | {
"verified": false,
"answer": 20328,
"timestamp": "2026-02-08T11:33:00.200494Z"
} | a1bed6 | ff7c8f | 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": 319,
"completion_tokens": 673
},
"timestamp": "2026-02-24T14:06:05.351Z",
"answer": 14684570
},
{
... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemm... | {
"lo": 3.25,
"mid": 5.68,
"hi": 8.81
} | |
169687 | comb_count_surjections_v1_717093673_1503 | Let $T$ be the set of all ordered pairs $(i, j)$ of positive integers such that $1 \leq i \leq 4$, $1 \leq j \leq 5$, and $i + j = 6$. Let $m$ be the number of elements in $T$. Let $k$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = m$. Let $n = 5$. Define $r = k! \cdot S(n, ... | 24 | graphs = [
Graph(
let={
"_n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(6)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(4)), right=IntegerRange(start=Const(1), end=Const(5))))),
"n": Co... | COMB | NT | COUNT | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS/COMB1"
] | 5b2e59 | comb_count_surjections_v1 | null | 5 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS"
] | 2 | 0.018 | 2026-02-08T16:07:44.455640Z | {
"verified": true,
"answer": 24,
"timestamp": "2026-02-08T16:07:44.473907Z"
} | 805d94 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 280,
"completion_tokens": 1461
},
"timestamp": "2026-02-24T20:00:20.352Z",
"answer": 24
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok_later"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
... | {
"lo": -2.4,
"mid": 1.57,
"hi": 5.75
} | ||
e8cb49_n | alg_qf_psd_min_v1_1218484723_4265 | A manufacturing company is optimizing a three-stage production process. They choose integer settings $a$ and $b$ for two machines, each between $1$ and $43$, and an integer setting $c$ for a shared control unit. The control setting $c$ must be at most
$$\min\{d : d \ge |T|,\ d \mid 4605859\},$$
where $|T|$ is the numbe... | 83,380 | ALG | null | COMPUTE | sympy | POLY_ORBIT_LEGENDRE | [
"POLY_ORBIT_LEGENDRE/MIN_PRIME_FACTOR"
] | fa2660 | alg_qf_psd_min_v1 | null | 7 | null | [
"MIN_PRIME_FACTOR",
"POLY_ORBIT_LEGENDRE"
] | 2 | 0.348 | 2026-02-25T05:54:25.238217Z | null | ec4db1 | e8cb49 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 510,
"completion_tokens": 11335
},
"timestamp": "2026-03-30T21:24:09.216Z",
"answer": 83380
},
{
... | 1 | [
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok_later"
},
{
"lemma": "POLY_ORBIT_LEGENDRE",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 1.5,
"mid": 4.69,
"hi": 7.23
} | |
a35d39 | algebra_poly_eval_v1_784195855_3841 | Let $y = 30$. Define $r = y^3 - 6y^2 - 2y - 7$. Let $k_{\max}$ be the largest integer $k$ such that $2^k \leq 2364$. Compute the Bell number of $|r| \bmod k_{\max}$. | 203 | graphs = [
Graph(
let={
"_n": Const(3),
"y": Const(30),
"result": Sum(Pow(Ref("y"), Ref("_n")), Mul(Const(-6), Pow(Ref("y"), Const(2))), Mul(Const(-2), Ref("y")), Const(-7)),
"Q": Bell(Mod(value=Abs(arg=Ref(name='result')), modulus=MaxOverSet(set=SolutionsSet(... | COMB | null | COMPUTE | sympy | MAX_VAL | [
"MAX_VAL"
] | 607073 | algebra_poly_eval_v1 | bell_mod | 3 | 0 | [
"MAX_VAL"
] | 1 | 0.001 | 2026-02-08T06:39:55.657685Z | {
"verified": true,
"answer": 203,
"timestamp": "2026-02-08T06:39:55.658974Z"
} | 57eda0 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 181,
"completion_tokens": 618
},
"timestamp": "2026-02-24T06:45:09.392Z",
"answer": 203
},
{
"id"... | 1 | [
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K16",
"status": "same_pattern_wrong"
},
{
"lemma": "MAX_VAL",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
... | {
"lo": -4.93,
"mid": -2.91,
"hi": -0.71
} | ||
b98bf2 | antilemma_k2_v1_1520064083_1296 | Compute the value of
$$
\sum_{k=1}^{213} \phi(k) \left\lfloor \frac{213}{k} \right\rfloor.
$$ | 22,791 | graphs = [
Graph(
let={
"x": Summation(var="k", start=Const(1), end=Const(213), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(213), Var("k"))))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | antilemma_k2_v1 | null | 4 | 0 | [
"K2"
] | 1 | 0 | 2026-02-08T03:54:51.222327Z | {
"verified": true,
"answer": 22791,
"timestamp": "2026-02-08T03:54:51.222701Z"
} | d6de24 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 149,
"completion_tokens": 500
},
"timestamp": "2026-02-10T16:09:57.705Z",
"answer": 22791
},
{
"i... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -3.53,
"mid": 1.02,
"hi": 5.49
} | ||
339e40 | comb_factorial_compute_v1_784195855_9247 | Let $m = 13013$ and $n$ be the smallest divisor of $m$ that is greater than or equal to 2. Define $A$ to be the set of positive integers $k$ such that $1 \leq k \leq 41409$ and $$ k \equiv \left\lfloor \frac{k}{2} \right\rfloor \pmod{5}. $$ Compute the number of elements in $A$ minus $n!$. | 3,241 | graphs = [
Graph(
let={
"_m": Const(13013),
"_n": Const(41409),
"n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Ref("_m"))))),
"result": Factorial(Ref("n")),
"Q": Sub(CountOve... | NT | null | COMPUTE | sympy | L3C | [
"L3C",
"MIN_PRIME_FACTOR"
] | dcc96d | comb_factorial_compute_v1 | negation_mod | 5 | 0 | [
"L3C",
"MIN_PRIME_FACTOR"
] | 2 | 0.004 | 2026-02-08T16:39:42.654487Z | {
"verified": true,
"answer": 3241,
"timestamp": "2026-02-08T16:39:42.658277Z"
} | 871b7f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 144,
"completion_tokens": 1395
},
"timestamp": "2026-02-17T09:22:34.640Z",
"answer": 3241
},
{... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
299a58 | nt_sum_gcd_range_mod_v1_1520064083_9642 | Let $N$ be the number of positive integers $t$ such that $5 \le t \le 3487$ and there exist positive integers $a$, $b$ with $1 \le a \le 343$, $1 \le b \le 1229$, and $t = 3a + 2b$. Let $k = 84$ and $M = 10867$. Compute the remainder when $\sum_{n=1}^{N} \gcd(n, k)$ is divided by $M$. | 10,640 | 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=343)), Geq(left=Var(name='b'), right=Const(value... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_sum_gcd_range_mod_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.314 | 2026-02-08T10:57:04.070343Z | {
"verified": true,
"answer": 10640,
"timestamp": "2026-02-08T10:57:04.383874Z"
} | cdbdc2 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 158,
"completion_tokens": 5233
},
"timestamp": "2026-02-14T09:30:29.295Z",
"answer": 10640
},
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
734836 | sequence_count_fib_divisible_v1_124444284_6126 | Let $r$ be the number of positive integers $n \leq 544$ such that the $n$-th Fibonacci number is divisible by $17$. Let $m = |r| + 2$. Determine the value of the smallest positive integer $k$ such that the $k$-th Fibonacci number is divisible by $m$. | 30 | graphs = [
Graph(
let={
"upper": Const(544),
"d": Const(17),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Divides(divisor=Ref("d"), dividend=Fibonacci(arg=Var(name='n')))))),
"Q": Fib... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"K14"
] | a49bcb | sequence_count_fib_divisible_v1 | null | 6 | 0 | [
"K14",
"MIN_PRIME_FACTOR"
] | 2 | 0.09 | 2026-02-08T08:08:38.596711Z | {
"verified": true,
"answer": 30,
"timestamp": "2026-02-08T08:08:38.686570Z"
} | 66f9e7 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 116,
"completion_tokens": 1918
},
"timestamp": "2026-02-13T15:28:33.473Z",
"answer": 30
},
{
... | 1 | [
{
"lemma": "K14",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
db6ffc | nt_count_coprime_and_v1_784195855_4246 | Let $u$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 2480625$. Let $k_1 = \sum_{k=1}^{2} \phi(k) \left\lfloor \frac{2}{k} \right\rfloor$ and $k_2 = 7$. Determine the number of positive integers $n$ with $1 \leq n \leq u$ such that $\gcd(n, k_1) = 1$ and $\gcd(n, k_2) = 1$... | 1,800 | graphs = [
Graph(
let={
"upper": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(2480625)))), expr=Sum(Var("x"), Var("y")))),
"k1": Summa... | NT | null | COUNT | sympy | B3 | [
"B3",
"K2"
] | f1ea07 | nt_count_coprime_and_v1 | null | 6 | 0 | [
"B3",
"K2"
] | 2 | 0.388 | 2026-02-08T06:56:33.783635Z | {
"verified": true,
"answer": 1800,
"timestamp": "2026-02-08T06:56:34.171306Z"
} | 2cfe58 | 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": 1455
},
"timestamp": "2026-02-13T07:10:07.866Z",
"answer": 1800
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lem... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
345828 | diophantine_fbi2_count_v1_2051736721_5965 | Let $T$ be the set of all positive integers $t$ such that $11 \leq t \leq 86$ and there exist integers $a$, $b$ with $1 \leq a \leq 6$, $1 \leq b \leq 11$, and $t = 7a + 4b$. Let $m = 57600$ and let $k$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = m$. Determine th... | 10 | graphs = [
Graph(
let={
"_m": Const(57600),
"_n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=6)), Geq(left=V... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/B3"
] | 05313e | diophantine_fbi2_count_v1 | null | 6 | 0 | [
"B3",
"LIN_FORM"
] | 2 | 0.012 | 2026-02-08T18:52:42.793368Z | {
"verified": true,
"answer": 10,
"timestamp": "2026-02-08T18:52:42.805201Z"
} | 9f6ce8 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 205,
"completion_tokens": 4696
},
"timestamp": "2026-02-18T20:18:31.628Z",
"answer": 10
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
},
{
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
fd7fb9 | diophantine_fbi2_count_v1_124444284_4397 | Let $k = 180$. Let $S$ be the set of all integers $d$ such that $d \geq 2$, $d \leq 122$, $d$ divides $k$, and $\frac{k}{d} \geq 4$. Furthermore, suppose $\frac{k}{d} \leq \min\left\{x + y \mid x, y \text{ are positive integers such that } xy = \min\left\{x + y \mid x, y \text{ are positive integers such that } xy = 36... | 29,592 | graphs = [
Graph(
let={
"_n": Const(2),
"k": Const(180),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Leq(Var("d"), Const(122)), Divides(divisor=Var("d"), dividend=Ref("k")), Geq(Div(Ref("k"), Var("d")), Const(4)), Leq(Div(... | NT | null | COUNT | sympy | B3 | [
"B3/B3"
] | 8ffef9 | diophantine_fbi2_count_v1 | null | 7 | 0 | [
"B3"
] | 1 | 0.012 | 2026-02-08T05:59:30.740636Z | {
"verified": true,
"answer": 29592,
"timestamp": "2026-02-08T05:59:30.752977Z"
} | 5a96db | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 240,
"completion_tokens": 1490
},
"timestamp": "2026-02-12T18:14:43.729Z",
"answer": 29592
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
c44c26 | alg_qf_psd_count_v1_1218484723_2307 | Let $Q$ be the number of ordered pairs $(a,b)$ of positive integers with $1 \le a \le 416$ and
$$1 \le b \le \left|\left\{(a_1,b_1) : 1 \le a_1,b_1 \le 30,\ 10a_1^{2} - 18a_1b_1 + 25b_1^{2} \le 5165 \right\}\right|$$
such that
$$-4ab + a^{2} + 4b^{2} = 275625.$$
Find $Q$. | 154 | 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"), Const(416)), Geq(Var("b"), Const(1)), Leq(Var("b"), CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a1... | ALG | null | COUNT | sympy | QF_PSD_COUNT_LEQ | [
"QF_PSD_COUNT_LEQ"
] | 009d0f | alg_qf_psd_count_v1 | null | 7 | 0 | [
"QF_PSD_COUNT_LEQ"
] | 1 | 0.674 | 2026-02-25T04:08:23.034609Z | {
"verified": true,
"answer": 154,
"timestamp": "2026-02-25T04:08:23.708356Z"
} | ee5667 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 245,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T04:05:52.821Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
}
] | {
"lo": 1.55,
"mid": 4.7,
"hi": 7.23
} | ||
e50c2e | alg_poly3_sum_v1_1218484723_1311 | Find the remainder when $$\sum_{\substack{1 \leq a \leq 13 \\ 1 \leq b \leq 13 \\ 1 \leq c \leq 13}} \left( 42a c^{2} + \left|\left\{ (a_1, b_1) : 1 \leq a_1, b_1 \leq 25,\ 17 a_1^{4} + 17 b_1^{4} + 102 a_1^{2} b_1^{2} + 68 a_1 b_1^{3} + 68 a_1^{3} b_1 = 7768592 \right\}\right| \cdot a^{3} - 120b c^{2} + 141 a b^{2} - ... | 1,218 | graphs = [
Graph(
let={
"_n": Const(141),
"result": Mod(value=SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b"), Var("c")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(13)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(13)), Geq(Var("c"... | ALG | null | COMPUTE | sympy | POLY4_COUNT | [
"POLY4_COUNT"
] | 861d91 | alg_poly3_sum_v1 | null | 7 | 0 | [
"POLY4_COUNT"
] | 1 | 0.025 | 2026-02-25T03:03:38.680725Z | {
"verified": true,
"answer": 1218,
"timestamp": "2026-02-25T03:03:38.706179Z"
} | f1a539 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 346,
"completion_tokens": 7055
},
"timestamp": "2026-03-29T00:23:53.077Z",
"answer": 58973
},
{
... | 1 | [
{
"lemma": "POLY4_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 0.8,
"mid": 3.7,
"hi": 5.71
} | ||
1deec7 | nt_sum_gcd_range_mod_v1_784195855_2253 | Let $A$ be the set of all ordered pairs of positive integers $(x, y)$ such that $xy = 1327104$. For each such pair, compute the sum $x + y$. Let $N$ be the minimum value among all such sums. Let $k = 288$ and $M = 11093$. Define
$$
\text{sum} = \sum_{i=1}^{N} \gcd(i, k).
$$
Let $r = \text{sum} \bmod M$. Given $\_n = 77... | 13,535 | graphs = [
Graph(
let={
"_n": Const(77621),
"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(1327104)))), expr=Sum(Var("x"), Var("y")... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_gcd_range_mod_v1 | null | 7 | 0 | [
"B3"
] | 1 | 0.119 | 2026-02-08T05:37:23.708296Z | {
"verified": true,
"answer": 13535,
"timestamp": "2026-02-08T05:37:23.826825Z"
} | 74a4ef | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 188,
"completion_tokens": 3549
},
"timestamp": "2026-02-12T12:06:15.589Z",
"answer": 13535
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
e0f8c0 | modular_mod_compute_v1_458359167_1314 | Let $a = -47961$. Consider the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 1020100$. Let $m$ be the minimum value of $x + y$ over all such pairs. Find the remainder when $a$ is divided by $m$. | 519 | graphs = [
Graph(
let={
"a": Const(-47961),
"m": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(1020100)))), expr=Sum(Var("x"), Var("y")... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | modular_mod_compute_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.001 | 2026-02-08T04:32:41.976506Z | {
"verified": true,
"answer": 519,
"timestamp": "2026-02-08T04:32:41.977579Z"
} | 18e8f4 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 175,
"completion_tokens": 787
},
"timestamp": "2026-02-10T17:01:06.764Z",
"answer": 519
},
{
"id... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
6d834f | comb_count_derangements_v1_601307018_845 | Let $n = \sum_{k=0}^{2} 2^{k}$. Compute the number of derangements $D_n$ of $n$ elements, and let $M = D_n$. Find the remainder when $89229 \cdot M$ is divided by $87314$. | 57,850 | graphs = [
Graph(
let={
"n": Summation(var="k", start=Const(0), end=Const(2), expr=Pow(Const(2), Var("k"))),
"result": Subfactorial(arg=Ref(name='n')),
"_c": Const(89229),
"Q": Mod(value=Mul(Ref("_c"), Ref("result")), modulus=Const(87314)),
},
... | COMB | null | COUNT | sympy | SUM_GEOM | [
"SUM_GEOM"
] | 04214c | comb_count_derangements_v1 | null | 3 | 0 | [
"SUM_GEOM"
] | 1 | 0.001 | 2026-03-10T01:27:55.973758Z | {
"verified": true,
"answer": 57850,
"timestamp": "2026-03-10T01:27:55.974954Z"
} | e47505 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 172,
"completion_tokens": 1542
},
"timestamp": "2026-03-29T00:20:03.587Z",
"answer": 57850
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "SUM_GEOM",
"status": "ok"
},
{
"lemma": "V8",
"sta... | {
"lo": -0.92,
"mid": 2.07,
"hi": 4.68
} | ||
78b597 | nt_count_digit_sum_v1_1520064083_5009 | Let $m = 24$. Consider the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = m$. Let $P$ be the maximum value of $xy$ over all such pairs. Now consider the set of all ordered pairs $(x, y)$ of positive integers such that $xy = P$. Let $n$ be the minimum value of $x + y$ over all such pairs. Let ... | 5,875 | graphs = [
Graph(
let={
"_m": Const(24),
"_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")), MaxOverSet(set=MapOverSet(set=SolutionsSet(var=T... | NT | null | COUNT | sympy | B1 | [
"B1/B3/COUNT_SUM_EQUALS"
] | 1fe134 | nt_count_digit_sum_v1 | null | 6 | 0 | [
"B1",
"B3",
"COUNT_SUM_EQUALS"
] | 3 | 7.398 | 2026-02-08T06:32:50.805854Z | {
"verified": true,
"answer": 5875,
"timestamp": "2026-02-08T06:32:58.203484Z"
} | 8c12b6 | 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": 1803
},
"timestamp": "2026-02-13T02:03:45.520Z",
"answer": 5875
},
{... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok_later"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
1d680e | modular_mod_compute_v1_349078426_427 | Let $a = 46225$. Let $m$ be the maximum value of $xy$ over all pairs of positive integers $(x, y)$ such that $x + y = 142$. Let $r$ be the remainder when $a$ is divided by $m$. Compute the remainder when $75731r$ is divided by $54375$. | 10,736 | graphs = [
Graph(
let={
"_n": Const(54375),
"a": Const(46225),
"m": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Const(142)))), ... | NT | null | COMPUTE | sympy | B1 | [
"B1"
] | 5b950e | modular_mod_compute_v1 | null | 3 | 0 | [
"B1"
] | 1 | 0.006 | 2026-02-08T13:02:42.154073Z | {
"verified": true,
"answer": 10736,
"timestamp": "2026-02-08T13:02:42.159762Z"
} | b7e8f4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 121,
"completion_tokens": 1047
},
"timestamp": "2026-02-15T09:22:03.464Z",
"answer": 10736
},
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
176daa | sequence_fibonacci_compute_v1_1978505735_1418 | Let $N$ be the number of positive integers $k$ such that $1 \leq k \leq 21964$ and $19$ divides $k$. Let $c = \sum_{d \mid N} \phi(d)$, where the sum is over all positive divisors $d$ of $N$, and $\phi$ denotes Euler's totient function. Let $F_{25}$ denote the 25th Fibonacci number. Compute the remainder when $c - F_{2... | 2,229 | graphs = [
Graph(
let={
"_n": CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(1)), Leq(Var("k"), Const(21964)), Divides(divisor=Const(19), dividend=Var("k"))), domain='positive_integers')),
"n": Const(25),
"result": Fibonacci(arg=Ref(name='n'... | NT | null | COMPUTE | sympy | C2 | [
"C2/K3"
] | 63d175 | sequence_fibonacci_compute_v1 | negation_mod | 4 | 0 | [
"C2",
"K3"
] | 2 | 0.003 | 2026-02-08T16:08:20.495932Z | {
"verified": true,
"answer": 2229,
"timestamp": "2026-02-08T16:08:20.498464Z"
} | e11ecb | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 161,
"completion_tokens": 925
},
"timestamp": "2026-02-16T22:14:49.648Z",
"answer": 2229
},
{
... | 1 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K3",
"status": "ok_later"
},
{
"lemma": "LTE_DIFF",
"status": ... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
f96382_n | algebra_poly_eval_v1_1218484723_6366 | A cryptographer fixes a base value $m = 7$ and defines a code number $R$ as follows. First, consider all ordered pairs $(a, b)$ of integers with $1 \le a \le 20$, $1 \le b \le 20$, and $a \le b$ that satisfy
$$5 \cdot a^{\left|\{ p : p > 0,\ \text{there exists an integer } q \text{ such that } pq = 108,\ \gcd(p, q) = 1... | 31,090 | ALG | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/QF_PSD_ORBIT"
] | 97daa7 | algebra_poly_eval_v1 | null | 7 | null | [
"COPRIME_PAIRS",
"QF_PSD_ORBIT"
] | 2 | 0.008 | 2026-02-25T07:54:56.326510Z | null | d546e9 | f96382 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 328,
"completion_tokens": 7503
},
"timestamp": "2026-03-31T01:16:07.913Z",
"answer": 31090
},
{
"... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_ORBIT",
"status": "ok_later"
}
] | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | |
e7fc1d | algebra_poly_eval_v1_898971024_2860 | Let $k = 27$. Compute the value of
$$
\frac{56k^5 - 170k^4 - 12k^3 + p k^2 - 291k + 54}{19635},
$$
where $p$ is the largest prime number between $2$ and $378$, inclusive. | 36,324 | graphs = [
Graph(
let={
"_n": Const(3),
"k": Const(27),
"result": Div(Sum(Mul(Const(56), Pow(Ref("k"), Const(5))), Mul(Const(-170), Pow(Ref("k"), Const(4))), Mul(Const(-12), Pow(Ref("k"), Ref("_n"))), Mul(MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | algebra_poly_eval_v1 | null | 5 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.004 | 2026-02-08T17:01:48.444078Z | {
"verified": true,
"answer": 36324,
"timestamp": "2026-02-08T17:01:48.448429Z"
} | a2291d | 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": 1766
},
"timestamp": "2026-02-17T17:39:03.403Z",
"answer": 36324
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"sta... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
e20f20 | algebra_poly_eval_v1_124444284_9505 | Let $ m = 4 $. Let $ n $ be the number of positive integers at most $ 16 $ that are even and relatively prime to $ 35 $. Let $ k $ be the maximum value of $ xy $ over all pairs of positive integers $ (x, y) $ such that $ x + y = n $. Let $ p $ be the number of unordered pairs $ (p, q) $ of positive integers such that $... | 303 | graphs = [
Graph(
let={
"_m": Const(4),
"_n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(16)), Divides(divisor=Const(2), dividend=Var("n")), Eq(GCD(a=Var("n"), b=Const(35)), Const(1))))),
"k": MaxOverSet(set=MapO... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS",
"C5/B1"
] | ead9e9 | algebra_poly_eval_v1 | null | 7 | 0 | [
"B1",
"C5",
"COPRIME_PAIRS"
] | 3 | 0.007 | 2026-02-08T12:32:28.436763Z | {
"verified": true,
"answer": 303,
"timestamp": "2026-02-08T12:32:28.443916Z"
} | d9a3ea | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 179,
"completion_tokens": 1319
},
"timestamp": "2026-02-15T02:17:57.770Z",
"answer": 303
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "C5",
"status": "ok"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
ed6510 | alg_poly4_sum_v1_1218484723_4278 | Let $P = \min\{ x + y : x, y > 0,\ xy = 665856 \}$. Compute the remainder when $$\sum_{a=1}^{298} \sum_{b=1}^{298} \left( P a^2 b^2 - 1088 a^3 b + 272 a^4 + 272 b^4 - 1088 a b^3 \right)$$ is divided by $50156$. | 49,516 | graphs = [
Graph(
let={
"_n": Const(272),
"result": Mod(value=SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(298)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(298)))), expr=Sum(Mul(MinO... | ALG | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | alg_poly4_sum_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.206 | 2026-02-25T05:54:59.779444Z | {
"verified": true,
"answer": 49516,
"timestamp": "2026-02-25T05:54:59.985185Z"
} | f34bfa | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 209,
"completion_tokens": 23473
},
"timestamp": "2026-03-29T14:47:32.567Z",
"answer": 760
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 1.55,
"mid": 4.7,
"hi": 7.23
} | ||
f776f1 | comb_binomial_compute_v1_1218484723_4625 | Let $n$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \le a \le 15$ and $1 \le b \le 15$ such that $16 \cdot b^2 = 1024$. Let $M = \binom{n}{8}$. Find the remainder when $44121M$ is divided by $97201$. | 91,715 | graphs = [
Graph(
let={
"_n": Const(15),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(15)), Geq(Var("b"), Const(1)), Leq(Var("b"), Ref("_n")), Eq(Mul(Const(16), Pow(Var("b"), Const(2))), Const(... | COMB | null | COMPUTE | sympy | QF_PSD_COUNT | [
"QF_PSD_COUNT"
] | 09ce67 | comb_binomial_compute_v1 | null | 3 | 0 | [
"QF_PSD_COUNT"
] | 1 | 0.003 | 2026-02-25T06:18:00.785956Z | {
"verified": true,
"answer": 91715,
"timestamp": "2026-02-25T06:18:00.788617Z"
} | e4e801 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 194,
"completion_tokens": 2535
},
"timestamp": "2026-03-29T16:34:58.017Z",
"answer": 91715
},
{
"... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no... | {
"lo": -3.33,
"mid": 1.03,
"hi": 5.26
} | ||
63b9a2 | lin_form_endings_v1_1526740231_466 | Let $a = 40$ and $b = 56$. Define $g = \gcd(a, b)$, and let $a' = \left\lfloor \frac{a}{g} \right\rfloor$ and $b' = \left\lfloor \frac{b}{g} \right\rfloor$. Let $A = 20$ and $B = 13$. Compute the value of $(a' \cdot A + b' \cdot B - a' \cdot b') \cdot 13700$, and find the remainder when this value is divided by $92576$... | 7,952 | graphs = [
Graph(
let={
"a_coeff": Const(40),
"b_coeff": Const(56),
"A_val": Const(20),
"B_val": Const(13),
"g_step": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"ap_node": Floor(Div(Ref("a_coeff"), Ref("g_step"))),
"bp_node": ... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 3 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T11:33:45.517108Z | {
"verified": true,
"answer": 7952,
"timestamp": "2026-02-08T11:33:45.517939Z"
} | 7a63a9 | 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": 684
},
"timestamp": "2026-02-14T16:14:19.243Z",
"answer": 7952
},
{
... | 1 | [
{
"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",
"status": "no"
},
{
"lemma": "V8_SUM",
... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
5c4af5 | nt_count_coprime_v1_677425708_1751 | Let $S$ be the set of positive integers $n$ such that $n \leq 27225$ and $\gcd(n, 23) = 1$. Let $r$ be the number of elements in $S$. Compute the remainder when $96817 \cdot r$ is divided by $83484$. | 8,030 | graphs = [
Graph(
let={
"upper": Const(27225),
"k": Const(23),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), SumOverDivisors(n=GCD(a=Const(value=3), b=Const(value=5)), var='d', expr=MoebiusMu(n=Var(name='d')))), Leq(Var("n"), Ref("upper... | NT | null | COUNT | sympy | MOBIUS_COPRIME | [
"MOBIUS_COPRIME"
] | ac54ac | nt_count_coprime_v1 | null | 3 | 0 | [
"MOBIUS_COPRIME"
] | 1 | 2.333 | 2026-02-08T04:24:57.137610Z | {
"verified": true,
"answer": 8030,
"timestamp": "2026-02-08T04:24:59.470233Z"
} | 050b5d | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 179,
"completion_tokens": 2407
},
"timestamp": "2026-02-10T00:28:36.682Z",
"answer": 8030
},
{
"i... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok"
},
{
"lemma": "V1",
"status": "n... | {
"lo": -6.5,
"mid": -0.2,
"hi": 6.11
} |
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