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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
ec4c78 | antilemma_v1_legendre_151522320_163 | Let $m = 33215$. Let $n$ be the number of nonnegative integers $j$ such that $0 \leq j \leq 65545$ and $\binom{65545}{j}$ is odd, increased by $5$. Let $x$ be the largest integer $k$ such that $n^k$ divides $m!$. Compute $x + \phi(|x| + 1) + \tau(|x| + 1)$, where $\phi$ denotes Euler's totient function and $\tau$ denot... | 4,153 | graphs = [
Graph(
let={
"_m": Const(33215),
"_n": Sum(CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(65545)), Eq(Mod(value=Binom(n=Const(65545), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')), Const(... | NT | null | COMPUTE | sympy | V8 | [
"V8/V1",
"V1"
] | b9ae67 | antilemma_v1_legendre | null | 7 | 0 | [
"V1",
"V8"
] | 2 | 0.002 | 2026-02-08T03:00:47.791124Z | {
"verified": true,
"answer": 4153,
"timestamp": "2026-02-08T03:00:47.792631Z"
} | f49723 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 239,
"completion_tokens": 2107
},
"timestamp": "2026-02-09T00:00:30.326Z",
"answer": 4153
},
{
"... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "same_pattern_wrong"
},
{
"lemma": "MOD_MUL",
"st... | {
"lo": -6.49,
"mid": 0.51,
"hi": 7.52
} | ||
42c9d2 | algebra_poly_eval_v1_601307018_4929 | Let $t = 5$. Compute
$$
\frac{9 t^{5} + 57 t^{4} + \left|\left\{ v : v \geq 40,\ v \leq \min\left\{ |x - y| : x > 0,\ y > 0,\ x y = 47156561 \right\},\ \exists\, a,b \in \mathbb{Z},\ 1 \leq a,b \leq 11\ \text{such that}\ 13b^2 + 17a^2 + 10ab = v \right\}\right| \cdot t^{3} + 93 t^{2} -90t + 72}{27}.
$$ | 2,961 | graphs = [
Graph(
let={
"_m": Const(72),
"_n": Const(3),
"t": Const(5),
"result": Div(Sum(Mul(Const(9), Pow(Ref("t"), Const(5))), Mul(Const(57), Pow(Ref("t"), Const(4))), Mul(CountOverSet(set=SolutionsSet(var=Var("v"), condition=And(Geq(Var("v"), Const(40)), L... | ALG | null | COMPUTE | sympy | B3_DIFF | [
"B3_DIFF/QF_PSD_DISTINCT"
] | d645fd | algebra_poly_eval_v1 | null | 7 | 0 | [
"B3_DIFF",
"QF_PSD_DISTINCT"
] | 2 | 0.021 | 2026-03-10T05:38:17.342713Z | {
"verified": true,
"answer": 2961,
"timestamp": "2026-03-10T05:38:17.363429Z"
} | 8ed207 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 270,
"completion_tokens": 13156
},
"timestamp": "2026-04-19T00:34:04.888Z",
"answer": 2961
},
{
... | 1 | [
{
"lemma": "B3_DIFF",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_DISTINCT",
"status": "ok_later"
}
] | {
"lo": -3.31,
"mid": 1.32,
"hi": 5.87
} | ||
3b14df | sequence_count_fib_divisible_v1_1439011603_2118 | Let $n = 44121$. Let $A$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 6$, $\gcd(p, q) = 1$, and $p < q$. Let $U$ be the number of integers $n$ with $1 \leq n \leq 1278$ such that $|A|$ divides $n$ and $\gcd(n, 35) = 1$. Let $d = 15$. Compute the remainder when $n... | 80,761 | graphs = [
Graph(
let={
"_n": Const(44121),
"upper": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(1278)), Divides(divisor=CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/C5"
] | 195cc1 | sequence_count_fib_divisible_v1 | null | 6 | 0 | [
"C5",
"COPRIME_PAIRS"
] | 2 | 0.07 | 2026-02-08T16:31:36.743747Z | {
"verified": true,
"answer": 80761,
"timestamp": "2026-02-08T16:31:36.814054Z"
} | b765d0 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 200,
"completion_tokens": 2271
},
"timestamp": "2026-02-17T05:59:36.558Z",
"answer": 80761
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "C5",
"status": "ok_later"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lem... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
bdfc9c | modular_count_residue_v1_1520064083_1260 | Let $p$ and $q$ be positive integers such that $pq = 1080$, $\gcd(p, q) = 1$, and $p < q$. Let $S$ be the set of all such integers $p$. Define $r = \sum_{k=1}^{|S|} \varphi(k) \left\lfloor \frac{4}{k} \right\rfloor$, where $\varphi$ denotes Euler's totient function. Let $N$ be the number of positive integers $n \leq 32... | 1,106 | graphs = [
Graph(
let={
"upper": Const(32057),
"m": Const(29),
"r": Summation(var="k", start=Const(1), end=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 | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/K2"
] | 846647 | modular_count_residue_v1 | null | 4 | 0 | [
"COPRIME_PAIRS",
"K2"
] | 2 | 8.483 | 2026-02-08T03:53:31.916253Z | {
"verified": true,
"answer": 1106,
"timestamp": "2026-02-08T03:53:40.398862Z"
} | 14083a | 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": 2118
},
"timestamp": "2026-02-10T16:05:19.118Z",
"answer": 1106
},
{
"i... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K2",
"status": "ok_later"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
... | {
"lo": -5.92,
"mid": -3.15,
"hi": 0.25
} | ||
a6cf08 | modular_mod_compute_v1_784195855_1366 | Let $a = 700$ and $m = 27889$. Let $r$ be the remainder when $a$ is divided by $m$. Let $c$ be the largest prime number $n$ such that $2 \leq n \leq 4650$. Compute the remainder when $c \cdot r$ is divided by $53866$. | 22,340 | graphs = [
Graph(
let={
"_n": Const(2),
"a": Const(700),
"m": Const(27889),
"result": Mod(value=Ref("a"), modulus=Ref("m")),
"_c": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Const(4650)), IsPrime... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | 183c11 | modular_mod_compute_v1 | affine_mod | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.001 | 2026-02-08T04:59:35.299540Z | {
"verified": true,
"answer": 22340,
"timestamp": "2026-02-08T04:59:35.300610Z"
} | 892b6f | 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": 1101
},
"timestamp": "2026-02-11T22:35:11.657Z",
"answer": 22340
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
62637b | nt_min_coprime_above_v1_48377204_1641 | Let $m$ be the number of integers $t$ with $30 \leq t \leq 666$ for which there exist integers $a$ and $b$ satisfying $1 \leq a \leq 24$, $1 \leq b \leq 18$, and $t = 21a + 9b$. Find the smallest integer $n$ such that $32761 < n \leq 32972$ and $\gcd(n, m) = 1$. Let this value be $k$. Compute $k + \left(2^{k \bmod 15} ... | 32,766 | graphs = [
Graph(
let={
"_n": Const(65022),
"start": Const(32761),
"upper": Const(32972),
"modulus": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_min_coprime_above_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.026 | 2026-02-08T16:16:46.516272Z | {
"verified": true,
"answer": 32766,
"timestamp": "2026-02-08T16:16:46.542535Z"
} | aa21ae | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 177,
"completion_tokens": 3938
},
"timestamp": "2026-02-17T00:53:13.582Z",
"answer": 32766
},
... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
e8dcd7 | geo_count_lattice_triangle_v1_784195855_2787 | Let $A = 2 \times \left| 120 \cdot 121 + 89 \cdot (-55) \right|$. Let $B = \gcd(|\sum_{k=1}^{15} \phi(k) \cdot \lfloor 15/k \rfloor|, 55) + \gcd(|89 - 120|, |121 - 55|) + \gcd(|0 - 89|, |0 - 121|)$, where $\phi$ denotes Euler's totient function. Compute $$\frac{A + 2 - B}{2}.$$ Find the value of this expression. | 4,810 | graphs = [
Graph(
let={
"_n": Const(55),
"area_2x": Abs(arg=Sum(Mul(Const(value=120), Const(value=121)), Mul(Const(value=89), Sub(left=Const(value=0), right=Ref(name='_n'))))),
"boundary": Sum(GCD(a=Abs(arg=Summation(expr=Mul(EulerPhi(n=Var(name='k')), Floor(arg=Div(left=... | NT | null | COUNT | sympy | K2 | [
"K2"
] | 6897ab | geo_count_lattice_triangle_v1 | null | 7 | 0 | [
"K2"
] | 1 | 0.006 | 2026-02-08T06:02:57.740641Z | {
"verified": true,
"answer": 4810,
"timestamp": "2026-02-08T06:02:57.746385Z"
} | aad4ad | 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": 3665
},
"timestamp": "2026-02-12T18:46:52.205Z",
"answer": 4810
},
{... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
a0cf56 | nt_count_divisible_v1_48377204_1838 | Let $N = 76788$. Let $A$ be the number of positive integers $n$ such that $1 \leq n \leq 66666$ and $n$ is divisible by $21$. Let $B$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 11118907800$, $\gcd(p, q) = 1$, and $p < q$. Compute the remainder when $B - A... | 73,678 | graphs = [
Graph(
let={
"_n": Const(76788),
"upper": Const(66666),
"divisor": Const(21),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(value=Var("n"), modulus=Ref("divisor")), C... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | c90628 | nt_count_divisible_v1 | negation_mod | 6 | 0 | [
"COPRIME_PAIRS"
] | 1 | 3.441 | 2026-02-08T16:26:56.701760Z | {
"verified": true,
"answer": 73678,
"timestamp": "2026-02-08T16:27:00.142950Z"
} | 2678b3 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 159,
"completion_tokens": 4056
},
"timestamp": "2026-02-17T04:34:57.963Z",
"answer": 73678
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "n... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
f8cb94 | nt_num_divisors_compute_v1_1742523217_5205 | Let $ n = 59049 $. Compute the number of positive divisors of $ n $. | 11 | graphs = [
Graph(
let={
"n": Const(59049),
"result": NumDivisors(n=Ref("n")),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_num_divisors_compute_v1 | null | 3 | 0 | [
"B3"
] | 1 | 0.009 | 2026-02-08T10:51:30.767396Z | {
"verified": true,
"answer": 11,
"timestamp": "2026-02-08T10:51:30.776775Z"
} | fca587 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 65,
"completion_tokens": 379
},
"timestamp": "2026-02-14T09:03:10.313Z",
"answer": 11
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -9.12,
"mid": -6.02,
"hi": -3.62
} | ||
1406df | nt_count_divisible_and_v1_784195855_7875 | Let $m = 2$. Let $n$ be the largest prime number satisfying $m \le n \le 5$. Let $d_1 = 12$ and $d_2 = \sum_{k=1}^{n} k$. Define $S$ as the set of all positive integers $n$ such that $1 \le n \le 238260$, $n$ is divisible by $d_1$, and $n$ is divisible by $d_2$. Let $c = |S|$, the number of elements in $S$. Compute $\s... | 33,527 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_m")), Leq(Var("n"), Const(5)), IsPrime(Var("n"))))),
"upper": Const(238260),
"d1": Const(12),
"d2": Summation(var="k", start=C... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW/SUM_ARITHMETIC"
] | 592103 | nt_count_divisible_and_v1 | null | 4 | 0 | [
"MAX_PRIME_BELOW",
"SUM_ARITHMETIC"
] | 2 | 12.18 | 2026-02-08T09:35:38.639872Z | {
"verified": true,
"answer": 33527,
"timestamp": "2026-02-08T09:35:50.820122Z"
} | 3511dc | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 195,
"completion_tokens": 3417
},
"timestamp": "2026-02-14T05:18:36.724Z",
"answer": 33527
},
... | 1 | [
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok_later"
},
{
"lemma": "V7",
"status": "no"
}... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
ad12aa | diophantine_fbi2_min_v1_1978505735_2553 | Let $k = 35$. Define $\text{upper}$ to be the number of positive integers $n$ with $1 \leq n \leq 90$ such that the sum of the decimal digits of $n$ is divisible by $2$. Determine the value of the smallest integer $d \geq 3$ such that $d \leq \text{upper}$, $d$ divides $k$, and $\frac{k}{d} \geq 5$. | 5 | graphs = [
Graph(
let={
"_n": Const(2),
"k": Const(35),
"upper": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(90)), Eq(Mod(value=DigitSum(Var("n")), modulus=Ref("_n")), Const(0))))),
"result": MinOverSe... | NT | null | EXTREMUM | sympy | L3B | [
"L3B"
] | cc148f | diophantine_fbi2_min_v1 | null | 5 | 0 | [
"L3B"
] | 1 | 0.005 | 2026-02-08T16:57:46.210048Z | {
"verified": true,
"answer": 5,
"timestamp": "2026-02-08T16:57:46.215044Z"
} | 7de9c2 | 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": 1522
},
"timestamp": "2026-02-17T16:00:22.553Z",
"answer": 5
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "L3B",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
55a35d | nt_count_divisible_and_v1_1918700295_3136 | Let $T$ be the set of all integers $t$ such that $12 \leq t \leq 161$ and $t = 7a + 5b$ for some positive integers $a \leq 18$ and $b \leq 7$. Let $d_2$ be the number of positive integers $k \leq |T|$ that are divisible by 7. Find the number of positive integers $n \leq 24696$ that are divisible by both 12 and $d_2$. C... | 686 | graphs = [
Graph(
let={
"upper": Const(24696),
"d1": Const(12),
"d2": CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(1)), Leq(Var("k"), CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(... | ALG | NT | COUNT | sympy | LIN_FORM | [
"LIN_FORM/C2"
] | 03e7fc | nt_count_divisible_and_v1 | null | 6 | 0 | [
"C2",
"LIN_FORM"
] | 2 | 0.821 | 2026-02-08T08:25:26.733944Z | {
"verified": true,
"answer": 686,
"timestamp": "2026-02-08T08:25:27.554648Z"
} | 46ef00 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 183,
"completion_tokens": 560
},
"timestamp": "2026-02-15T20:13:51.162Z",
"answer": 411
},
{
"id": 11,
... | 1 | [
{
"lemma": "C2",
"status": "ok_later"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.34
} | ||
ffdb84 | nt_max_prime_below_v1_784195855_7646 | Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 12$, $\gcd(p, q) = 1$, and $p < q$. Let $T$ be the set of all prime numbers $n$ such that $n \geq |S|$ and $n \leq 54756$. Compute the maximum element of $T$. | 54,751 | graphs = [
Graph(
let={
"upper": Const(54756),
"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 | 1.212 | 2026-02-08T09:26:00.087803Z | {
"verified": true,
"answer": 54751,
"timestamp": "2026-02-08T09:26:01.300187Z"
} | 203c67 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 136,
"completion_tokens": 3049
},
"timestamp": "2026-02-14T03:51:31.803Z",
"answer": 54751
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
9e71b4 | nt_count_divisors_in_range_v1_1125832087_1668 | Let $n = 27720$. Let $A$ be the number of positive integers $k$ such that $1 \leq k \leq 27765$, $9$ divides $k$, and $\gcd(k, 14) = 1$. Let $B$ be the number of positive divisors $d$ of $n$ such that $58 \leq d \leq A$. Compute $14884 - B$. | 14,834 | graphs = [
Graph(
let={
"n": Const(27720),
"a": Const(58),
"b": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(27765)), Divides(divisor=Const(9), dividend=Var("n")), Eq(GCD(a=Var("n"), b=Const(14)), Const(1))))),
... | NT | null | COUNT | sympy | C5 | [
"C5"
] | 1d9668 | nt_count_divisors_in_range_v1 | null | 5 | 0 | [
"C5"
] | 1 | 0.016 | 2026-02-08T03:52:23.503687Z | {
"verified": true,
"answer": 14834,
"timestamp": "2026-02-08T03:52:23.519381Z"
} | 2f4761 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 204,
"completion_tokens": 5426
},
"timestamp": "2026-02-10T14:37:10.276Z",
"answer": 14834
},
{
... | 1 | [
{
"lemma": "C5",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
475cdb | comb_count_permutations_fixed_v1_865884756_1397 | Let $n$ be the number of integers $j$ with $0 \leq j \leq 32804$ such that $\binom{32804}{j}$ is odd. Let $k = 3$. Define $\text{result} = \binom{n}{k} \cdot !(n - k)$, where $!m$ denotes the number of derangements of $m$ elements. Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 62... | 92,158 | graphs = [
Graph(
let={
"_n": Const(32804),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Ref("_n")), Eq(Mod(value=Binom(n=Const(32804), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')),
"k... | COMB | null | COUNT | sympy | B3 | [
"B3",
"V8"
] | 7c01c3 | comb_count_permutations_fixed_v1 | negation_mod | 6 | 0 | [
"B3",
"V8"
] | 2 | 0.007 | 2026-02-08T16:02:57.355050Z | {
"verified": true,
"answer": 92158,
"timestamp": "2026-02-08T16:02:57.362158Z"
} | bdf9d0 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 281,
"completion_tokens": 1251
},
"timestamp": "2026-02-24T19:44:22.116Z",
"answer": 92158
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
},
{
"lemma... | {
"lo": -2.4,
"mid": 1.57,
"hi": 5.75
} | ||
99391c_n | algebra_poly_eval_v1_1218484723_2836 | A digital lock requires a code calculated by the formula $8m^3 - 3m^2 - 2m - 3$, where $m$ is the number of sectors on the lock's dial. If the dial has $16$ sectors, what is the code? | 31,965 | ALG | null | COMPUTE | sympy | QF_PSD_ORBIT | [
"QF_PSD_ORBIT/POLY_ORBIT_HENSEL",
"STARS_BARS/POLY_ORBIT_HENSEL",
"B1/POLY_ORBIT_HENSEL"
] | f8a9a8 | algebra_poly_eval_v1 | null | 2 | null | [
"B1",
"POLY_ORBIT_HENSEL",
"QF_PSD_ORBIT",
"STARS_BARS"
] | 4 | 0.659 | 2026-02-25T04:33:43.276075Z | null | e31536 | 99391c | narrative | 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": 803
},
"timestamp": "2026-03-30T19:08:11.333Z",
"answer": 31965
},
{
"i... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "POLY_ORBIT_HENSEL",
"status": "ok_later"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_ORBIT",
"status": "ok"
},
{
"lemma": "STARS_BARS",
"status": "ok"
}
] | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | |
780125 | comb_bell_compute_v1_168721529_1270 | Let $n$ be the smallest positive integer such that the highest power of $2$ dividing $n!$ is at least $7$. Compute the number of partitions of a set with $n$ elements. | 4,140 | graphs = [
Graph(
let={
"_n": Const(2),
"n": MinOverSet(set=SolutionsSet(var=Var("n"), condition=Geq(MaxKDivides(target=Factorial(Var("n")), base=Ref("_n")), Const(7)), domain='Z_{>0}')),
"result": Bell(Ref("n")),
},
goal=Ref("result"),
)
] | NT | COMB | COMPUTE | sympy | V5 | [
"V5"
] | 79df37 | comb_bell_compute_v1 | null | 6 | 0 | [
"V5"
] | 1 | 0.001 | 2026-02-08T13:33:22.603031Z | {
"verified": true,
"answer": 4140,
"timestamp": "2026-02-08T13:33:22.604529Z"
} | 6beb81 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 157,
"completion_tokens": 577
},
"timestamp": "2026-02-09T15:06:22.406Z",
"answer": 4140
},
{
"id... | 1 | [
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "ok"
}
] | {
"lo": -6.69,
"mid": -2.39,
"hi": 1.83
} | ||
5b3bbe | alg_poly_preperiod_count_v1_1218484723_6396 | For a non-negative integer $a$, define the sequence $N = (a^2 + a - 2) \bmod 83$, $M = (N^2 + N - 2) \bmod 83$, $R = (M^2 + M - 2) \bmod 83$, $S = (R^2 + R - 2) \bmod 83$. Find the number of integers $a$ with $0 \leq a \leq 53036$ such that $S = N$, $M \neq N$, and $R \neq N$. | 3,834 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Pow(Var("a"), Const(2)), Var("a"), Const(-2)), modulus=Const(83)),
"p2": Mod(value=Sum(Pow(Ref("p1"), Const(2)), Ref("p1"), Const(-2)), modulus=Const(83)),
"p3": Mod(value=Sum(Pow(Ref("p2"), Const(2)), Ref("p2"), Const(-2)), mod... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_preperiod_count_v1 | null | 6 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.024 | 2026-02-25T07:58:14.099420Z | {
"verified": true,
"answer": 3834,
"timestamp": "2026-02-25T07:58:14.123778Z"
} | 1af15f | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 239,
"completion_tokens": 27708
},
"timestamp": "2026-03-30T01:34:42.040Z",
"answer": 3834
},
{
"... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 1.53,
"mid": 4.7,
"hi": 7.23
} | ||
31725d | antilemma_sum_equals_v1_1520064083_7649 | Let $s$ be the number of ordered pairs of positive odd integers $(x_1, x_2)$ such that $x_1 + x_2 = 188$. Let $x$ be the number of ordered pairs of positive integers $(i, j)$ with $1 \leq i, j \leq 93$ such that $i + j = s$. Compute the remainder when $74144 \cdot x$ is divided by $89175$. | 28,917 | graphs = [
Graph(
let={
"_m": Const(89175),
"_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 | GEOM | COMPUTE | sympy | COMB1 | [
"COMB1/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | 3e1adf | antilemma_sum_equals_v1 | null | 4 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS"
] | 2 | 0.003 | 2026-02-08T09:13:54.244663Z | {
"verified": true,
"answer": 28917,
"timestamp": "2026-02-08T09:13:54.248083Z"
} | 43b5e5 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 208,
"completion_tokens": 2827
},
"timestamp": "2026-02-24T10:46:35.039Z",
"answer": 28917
},
{
"... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status":... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
39b1b3 | sequence_fibonacci_compute_v1_458359167_5133 | Let $n$ be the sum of $\phi(d)$ over all positive divisors $d$ of $24$, where $\phi$ denotes Euler's totient function. Let $F_n$ denote the $n$-th Fibonacci number, where $F_0 = 0$, $F_1 = 1$, and $F_k = F_{k-1} + F_{k-2}$ for $k \geq 2$. Compute the remainder when $38809 - F_n$ is divided by $59353$. | 51,794 | graphs = [
Graph(
let={
"_n": Const(59353),
"n": SumOverDivisors(n=Const(value=24), var='d', expr=EulerPhi(n=Var(name='d'))),
"result": Fibonacci(arg=Ref(name='n')),
"Q": Mod(value=Sub(Const(38809), Ref("result")), modulus=Ref("_n")),
},
goal=R... | NT | null | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | sequence_fibonacci_compute_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0.002 | 2026-02-08T12:17:22.449799Z | {
"verified": true,
"answer": 51794,
"timestamp": "2026-02-08T12:17:22.451591Z"
} | 405da0 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 155,
"completion_tokens": 837
},
"timestamp": "2026-02-14T23:56:41.252Z",
"answer": 51794
},
{... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
94e75d | sequence_fibonacci_compute_v1_397696148_2543 | Let $n = 5$. For each ordered pair $(k, j)$ with $k$ an integer from 1 to 6 and $j$ an integer from 1 to 4, compute the value of $k$. Let $S$ be the set of all such values of $k$. Define
$$
N = \frac{n \cdot \sum S}{20}.
$$
Let $F_N$ denote the $N$-th Fibonacci number, with $F_1 = F_2 = 1$ and $F_k = F_{k-1} + F_{k-2}$... | 90,338 | graphs = [
Graph(
let={
"_n": Const(5),
"n": Div(Mul(Ref("_n"), SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("k"), Var("_j")]), condition=Const(1), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(6)), right=IntegerRange(start=Const(1), end=Co... | NT | null | COMPUTE | sympy | SUM_INDEPENDENT | [
"SUM_INDEPENDENT/SUM_ARITHMETIC"
] | 87e6cf | sequence_fibonacci_compute_v1 | null | 3 | 0 | [
"SUM_ARITHMETIC",
"SUM_INDEPENDENT"
] | 2 | 0.001 | 2026-02-08T13:24:33.475911Z | {
"verified": true,
"answer": 90338,
"timestamp": "2026-02-08T13:24:33.477158Z"
} | 3f3284 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 199,
"completion_tokens": 2649
},
"timestamp": "2026-02-15T14:42:30.334Z",
"answer": 90338
},
... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok_later"
},
{
"lemma": "SUM_INDEPENDENT",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
9dd43e | nt_count_with_divisor_count_v1_1520064083_1880 | Let $S$ be the set of all positive integers $n$ such that $1 \leq n \leq 48841$ and the number of positive divisors of $n$ is 5. Let $d_{\text{min}}$ be the smallest integer $d \geq 2$ that divides 17303. Compute the Bell number $B_r$, where $r$ is the remainder when the number of elements in $S$ is divided by $d_{\tex... | 203 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": Const(48841),
"div_count": Const(5),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(NumDivisors(n=Var("n")), Ref("div_count"))))),
... | NT | COMB | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | 58d7e9 | nt_count_with_divisor_count_v1 | bell_mod | 6 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 2.037 | 2026-02-08T04:21:19.175918Z | {
"verified": true,
"answer": 203,
"timestamp": "2026-02-08T04:21:21.213339Z"
} | 4858a9 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 216,
"completion_tokens": 1204
},
"timestamp": "2026-02-10T16:20:47.394Z",
"answer": 203
},
{
"i... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
5415d6 | comb_bell_compute_v1_124444284_6556 | Let $n$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 52920$, $\gcd(p, q) = 1$, and $p < q$. Let $\text{result} = B_n$, the $n$-th Bell number. Let $c = 51984$ and $Q = c - \text{result}$. Find the value of $Q$. | 47,844 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=52920)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(value=1))... | NT | COMB | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_bell_compute_v1 | null | 6 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.002 | 2026-02-08T08:31:57.725389Z | {
"verified": true,
"answer": 47844,
"timestamp": "2026-02-08T08:31:57.727117Z"
} | 4821e0 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 142,
"completion_tokens": 1651
},
"timestamp": "2026-02-13T19:21:58.692Z",
"answer": 47844
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
}
] | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
f69666 | comb_bell_compute_v1_124444284_3286 | Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $p < q$, $\gcd(p, q) = 1$, and $p \cdot q = 29348550$. Let $n$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $x \cdot y = |S|$. Compute the $n$th Bell number. Determine the va... | 4,140 | graphs = [
Graph(
let={
"_n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=29348550)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(value... | NT | COMB | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/B3"
] | 3f0fb0 | comb_bell_compute_v1 | null | 6 | 0 | [
"B3",
"COPRIME_PAIRS"
] | 2 | 0.002 | 2026-02-08T05:20:26.169951Z | {
"verified": true,
"answer": 4140,
"timestamp": "2026-02-08T05:20:26.171654Z"
} | 178bd9 | 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": 1485
},
"timestamp": "2026-02-12T06:42:25.415Z",
"answer": 4140
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
1823cf | sequence_count_fib_divisible_v1_601307018_3261 | Let $M$ be the number of positive integers $p$ for which there exists an integer $q$ such that $p \cdot q = 216$, $\gcd(p, q) = 1$, and $p < q$. Let $R$ be the largest prime number $n$ satisfying $M \le n \le \max\{ d \mid d \ge 1,\, d \mid 359999,\, d^2 \le 359999 \}$. Let $S$ be the number of positive integers $n_1$ ... | 74,069 | graphs = [
Graph(
let={
"_m": Const(44121),
"_n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=216)), Eq(left=GCD(a=Var(name='p'), b=Var(na... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/MAX_PRIME_BELOW",
"B3_CLOSEST/MAX_PRIME_BELOW"
] | c05b12 | sequence_count_fib_divisible_v1 | null | 7 | 0 | [
"B3_CLOSEST",
"COPRIME_PAIRS",
"MAX_PRIME_BELOW"
] | 3 | 0.01 | 2026-03-10T03:47:23.956490Z | {
"verified": true,
"answer": 74069,
"timestamp": "2026-03-10T03:47:23.966483Z"
} | a46b5d | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 288,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T08:02:48.020Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "B3_CLOSEST",
"status": "ok"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MOD_SUB",
... | {
"lo": 1.23,
"mid": 4.27,
"hi": 6.7
} | ||
d460e0 | comb_bell_compute_v1_1918700295_2461 | Let $n$ be the maximum value of $xy$ over all ordered pairs $(x, y)$ of positive integers such that $x + y = 6$. Let $r = B_n$, the $n$th Bell number. Compute $r + \phi(|r| + 1) + \tau(|r| + 1)$, where $\phi$ denotes Euler's totient function and $\tau(k)$ denotes the number of positive divisors of $k$. | 31,079 | graphs = [
Graph(
let={
"_n": Const(6),
"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("_n")))), expr=Mul(Var("x"), Var("y")))),
... | NT | COMB | COMPUTE | sympy | B1 | [
"B1"
] | 5b950e | comb_bell_compute_v1 | null | 5 | 0 | [
"B1"
] | 1 | 0.001 | 2026-02-08T07:54:18.336668Z | {
"verified": true,
"answer": 31079,
"timestamp": "2026-02-08T07:54:18.338022Z"
} | cf0f3b | 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": 7089
},
"timestamp": "2026-02-13T13:16:53.307Z",
"answer": 31079
},
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
a846bc | nt_count_gcd_equals_v1_397696148_2158 | Let $k$ be the number of integers $t$ with $7 \leq t \leq 185$ for which there exist positive integers $a \leq 39$ and $b \leq 17$ such that $t = 3a + 4b$. Let $S$ be the set of positive integers $n \leq 7225$ such that $\gcd(n, k) = 1$. Find the number of elements in $S$. | 7,184 | graphs = [
Graph(
let={
"upper": Const(7225),
"k": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=39)), Geq(left... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_count_gcd_equals_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.585 | 2026-02-08T12:58:18.168246Z | {
"verified": true,
"answer": 7184,
"timestamp": "2026-02-08T12:58:18.753006Z"
} | 700363 | 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": 3232
},
"timestamp": "2026-02-15T08:15:57.371Z",
"answer": 7184
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
507554 | antilemma_sum_equals_v1_124444284_1113 | Let $n$ be the number of integers $t$ such that $18 \leq t \leq 158$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 6$, $1 \leq b \leq 11$, and $t = 8a + 10b$. Let $x$ be the number of ordered pairs $(i, j)$ of positive integers such that $1 \leq i \leq 57$, $1 \leq j \leq 58$, and $i + j = n$. Compu... | 57 | 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 | COUNT_SUM_EQUALS | [
"LIN_FORM/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | ada383 | antilemma_sum_equals_v1 | null | 4 | 0 | [
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 2 | 0.024 | 2026-02-08T03:41:12.170908Z | {
"verified": true,
"answer": 57,
"timestamp": "2026-02-08T03:41:12.194810Z"
} | 8ff2c4 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 241,
"completion_tokens": 2994
},
"timestamp": "2026-02-23T22:43:58.229Z",
"answer": 57
},
{
"id"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status... | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
ebc9c0 | antilemma_k3_v1_655260480_3243 | Let $ n = 35485 $. Define $ x $ to be the sum of $ \phi(d) $ over all positive divisors $ d $ of $ n $, where $ \phi $ denotes Euler's totient function. Compute $ x $. | 35,485 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=35485), var='d', expr=EulerPhi(n=Var(name='d'))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T17:17:06.120099Z | {
"verified": true,
"answer": 35485,
"timestamp": "2026-02-08T17:17:06.120610Z"
} | bbe5e3 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 97,
"completion_tokens": 905
},
"timestamp": "2026-02-17T22:46:35.242Z",
"answer": 35485
},
{
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
ab75f2 | diophantine_fbi2_min_v1_655260480_6198 | Let $k = 24$. Determine the smallest integer $d$ such that $3 \leq d \leq 34$, $d$ divides $k$, and $\frac{k}{d} \geq 2$. | 3 | graphs = [
Graph(
let={
"k": Const(24),
"a": Const(2),
"b": Const(1),
"upper": Const(34),
"result": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(3)), Leq(Var("d"), Ref("upper")), Divides(divisor=Var("d"), dividend=Ref... | NT | null | EXTREMUM | sympy | B3 | [
"C5"
] | 1d9668 | diophantine_fbi2_min_v1 | null | 3 | 0 | [
"B3",
"C5"
] | 2 | 0.064 | 2026-02-08T18:54:54.581415Z | {
"verified": true,
"answer": 3,
"timestamp": "2026-02-08T18:54:54.644961Z"
} | ff55de | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 92,
"completion_tokens": 677
},
"timestamp": "2026-02-18T20:29:06.077Z",
"answer": 3
},
{
... | 1 | [
{
"lemma": "C5",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
e63acd | diophantine_fbi2_min_v1_1874849503_914 | Let $k = 77$. Find the smallest integer $d$ such that $2 \leq d \leq 87$, $d$ divides $k$, and $\frac{k}{d} \geq 4$. | 7 | graphs = [
Graph(
let={
"k": Const(77),
"a": Const(1),
"b": Const(3),
"upper": Const(87),
"result": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Leq(Var("d"), Ref("upper")), Divides(divisor=Var("d"), dividend=Ref... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"ONE_PHI_2",
"K2"
] | 92c96e | diophantine_fbi2_min_v1 | null | 2 | 0 | [
"COPRIME_PAIRS",
"K2",
"ONE_PHI_2"
] | 3 | 0.067 | 2026-02-08T13:24:47.024411Z | {
"verified": true,
"answer": 7,
"timestamp": "2026-02-08T13:24:47.091848Z"
} | cde85e | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 158,
"completion_tokens": 333
},
"timestamp": "2026-02-09T22:39:41.937Z",
"answer": 7
},
{
"id": ... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
... | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
87a85c | diophantine_fbi2_count_v1_784195855_283 | Let $d_{\min}$ be the smallest divisor $d \ge 2$ of $11021$. Let $k = 180$. Let $D$ be the set of all integers $d$ such that $5 \le d \le d_{\min}$, $d$ divides $k$, $k/d \ge 3$, and $k/d \le 101$, where $101$ is the smallest divisor $\ge 2$ of $10403$. Let $\text{result} = |D|$. Let $Q = 33489 - \text{result}$. Comput... | 33,477 | graphs = [
Graph(
let={
"_n": Const(11021),
"k": Const(180),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(5)), Leq(Var("d"), MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | diophantine_fbi2_count_v1 | null | 4 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.009 | 2026-02-08T03:04:30.839366Z | {
"verified": true,
"answer": 33477,
"timestamp": "2026-02-08T03:04:30.848094Z"
} | e9549f | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 237,
"completion_tokens": 2249
},
"timestamp": "2026-02-10T12:38:30.653Z",
"answer": 33477
},
{
... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.02,
"hi": 0.32
} | ||
436bfa | antilemma_sum_equals_v1_48377204_2478 | Let $m = 9$. Let $n$ be the number of ordered pairs $(i, j)$ of integers with $1 \leq i \leq 8$ and $1 \leq j \leq 8$ such that $i + j = m$. Let $x$ be the number of ordered pairs $(i_1, j_1)$ of integers with $1 \leq i_1 \leq 8$ and $1 \leq j_1 \leq 8$ such that $i_1 + j_1 = n$. Define
$$
Q = \sum_{n=1}^{|x|} \phi(n),... | 18 | graphs = [
Graph(
let={
"_m": Const(9),
"_n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref("_m")), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(8)), right=IntegerRange(start=Const(1), end=Cons... | COMB | GEOM | COMPUTE | sympy | LIN_FORM | [
"COUNT_SUM_EQUALS/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | ae9919 | antilemma_sum_equals_v1 | null | 4 | 0 | [
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 2 | 0.042 | 2026-02-08T16:47:18.472148Z | {
"verified": true,
"answer": 18,
"timestamp": "2026-02-08T16:47:18.514123Z"
} | 364156 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 213,
"completion_tokens": 983
},
"timestamp": "2026-02-17T12:05:32.375Z",
"answer": 16
},
{... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SU... | {
"lo": -5.64,
"mid": -3.17,
"hi": -0.81
} | ||
97e008 | nt_min_with_divisor_count_v1_971394319_1332 | Let $u = 52441$ and $d = 8$. Define $r$ to be the smallest positive integer $n$ such that $n \leq u$ and $n$ has exactly $8$ positive divisors. Let $A$ be the set of all positive integers $p$ such that there exists a positive integer $q$ with $p \cdot q = 6$, $\gcd(p, q) = 1$, and $p < q$. Let $a = |A|$. Let $B$ be the... | 1,048 | graphs = [
Graph(
let={
"_n": Const(54383),
"upper": Const(52441),
"div_count": Const(8),
"result": MinOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(NumDivisors(n=Var("n")), Ref("div_count"))))),
... | NT | null | EXTREMUM | sympy | V1 | [
"COPRIME_PAIRS",
"C4"
] | 583d7c | nt_min_with_divisor_count_v1 | mod_exp | 5 | 0 | [
"C4",
"COPRIME_PAIRS",
"V1"
] | 3 | 3.353 | 2026-02-08T13:37:02.977148Z | {
"verified": true,
"answer": 1048,
"timestamp": "2026-02-08T13:37:06.330422Z"
} | 907ac9 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 238,
"completion_tokens": 1405
},
"timestamp": "2026-02-15T18:49:56.324Z",
"answer": 1048
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
be46ff | nt_count_with_divisor_count_v1_151522320_1653 | Let $P$ be the set of all prime numbers $n$ such that $2 \le n \le 227$. Let $d$ be the number of elements in $P$.
Consider the set of all ordered pairs $(x,y)$ of positive integers such that $xy = d$. For each such pair, compute $x + y$, and let $k$ be the minimum value of $x + y$ over all such pairs.
Compute the nu... | 218 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": Const(73984),
"div_count": 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")), CountOv... | NT | null | COUNT | sympy | COUNT_PRIMES | [
"COUNT_PRIMES/B3"
] | 3caaca | nt_count_with_divisor_count_v1 | null | 6 | 0 | [
"B3",
"COUNT_PRIMES"
] | 2 | 4.616 | 2026-02-08T04:10:09.381578Z | {
"verified": true,
"answer": 218,
"timestamp": "2026-02-08T04:10:13.998074Z"
} | 4ad82b | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 247,
"completion_tokens": 4436
},
"timestamp": "2026-02-10T15:38:18.621Z",
"answer": 218
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
867be8 | geo_count_lattice_rect_v1_1125832087_929 | Compute the number of lattice points $(x, y)$ such that $0 \leq x \leq 100$ and $0 \leq y \leq 295$. | 29,896 | graphs = [
Graph(
let={
"a": Const(100),
"b": Const(295),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 2 | 0 | null | null | 0.001 | 2026-02-08T03:22:07.264784Z | {
"verified": true,
"answer": 29896,
"timestamp": "2026-02-08T03:22:07.266278Z"
} | 5a2655 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 148,
"completion_tokens": 155
},
"timestamp": "2026-02-10T14:04:03.154Z",
"answer": 29896
},
{
"i... | 1 | [] | {
"lo": -5.97,
"mid": -3.96,
"hi": -1.93
} | ||||
6b29ed | antilemma_k3_v1_2051736721_1404 | Let $x = \sum_{d \mid 99879} \phi(d)$, where the sum is over all positive divisors $d$ of $99879$. Let $c$ be the sum of all real numbers $x_1$ such that $x_1^2 - 44x_1 - 12512 = 0$. Compute the remainder when $c - x$ is divided by $78685$. | 57,535 | graphs = [
Graph(
let={
"_n": Const(2),
"x": SumOverDivisors(n=Const(value=99879), var='d', expr=EulerPhi(n=Var(name='d'))),
"_c": SumOverSet(set=SolutionsSet(var=Var("x1"), condition=Eq(Sum(Pow(Var("x1"), Ref("_n")), Mul(Const(-44), Var("x1")), Const(-12512)), Sub(Const(... | NT | COMB | COMPUTE | sympy | K13 | [
"VIETA_SUM",
"IDENTITY_SUB_SELF",
"K3"
] | 5061b4 | antilemma_k3_v1 | negation_mod | 3 | 0 | [
"IDENTITY_SUB_SELF",
"K13",
"K3",
"VIETA_SUM"
] | 4 | 0.005 | 2026-02-08T16:02:03.109522Z | {
"verified": true,
"answer": 57535,
"timestamp": "2026-02-08T16:02:03.114493Z"
} | 715d1d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 135,
"completion_tokens": 533
},
"timestamp": "2026-02-16T19:43:52.061Z",
"answer": 57535
},
{... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "IDENTITY_SUB_SELF",
"status": "ok"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
0056e2 | algebra_poly_eval_v1_601307018_713 | Let $n = 9$. Compute $$2n^3 - 2n^2 + n + \min_{\substack{1 \le a \le 8 \\ 1 \le b \le 8}} \left( 5a^2 + \left| \left\{ (a_1, b_1) \in [1,30]^2 : -9a_1^3 - 27a_1 b_1^2 + 27a_1^2 b_1 + 9b_1^3 = \min_{\substack{1 \le a_2 \le 26 \\ 1 \le b_2 \le 26}} (65a_2^3 + 219a_2 b_2^2 + 201a_2^2 b_2 + 91b_2^3) \right\} \right| \cdot ... | 1,315 | graphs = [
Graph(
let={
"_m": Const(30),
"_n": Const(2),
"n": Const(9),
"result": Sum(Mul(Const(2), Pow(Ref("n"), Const(3))), Mul(Const(-2), Pow(Ref("n"), Ref("_n"))), Ref("n"), MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]... | ALG | null | COMPUTE | sympy | POLY3_MIN | [
"POLY3_MIN/POLY3_COUNT/QF_PSD_MIN"
] | ec843a | algebra_poly_eval_v1 | null | 6 | 0 | [
"POLY3_COUNT",
"POLY3_MIN",
"QF_PSD_MIN"
] | 3 | 0.031 | 2026-03-10T01:21:53.091715Z | {
"verified": true,
"answer": 1315,
"timestamp": "2026-03-10T01:21:53.122820Z"
} | 253c5c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 317,
"completion_tokens": 2521
},
"timestamp": "2026-03-28T23:54:18.706Z",
"answer": 1315
},
{
"i... | 1 | [
{
"lemma": "POLY3_COUNT",
"status": "ok_later"
},
{
"lemma": "POLY3_MIN",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_MIN",
"status": "ok_later"
}
] | {
"lo": -0.92,
"mid": 2.07,
"hi": 4.68
} | ||
bfc283 | nt_count_gcd_equals_v1_349078426_606 | Let $k = 378$. Let $d$ be the number of positive integers $k'$ such that $1 \leq k' \leq 432$ and $16$ divides $k'$. Let $N$ be the number of positive integers $n$ such that $1 \leq n \leq 32400$ and $\gcd(n, k) = d$. Find the remainder when $44121 \cdot N$ is divided by $76000$. | 30,194 | graphs = [
Graph(
let={
"upper": Const(32400),
"k": Const(378),
"d": CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(1)), Leq(Var("k"), Const(432)), Divides(divisor=Const(16), dividend=Var("k"))), domain='positive_integers')),
"re... | NT | null | COUNT | sympy | C2 | [
"C2"
] | 9685eb | nt_count_gcd_equals_v1 | null | 5 | 0 | [
"C2"
] | 1 | 3.437 | 2026-02-08T13:10:04.900290Z | {
"verified": true,
"answer": 30194,
"timestamp": "2026-02-08T13:10:08.337123Z"
} | 29defb | 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": 1645
},
"timestamp": "2026-02-15T10:23:33.463Z",
"answer": 30194
},
... | 1 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
9582f5 | nt_count_divisors_in_range_v1_48377204_1251 | Let $A$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 24$, $\gcd(p, q) = 1$, and $p < q$. Let $n$ be the number of elements in $A$. Define $a$ to be the largest integer $k$ such that $n^k \leq 133737864$. Let $N = 332640$ and $b = 15849$. Compute the number... | 155 | graphs = [
Graph(
let={
"_n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=24)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(value=1)), ... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/MAX_VAL"
] | aa93c6 | nt_count_divisors_in_range_v1 | null | 5 | 0 | [
"COPRIME_PAIRS",
"MAX_VAL"
] | 2 | 0.197 | 2026-02-08T16:00:09.001760Z | {
"verified": true,
"answer": 155,
"timestamp": "2026-02-08T16:00:09.198292Z"
} | 47eed3 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 175,
"completion_tokens": 2119
},
"timestamp": "2026-02-16T18:26:25.023Z",
"answer": 155
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "ok_later"
},
{
"lemma": "MOD_MUL",
"s... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
149d14 | comb_sum_binomial_row_v1_124444284_5950 | Let $c = 320$ and $m = 2$. Let $S$ be the set of all positive integers $t$ such that there exist positive integers $a$ and $b$ with $1 \le a \le 4$, $1 \le b \le 20$, $27 \le t \le 300$, and $t = 15a + 12b$. Let $n$ be the number of elements in $S$. Let $T$ be the set of all positive integers $k$ such that $1 \le k \le... | 1,024 | graphs = [
Graph(
let={
"_c": Const(320),
"_m": Const(2),
"_n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=C... | NT | null | SUM | sympy | SUM_DIVISIBLE | [
"SUM_DIVISIBLE/C2",
"LIN_FORM/C2"
] | e29d1e | comb_sum_binomial_row_v1 | null | 6 | 0 | [
"C2",
"LIN_FORM",
"SUM_DIVISIBLE"
] | 3 | 0.003 | 2026-02-08T06:57:21.667450Z | {
"verified": true,
"answer": 1024,
"timestamp": "2026-02-08T06:57:21.670808Z"
} | 439284 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 251,
"completion_tokens": 3109
},
"timestamp": "2026-02-13T06:18:14.230Z",
"answer": 4
},
{... | 1 | [
{
"lemma": "C2",
"status": "ok_later"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
}... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
99141d | alg_sum_powers_v1_1218484723_5562 | Let $C$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 40$ such that $25b^2 + 22ab + 34a^2 \le 61513$. Let $M$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ with $xy = 1806336$. Define $R = \left(\sum_{k=1}^{C} k^2\right) \bmod M$. Find the remainder whe... | 2,002 | graphs = [
Graph(
let={
"_m": Const(40),
"_n": Const(68585),
"result": Mod(value=Summation(var="k", start=Const(1), end=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"), C... | ALG | null | COMPUTE | sympy | QF_PSD_COUNT_LEQ | [
"QF_PSD_COUNT_LEQ",
"B3"
] | 3a349f | alg_sum_powers_v1 | null | 5 | 0 | [
"B3",
"QF_PSD_COUNT_LEQ"
] | 2 | 0.057 | 2026-02-25T07:04:17.019477Z | {
"verified": true,
"answer": 2002,
"timestamp": "2026-02-25T07:04:17.076031Z"
} | e9f12e | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 240,
"completion_tokens": 12042
},
"timestamp": "2026-03-29T21:43:57.636Z",
"answer": 2002
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
}
] | {
"lo": 1.53,
"mid": 4.7,
"hi": 7.23
} | ||
7764bb | nt_sum_over_divisible_v1_458359167_2633 | Let $n = 13$. Let the upper bound be $45360$. Define $d$ to be the largest positive divisor of $33616$ that is at most $176$. Let $S$ be the set of all positive integers $k$ such that $1 \leq k \leq 45360$ and $k$ is divisible by $d$. Let $R$ be the sum of all elements in $S$. Compute the value of $n - R$, and then fin... | 28,735 | graphs = [
Graph(
let={
"_n": Const(13),
"upper": Const(45360),
"divisor": MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Leq(Var("d"), Const(176)), Divides(divisor=Var("d"), dividend=Const(33616))))),
"result": SumOverSet(set... | NT | null | SUM | sympy | MAX_DIVISOR | [
"MAX_DIVISOR"
] | 51757e | nt_sum_over_divisible_v1 | null | 3 | 0 | [
"MAX_DIVISOR"
] | 1 | 3.798 | 2026-02-08T06:23:06.882224Z | {
"verified": true,
"answer": 28735,
"timestamp": "2026-02-08T06:23:10.680070Z"
} | e98d39 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 167,
"completion_tokens": 6390
},
"timestamp": "2026-02-13T03:18:32.304Z",
"answer": 28735
},
... | 1 | [
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
27a4cd | nt_count_digit_sum_v1_1125832087_420 | Let $T$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 121$. Let $s$ be the minimum value of $x + y$ over all pairs in $T$. Determine the number of positive integers $n$ less than or equal to $99999$ such that the sum of the digits of $n$ is equal to $s$. | 6,000 | graphs = [
Graph(
let={
"upper": Const(99999),
"target_sum": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(121)))), expr=Sum(Var("x"), ... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | nt_count_digit_sum_v1 | null | 5 | 0 | [
"B3"
] | 1 | 4.748 | 2026-02-08T03:03:52.314966Z | {
"verified": true,
"answer": 6000,
"timestamp": "2026-02-08T03:03:57.063457Z"
} | 284f72 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 193,
"completion_tokens": 1595
},
"timestamp": "2026-02-10T12:34:57.713Z",
"answer": 6000
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -3.47,
"mid": 0.81,
"hi": 4.81
} | ||
c9354c | nt_count_coprime_v1_1742523217_36 | Let $m = 41$. Let $n$ be the largest prime number less than or equal to $12$. Let $k$ be the largest prime number less than or equal to $m$. Let $S$ be the set of all positive integers $x$ such that $1 \leq x \leq 73984$ and $\gcd(x, k) = 1$. Let $r$ be the number of elements in $S$. Let $q$ be the remainder when $r$ i... | 21,147 | graphs = [
Graph(
let={
"_m": Const(41),
"_n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(12)), IsPrime(Var("n"))))),
"upper": Const(73984),
"k": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(... | NT | COMB | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW/MAX_PRIME_BELOW"
] | 9daedf | nt_count_coprime_v1 | bell_mod | 6 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 5.303 | 2026-02-08T02:50:38.985103Z | {
"verified": true,
"answer": 21147,
"timestamp": "2026-02-08T02:50:44.288113Z"
} | 126b35 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 247,
"completion_tokens": 622
},
"timestamp": "2026-02-09T12:43:39.353Z",
"answer": 21147
},
{
"i... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -4.32,
"mid": -2.03,
"hi": 0.23
} | ||
67c438 | nt_count_digit_sum_v1_458359167_4822 | Let $S$ be the set of all ordered pairs $(a, b)$ where $a$ is an integer from 1 to 99 and $b$ is an integer from 1 to 101. Let $N$ be the number of positive integers $n$ such that $1 \leq n \leq |S|$ and the sum of the decimal digits of $n$ is 18. Let $c = 53712$. Compute the remainder when $c \cdot N$ is divided by 73... | 31,188 | graphs = [
Graph(
let={
"upper": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(99)), right=IntegerRange(start=Const(1), end=Const(101)))),
"target_sum": Const(18),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var(... | NT | null | COUNT | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | nt_count_digit_sum_v1 | null | 4 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.371 | 2026-02-08T12:05:29.093897Z | {
"verified": true,
"answer": 31188,
"timestamp": "2026-02-08T12:05:29.465185Z"
} | 204091 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 163,
"completion_tokens": 1071
},
"timestamp": "2026-02-14T22:15:50.669Z",
"answer": 31188
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
84a6f8 | diophantine_fbi2_count_v1_1915831931_2237 | Let $k = 240$. Let $P$ be the set of prime numbers $n$ such that $2 \leq n \leq 105$, and let $M$ be the largest element of $P$. Let $Q$ be the set of prime numbers $n_1$ such that $2 \leq n_1 \leq 4$, and let $m$ be the largest element of $Q$. Determine the number of integers $d$ such that $3 \leq d \leq M$, $d$ divid... | 16 | graphs = [
Graph(
let={
"_n": Const(4),
"k": Const(240),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(3)), Leq(Var("d"), MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(105)), ... | NT | null | COUNT | sympy | C2 | [
"MAX_PRIME_BELOW"
] | dc3ad3 | diophantine_fbi2_count_v1 | null | 4 | 0 | [
"C2",
"MAX_PRIME_BELOW"
] | 2 | 0.142 | 2026-02-08T16:40:59.683103Z | {
"verified": true,
"answer": 16,
"timestamp": "2026-02-08T16:40:59.824923Z"
} | bd32cc | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 189,
"completion_tokens": 1382
},
"timestamp": "2026-02-17T09:54:03.420Z",
"answer": 16
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
47ad21 | sequence_lucas_compute_v1_2051736721_1120 | Let $n$ be the largest prime number less than or equal to 22. Compute the $n$-th Lucas number. | 9,349 | graphs = [
Graph(
let={
"_n": Const(22),
"n": MaxOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(2)), Leq(Var("n1"), Ref("_n")), IsPrime(Var("n1"))))),
"result": Lucas(arg=Ref(name='n')),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | sequence_lucas_compute_v1 | null | 2 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.001 | 2026-02-08T15:50:59.676972Z | {
"verified": true,
"answer": 9349,
"timestamp": "2026-02-08T15:50:59.678448Z"
} | 22d29e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 73,
"completion_tokens": 601
},
"timestamp": "2026-02-16T14:38:20.781Z",
"answer": 9349
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8_SUM",... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
cd5f5e | alg_poly_preperiod_count_v1_1218484723_6251 | Let $N = a^3 - 2a \bmod 29$, $M = N^3 - 2N \bmod 29$, and $R = M^3 - 2M \bmod 29$. Find the number of non-negative integers $a$ with $0 \le a \le 9366$ such that $R = N$ and $M \neq N$. | 1,938 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Pow(Var("a"), Const(3)), Mul(Const(-2), Var("a"))), modulus=Const(29)),
"p2": Mod(value=Sum(Pow(Ref("p1"), Const(3)), Mul(Const(-2), Ref("p1"))), modulus=Const(29)),
"p3": Mod(value=Sum(Pow(Ref("p2"), Const(3)), Mul(Const(-2), R... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_preperiod_count_v1 | null | 6 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.013 | 2026-02-25T07:49:10.354566Z | {
"verified": true,
"answer": 1938,
"timestamp": "2026-02-25T07:49:10.367068Z"
} | bae171 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 196,
"completion_tokens": 8166
},
"timestamp": "2026-03-30T00:54:47.505Z",
"answer": 1938
},
{
"i... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -3.33,
"mid": 1.03,
"hi": 5.26
} | ||
85699c | comb_catalan_compute_v1_151522320_269 | Let $N = 49571$. Let $S$ be the set of all positive integers $t$ such that $15 \leq t \leq 51$ and $t = 6a + 9b$ for some integers $a$ and $b$ with $1 \leq a \leq 4$ and $1 \leq b \leq 3$. Let $n = |S|$. Let $C_n$ denote the $n$-th Catalan number. Compute the remainder when $N \cdot C_n$ is divided by $86812$. | 62,402 | graphs = [
Graph(
let={
"_n": Const(49571),
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=4)), Geq(left=Va... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_catalan_compute_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T03:07:07.418608Z | {
"verified": true,
"answer": 62402,
"timestamp": "2026-02-08T03:07:07.420218Z"
} | 19557c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 237,
"completion_tokens": 4360
},
"timestamp": "2026-02-10T13:06:38.405Z",
"answer": 62402
},
{
"... | 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": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
... | {
"lo": -0.05,
"mid": 2.89,
"hi": 5.27
} | ||
31d6b2 | nt_sum_divisors_range_v1_1520064083_8405 | Let $N = 33$. Define $\text{upper}$ to be the number of positive integers $k$ such that $1 \leq k \leq 216513$ and $N$ divides $k$. Let $\text{result}$ be the sum of the number of positive divisors of $n$, taken over all positive integers $n$ from $1$ to $\text{upper}$. Let $Q$ be the remainder when $44121 \cdot \text{... | 35,051 | graphs = [
Graph(
let={
"_n": Const(33),
"upper": CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(1)), Leq(Var("k"), Const(216513)), Divides(divisor=Ref("_n"), dividend=Var("k"))), domain='positive_integers')),
"result": SumOverSet(set=MapOve... | NT | null | SUM | sympy | C2 | [
"C2"
] | 9685eb | nt_sum_divisors_range_v1 | null | 5 | 0 | [
"C2"
] | 1 | 0.469 | 2026-02-08T10:10:22.793820Z | {
"verified": true,
"answer": 35051,
"timestamp": "2026-02-08T10:10:23.262856Z"
} | c94d76 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 157,
"completion_tokens": 4603
},
"timestamp": "2026-02-14T06:39:17.935Z",
"answer": 35051
},
... | 1 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
e1122d | diophantine_product_count_v1_458359167_2079 | Let $n = 9$. Consider the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = 6$. Let $M$ be the maximum value of $xy$ over all such pairs. Define
$$
\text{upper} = \sum_{k=1}^{M} \varphi(k) \left\lfloor \frac{n}{k} \right\rfloor,
$$
where $\varphi(k)$ denotes Euler's totient function. Let $k = 60... | 10 | graphs = [
Graph(
let={
"_n": Const(9),
"k": Const(60),
"upper": Summation(var="k", start=Const(1), end=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(... | NT | null | COUNT | sympy | L3B | [
"B1/K2"
] | ebd04c | diophantine_product_count_v1 | null | 6 | 0 | [
"B1",
"K2",
"L3B"
] | 3 | 0.143 | 2026-02-08T05:07:09.733939Z | {
"verified": true,
"answer": 10,
"timestamp": "2026-02-08T05:07:09.877375Z"
} | e0ec13 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 269,
"completion_tokens": 1875
},
"timestamp": "2026-02-11T22:54:55.445Z",
"answer": 10
},
{
"id"... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K2",
"status": "ok_later"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
... | {
"lo": -3.45,
"mid": 1.15,
"hi": 6.18
} | ||
9f1409 | nt_count_divisors_in_range_v1_458359167_2114 | Let $n = 1680$. Let $a = 8$. Let $b$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 850$. Let $r$ be the number of positive divisors $d$ of $n$ such that $a \leq d \leq b$. Compute the remainder when $57081 \cdot r$ is divided by $55852$. | 36,870 | graphs = [
Graph(
let={
"n": Const(1680),
"a": Const(8),
"b": 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(S... | NT | null | COUNT | sympy | COMB1 | [
"COMB1"
] | 567f58 | nt_count_divisors_in_range_v1 | null | 5 | 0 | [
"COMB1"
] | 1 | 0.007 | 2026-02-08T05:08:40.715297Z | {
"verified": true,
"answer": 36870,
"timestamp": "2026-02-08T05:08:40.722202Z"
} | 88b14b | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 212,
"completion_tokens": 2422
},
"timestamp": "2026-02-11T22:56:26.271Z",
"answer": 36870
},
{
... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
b58795 | antilemma_sum_primes_v1_1874849503_220 | Let $M$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that
$$pq=18, \quad \gcd(p,q)=1, \quad p<q.$$
Let $S$ be the sum of all prime numbers $n$ with $M\le n\le 154$.
Write $|S|$ in base $10$ as $\sum_{i=0}^{t} a_i 10^i$ with digits $a_i\in\{0,1,\dots,9\}$ and $a_t\ne 0$. De... | 102 | graphs = [
Graph(
let={
"_c": Const(2),
"_m": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=18)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/L3C/SUM_PRIMES",
"L3C",
"SUM_PRIMES"
] | 158d3b | antilemma_sum_primes_v1 | digits_weighted_mod | 7 | 0 | [
"COPRIME_PAIRS",
"L3C",
"SUM_PRIMES"
] | 3 | 0.007 | 2026-02-08T12:53:11.792349Z | {
"verified": true,
"answer": 102,
"timestamp": "2026-02-08T12:53:11.798882Z"
} | 13fdce | 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": 5078
},
"timestamp": "2026-02-09T14:48:19.437Z",
"answer": 102
},
{
"id... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
... | {
"lo": -6.51,
"mid": -0.31,
"hi": 5.43
} | ||
9559a0 | sequence_lucas_compute_v1_784195855_4333 | Let $m = 4$. Consider the set of all prime numbers $n$ such that $2 \leq n \leq m$. Let $n_{\text{max}}$ be the largest element of this set. Now, let $k$ be the largest positive integer such that $n_{\text{max}}^k \leq 784719429$. Compute the $k$-th Lucas number. | 5,778 | graphs = [
Graph(
let={
"_m": Const(4),
"_n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_m")), IsPrime(Var("n"))))),
"n": MaxOverSet(set=SolutionsSet(var=Var("k"), condition=Leq(Pow(Ref("_n"), Var("k")), Const(7847... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW/MAX_VAL"
] | b2f06b | sequence_lucas_compute_v1 | null | 5 | 0 | [
"MAX_PRIME_BELOW",
"MAX_VAL"
] | 2 | 0.002 | 2026-02-08T07:02:16.487819Z | {
"verified": true,
"answer": 5778,
"timestamp": "2026-02-08T07:02:16.490043Z"
} | 1b328a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 129,
"completion_tokens": 984
},
"timestamp": "2026-02-13T07:19:39.000Z",
"answer": 5778
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "ok_later"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
f61b06 | nt_count_intersection_v1_548369836_410 | Let $N = 20000$. Define $a$ to be the number of integers $t$ such that $5 \leq t \leq 15$ and there exist integers $a$ and $b$ with $1 \leq a \leq 3$, $1 \leq b \leq 3$, and $t = 3a + 2b$. Let $b = 22$. Define $S$ to be the set of all positive integers $n \leq N$ such that $a$ divides $n$ and $\gcd(n, b) = 1$. Compute ... | 1,010 | graphs = [
Graph(
let={
"N": Const(20000),
"a": 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... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_count_intersection_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 6.305 | 2026-02-08T02:54:04.185750Z | {
"verified": true,
"answer": 1010,
"timestamp": "2026-02-08T02:54:10.491104Z"
} | 1ae278 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 253,
"completion_tokens": 825
},
"timestamp": "2026-02-08T20:26:26.555Z",
"answer": 1010
},
{
"id... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"... | {
"lo": -0.87,
"mid": 0.99,
"hi": 2.61
} | ||
6f6b37 | nt_max_prime_below_v1_677425708_592 | Let $ S $ be the set of all positive integers $ p $ for which there exists a positive integer $ q $ such that $ pq = 18 $, $ \gcd(p, q) = 1 $, and $ p < q $. Let $ t $ be the number of elements in $ S $. Determine the largest prime number $ n $ such that $ t \leq n \leq 40000 $. | 39,989 | graphs = [
Graph(
let={
"upper": Const(40000),
"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 | 1.494 | 2026-02-08T03:36:18.986076Z | {
"verified": true,
"answer": 39989,
"timestamp": "2026-02-08T03:36:20.480252Z"
} | 3be7e4 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 201,
"completion_tokens": 3760
},
"timestamp": "2026-02-08T20:48:23.238Z",
"answer": 39989
},
{
"... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V1",
"... | {
"lo": -3.53,
"mid": 1.02,
"hi": 5.49
} | ||
30c3c3 | sequence_fibonacci_compute_v1_1520064083_9696 | Let $n$ be the number of integers $t$ such that $14 \leq t \leq 68$ and there exist positive integers $a$, $b$ with $1 \leq a \leq 6$, $1 \leq b \leq 4$, satisfying $t = 6a + 8b$. Compute the value of the $n$-th Fibonacci number. | 17,711 | 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=1... | NT | null | COMPUTE | sympy | C3 | [
"LIN_FORM"
] | 7b2633 | sequence_fibonacci_compute_v1 | null | 5 | 0 | [
"C3",
"LIN_FORM"
] | 2 | 0.01 | 2026-02-08T10:58:39.827216Z | {
"verified": true,
"answer": 17711,
"timestamp": "2026-02-08T10:58:39.836759Z"
} | 0d7860 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 127,
"completion_tokens": 1912
},
"timestamp": "2026-02-14T09:37:05.031Z",
"answer": 17711
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": ... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
4a774e | sequence_count_fib_divisible_v1_1125832087_112 | Let $n$ be a positive integer. Define $f(n)$ to be the largest integer $k$ such that $3^k$ divides $n!$. Let $N$ be the smallest positive integer $n$ for which $f(n) \geq 458$. Determine the number of positive integers $n$ such that $1 \leq n \leq N$ and the $n$-th Fibonacci number is divisible by 3. (Define the Fibona... | 230 | graphs = [
Graph(
let={
"upper": MinOverSet(set=SolutionsSet(var=Var("n"), condition=Geq(MaxKDivides(target=Factorial(Var("n")), base=Const(3)), Const(458)), domain='Z_{>0}')),
"d": Const(3),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n")... | NT | null | COUNT | sympy | LIN_FORM | [
"V5"
] | 79df37 | sequence_count_fib_divisible_v1 | null | 7 | 0 | [
"LIN_FORM",
"V5"
] | 2 | 0.061 | 2026-02-08T02:52:24.829070Z | {
"verified": true,
"answer": 230,
"timestamp": "2026-02-08T02:52:24.890028Z"
} | 310400 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 247,
"completion_tokens": 876
},
"timestamp": "2026-02-17T14:53:30.813Z",
"answer": 113
}
] | 0 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V5",
"status": "ok"
}
] | {
"lo": -6.48,
"mid": 1.54,
"hi": 9.56
} | ||
ee45de | lin_form_endings_v1_1915831931_3223 | Let $d$ be the greatest common divisor of $16$ and $28$. Let $k = 12419 \cdot d$. Compute the remainder when $k$ is divided by $58825$. | 49,676 | graphs = [
Graph(
let={
"a_coeff": Const(16),
"b_coeff": Const(28),
"_inner_result": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"_scale_k": Const(12419),
"_scaled": Mul(Ref("_scale_k"), Ref("_inner_result")),
"_mod_M": Const(58825),
... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 2 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T17:25:55.705841Z | {
"verified": true,
"answer": 49676,
"timestamp": "2026-02-08T17:25:55.706647Z"
} | 5a4bb6 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 89,
"completion_tokens": 258
},
"timestamp": "2026-02-18T02:52:56.673Z",
"answer": 49676
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
b2130b | alg_qf_psd_orbit_v1_1218484723_4407 | Find the number of ordered pairs $(a, b)$ of positive integers with $1 \le a \le b \le 102$ such that
$$
-144ab + \left( \sum_{\substack{a_1^2 + b_1^2 + c^2 = a_1b_1 + b_1c + ca_1 \\ 2a_1 + 8b_1 + 6c = 80 \\ a_1, b_1, c \ge 1}} (a_1^2 + b_1^2 + c^2) \right) a^2 + 75b^2 = 47775.
$$ | 6 | 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(102)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(102)), Leq(Var("a"), Var("b")), Eq(Sum(Mul(Const(-1... | ALG | null | COUNT | sympy | LIN_FORM | [
"SUM_SQUARES_IDENTITY"
] | 9879b8 | alg_qf_psd_orbit_v1 | null | 6 | 0 | [
"LIN_FORM",
"SUM_SQUARES_IDENTITY"
] | 2 | 7.014 | 2026-02-25T06:01:51.582629Z | {
"verified": true,
"answer": 6,
"timestamp": "2026-02-25T06:01:58.596335Z"
} | fbec1e | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 256,
"completion_tokens": 8401
},
"timestamp": "2026-03-29T15:31:16.807Z",
"answer": 6
},
{
"id":... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_SQUARES_IDENTITY",
"status": "ok"
}
] | {
"lo": -2.45,
"mid": 1.37,
"hi": 5.29
} | ||
aa1274 | nt_max_prime_below_v1_1918700295_2530 | Let $k$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p < q$, $\gcd(p, q) = 1$, and $pq = 54$. Determine the value of the largest prime number $n$ such that $n \geq k$ and $n \leq 89401$. | 89,399 | graphs = [
Graph(
let={
"upper": Const(89401),
"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 | 2.95 | 2026-02-08T07:56:50.579198Z | {
"verified": true,
"answer": 89399,
"timestamp": "2026-02-08T07:56:53.528896Z"
} | 1464b2 | 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": 2603
},
"timestamp": "2026-02-13T13:50:59.284Z",
"answer": 89399
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
}
] | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
a92bd5 | comb_sum_binomial_row_v1_1978505735_2738 | Let $n$ be the smallest integer greater than or equal to $2$ that divides $65007371$. Compute $2^n$. | 2,048 | 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(65007371))))),
"result": Pow(Const(2), Ref("n")),
},
goal=Ref("result"),
)
] | NT | null | SUM | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | comb_sum_binomial_row_v1 | null | 4 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.001 | 2026-02-08T17:08:56.814409Z | {
"verified": true,
"answer": 2048,
"timestamp": "2026-02-08T17:08:56.815282Z"
} | 9a022d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 75,
"completion_tokens": 684
},
"timestamp": "2026-02-17T20:13:04.287Z",
"answer": 2048
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
e6fa01 | modular_min_linear_v1_1918700295_128 | Let $a = 12574$, $b = 13128$, and $m = 20773$. Let $S$ be the set of all integers $x$ such that $$x \geq \sum_{d \mid \gcd(7,11)} \mu(d),$$ $$x \leq m,$$ and $$ax \equiv b \pmod{m}.$$ Determine the value of the smallest element of $S$. | 18,894 | graphs = [
Graph(
let={
"a": Const(12574),
"b": Const(13128),
"m": Const(20773),
"result": MinOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), SumOverDivisors(n=GCD(a=Const(value=7), b=Const(value=11)), var='d', expr=MoebiusMu(n=Var(name='d')... | NT | null | EXTREMUM | sympy | MOBIUS_COPRIME | [
"MOBIUS_COPRIME"
] | ac54ac | modular_min_linear_v1 | null | 5 | 0 | [
"MOBIUS_COPRIME"
] | 1 | 1.627 | 2026-02-08T03:00:48.187861Z | {
"verified": true,
"answer": 18894,
"timestamp": "2026-02-08T03:00:49.814988Z"
} | f283c5 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 209,
"completion_tokens": 2385
},
"timestamp": "2026-02-08T23:01:56.398Z",
"answer": 18894
},
{
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -6.49,
"mid": 0.51,
"hi": 7.52
} | ||
573a18 | lin_form_endings_v1_1248542787_129 | Let $a = 40$, $b = 32$, $A = 34$, and $B = 50$. Let $g = \gcd(a, b)$. Compute the value of
$$
\left\lfloor \frac{aA + bB - (a + b)}{g} \right\rfloor + 1.
$$
Let $k = 7364$ and multiply the result above by $k$. Let $x$ be the remainder when this product is divided by $53104$. Compute $x$. | 10,568 | graphs = [
Graph(
let={
"a_coeff": Const(40),
"b_coeff": Const(32),
"A_val": Const(34),
"B_val": Const(50),
"g_step": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"numerator": Sub(Sum(Mul(Ref("a_coeff"), Ref("A_val")), Mul(Ref("b_coeff"), R... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 3 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T02:57:56.337559Z | {
"verified": true,
"answer": 10568,
"timestamp": "2026-02-08T02:57:56.338329Z"
} | 812caf | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 230,
"completion_tokens": 963
},
"timestamp": "2026-02-09T00:28:30.461Z",
"answer": 10568
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -1,
"mid": 0.95,
"hi": 2.6
} | ||
551f87 | nt_count_divisible_and_v1_798873815_51 | Let $m = 79386$ and let $r$ be the number of positive integers $n \leq 3$ such that $\gcd(n, 10) = 1$. Let $s$ be the number of positive integers $n \leq 114960$ that are divisible by both $10$ and $12$. Let $T$ be the set of all real numbers $x$ such that $x^r - 64x - 1577 = 0$. Compute the remainder when $\left(\sum_... | 77,534 | graphs = [
Graph(
let={
"_m": Const(79386),
"_n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(3)), Eq(GCD(a=Var("n"), b=Const(10)), Const(1))))),
"upper": Const(114960),
"d1": Const(10),
"d... | NT | null | COUNT | sympy | C4 | [
"C4/VIETA_SUM"
] | 173fcf | nt_count_divisible_and_v1 | negation_mod | 4 | 0 | [
"C4",
"VIETA_SUM"
] | 2 | 5.709 | 2026-02-08T02:25:23.335670Z | {
"verified": true,
"answer": 77534,
"timestamp": "2026-02-08T02:25:29.044246Z"
} | 433d67 | 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": 811
},
"timestamp": "2026-02-08T18:32:06.603Z",
"answer": 77534
},
{
"i... | 1 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
... | {
"lo": -5.53,
"mid": -3.77,
"hi": -1.89
} | ||
5d886f | geo_count_lattice_rect_v1_1918700295_4618 | Let $a = 128$ and $b = 73$. Compute the number of lattice points $(x, y)$ such that $0 \leq x \leq a$ and $0 \leq y \leq b$. | 9,546 | graphs = [
Graph(
let={
"a": Const(128),
"b": Const(73),
"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 | 2026-02-08T09:29:14.418469Z | {
"verified": true,
"answer": 9546,
"timestamp": "2026-02-08T09:29:14.419076Z"
} | e5e527 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 160,
"completion_tokens": 290
},
"timestamp": "2026-02-24T11:23:45.033Z",
"answer": 9546
},
{
"id... | 1 | [] | {
"lo": -4.92,
"mid": -2.91,
"hi": -0.68
} | ||||
97ca34 | nt_count_digit_sum_v1_971394319_964 | Let $S$ be the set of all integers $n$ such that $1 \leq n \leq 19998$ and the sum of the digits of $n$ is even. Let $T$ be the set of all positive integers $n$ such that $1 \leq n \leq |S|$ and the sum of the digits of $n$ is 21. Compute the number of elements in $T$. Let this number be $r$. Find the remainder when $4... | 35,582 | graphs = [
Graph(
let={
"upper": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(19998)), Eq(Mod(value=DigitSum(Var("n")), modulus=Const(2)), Const(0))))),
"target_sum": Const(21),
"result": CountOverSet(set=Solutions... | NT | null | COUNT | sympy | L3B | [
"L3B"
] | cc148f | nt_count_digit_sum_v1 | null | 4 | 0 | [
"L3B"
] | 1 | 0.555 | 2026-02-08T13:24:11.563024Z | {
"verified": true,
"answer": 35582,
"timestamp": "2026-02-08T13:24:12.117818Z"
} | a3e171 | 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": 2459
},
"timestamp": "2026-02-15T15:45:38.969Z",
"answer": 35582
},
... | 1 | [
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3B",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
ee2792 | comb_bell_compute_v1_784195855_8232 | Let $n$ be the number of nonnegative integers $j$ such that $0 \leq j \leq 2096$ and $\binom{2096}{j} \equiv 1 \pmod{2}$. Let $\text{result} = B_n$, the $n$th Bell number, which counts the number of partitions of a set of $n$ elements. Let $Q$ be the remainder when $26003 \cdot \text{result}$ is divided by $74529$. Com... | 32,544 | graphs = [
Graph(
let={
"_n": Const(2),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(2096)), Eq(Mod(value=Binom(n=Const(2096), k=Var("j")), modulus=Ref("_n")), Const(1))), domain='nonnegative_integers')),
"res... | COMB | null | COMPUTE | sympy | V8 | [
"V8"
] | 86348e | comb_bell_compute_v1 | null | 7 | 0 | [
"V8"
] | 1 | 0.001 | 2026-02-08T15:58:03.952343Z | {
"verified": true,
"answer": 32544,
"timestamp": "2026-02-08T15:58:03.953764Z"
} | ef69c8 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 224,
"completion_tokens": 1082
},
"timestamp": "2026-02-24T19:12:03.005Z",
"answer": 32544
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
}
] | {
"lo": -2.4,
"mid": 1.57,
"hi": 5.75
} | ||
020b88 | comb_binomial_compute_v1_1439011603_2727 | Let $n$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p < q$, $\gcd(p, q) = 1$, and $pq = 5659500$. Compute $\binom{n}{9}$. | 11,440 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=5659500)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(value=1... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_binomial_compute_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.004 | 2026-02-08T16:55:39.141358Z | {
"verified": true,
"answer": 11440,
"timestamp": "2026-02-08T16:55:39.145118Z"
} | 193bf4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 103,
"completion_tokens": 2173
},
"timestamp": "2026-02-17T16:25:28.370Z",
"answer": 11440
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
959af3 | antilemma_k2_v1_397696148_1543 | Let
$$
x = \sum_{k=1}^{154} \phi(k) \left\lfloor \frac{154}{k} \right\rfloor.
$$
Compute the remainder when $x^2 + 25x + 2401$ is divided by $61414$. | 18,865 | graphs = [
Graph(
let={
"x": Summation(var="k", start=Const(1), end=Const(154), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(154), Var("k"))))),
"_c": Const(2401),
"Q": Mod(value=Sum(Pow(Ref("x"), Const(2)), Mul(Const(25), Ref("x")), Ref("_c")), modulus=Const(61414)),
... | NT | COMB | COMPUTE | sympy | K13 | [
"K2"
] | 6897ab | antilemma_k2_v1 | null | 7 | 0 | [
"K13",
"K2"
] | 2 | 0.006 | 2026-02-08T12:38:18.692883Z | {
"verified": true,
"answer": 18865,
"timestamp": "2026-02-08T12:38:18.699038Z"
} | 803e82 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 106,
"completion_tokens": 1714
},
"timestamp": "2026-02-15T03:03:41.666Z",
"answer": 18865
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
16b038 | geo_count_lattice_triangle_v1_1431428450_1254 | Let $A$ be the area of the triangle with vertices at $(0,0)$, $(121,23)$, and $(233,128)$, multiplied by $2$. Let $B$ be the number of lattice points on the boundary of this triangle, computed as the sum of the greatest common divisors of the absolute differences of the coordinates along each edge:
\begin{align*}
B &= ... | 5,061 | graphs = [
Graph(
let={
"area_2x": Abs(arg=Sum(Mul(Const(value=121), Const(value=128)), Mul(Const(value=233), Sub(left=Const(value=0), right=Const(value=23))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=121)), b=Abs(arg=Const(value=23))), GCD(a=Abs(arg=Sub(left=Const(value=233), rig... | ALG | NT | COUNT | sympy | [] | geo_count_lattice_triangle_v1 | null | 4 | 0 | null | null | 0.002 | 2026-02-08T13:58:56.664582Z | {
"verified": true,
"answer": 5061,
"timestamp": "2026-02-08T13:58:56.666963Z"
} | 422cb6 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 233,
"completion_tokens": 836
},
"timestamp": "2026-02-15T22:15:22.920Z",
"answer": 5061
},
{
... | 1 | [] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||||
a822c6 | comb_count_surjections_v1_1978505735_7410 | Let $S$ be the set of all ordered triples $(x_1, x_2, x_3)$ of positive odd integers such that $x_1 + x_2 + x_3 = 7$. Let $n$ be the number of elements in $S$. Let $T$ be the set of all ordered pairs $(i, j)$ with $i, j \in \{1, 2\}$ such that $i + j = 3$. Let $k$ be the number of elements in $T$. Define $\text{result}... | 48 | graphs = [
Graph(
let={
"_n": Const(7),
"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... | COMB | NT | COUNT | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS",
"COMB1"
] | 938829 | comb_count_surjections_v1 | null | 6 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS"
] | 2 | 0.012 | 2026-02-08T20:15:03.625692Z | {
"verified": true,
"answer": 48,
"timestamp": "2026-02-08T20:15:03.637831Z"
} | ba77c8 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 238,
"completion_tokens": 5721
},
"timestamp": "2026-02-19T00:13:06.596Z",
"answer": 48
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
... | {
"lo": -3.12,
"mid": 1.47,
"hi": 6.57
} | ||
5b89cf | lin_form_endings_v1_1440796553_695 | Let $a = 4$, $b = 14$, $A = 57$, and $B = 32$. 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 $T$ be the integer defined by
$$
|T| = a'A + b'B - a'b'.
$$
Define the quantity
$$
S = aA + bB - a - b + 1.
$$
Let $D = S - |T|$. Compute $... | 213 | graphs = [
Graph(
let={
"a_coeff": Const(4),
"b_coeff": Const(14),
"A_val": Const(57),
"B_val": Const(32),
"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 | 6 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T11:55:19.431537Z | {
"verified": true,
"answer": 213,
"timestamp": "2026-02-08T11:55:19.432811Z"
} | 1c77f3 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 215,
"completion_tokens": 1441
},
"timestamp": "2026-02-14T20:41:47.875Z",
"answer": 213
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
6b445b | nt_min_coprime_above_v1_2051736721_4682 | Let $s$ be the maximum value of $xy$ over all pairs of positive integers $(x,y)$ such that $x + y = 116$. Let $r$ be the smallest integer $n$ such that $s < n \leq 3865$ and $\gcd(n, 491) = 1$. Compute the remainder when $34567 \cdot r$ is divided by $69952$. | 57,731 | graphs = [
Graph(
let={
"_n": Const(69952),
"start": 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(116)))), expr=Mul(Var("x"), Var("y")... | NT | null | EXTREMUM | sympy | B1 | [
"B1"
] | 5b950e | nt_min_coprime_above_v1 | null | 5 | 0 | [
"B1"
] | 1 | 0.043 | 2026-02-08T18:06:16.926842Z | {
"verified": true,
"answer": 57731,
"timestamp": "2026-02-08T18:06:16.969577Z"
} | e9a3d6 | 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": 1982
},
"timestamp": "2026-02-18T13:27:30.033Z",
"answer": 57731
},
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
f9e949 | comb_factorial_compute_v1_1520064083_6219 | Let $n$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 14$. Let $r = n!$. Compute the remainder when $67209 \cdot r$ is divided by $80740$. | 29,060 | graphs = [
Graph(
let={
"_n": Const(14),
"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... | ALG | COMB | COMPUTE | sympy | COMB1 | [
"COMB1"
] | 567f58 | comb_factorial_compute_v1 | null | 4 | 0 | [
"COMB1"
] | 1 | 0.003 | 2026-02-08T07:55:46.511345Z | {
"verified": true,
"answer": 29060,
"timestamp": "2026-02-08T07:55:46.514577Z"
} | ee454b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 173,
"completion_tokens": 2624
},
"timestamp": "2026-02-24T08:39:46.732Z",
"answer": 29060
},
{
"... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 1.15,
"mid": 4.18,
"hi": 6.61
} | ||
fcd09b | diophantine_fbi2_count_v1_124444284_470 | Let $k = 180$. Define $\text{result}$ to be the number of integers $d$ with $4 \leq d \leq 80$ such that $d$ divides $k$, and $5 \leq \frac{k}{d} \leq 81$. Define $c$ to be the number of nonnegative integers $j$ with $0 \leq j \leq 75103$ such that $\binom{75103}{j}$ is odd. Compute $\text{result}^2 + 7 \cdot \text{res... | 1,222 | graphs = [
Graph(
let={
"k": Const(180),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(4)), Leq(Var("d"), Const(80)), Divides(divisor=Var("d"), dividend=Ref("k")), Geq(Div(Ref("k"), Var("d")), Const(5)), Leq(Div(Ref("k"), Var("d")), Const(81)... | NT | null | COUNT | sympy | V8 | [
"V8"
] | 4109e4 | diophantine_fbi2_count_v1 | quadratic_mod | 4 | 0 | [
"V8"
] | 1 | 0.008 | 2026-02-08T03:18:08.434939Z | {
"verified": true,
"answer": 1222,
"timestamp": "2026-02-08T03:18:08.442789Z"
} | 93f8c9 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 237,
"completion_tokens": 1937
},
"timestamp": "2026-02-09T18:06:51.591Z",
"answer": 1222
},
{
"i... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
}
] | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
36bd1f | antilemma_cartesian_v1_1520064083_4344 | Compute the number of ordered pairs $(a,b)$ of positive integers such that $1 \leq a \leq 20$ and $1 \leq b \leq 101$. Subtract from this the number of ordered pairs $(i,j)$ such that $1 \leq i \leq 29$ and $1 \leq j \leq 37$. Find the value of this difference. | 947 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(29)), right=IntegerRange(start=Const(1), end=Const(37)))),
"Q": Sub(CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(20)), right=IntegerRange(start=... | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN",
"COUNT_CARTESIAN"
] | f9c395 | antilemma_cartesian_v1 | negation_mod | 2 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.002 | 2026-02-08T06:14:05.406295Z | {
"verified": true,
"answer": 947,
"timestamp": "2026-02-08T06:14:05.408022Z"
} | 3f712d | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 197,
"completion_tokens": 224
},
"timestamp": "2026-02-24T05:39:22.691Z",
"answer": 947
},
{
"id"... | 2 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SU... | {
"lo": -10,
"mid": -7.79,
"hi": -5.57
} | ||
c5cf2d | lin_form_endings_v1_784195855_4738 | Let $a = 42$ and $b = 30$. Compute $\gcd(a, b)$. Multiply this greatest common divisor by $15988$, and let the result be $x$. Compute the remainder when $x$ is divided by $89006$. Find the value of this remainder. | 6,922 | graphs = [
Graph(
let={
"a_coeff": Const(42),
"b_coeff": Const(30),
"_inner_result": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"_scale_k": Const(15988),
"_scaled": Mul(Ref("_scale_k"), Ref("_inner_result")),
"_mod_M": Const(89006),
... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 2 | null | [
"LIN_FORM"
] | 1 | 0 | 2026-02-08T07:19:33.097156Z | {
"verified": true,
"answer": 6922,
"timestamp": "2026-02-08T07:19:33.097651Z"
} | 3c8f1d | 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": 352
},
"timestamp": "2026-02-13T09:33:56.750Z",
"answer": 6922
},
{
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"sta... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
a96ffb | comb_count_derangements_v1_898971024_2395 | Let $n$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p < q$, $\gcd(p, q) = 1$, and $pq = 10500$. Compute the subfactorial of $n$. | 14,833 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=10500)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(value=1))... | NT | COMB | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_count_derangements_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.003 | 2026-02-08T16:43:01.717387Z | {
"verified": true,
"answer": 14833,
"timestamp": "2026-02-08T16:43:01.720099Z"
} | 4d5fd8 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 104,
"completion_tokens": 1316
},
"timestamp": "2026-02-17T10:49:17.450Z",
"answer": 14833
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
08a89d | modular_min_modexp_v1_124444284_277 | Let $ a = 13 $, $ b = 130 $, and $ m = 137 $. Let $ u $ be the number of integers $ n $ such that $ 1 \leq n \leq 271 $ and the sum of the decimal digits of $ n $ is odd.
Determine the smallest positive integer $ x $ such that $ 1 \leq x \leq u $ and
$$
13^x \equiv 130 \pmod{137}.
$$ | 86 | graphs = [
Graph(
let={
"a": Const(13),
"b": Const(130),
"m": Const(137),
"upper": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(271)), Eq(Mod(value=DigitSum(Var("n")), modulus=Const(2)), Const(1))))),
... | NT | null | EXTREMUM | sympy | L3B | [
"L3B"
] | cc148f | modular_min_modexp_v1 | null | 6 | 0 | [
"L3B"
] | 1 | 0.161 | 2026-02-08T03:08:40.940574Z | {
"verified": true,
"answer": 86,
"timestamp": "2026-02-08T03:08:41.101398Z"
} | 93321d | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 212,
"completion_tokens": 4969
},
"timestamp": "2026-02-09T15:36:58.902Z",
"answer": 86
},
{
"id"... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3B",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
6c6bfe | alg_poly_preperiod_count_v1_1218484723_75 | Let $N = (a^2 + a + 16) \bmod 83$, $M = (N^2 + N + 16) \bmod 83$, $R = (M^2 + M + 16) \bmod 83$, and $S = (R^2 + R + 16) \bmod 83$. Find the number of non-negative integers $a$ with $0 \le a \le 62083$ such that $S = N$, $M \ne N$, and $R \ne N$. | 4,488 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Pow(Var("a"), Const(2)), Var("a"), Const(16)), modulus=Const(83)),
"p2": Mod(value=Sum(Pow(Ref("p1"), Const(2)), Ref("p1"), Const(16)), modulus=Const(83)),
"p3": Mod(value=Sum(Pow(Ref("p2"), Const(2)), Ref("p2"), Const(16)), mod... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_preperiod_count_v1 | null | 6 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.024 | 2026-02-25T01:46:52.028032Z | {
"verified": true,
"answer": 4488,
"timestamp": "2026-02-25T01:46:52.052038Z"
} | 4997b8 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 231,
"completion_tokens": 29016
},
"timestamp": "2026-03-10T08:06:39.845Z",
"answer": 0
},
{
"i... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 1.39,
"mid": 3.79,
"hi": 5.74
} | ||
211a98 | alg_qf_psd_orbit_v1_1419126231_693 | Let $c = \left|\left\{ (a_2, b_2) : 1 \le a_2, b_2 \le 35,\ 5a_2^2 + 10a_2b_2 + 5b_2^2 = 3920 \right\}\right|$. Let $f = \left|\left\{ (a_1, b_1) : 1 \le a_1, b_1 \le 30,\ -9a_1^3 + c a_1^2 b_1 - 27a_1 b_1^2 + 9b_1^3 = -9 \right\}\right|$. Find the number of ordered pairs $(a, b)$ of positive integers with $1 \le a \le... | 5 | graphs = [
Graph(
let={
"_m": Const(35),
"_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(393)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(393)), Leq(Var("a"), V... | ALG | null | COUNT | sympy | MAX_DIVISOR | [
"QF_PSD_COUNT/POLY3_COUNT"
] | cbf254 | alg_qf_psd_orbit_v1 | null | 6 | 0 | [
"MAX_DIVISOR",
"POLY3_COUNT",
"QF_PSD_COUNT"
] | 3 | 2.022 | 2026-02-25T10:09:42.341391Z | {
"verified": true,
"answer": 5,
"timestamp": "2026-02-25T10:09:44.363631Z"
} | 6085c1 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 313,
"completion_tokens": 32768
},
"timestamp": "2026-03-30T09:44:20.253Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "POLY3_COUNT",
"status": "ok_later"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT",
"status": "ok"
}
] | {
"lo": 3.8,
"mid": 6.33,
"hi": 9.49
} | ||
f765fd | comb_count_derangements_v1_124444284_4261 | Let $n$ be the smallest divisor of $77$ that is at least $2$. Define $Q$ as the remainder when $62426 \cdot !n$ is divided by $51963$, where $!n$ denotes the number of derangements of $n$ elements. Compute $Q$. | 16,203 | graphs = [
Graph(
let={
"n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(77))))),
"result": Subfactorial(arg=Ref(name='n')),
"_c": Const(62426),
"Q": Mod(value=Mul(Ref("_c"), Ref("re... | NT | COMB | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | comb_count_derangements_v1 | null | 2 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.002 | 2026-02-08T05:53:17.485007Z | {
"verified": true,
"answer": 16203,
"timestamp": "2026-02-08T05:53:17.486629Z"
} | 4a22e5 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 110,
"completion_tokens": 1472
},
"timestamp": "2026-02-12T16:31:09.416Z",
"answer": 16203
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
beef73 | alg_poly_orbit_count_v1_601307018_4416 | Let $N = a^3 + a \bmod 19$ and $M = N^3 + N \bmod 19$. Find the number of non-negative integers $a$ with $0 \le a \le 12881$ such that $M = a$ and $N \ne a$. | 4,068 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Pow(Var("a"), Const(3)), Var("a")), modulus=Const(19)),
"p2": Mod(value=Sum(Pow(Ref("p1"), Const(3)), Ref("p1")), modulus=Const(19)),
"result": CountOverSet(set=SolutionsSet(var=Var("a"), condition=And(Geq(Var("a"), Const(0)), L... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_orbit_count_v1 | null | 4 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.011 | 2026-03-10T04:58:40.659176Z | {
"verified": true,
"answer": 4068,
"timestamp": "2026-03-10T04:58:40.669863Z"
} | 2b98fb | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 176,
"completion_tokens": 5315
},
"timestamp": "2026-03-29T12:10:29.896Z",
"answer": 4
},
{
"i... | 0 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 3.34,
"mid": 5.77,
"hi": 8.89
} | ||
dcbaaa | nt_sum_totient_over_divisors_v1_1742523217_288 | Let $n_2$ be the largest prime number satisfying $2 \le n_2 \le 28$. Let $u = \lambda(n_2) + 1$, where $\lambda$ is the Liouville function, and let $p = 29 + u$. Let $q = 73$ and $n_1 = p \cdot q$. Define $c = \lambda(n_1)$ and $n = 53332 \cdot c$. Compute the sum of $\phi(d)$ over all positive divisors $d$ of $n$, whe... | 53,332 | graphs = [
Graph(
let={
"_n": Const(29),
"n2": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(28)), IsPrime(Var("n"))))),
"u": Sum(LiouvilleLambda(n=Ref(name='n2')), Const(1)),
"p": Sum(Ref("_n"), Ref("u"))... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW/LIOUVILLE_MINUS_ONE",
"LIOUVILLE_ONE"
] | 9bd2a3 | nt_sum_totient_over_divisors_v1 | null | 5 | 2 | [
"LIOUVILLE_MINUS_ONE",
"LIOUVILLE_ONE",
"MAX_PRIME_BELOW"
] | 3 | 0.004 | 2026-02-08T02:57:52.531508Z | {
"verified": true,
"answer": 53332,
"timestamp": "2026-02-08T02:57:52.535332Z"
} | 925fad | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 241,
"completion_tokens": 1119
},
"timestamp": "2026-02-09T15:58:52.235Z",
"answer": 53332
},
{
"... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIOUVILLE_MINUS_ONE",
"status": "ok_later"
},
{
"lemma": "LIOUVILLE_ONE",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BE... | {
"lo": -6.51,
"mid": -0.31,
"hi": 5.43
} | ||
884de7 | nt_num_divisors_compute_v1_1431428450_98 | Let $d$ be the smallest integer greater than or equal to $2$ that divides $12673$. Compute the number of positive divisors of this integer $d$. | 2 | graphs = [
Graph(
let={
"_n": Const(2),
"n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(12673))))),
"result": NumDivisors(n=Ref("n")),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | B1 | [
"MIN_PRIME_FACTOR"
] | bc3776 | nt_num_divisors_compute_v1 | null | 3 | 0 | [
"B1",
"MIN_PRIME_FACTOR"
] | 2 | 0.017 | 2026-02-08T13:12:20.558925Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-02-08T13:12:20.575874Z"
} | 700db4 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 94,
"completion_tokens": 530
},
"timestamp": "2026-02-16T04:27:47.688Z",
"answer": 2
},
{
"id": 11,
"m... | 2 | [
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -9.12,
"mid": -6.02,
"hi": -3.62
} | ||
d09f6f | geo_count_lattice_rect_v1_1742523217_5588 | Let $a = 120$ and $b = 55$. A lattice point is a point in the plane with integer coordinates.
Compute the number of lattice points $(x, y)$ such that $0 \leq x \leq a$ and $0 \leq y \leq b$. | 6,776 | graphs = [
Graph(
let={
"a": Const(120),
"b": Const(55),
"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 | 2026-02-08T11:05:11.276336Z | {
"verified": true,
"answer": 6776,
"timestamp": "2026-02-08T11:05:11.277345Z"
} | 0ca0f0 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 173,
"completion_tokens": 269
},
"timestamp": "2026-02-24T12:50:11.739Z",
"answer": 6776
},
{
"id... | 2 | [] | {
"lo": -9.23,
"mid": -6.18,
"hi": -4.06
} | ||||
7adecd | nt_count_coprime_and_v1_809748730_72 | Let $\text{upper} = 37512$. Let $S$ be the set of all positive integers $n$ such that $1 \leq n \leq \text{upper}$, $\gcd(n, 3) = 1$, and $\gcd(n, 11) = 1$.
Let $A$ be the number of elements in $S$. Let $T$ be the set of all positive integers $n$ such that $1 \leq n \leq 52490$, $10$ divides $n$, and $\gcd(n, 21) = 1$... | 48,185 | graphs = [
Graph(
let={
"_n": Const(69917),
"upper": Const(37512),
"k1": Const(3),
"k2": Const(11),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(GCD(a=Var("n"), b=Ref("... | NT | null | COUNT | sympy | C5 | [
"C5"
] | d9890f | nt_count_coprime_and_v1 | quadratic_mod | 4 | 0 | [
"C5"
] | 1 | 8.703 | 2026-02-08T11:18:54.714271Z | {
"verified": true,
"answer": 48185,
"timestamp": "2026-02-08T11:19:03.417284Z"
} | 5212b0 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 209,
"completion_tokens": 2688
},
"timestamp": "2026-02-14T11:39:54.348Z",
"answer": 48185
},
... | 1 | [
{
"lemma": "C5",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
e327cb | geo_count_lattice_triangle_v1_458359167_1199 | Let $n = 109$. Let $\text{area}_{2x} = \left|136n - 77\right|$. Let $\text{boundary}$ be the sum of $\gcd\left(\left|\sum_{k=1}^{16} \varphi(k) \left\lfloor \frac{16}{k} \right\rfloor\right|, 7\right)$, $\gcd\left(125, 102\right)$, and $\gcd\left(11, 109\right)$. Let $\text{result} = \frac{\text{area}_{2x} + 2 - \text{... | 42,197 | graphs = [
Graph(
let={
"_n": Const(109),
"area_2x": Abs(arg=Sum(Mul(Const(value=136), Ref(name='_n')), Mul(Const(value=11), Sub(left=Const(value=0), right=Const(value=7))))),
"boundary": Sum(GCD(a=Abs(arg=Summation(expr=Mul(EulerPhi(n=Var(name='k')), Floor(arg=Div(left=C... | NT | null | COUNT | sympy | K2 | [
"K2"
] | 6897ab | geo_count_lattice_triangle_v1 | null | 6 | 0 | [
"K2"
] | 1 | 0.005 | 2026-02-08T04:29:20.994828Z | {
"verified": true,
"answer": 42197,
"timestamp": "2026-02-08T04:29:21.000138Z"
} | 95c99a | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 278,
"completion_tokens": 1978
},
"timestamp": "2026-02-10T16:53:35.099Z",
"answer": 42197
},
{
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "n... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
19e2e3 | nt_count_primes_v1_2051736721_1998 | Let $P$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 108$, $\gcd(p, q) = 1$, and $p < q$. Let $L$ be the number of elements in $P$. Let $n$ be an integer satisfying $L \leq n \leq 16384$ and such that $n$ is prime. Let $R$ be the number of such primes $n$. Comput... | 72,629 | graphs = [
Graph(
let={
"_n": Const(74529),
"upper": Const(16384),
"result": CountOverSet(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'), conditio... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_count_primes_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.461 | 2026-02-08T16:24:49.784585Z | {
"verified": true,
"answer": 72629,
"timestamp": "2026-02-08T16:24:50.245927Z"
} | edd66c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 156,
"completion_tokens": 2357
},
"timestamp": "2026-02-17T04:07:16.794Z",
"answer": 72629
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
9117c2 | comb_binomial_compute_v1_865884756_1477 | Let $n$ be the sum of $\phi(d)$ over all positive divisors $d$ of $13$. Compute $\binom{n}{6}$. | 1,716 | graphs = [
Graph(
let={
"_n": Const(13),
"n": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"k": Const(6),
"result": Binom(n=Ref("n"), k=Ref("k")),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | comb_binomial_compute_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T16:04:39.467035Z | {
"verified": true,
"answer": 1716,
"timestamp": "2026-02-08T16:04:39.468336Z"
} | 327546 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 90,
"completion_tokens": 442
},
"timestamp": "2026-02-16T06:53:09.750Z",
"answer": 1716
},
{
"id": 11,
... | 2 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
1164fe | antilemma_k2_v1_2051736721_24 | Let $n = 322$. Compute
$$
\sum_{k=1}^{\sum_{d\mid n} \phi(d)} \phi(k) \cdot \left\lfloor \frac{322}{k} \right\rfloor,
$$
where $\phi(m)$ denotes Euler's totient function. | 52,003 | graphs = [
Graph(
let={
"_n": Const(322),
"x": Summation(var="k", start=Const(1), end=SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(322), Var("k"))))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3/K2",
"K2"
] | c7f244 | antilemma_k2_v1 | null | 6 | 0 | [
"K2",
"K3"
] | 2 | 0.003 | 2026-02-08T15:07:53.434235Z | {
"verified": true,
"answer": 52003,
"timestamp": "2026-02-08T15:07:53.436972Z"
} | 993aa8 | 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": 809
},
"timestamp": "2026-02-16T01:02:50.794Z",
"answer": 52003
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "M... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
b1d28f | comb_factorial_compute_v1_601307018_5844 | Let $S$ be the set of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 5248$. Let $n$ be the number of positive integers $v$ with $41 \leq v \leq |S|$ for which there exist integers $a, b$ satisfying $1 \leq a \leq 8$, $1 \leq b \leq 8$, and $41 \cdot b^2 = v$. Compute $n!$. | 40,320 | graphs = [
Graph(
let={
"_m": Const(5248),
"_n": Const(41),
"n": CountOverSet(set=SolutionsSet(var=Var("v"), condition=And(Geq(Var("v"), Ref("_n")), Leq(Var("v"), CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(na... | COMB | null | COMPUTE | sympy | COMB1 | [
"COMB1/QF_PSD_DISTINCT"
] | 555ca3 | comb_factorial_compute_v1 | null | 4 | 0 | [
"COMB1",
"QF_PSD_DISTINCT"
] | 2 | 0.005 | 2026-03-10T06:24:42.618666Z | {
"verified": true,
"answer": 40320,
"timestamp": "2026-03-10T06:24:42.623929Z"
} | 3f71e3 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 227,
"completion_tokens": 1246
},
"timestamp": "2026-04-19T03:00:37.112Z",
"answer": 40320
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "QF_PSD_DISTINCT",
"status": "ok_later"
},
{
"lemma": "V7",
"... | {
"lo": -5.35,
"mid": 0.52,
"hi": 5.84
} | ||
897b49 | nt_max_prime_below_v1_2051736721_2640 | Let $c$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq = 12$, $\gcd(p, q) = 1$, and $p < q$. Let $n$ be the largest prime number satisfying $c \leq n \leq 11449$. Compute the remainder when $52181 \cdot n$ is divided by $50077$. | 47,528 | graphs = [
Graph(
let={
"upper": Const(11449),
"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 | 0.441 | 2026-02-08T16:49:43.046916Z | {
"verified": true,
"answer": 47528,
"timestamp": "2026-02-08T16:49:43.487969Z"
} | 42f7c6 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 133,
"completion_tokens": 2878
},
"timestamp": "2026-02-17T13:08:40.044Z",
"answer": 47528
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
d3122f | nt_count_with_divisor_count_v1_1918700295_1262 | Let $d$ be the value of
$$
\sum_{k=1}^{5} \phi(k) \left\lfloor \frac{5}{k} \right\rfloor,
$$
where $\phi$ denotes Euler's totient function. Compute the number of positive integers $n$ such that $1 \leq n \leq 44944$ and the number of positive divisors of $n$ is equal to $d$. | 29 | graphs = [
Graph(
let={
"_n": Const(5),
"upper": Const(44944),
"div_count": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(5), Var("k"))))),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(G... | NT | null | COUNT | sympy | ONE_PHI_1 | [
"K2"
] | 6897ab | nt_count_with_divisor_count_v1 | null | 6 | 0 | [
"K2",
"ONE_PHI_1"
] | 2 | 12.006 | 2026-02-08T05:44:36.076978Z | {
"verified": true,
"answer": 29,
"timestamp": "2026-02-08T05:44:48.082771Z"
} | 9c16ce | 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": 2286
},
"timestamp": "2026-02-12T13:26:57.026Z",
"answer": 29
},
{
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
6cab26 | nt_min_crt_v1_1248542787_292 | Let $a$ be the largest integer $k$ such that $d^k$ divides $21!$, where $d$ is the smallest integer greater than or equal to 2 that divides 77. Let $b = 2$, $m = 4$, $k = 9$, and $n = 8$. Define $s = \sum_{j=1}^{n} j$. Find the smallest positive integer $t$ such that $1 \leq t \leq s$, $t \equiv a \pmod{4}$, and $t \eq... | 11 | graphs = [
Graph(
let={
"_n": Const(8),
"m": Const(4),
"k": Const(9),
"a": MaxKDivides(target=Factorial(Const(21)), base=MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(77)))))),
... | NT | null | EXTREMUM | sympy | COMB1 | [
"MIN_PRIME_FACTOR/V1",
"SUM_ARITHMETIC"
] | 71eae7 | nt_min_crt_v1 | null | 6 | 0 | [
"COMB1",
"MIN_PRIME_FACTOR",
"SUM_ARITHMETIC",
"V1"
] | 4 | 0.224 | 2026-02-08T03:02:55.962506Z | {
"verified": true,
"answer": 11,
"timestamp": "2026-02-08T03:02:56.186458Z"
} | 21b1b1 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 246,
"completion_tokens": 969
},
"timestamp": "2026-02-09T02:23:59.216Z",
"answer": 11
},
{
"id":... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"... | {
"lo": -6.51,
"mid": -0.38,
"hi": 5.12
} | ||
0efde2 | nt_count_coprime_v1_1918700295_2990 | Let $r$ be the number of positive integers $n$ with $1 \leq n \leq 36864$ such that $\gcd(n, 16) = 1$. Let $p$ be the largest prime number at most $256$. Let $s$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 6265009$, and let $c$ be the largest prime number $n$ with $2 \le... | 65,099 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(2),
"upper": Const(36864),
"k": Const(16),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(GCD(a=Var("n"), b=Ref("k")),... | NT | null | COUNT | sympy | B3 | [
"B3/MAX_PRIME_BELOW"
] | 9bfb92 | nt_count_coprime_v1 | two_moduli | 6 | 0 | [
"B3",
"MAX_PRIME_BELOW"
] | 2 | 10.268 | 2026-02-08T08:20:45.419586Z | {
"verified": true,
"answer": 65099,
"timestamp": "2026-02-08T08:20:55.687993Z"
} | 76f810 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 200,
"completion_tokens": 1764
},
"timestamp": "2026-02-13T17:43:07.107Z",
"answer": 65099
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"stat... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
d8b027 | nt_count_with_divisor_count_v1_151522320_1176 | Let $A$ be the number of positive integers $n$ such that $1 \leq n \leq 8192$ and $n$ has exactly $2$ positive divisors. Let $B$ be the number of integers $t$ such that $7 \leq t \leq 5050$ and there exist positive integers $a \leq 528$ and $b \leq 1205$ satisfying $t = 5a + 2b$. Compute $B - A$. | 4,012 | graphs = [
Graph(
let={
"upper": Const(8192),
"div_count": Const(2),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(NumDivisors(n=Var("n")), Ref("div_count"))))),
"Q": Sub(CountOverS... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 324ba4 | nt_count_with_divisor_count_v1 | negation_mod | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.686 | 2026-02-08T03:49:52.785004Z | {
"verified": true,
"answer": 4012,
"timestamp": "2026-02-08T03:49:53.471142Z"
} | 87d500 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 149,
"completion_tokens": 2994
},
"timestamp": "2026-02-11T19:34:47.823Z",
"answer": 4012
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
a65502 | comb_count_partitions_v1_784195855_7255 | Let $v = \sum_{k=0}^{0} (-1)^k \binom{0}{k}$ and $n_1 = \left( \sum_{k=0}^{9} (-1)^k \binom{9}{k} \right) \cdot v$. Let $e = \sum_{k=\binom{8}{8}-1}^{n_1} (-1)^k \binom{n_1}{k}$. Define $n$ to be $e$ multiplied by the number of elements in the Cartesian product of the sets $\{1, 2, 3\}$ and $\{1, 2, \dots, 13\}$. Let $... | 14,850 | graphs = [
Graph(
let={
"_n": Const(62469),
"n2": Const(0),
"v": Summation(var="k", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n2"), k=Var("k")))),
"n1": Mul(Summation(var="k", start=Const(0), end=Const(9), expr=Mul(Pow(Cons... | COMB | null | COUNT | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN/BINOMIAL_ALTERNATING",
"ZERO_BINOM_N"
] | d4ecfa | comb_count_partitions_v1 | null | 4 | 2 | [
"BINOMIAL_ALTERNATING",
"COUNT_CARTESIAN",
"ZERO_BINOM_N"
] | 3 | 0.005 | 2026-02-08T09:10:13.667621Z | {
"verified": true,
"answer": 14850,
"timestamp": "2026-02-08T09:10:13.672725Z"
} | b27626 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 294,
"completion_tokens": 2795
},
"timestamp": "2026-02-24T10:35:37.208Z",
"answer": 14850
},
{
"... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma"... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.