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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
696f0b | nt_sum_over_divisible_v1_784195855_1593 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 14288400$. Let $\text{upper}$ be the minimum value of $x + y$ over all such pairs. Let $\text{result}$ be the sum of all positive integers $n$ such that $n \leq \text{upper}$ and $n$ is divisible by $50$. Let $c = 23104$ and let $Q$ b... | 30,488 | graphs = [
Graph(
let={
"upper": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(14288400)))), expr=Sum(Var("x"), Var("y")))),
"divisor":... | NT | null | SUM | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_over_divisible_v1 | null | 6 | 0 | [
"B3"
] | 1 | 1.402 | 2026-02-08T05:09:13.492010Z | {
"verified": true,
"answer": 30488,
"timestamp": "2026-02-08T05:09:14.894198Z"
} | 8b2eb6 | 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": 3779
},
"timestamp": "2026-02-11T23:02:26.431Z",
"answer": 30488
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
}
] | {
"lo": -3.52,
"mid": 1.14,
"hi": 6.18
} | ||
da86c5 | antilemma_k3_v1_458359167_174 | Let $n = 46966$. Let $x = \sum_{d \mid n} \phi(d)$, where $\phi$ denotes Euler's totient function. Compute $x + \phi(|x| + 1) + \tau\left(|x| + \frac{85}{\sum_{d \mid 85} \phi(d)}\right)$, where $\tau(m)$ denotes the number of positive divisors of $m$. | 93,170 | graphs = [
Graph(
let={
"_n": Const(46966),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Sum(Ref("x"), EulerPhi(n=Sum(Abs(arg=Ref(name='x')), Const(1))), NumDivisors(n=Sum(Abs(arg=Ref(name='x')), Div(Const(85), SumOverDivisors(n=Co... | NT | COMB | COMPUTE | sympy | K3 | [
"K3/IDENTITY_DIV_SELF",
"K3"
] | 4f02be | antilemma_k3_v1 | arith_invariants | 5 | 0 | [
"IDENTITY_DIV_SELF",
"K3"
] | 2 | 0.001 | 2026-02-08T03:03:09.471429Z | {
"verified": true,
"answer": 93170,
"timestamp": "2026-02-08T03:03:09.472773Z"
} | bd7ae8 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 206,
"completion_tokens": 1180
},
"timestamp": "2026-02-10T12:31:48.931Z",
"answer": 93170
},
{
"... | 1 | [
{
"lemma": "IDENTITY_DIV_SELF",
"status": "ok_later"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"... | {
"lo": -3.47,
"mid": 0.81,
"hi": 4.81
} | ||
fc704b | geo_count_lattice_triangle_v1_677425708_863 | Let $P_1=(0,0)$, $P_2=(111,0)$, and $P_3=(111,7)$ be three points in the plane. Let $P_4=(0,7)$, and consider the quadrilateral $P_1P_2P_3P_4$.
Let
$$A=120\cdot 111+144\cdot(0-7).$$
Define $K$ to be $|A|$, and let
$$B_1=\gcd\left(\left|\sum_{k=1}^{15} \varphi(k)\left\lfloor\frac{15}{k}\right\rfloor\right|,|7|\right),$... | 55,458 | graphs = [
Graph(
let={
"_m": Const(61529),
"_n": Const(111),
"area_2x": Abs(arg=Sum(Mul(Const(value=120), Const(value=111)), Mul(Const(value=144), Sub(left=Const(value=0), right=Const(value=7))))),
"boundary": Sum(GCD(a=Abs(arg=Summation(expr=Mul(EulerPhi(n=V... | NT | null | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC",
"K2"
] | 2a0f86 | geo_count_lattice_triangle_v1 | null | 8 | 0 | [
"K2",
"SUM_ARITHMETIC"
] | 2 | 0.013 | 2026-02-08T03:49:35.613835Z | {
"verified": true,
"answer": 55458,
"timestamp": "2026-02-08T03:49:35.627119Z"
} | b970f9 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 412,
"completion_tokens": 1090
},
"timestamp": "2026-02-09T13:39:04.642Z",
"answer": 55458
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
... | {
"lo": -5.54,
"mid": -3.02,
"hi": -0.25
} | ||
730b5f | geo_visible_lattice_v1_1742523217_3839 | Let $n = 88$. Define a lattice point $(x, y)$ to be visible from the origin if $\gcd(x, y) = 1$. Let $R$ be the number of visible lattice points $(x, y)$ with $1 \leq x, y \leq n$. Compute $12769 - R$. | 8,034 | graphs = [
Graph(
let={
"n": Const(88),
"result": VisibleLatticePoints(n=Ref(name='n')),
"Q": Sub(Const(12769), Ref("result")),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 3 | 0 | null | null | 1.031 | 2026-02-08T06:06:52.250837Z | {
"verified": true,
"answer": 8034,
"timestamp": "2026-02-08T06:06:53.281756Z"
} | 1f84b1 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 181,
"completion_tokens": 11306
},
"timestamp": "2026-02-24T05:21:13.490Z",
"answer": 8034
},
{
"... | 1 | [] | {
"lo": -0.06,
"mid": 2.89,
"hi": 5.27
} | ||||
399831 | nt_sum_gcd_range_mod_v1_1520064083_6649 | Let $m = 14793$. Define $N$ to be the number of integers $n$ such that $1 \leq n \leq m$ and the sum of the decimal digits of $n$ is divisible by 2.
Let $k$ be the largest positive divisor of 113232 that does not exceed 336.
Let $M = 11633$. Compute the sum $$\sum_{n=1}^{N} \gcd(n, k),$$ and let this sum be $S$. Let ... | 2 | graphs = [
Graph(
let={
"_m": Const(14793),
"_n": Const(2),
"N": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_m")), Eq(Mod(value=DigitSum(Var("n")), modulus=Ref("_n")), Const(0))))),
"k": MaxOverSet(set... | NT | COMB | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW",
"MAX_DIVISOR",
"L3B"
] | 518c22 | nt_sum_gcd_range_mod_v1 | bell_mod | 7 | 0 | [
"L3B",
"MAX_DIVISOR",
"MAX_PRIME_BELOW"
] | 3 | 0.346 | 2026-02-08T08:15:25.683764Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-02-08T08:15:26.029572Z"
} | 2188ee | 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": 4146
},
"timestamp": "2026-02-13T16:50:15.272Z",
"answer": 2
},
{
... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3B",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
"... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
25455b | comb_count_permutations_fixed_v1_349078426_502 | Let $n = 7$ and $k = 0$. Define $\binom{n}{k}$ to be the number of ways to choose $k$ elements from a set of $n$ elements, and let $!m$ denote the number of derangements of $m$ elements. Compute $\binom{7}{0} \cdot !(7 - 0)$. Let $p$ be the largest prime number less than or equal to $12$ that is at least $2$. Find the ... | 203 | graphs = [
Graph(
let={
"_n": Const(2),
"n": Const(7),
"k": Const(0),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub(left=Ref(name='n'), right=Ref(name='k')))),
"Q": Bell(Mod(value=Abs(arg=Ref(name='result')), modulus=MaxOverSet(... | NT | COMB | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | 88ea9c | comb_count_permutations_fixed_v1 | bell_mod | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.002 | 2026-02-08T13:06:11.616862Z | {
"verified": true,
"answer": 203,
"timestamp": "2026-02-08T13:06:11.619190Z"
} | e50476 | 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": 1097
},
"timestamp": "2026-02-15T09:27:03.616Z",
"answer": 203
},
{
... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
52ccf6 | nt_max_prime_below_v1_238844314_506 | Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $p < q$, $pq = 72$, and $\gcd(p, q) = 1$. Let $L$ be the number of elements in $S$. Determine the largest prime number $n$ such that $L \leq n \leq 10753$. | 10,753 | graphs = [
Graph(
let={
"upper": Const(10753),
"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 | 0.249 | 2026-02-08T13:22:57.331415Z | {
"verified": true,
"answer": 10753,
"timestamp": "2026-02-08T13:22:57.580691Z"
} | 0c3970 | 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": 2483
},
"timestamp": "2026-02-15T13:49:36.305Z",
"answer": 10753
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
5b6f18 | antilemma_sum_equals_v1_1125832087_2232 | Let $x$ be the number of ordered pairs $(i, j)$ of positive integers such that $1 \leq i \leq 70$, $1 \leq j \leq 71$, and $i + j = 72$. Compute the value of
$$
x + \varphi(|x| + 1) + \tau(|x| + 1),
$$
where $\varphi$ denotes Euler's totient function and $\tau(m)$ denotes the number of positive divisors of $m$. | 142 | graphs = [
Graph(
let={
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(72)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(70)), right=IntegerRange(start=Const(1), end=Const(71))))),
"Q": ... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 3 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.166 | 2026-02-08T04:25:31.087802Z | {
"verified": true,
"answer": 142,
"timestamp": "2026-02-08T04:25:31.253927Z"
} | 02edfb | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 221,
"completion_tokens": 875
},
"timestamp": "2026-02-24T00:45:09.092Z",
"answer": 142
},
{
"id"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status"... | {
"lo": -9.23,
"mid": -6.18,
"hi": -4.06
} | ||
190e26 | alg_poly3_min_v1_601307018_1384 | For integers $a, b$ with $1 \le a, b \le 56$, define
$$
f(a, b) = -117a^3 - 216ab^2 + 276a^2b + b^3 \cdot \min_{\substack{a_1, b_1 = 1 \\ a_1, b_1 \le 14}}\left\{ 2b_1^3 + 54a_1^k b_1 \right\},
$$
where $k = \left|\left\{ p > 0 : \exists\, q \in \mathbb{Z},\, pq = 12,\, \gcd(p, q) = 1,\, p < q \right\}\right|$. Find th... | 57,378 | graphs = [
Graph(
let={
"_m": Const(14),
"_n": Const(2),
"result": Mod(value=MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(56)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/POLY3_MIN"
] | 00eaa8 | alg_poly3_min_v1 | null | 7 | 0 | [
"COPRIME_PAIRS",
"POLY3_MIN"
] | 2 | 0.028 | 2026-03-10T02:05:31.965931Z | {
"verified": true,
"answer": 57378,
"timestamp": "2026-03-10T02:05:31.993708Z"
} | 86eea6 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 310,
"completion_tokens": 5490
},
"timestamp": "2026-03-29T02:05:39.892Z",
"answer": 57378
},
{
"... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "POLY3_MIN",
"status": "ok_later"
},
{
... | {
"lo": 2.84,
"mid": 4.95,
"hi": 7.12
} | ||
dc4faa | comb_factorial_compute_v1_601307018_6265 | Let $S = a^3 \bmod 4913$, $T = S^3 \bmod 4913$, and $K = T^3 \bmod d$, where $d$ is the largest positive divisor of $24167047$ such that $d^2 \le 24167047$. Define $L = K^3 \bmod 4913$. Let $n$ be the number of non-negative integers $a$ with $0 \le a \le 4912$ satisfying $L = a$, $S \ne a$, $T \ne a$, and $K \ne a$. Co... | 15,849 | graphs = [
Graph(
let={
"_m": Const(4913),
"_n": Const(4913),
"n": CountOverSet(set=SolutionsSet(var=Var("a"), condition=And(Geq(Var("a"), Const(0)), Leq(Var("a"), Const(4912)), Eq(Ref("_po_p4"), Var("a")), Neq(Ref("_po_p1"), Var("a")), Neq(Ref("_po_p2"), Var("a")), Neq(R... | COMB | NT | COMPUTE | sympy | B3_CLOSEST | [
"B3_CLOSEST/POLY_ORBIT_HENSEL"
] | 253c25 | comb_factorial_compute_v1 | null | 7 | 0 | [
"B3_CLOSEST",
"POLY_ORBIT_HENSEL"
] | 2 | 0.006 | 2026-03-10T06:51:57.229032Z | {
"verified": true,
"answer": 15849,
"timestamp": "2026-03-10T06:51:57.234621Z"
} | ac88bc | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 250,
"completion_tokens": 8301
},
"timestamp": "2026-04-19T04:02:41.398Z",
"answer": 15849
},
{
... | 1 | [
{
"lemma": "B3_CLOSEST",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "POLY_ORBIT_HENSEL",
"status": "ok_later"
},
{
"lemma": "V7"... | {
"lo": -5.35,
"mid": 0.52,
"hi": 5.84
} | ||
4e5d62 | nt_count_coprime_v1_655260480_5698 | Let $t$ be an integer. Define $N$ to be the number of integers $t$ with $10 \leq t \leq 345$ for which there exist positive integers $a \leq 9$ and $b \leq 94$ such that $t = 7a + 3b$. Let $m$ be the minimum value of $x_1 + y_1$ over all pairs of positive integers $(x_1, y_1)$ such that $x_1 y_1 = N$. Let $k$ be the mi... | 7,203 | 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=9)), Geq(left=Var(name='b'), right=Const(value=... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/B3",
"B3/B3"
] | a40c9e | nt_count_coprime_v1 | null | 7 | 0 | [
"B3",
"LIN_FORM"
] | 2 | 3.415 | 2026-02-08T18:37:51.126971Z | {
"verified": true,
"answer": 7203,
"timestamp": "2026-02-08T18:37:54.542387Z"
} | 683edd | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 216,
"completion_tokens": 5331
},
"timestamp": "2026-02-18T18:15:14.446Z",
"answer": 7203
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
00e663 | diophantine_fbi2_count_v1_1978505735_2709 | Let $d$ be a positive integer. Consider the set of all integers $d$ such that $2 \le d \le 197$, $d$ divides $240$, and $4 \le \frac{240}{d} \le 199$. Let $r$ be the number of elements in this set. Compute the remainder when $22899r$ is divided by $92185$. | 89,829 | graphs = [
Graph(
let={
"_n": Const(199),
"k": Const(240),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Leq(Var("d"), Const(197)), Divides(divisor=Var("d"), dividend=Ref("k")), Geq(Div(Ref("k"), Var("d")), Const(4)), Leq(Div... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | diophantine_fbi2_count_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.019 | 2026-02-08T17:07:38.544489Z | {
"verified": true,
"answer": 89829,
"timestamp": "2026-02-08T17:07:38.563791Z"
} | 6302b0 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 130,
"completion_tokens": 1514
},
"timestamp": "2026-02-17T20:09:42.032Z",
"answer": 89829
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
585926 | nt_count_intersection_v1_784195855_5710 | Let $T$ be the set of all integers $t$ such that $11 \leq t \leq 84$ and there exist positive integers $a$, $b$ with $1 \leq a \leq 8$, $1 \leq b \leq 7$, satisfying $t = 7a + 4b$. Let $n = |T|$, the number of elements in $T$. Let $N = 20000$. Define $b$ as the number of positive integers $k$ with $1 \leq k \leq n$ suc... | 4,120 | graphs = [
Graph(
let={
"_m": Const(94967),
"_n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=8)), Geq(left=V... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/COUNT_FIB_DIVISIBLE"
] | 95eec8 | nt_count_intersection_v1 | null | 7 | 0 | [
"COUNT_FIB_DIVISIBLE",
"LIN_FORM"
] | 2 | 0.942 | 2026-02-08T08:04:16.929090Z | {
"verified": true,
"answer": 4120,
"timestamp": "2026-02-08T08:04:17.871255Z"
} | fa6c00 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 245,
"completion_tokens": 4041
},
"timestamp": "2026-02-13T14:28:20.366Z",
"answer": 4120
},
{... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok_later"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V3",
"status": "... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
f77ca0 | algebra_poly_eval_v1_717093673_3352 | Let $m = 50$, $n = 5$, and $t = 20$. Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = \sum_{d\mid 4} \phi(d)$. Let $e$ be the minimum value of $x + y$ as $(x, y)$ ranges over $S$. Compute
$$
\left| \frac{m t^n + 275 t^e + 993 t^3 + 2136 t^2 + 1780 t + 286}{23643} \right|.
$$ | 9,002 | graphs = [
Graph(
let={
"_m": Const(50),
"_n": Const(5),
"t": Const(20),
"result": Div(Sum(Mul(Ref("_m"), Pow(Ref("t"), Ref("_n"))), Mul(Const(275), Pow(Ref("t"), MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=An... | NT | null | COMPUTE | sympy | K3 | [
"K3/B3"
] | f0a0b3 | algebra_poly_eval_v1 | null | 5 | 0 | [
"B3",
"K3"
] | 2 | 0.01 | 2026-02-08T17:30:28.020273Z | {
"verified": true,
"answer": 9002,
"timestamp": "2026-02-08T17:30:28.030305Z"
} | cd9bfa | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 174,
"completion_tokens": 1604
},
"timestamp": "2026-02-18T03:53:31.308Z",
"answer": 9002
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": ... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
7a8c44 | sequence_count_fib_divisible_v1_1116507919_206 | Let $m = 5$. Let $n$ be the number of positive integers $k \leq 4095$ such that $m$ divides the $k$-th Fibonacci number. Let $s = \sum_{d \mid n} \varphi(d)$. Let $d = 14$. Compute the number of positive integers $k \leq s$ such that $d$ divides the $k$-th Fibonacci number. | 34 | graphs = [
Graph(
let={
"_m": Const(5),
"_n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(4095)), Divides(divisor=Ref("_m"), dividend=Fibonacci(arg=Var(name='n')))))),
"upper": SumOverDivisors(n=Ref(name='_n'), va... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"COUNT_FIB_DIVISIBLE/K3"
] | b811b7 | sequence_count_fib_divisible_v1 | null | 7 | 0 | [
"COUNT_FIB_DIVISIBLE",
"K3",
"MAX_PRIME_BELOW"
] | 3 | 0.093 | 2026-02-08T02:27:55.572551Z | {
"verified": true,
"answer": 34,
"timestamp": "2026-02-08T02:27:55.665494Z"
} | 6e5978 | 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": 5826
},
"timestamp": "2026-02-08T19:13:30.773Z",
"answer": 34
},
{
"id"... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K3",
"status": "ok_later"
},
{
"lemma": "LTE_DIFF_P2",
"status": "n... | {
"lo": 0.06,
"mid": 1.74,
"hi": 3.24
} | ||
e3442f | algebra_quadratic_discriminant_v1_971394319_1346 | Let $a = 1$, $b = -20$, and $c = 100$. Define $\Delta = b^2 - 4ac$. Compute the sum of the number of positive divisors of all integers from 1 to $|\Delta|$. That is, compute
$$
\sum_{n=1}^{|\Delta|} \tau(n),
$$
where $\tau(n)$ denotes the number of positive divisors of $n$. | 0 | graphs = [
Graph(
let={
"a": Const(1),
"b": Const(-20),
"c": Const(100),
"result": Sub(Pow(Ref("b"), Const(2)), Mul(Const(4), Ref("a"), Ref("c"))),
"Q": Summation(var="n", start=Const(1), end=Abs(arg=Ref(name='result')), expr=NumDivisors(n=Var("n")... | NT | null | COMPUTE | sympy | MOBIUS_COPRIME | [
"MOBIUS_COPRIME"
] | ac54ac | algebra_quadratic_discriminant_v1 | null | 2 | 0 | [
"MOBIUS_COPRIME"
] | 1 | 0.016 | 2026-02-08T13:38:17.817902Z | {
"verified": true,
"answer": 0,
"timestamp": "2026-02-08T13:38:17.834365Z"
} | 7e2149 | 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": 244
},
"timestamp": "2026-02-15T18:51:24.553Z",
"answer": 0
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
920f55 | nt_sum_divisors_compute_v1_1080341949_510 | Let $n = 30276$. Let $s$ be the sum of the positive divisors of $n$. Let $p$ be the largest prime number between $2$ and $12$, inclusive. Compute the Bell number $B_k$, where $k$ is the remainder when $|s|$ is divided by $p$. | 203 | graphs = [
Graph(
let={
"n": Const(30276),
"result": SumDivisors(n=Ref("n")),
"Q": Bell(Mod(value=Abs(arg=Ref(name='result')), modulus=MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(12)), IsPrime(Var("n"))))))),
... | NT | COMB | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | 88ea9c | nt_sum_divisors_compute_v1 | bell_mod | 5 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.002 | 2026-02-08T13:32:49.727948Z | {
"verified": true,
"answer": 203,
"timestamp": "2026-02-08T13:32:49.729677Z"
} | f08f5d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 116,
"completion_tokens": 1238
},
"timestamp": "2026-02-15T17:23:29.786Z",
"answer": 203
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
6c551d | nt_gcd_compute_v1_798873815_409 | Let $n = 46$. Let $k$ be the number of positive integers less than or equal to $n$ that are divisible by 23. Let $\phi(k)$ denote Euler's totient function evaluated at $k$. Define $$e = \sum_{d \mid \phi(k)} \mu(d),$$ where $\mu$ is the Möbius function. Now define $$s = \sum_{d \mid 1} \mu(d).$$ Let $a = 364705 \cdot s... | 33,155 | graphs = [
Graph(
let={
"_n": Const(46),
"n1": EulerPhi(n=CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(1)), Leq(Var("k"), Ref("_n")), Divides(divisor=Const(23), dividend=Var("k"))), domain='positive_integers'))),
"e": SumOverDivisors(n=Ref... | NT | null | COMPUTE | sympy | C2 | [
"C2/ONE_PHI_2/MOBIUS_SUM"
] | 251b17 | nt_gcd_compute_v1 | null | 4 | 2 | [
"C2",
"MOBIUS_SUM",
"ONE_PHI_2"
] | 3 | 0.002 | 2026-02-08T02:38:11.529495Z | {
"verified": true,
"answer": 33155,
"timestamp": "2026-02-08T02:38:11.531234Z"
} | 35ae37 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 240,
"completion_tokens": 689
},
"timestamp": "2026-02-09T16:41:10.246Z",
"answer": 33155
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MOBIUS_SUM",
"status": "ok_later"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "ONE_PHI_2",
"status": "o... | {
"lo": -4.84,
"mid": -1.64,
"hi": 2
} | ||
929550 | diophantine_sum_product_min_v1_1520064083_4356 | Let $S$ be the number of positive integers $j$ such that $1 \leq j \leq 43$ and $j^4 \leq 3418801$. Let $P = 456$. Determine the value of the smallest positive integer $x$ such that $1 \leq x \leq 42$ and $x(S - x) = P$. | 19 | graphs = [
Graph(
let={
"_n": Const(4),
"S": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(1)), Leq(Var("j"), Const(43)), Leq(Pow(Var("j"), Ref("_n")), Const(3418801))), domain='positive_integers')),
"P": Const(456),
"result": M... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"C3"
] | 8a214c | diophantine_sum_product_min_v1 | null | 5 | 0 | [
"C3",
"LIN_FORM"
] | 2 | 0.334 | 2026-02-08T06:14:07.859464Z | {
"verified": true,
"answer": 19,
"timestamp": "2026-02-08T06:14:08.193209Z"
} | dbfca7 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 124,
"completion_tokens": 688
},
"timestamp": "2026-02-12T22:01:19.736Z",
"answer": 19
},
{
... | 1 | [
{
"lemma": "C3",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
d509de | v7_endings_v1_1742523217_1129 | Let $k$ be a nonnegative integer such that $0 \leq k \leq 2094$ and $\binom{2094}{k}$ is odd. Let $x$ be the sum of all such integers $k$. Compute $x$. | 33,504 | graphs = [
Graph(
let={
"_n": Const(2094),
"x": SumOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(0)), Leq(Var("k"), Const(2094)), Not(Divides(divisor=Const(2), dividend=Binom(n=Ref("_n"), k=Var("k"))))))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | V7 | [
"V7"
] | 0672d4 | v7_endings_v1 | null | 7 | 0 | [
"V7"
] | 1 | 0.001 | 2026-02-08T03:26:57.450059Z | {
"verified": true,
"answer": 33504,
"timestamp": "2026-02-08T03:26:57.450676Z"
} | d7834d | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 165,
"completion_tokens": 679
},
"timestamp": "2026-02-10T03:49:48.861Z",
"answer": 33504
},
{
"i... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V7",
"status": "ok"
}
] | {
"lo": -6.51,
"mid": -0.31,
"hi": 5.43
} | ||
dac93e | alg_qf_psd_min_v1_1419126231_616 | Find the minimum value of $$2808cd + 2322a^2 + 3996bd + 3402b^2 - 216bc + 1296ad + 2484d^2 - 2376ab + 2376ac + 1890c^2$$ over all ordered quadruples $(a, b, c, d)$ of positive integers with $1 \leq a, b, c, d \leq 24$. | 17,982 | graphs = [
Graph(
let={
"result": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b"), Var("c"), Var("d")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(24)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(24)), Geq(Var("c"), Const(1)), Leq(Var("c"), Co... | ALG | null | COMPUTE | sympy | K13 | [
"K13/STARS_BARS"
] | f7b8f1 | alg_qf_psd_min_v1 | null | 3 | null | [
"K13",
"STARS_BARS"
] | 2 | 2.233 | 2026-02-25T10:07:12.968904Z | {
"verified": true,
"answer": 17982,
"timestamp": "2026-02-25T10:07:15.201924Z"
} | ca71ec | 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": 20132
},
"timestamp": "2026-03-30T09:12:17.437Z",
"answer": 17982
},
{
... | 1 | [
{
"lemma": "K13",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "STARS_BARS",
"status": "ok_later"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma"... | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | ||
65490a | geo_visible_lattice_v1_48377204_3200 | A lattice point $(x,y)$ is said to be visible from the origin if $\gcd(x,y) = 1$. Let $N$ be the number of visible lattice points $(x,y)$ with $1 \le x, y \le 77$. Compute the remainder when $44121 \cdot N$ is divided by $51740$. | 31,203 | graphs = [
Graph(
let={
"n": Const(77),
"result": VisibleLatticePoints(n=Ref(name='n')),
"Q": Mod(value=Mul(Const(44121), Ref("result")), modulus=Const(51740)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 4 | 0 | null | null | 0.266 | 2026-02-08T17:14:13.325274Z | {
"verified": true,
"answer": 31203,
"timestamp": "2026-02-08T17:14:13.590992Z"
} | cab6d4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 118,
"completion_tokens": 4941
},
"timestamp": "2026-02-17T21:46:57.747Z",
"answer": 31203
},
... | 1 | [] | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||||
7cb7f7 | alg_sum_ap_v1_1218484723_1235 | Let $S$ be the set of integers $t$ such that $10 \le t \le 1843$ and $t = 7a + 3b$ for some integers $a, b$ with $1 \le a \le 226$, $1 \le b \le 87$. Let $M = \sum_{k=0}^{|S|} (7k + 21) \bmod{5880}$, and let $Q = |M|$. Compute $Q$. | 3,514 | graphs = [
Graph(
let={
"_n": Const(21),
"result": Mod(value=Summation(var="k", start=Const(0), end=CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(lef... | ALG | null | COMPUTE | sympy | POLY_ORBIT_HENSEL | [
"LIN_FORM"
] | 7b2633 | alg_sum_ap_v1 | null | 5 | 0 | [
"LIN_FORM",
"POLY_ORBIT_HENSEL"
] | 2 | 0.569 | 2026-02-25T02:59:44.054096Z | {
"verified": true,
"answer": 3514,
"timestamp": "2026-02-25T02:59:44.623150Z"
} | cf5b80 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 219,
"completion_tokens": 9159
},
"timestamp": "2026-03-10T06:12:36.006Z",
"answer": 3514
},
{
"i... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 4.76,
"mid": 6.79,
"hi": 9.83
} | ||
a4c308 | nt_sum_totient_over_divisors_v1_655260480_5187 | Let $n$ be the largest prime number less than or equal to 2777. Compute the sum of $\phi(d)$ over all positive divisors $d$ of $n$. | 2,777 | graphs = [
Graph(
let={
"_n": Const(2777),
"n": MaxOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(2)), Leq(Var("n1"), Ref("_n")), IsPrime(Var("n1"))))),
"result": SumOverDivisors(n=Ref(name='n'), var='d', expr=EulerPhi(n=Var(name='d'))),
... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | nt_sum_totient_over_divisors_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.002 | 2026-02-08T18:20:34.477151Z | {
"verified": true,
"answer": 2777,
"timestamp": "2026-02-08T18:20:34.479158Z"
} | 60789d | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 96,
"completion_tokens": 440
},
"timestamp": "2026-02-16T12:18:34.539Z",
"answer": 2773
},
{
"id": 11,
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
639089_n | comb_count_partitions_v1_601307018_2538 | A composer writes a piece using rhythmic units of lengths that are powers of $6$, specifically $6^0$, $6^1$, and $6^2$, since $\binom{13}{13} = 1$ and the sum starts at $k = 0$. The total duration of the piece is $n = 6^0 + 6^1 + 6^2$. The musician then explores all possible ways to subdivide this total duration into a... | 63,261 | COMB | null | COUNT | sympy | SUM_GEOM | [
"SUM_GEOM",
"ZERO_BINOM_N"
] | 4e18d8 | comb_count_partitions_v1 | null | 3 | null | [
"SUM_GEOM",
"ZERO_BINOM_N"
] | 2 | 0.002 | 2026-03-10T03:14:03.483259Z | null | da68da | 639089 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 234,
"completion_tokens": 1126
},
"timestamp": "2026-03-29T16:20:22.730Z",
"answer": 63261
},
{
"... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "SUM_GEOM",
"status": "ok"
},
{
"lemma": ... | {
"lo": 1.7,
"mid": 5.03,
"hi": 8.38
} | |
04a546 | alg_poly3_sum_v1_1218484723_2399 | Let $S$ be the sum
$$S = \sum_{\substack{(a, b)\\ 1 \le a \le 161,\\ 1 \le b \le \left|\{ v : v \ge 9,\ v \le \left|\{ t : \text{there exist integers } a, b \text{ with } 1 \le a \le 353,\ 1 \le b \le 872 \\ \text{such that } t = 14a + 6b,\ t \ge 20,\ t \le 10174 \}\right|,\\ \text{there exist integers } a, b \text{ wi... | 60,501 | graphs = [
Graph(
let={
"_m": Const(27),
"_n": Const(65031),
"result": Mod(value=SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(161)), Geq(Var("b"), Const(1)), Leq(Var("b"), C... | ALG | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/QF_PSD_DISTINCT"
] | e187db | alg_poly3_sum_v1 | null | 7 | 0 | [
"LIN_FORM",
"QF_PSD_DISTINCT"
] | 2 | 0.062 | 2026-02-25T04:11:37.181777Z | {
"verified": true,
"answer": 60501,
"timestamp": "2026-02-25T04:11:37.243633Z"
} | ad954d | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 354,
"completion_tokens": 25321
},
"timestamp": "2026-03-29T04:32:24.011Z",
"answer": 10805
},
{
... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_DISTINCT",
"status": "ok_later"
}
] | {
"lo": 3.81,
"mid": 6.33,
"hi": 9.49
} | ||
74635e | diophantine_fbi2_count_v1_151522320_2305 | Let $k = 1260$, $a = 3$, and $b = 1$. Compute the number of positive integers $d$ such that $4 \leq d \leq 203$, $d$ divides $k$, $\frac{k}{d} \geq 2$, and $\frac{k}{d} \leq 201$. | 24 | graphs = [
Graph(
let={
"k": Const(1260),
"a": Const(3),
"b": Const(1),
"upper": Const(200),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(4)), Leq(Var("d"), Const(203)), Divides(divisor=Var("d"), dividend=... | NT | null | COUNT | sympy | EULER_TOTIENT_SUM | [
"C4/C4",
"B3/C4"
] | 58817b | diophantine_fbi2_count_v1 | null | 4 | 0 | [
"B3",
"C4",
"EULER_TOTIENT_SUM"
] | 3 | 0.107 | 2026-02-08T04:43:52.302831Z | {
"verified": true,
"answer": 24,
"timestamp": "2026-02-08T04:43:52.410288Z"
} | b09d9f | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 186,
"completion_tokens": 2103
},
"timestamp": "2026-02-11T21:48:57.584Z",
"answer": 24
},
{
"id... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemm... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
e02adc | modular_min_linear_v1_1116507919_340 | Let $a = 31745$, $b = 27910$, and $m = 65767$. Let $S$ be the set of all ordered pairs of positive integers $(p, q)$ such that $p \cdot q = 12$, $\gcd(p, q) = 1$, and $p < q$. Let $\phi = \varphi(|S|)$, where $\varphi$ is Euler's totient function. Find the smallest integer $x$ such that $x \geq \phi$, $x \leq m$, and $... | 9,738 | graphs = [
Graph(
let={
"a": Const(31745),
"b": Const(27910),
"m": Const(65767),
"result": MinOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), EulerPhi(n=CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')),... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/ONE_PHI_2"
] | 761f00 | modular_min_linear_v1 | null | 6 | 0 | [
"COPRIME_PAIRS",
"ONE_PHI_2"
] | 2 | 3.66 | 2026-02-08T02:31:44.718867Z | {
"verified": true,
"answer": 9738,
"timestamp": "2026-02-08T02:31:48.378405Z"
} | 5d6020 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 258,
"completion_tokens": 7178
},
"timestamp": "2026-02-08T19:24:03.902Z",
"answer": 9738
},
{
"i... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "ONE_PHI_2",
"status": "ok_later"... | {
"lo": -4.59,
"mid": 0.41,
"hi": 5.45
} | ||
cfdf5d | diophantine_product_count_v1_1918700295_293 | Let $t$ be an integer satisfying $10 \leq t \leq 79$. Define $T$ as the set of all such $t$ for which there exist integers $a$ and $b$ with $1 \leq a \leq 10$, $1 \leq b \leq 7$, and $t = 3a + 7b$. Let $N$ be the number of elements in $T$. Let $k = 60$. Determine the number of positive integers $x$ such that $1 \leq x ... | 13,535 | graphs = [
Graph(
let={
"k": Const(60),
"upper": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=10)), Geq(left=V... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | diophantine_product_count_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.006 | 2026-02-08T03:08:50.949779Z | {
"verified": true,
"answer": 13535,
"timestamp": "2026-02-08T03:08:50.955897Z"
} | 9f5b7f | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 278,
"completion_tokens": 3049
},
"timestamp": "2026-02-10T13:11:46.497Z",
"answer": 13535
},
{
"... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.02,
"hi": 0.31
} | ||
aecf40 | comb_binomial_compute_v1_1353956133_108 | Let $j$ range over the nonnegative integers. Define $m$ to be the number of integers $j$ with $0 \leq j \leq 82544$ such that $\binom{82544}{j}$ is odd. Let $n$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers satisfying $xy = m$. Compute the remainder when $11369 \cdot \binom{n}{9}$... | 42,305 | graphs = [
Graph(
let={
"_m": Const(63579),
"_n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(82544)), Eq(Mod(value=Binom(n=Const(82544), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')),
... | ALG | COMB | COMPUTE | sympy | V8 | [
"V8/B3"
] | b4fc86 | comb_binomial_compute_v1 | null | 7 | 0 | [
"B3",
"V8"
] | 2 | 0.002 | 2026-02-08T11:18:56.755569Z | {
"verified": true,
"answer": 42305,
"timestamp": "2026-02-08T11:18:56.757801Z"
} | 120c05 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 219,
"completion_tokens": 18143
},
"timestamp": "2026-02-24T13:18:41.333Z",
"answer": 42305
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
411dcc | diophantine_product_count_v1_1353956133_706 | Let $u$ be the number of positive integers $n \leq 448$ such that the $n$th Fibonacci number is divisible by 21. Let $d$ be the number of positive divisors $x$ of 120 such that both $x \leq u$ and $\frac{120}{x} \leq u$. Let $s$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such t... | 4,108 | graphs = [
Graph(
let={
"_n": Const(21),
"k": Const(120),
"upper": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(448)), Divides(divisor=Ref("_n"), dividend=Fibonacci(arg=Var(name='n')))))),
"result": Cou... | NT | null | COUNT | sympy | B3 | [
"COUNT_FIB_DIVISIBLE",
"B3"
] | fa3da5 | diophantine_product_count_v1 | mod_exp | 6 | 0 | [
"B3",
"COUNT_FIB_DIVISIBLE"
] | 2 | 0.039 | 2026-02-08T11:48:07.854233Z | {
"verified": true,
"answer": 4108,
"timestamp": "2026-02-08T11:48:07.893355Z"
} | d08041 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 168,
"completion_tokens": 1575
},
"timestamp": "2026-02-14T18:59:40.918Z",
"answer": 4108
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
681388 | comb_binomial_compute_v1_898971024_1907 | Let $n_1$ range over the positive integers from 1 to 52 inclusive that are divisible by 4 and relatively prime to 15. Let $m$ be the number of such integers. Let $k$ be the largest positive divisor of 77 that is at most $m$. Compute $\binom{12}{k}$. Let $c = 23274$. Find the remainder when $c \cdot \binom{12}{k}$ is di... | 39,347 | graphs = [
Graph(
let={
"_n": CountOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(1)), Leq(Var("n1"), Const(52)), Divides(divisor=Const(4), dividend=Var("n1")), Eq(GCD(a=Var("n1"), b=Const(15)), Const(1))))),
"n": Const(12),
"k": MaxOverSet(set... | NT | null | COMPUTE | sympy | C5 | [
"C5/MAX_DIVISOR"
] | 454bdd | comb_binomial_compute_v1 | null | 3 | 0 | [
"C5",
"MAX_DIVISOR"
] | 2 | 0.004 | 2026-02-08T16:24:54.713664Z | {
"verified": true,
"answer": 39347,
"timestamp": "2026-02-08T16:24:54.717495Z"
} | bea375 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 146,
"completion_tokens": 1398
},
"timestamp": "2026-02-17T02:47:54.709Z",
"answer": 39347
},
... | 1 | [
{
"lemma": "C5",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok_later"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
7072ba | antilemma_sum_equals_v1_124444284_832 | Let $n = 58$. Compute the number of ordered pairs $(i, j)$ of positive integers such that $i + j = n$, $1 \le i \le 56$, and $1 \le j \le 57$. | 56 | graphs = [
Graph(
let={
"_n": Const(58),
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref("_n")), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(56)), right=IntegerRange(start=Const(1), end=Con... | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 2 | 0 | [
"COUNT_CARTESIAN",
"COUNT_SUM_EQUALS"
] | 2 | 0.038 | 2026-02-08T03:32:54.161981Z | {
"verified": true,
"answer": 56,
"timestamp": "2026-02-08T03:32:54.200250Z"
} | d6c073 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 161,
"completion_tokens": 717
},
"timestamp": "2026-02-09T22:45:08.607Z",
"answer": 56
},
{
"id":... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "n... | {
"lo": -9.23,
"mid": -6.18,
"hi": -4.06
} | ||
fe6279 | antilemma_k3_v1_124444284_9072 | Let $n = 99332$. Define $x = \sum_{d \mid n} \phi(d)$, where the sum is taken over all positive divisors $d$ of $n$, and $\phi$ denotes Euler's totient function. Compute $x$. | 99,332 | graphs = [
Graph(
let={
"_n": Const(99332),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 4 | 0 | [
"K3"
] | 1 | 0.002 | 2026-02-08T12:11:05.010584Z | {
"verified": true,
"answer": 99332,
"timestamp": "2026-02-08T12:11:05.012487Z"
} | 00fcb7 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 117,
"completion_tokens": 556
},
"timestamp": "2026-02-16T03:32:24.230Z",
"answer": 29472
},
{
"id": 11,... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
9e9c5e | geo_count_lattice_rect_v1_124444284_3828 | Let $a = 144$ and $b = 272$. Define the rectangle $R$ as the set of all points $(x, y)$ such that $0 \leq x \leq a$ and $0 \leq y \leq b$. Compute the number of lattice points (points with integer coordinates) in $R$. | 39,585 | graphs = [
Graph(
let={
"a": Const(144),
"b": Const(272),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 2 | 0 | null | null | 0.002 | 2026-02-08T05:37:50.681003Z | {
"verified": true,
"answer": 39585,
"timestamp": "2026-02-08T05:37:50.682967Z"
} | dbc8ee | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 182,
"completion_tokens": 321
},
"timestamp": "2026-02-24T04:05:12.788Z",
"answer": 39585
},
{
"i... | 1 | [] | {
"lo": -4.93,
"mid": -2.91,
"hi": -0.71
} | ||||
087a34 | comb_count_surjections_v1_124444284_1074 | Let $n = 4$ and $k = 4$. The Stirling number of the second kind $S(n, k)$ counts the number of ways to partition a set of $n$ elements into $k$ nonempty unlabeled subsets. Compute $k! \cdot S(n, k)$, and let this value be $r$.
Now consider the set of all ordered pairs $(i, j)$ such that $1 \leq i \leq 44$ and $1 \leq ... | 2,000 | graphs = [
Graph(
let={
"n": Const(4),
"k": Const(4),
"result": Mul(Factorial(Ref("k")), Stirling2(n=Ref(name='n'), k=Ref(name='k'))),
"Q": Sub(CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(44)), right=IntegerRange(start=Const(1... | COMB | null | COUNT | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 009729 | comb_count_surjections_v1 | negation_mod | 4 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.004 | 2026-02-08T03:40:55.549669Z | {
"verified": true,
"answer": 2000,
"timestamp": "2026-02-08T03:40:55.554030Z"
} | 34561a | 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": 333
},
"timestamp": "2026-02-10T02:18:29.740Z",
"answer": 2000
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.97,
"mid": -3.96,
"hi": -1.93
} | ||
bfd49f | antilemma_k3_v1_717093673_2626 | Let $n = 91994$. Define $x$ to be the sum of Euler's totient function $\phi(d)$ over all positive divisors $d$ of $n$. Compute $x$. | 91,994 | graphs = [
Graph(
let={
"_n": Const(91994),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 2 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T17:00:58.680568Z | {
"verified": true,
"answer": 91994,
"timestamp": "2026-02-08T17:00:58.681324Z"
} | bb3331 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 103,
"completion_tokens": 727
},
"timestamp": "2026-02-16T08:53:42.782Z",
"answer": 13084
},
{
"id": 11,... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
d894f7 | comb_binomial_compute_v1_601307018_3893 | Let $k$ be the minimum value of $3a^2b + 3ab^2 + b^3$ over all ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 11$. Let $n$ be the number of non-negative integers $j$ with $0 \le j \le 65732$ such that $\binom{65732}{j} \bmod 2 = 1$. Let $R = \binom{n}{k}$. Find the remainder when $98451R$ is divided b... | 16,204 | graphs = [
Graph(
let={
"_n": Const(2),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(65732)), Eq(Mod(value=Binom(n=Const(65732), k=Var("j")), modulus=Ref("_n")), Const(1))), domain='nonnegative_integers')),
"k... | COMB | null | COMPUTE | sympy | POLY3_MIN | [
"POLY3_MIN",
"V8"
] | d933ba | comb_binomial_compute_v1 | null | 5 | 0 | [
"POLY3_MIN",
"V8"
] | 2 | 0.006 | 2026-03-10T04:30:50.051175Z | {
"verified": true,
"answer": 16204,
"timestamp": "2026-03-10T04:30:50.056720Z"
} | a07f1c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 236,
"completion_tokens": 5594
},
"timestamp": "2026-03-29T10:18:08.864Z",
"answer": 16204
},
{
"... | 1 | [
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "POLY3_MIN",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"s... | {
"lo": -3.34,
"mid": 0.9,
"hi": 4.9
} | ||
5c5011 | alg_poly_orbit_hensel_v1_601307018_1435 | Let $N \equiv a^2 - 22 \pmod{1849}$, $M \equiv N^2 - 22 \pmod{1849}$, $R \equiv M^2 - 22 \pmod{1849}$, $S \equiv R^2 - 22 \pmod{1849}$, and $T \equiv S^2 - 22 \pmod{1849}$. Find the number of non-negative integers $a$ with $0 \leq a \leq 1996919$ such that $T = a$, but $N \ne a$, $M \ne a$, $R \ne a$, and $S \ne a$. | 5,400 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Pow(Var("a"), Const(2)), Const(-22)), modulus=Const(1849)),
"p2": Mod(value=Sum(Pow(Ref("p1"), Const(2)), Const(-22)), modulus=Const(1849)),
"p3": Mod(value=Sum(Pow(Ref("p2"), Const(2)), Const(-22)), modulus=Const(1849)),
... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_orbit_hensel_v1 | null | 7 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.032 | 2026-03-10T02:09:25.848427Z | {
"verified": true,
"answer": 5400,
"timestamp": "2026-03-10T02:09:25.880049Z"
} | df7b15 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 265,
"completion_tokens": 20424
},
"timestamp": "2026-03-29T02:11:25.636Z",
"answer": 5
},
{
"i... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 2.84,
"mid": 4.95,
"hi": 7.12
} | ||
a6a539 | comb_sum_binomial_row_v1_717093673_1945 | Let $m = 44121$. Let $T$ be the set of all integers $t$ with $9 \leq t \leq 45$ for which there exist integers $a$ and $b$ such that $1 \leq a \leq 12$, $1 \leq b \leq 3$, and $t = 2a + 7b$. Let $n$ be the number of prime numbers less than or equal to the number of elements in $T$. Compute $2^n$, then find the remainde... | 79,521 | graphs = [
Graph(
let={
"_m": Const(44121),
"_n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=12)), Geq(left=... | NT | null | SUM | sympy | LIN_FORM | [
"LIN_FORM/COUNT_PRIMES"
] | a88a1b | comb_sum_binomial_row_v1 | null | 5 | 0 | [
"COUNT_PRIMES",
"LIN_FORM"
] | 2 | 0.006 | 2026-02-08T16:24:52.425621Z | {
"verified": true,
"answer": 79521,
"timestamp": "2026-02-08T16:24:52.432007Z"
} | c021fb | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 173,
"completion_tokens": 3098
},
"timestamp": "2026-02-17T03:04:08.036Z",
"answer": 79521
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "ok_later"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
c19bc5 | comb_sum_binomial_row_v1_865884756_4139 | Let $ n_1 $ be a positive integer. Consider the set of all integers $ n_1 $ such that $ 1 \leq n_1 \leq 16 $ and $ 7 $ divides the $ n_1 $-th Fibonacci number. Let $ c $ be the number of elements in this set. Define $ \alpha = c^{12} $. Compute the remainder when $ 92221 \cdot \alpha $ is divided by $ 64777 $. | 22,529 | graphs = [
Graph(
let={
"_n": Const(64777),
"n": Const(12),
"result": Pow(CountOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(1)), Leq(Var("n1"), Const(16)), Divides(divisor=Const(7), dividend=Fibonacci(arg=Var(name='n1')))))), Ref("n")),
... | ALG | NT | SUM | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE"
] | 66de3c | comb_sum_binomial_row_v1 | null | 5 | 0 | [
"COUNT_FIB_DIVISIBLE"
] | 1 | 0.002 | 2026-02-08T17:45:47.090254Z | {
"verified": true,
"answer": 22529,
"timestamp": "2026-02-08T17:45:47.091840Z"
} | c9e73c | 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": 1641
},
"timestamp": "2026-02-18T07:01:05.414Z",
"answer": 22529
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V3",... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
eb8fe4 | antilemma_k3_v1_1918700295_795 | Let $n = 13213$. Compute the sum of $\phi(d)$ over all positive divisors $d$ of $n$, where $\phi$ denotes Euler's totient function. | 13,213 | graphs = [
Graph(
let={
"_n": Const(13213),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T03:30:22.572423Z | {
"verified": true,
"answer": 13213,
"timestamp": "2026-02-08T03:30:22.572970Z"
} | a34ad0 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 149,
"completion_tokens": 745
},
"timestamp": "2026-02-10T14:44:38.932Z",
"answer": 13213
},
{
"i... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V5",
"sta... | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
247777 | diophantine_product_count_v1_898971024_3079 | Let $k = 240$ and $U = 125$. Compute the number of positive integers $x \leq U$ such that $x$ divides $k$ and $\frac{k}{x} \leq U$. | 18 | graphs = [
Graph(
let={
"k": Const(240),
"upper": Const(125),
"result": CountOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), Const(1)), Leq(Var("x"), Ref("upper")), Divides(divisor=Var("x"), dividend=Ref("k")), Leq(Div(Ref("k"), Var("x")), Ref("upper"))... | NT | null | COUNT | sympy | VIETA_SUM | [
"B3"
] | 0cd20d | diophantine_product_count_v1 | null | 4 | 0 | [
"B3",
"VIETA_SUM"
] | 2 | 0.133 | 2026-02-08T17:08:44.990167Z | {
"verified": true,
"answer": 18,
"timestamp": "2026-02-08T17:08:45.123567Z"
} | d3faa2 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 93,
"completion_tokens": 1959
},
"timestamp": "2026-02-17T19:30:22.749Z",
"answer": 18
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
73b65a | modular_count_residue_v1_1520064083_4290 | Let $m = 1 + 2 + 3 + 4 + 5$ and $r = 8$. Let $\text{result}$ be the number of positive integers $n$ such that $1 \leq n \leq 32099$ and $n \equiv r \pmod{m}$. Compute the remainder when $68347 \cdot \text{result}$ is divided by $84295$. | 10,755 | graphs = [
Graph(
let={
"upper": Const(32099),
"m": Summation(var="k", start=Const(1), end=Const(5), expr=Var("k")),
"r": Const(8),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod... | NT | null | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | modular_count_residue_v1 | null | 3 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 3.076 | 2026-02-08T06:11:33.102419Z | {
"verified": true,
"answer": 10755,
"timestamp": "2026-02-08T06:11:36.178328Z"
} | 334000 | 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": 1739
},
"timestamp": "2026-02-12T21:19:10.870Z",
"answer": 10755
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
6ff308 | nt_num_divisors_compute_v1_458359167_1725 | Let $n = 12544$. Let $r$ be the number of positive divisors of $n$. Compute the value of $$\sum_{i=0}^{\text{num\_digits}(r) - 1} \left( \text{digit}_i(r) \cdot (i+1)^{\sum_{d \mid 2} \phi(d)} \right) + 26896$$ where $\text{digit}_i(r)$ denotes the $i$-th decimal digit of $r$ (starting from the units place at $i=0$), a... | 26,911 | graphs = [
Graph(
let={
"n": Const(12544),
"result": NumDivisors(n=Ref("n")),
"_c": Const(26896),
"Q": Sum(Summation(var="i", start=Const(0), end=Sub(NumDigits(x=Abs(arg=Ref(name='result')), base=None), Const(1)), expr=Mul(Digit(x=Abs(arg=Ref(name='result')), ... | NT | null | COMPUTE | sympy | K3 | [
"K3"
] | 57059b | nt_num_divisors_compute_v1 | digits_weighted_mod | 3 | 0 | [
"K3"
] | 1 | 0.002 | 2026-02-08T04:49:21.224054Z | {
"verified": true,
"answer": 26911,
"timestamp": "2026-02-08T04:49:21.226224Z"
} | 85671d | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 256,
"completion_tokens": 774
},
"timestamp": "2026-02-11T22:10:51.387Z",
"answer": 26911
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
817226 | geo_count_lattice_rect_v1_2051736721_3146 | Compute the number of lattice points $(x, y)$ such that $0 \leq x \leq 240$ and $0 \leq y \leq 222$. | 53,743 | graphs = [
Graph(
let={
"a": Const(240),
"b": Const(222),
"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 | 2026-02-08T17:08:32.828311Z | {
"verified": true,
"answer": 53743,
"timestamp": "2026-02-08T17:08:32.829624Z"
} | 92cc2e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 81,
"completion_tokens": 465
},
"timestamp": "2026-02-17T20:41:24.560Z",
"answer": 53743
},
{
... | 1 | [] | {
"lo": -4.1,
"mid": -1.76,
"hi": 1.32
} | ||||
0f1b45 | algebra_poly_eval_v1_1218484723_5911 | Let $z$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 25$ such that $50a^2 + 50b^2 = 16250$. Let $R = z^2 + 3z - 7$. Find the remainder when $93617R$ is divided by $85955$. | 16,294 | graphs = [
Graph(
let={
"_n": Const(25),
"z": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(25)), Geq(Var("b"), Const(1)), Leq(Var("b"), Ref("_n")), Eq(Sum(Mul(Const(50), Pow(Var("a"), Const(2))), Mu... | ALG | null | COMPUTE | sympy | QF_PSD_COUNT | [
"QF_PSD_COUNT"
] | 09ce67 | algebra_poly_eval_v1 | null | 3 | 0 | [
"QF_PSD_COUNT"
] | 1 | 0.002 | 2026-02-25T07:30:03.605410Z | {
"verified": true,
"answer": 16294,
"timestamp": "2026-02-25T07:30:03.607827Z"
} | 3d32db | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 190,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T23:26:26.892Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT",
"status": "ok"
}
] | {
"lo": 1.53,
"mid": 4.7,
"hi": 7.23
} | ||
2cbd22 | geo_count_lattice_rect_v1_1520064083_7584 | Compute the number of lattice points $(x,y)$ such that $0 \leq x \leq 190$ and $0 \leq y \leq 84$. | 16,235 | graphs = [
Graph(
let={
"a": Const(190),
"b": Const(84),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 4 | 0 | null | null | 0 | 2026-02-08T09:10:23.600841Z | {
"verified": true,
"answer": 16235,
"timestamp": "2026-02-08T09:10:23.601303Z"
} | 23f5b5 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 147,
"completion_tokens": 160
},
"timestamp": "2026-02-24T10:45:15.788Z",
"answer": 16235
},
{
"i... | 1 | [] | {
"lo": -5.97,
"mid": -3.97,
"hi": -1.93
} | ||||
ed7a5b | lin_form_endings_v1_677425708_2943 | Let $a = 98$ and $b = 56$. Define $\step = \gcd(a, b)$. Let $k = 497$ and compute $r = \left\lfloor \frac{k}{\gcd(k, \step)} \right\rfloor$. Multiply $r$ by $7622$, and let the result be $s$. Find the remainder when $s$ is divided by $59380$. | 6,742 | graphs = [
Graph(
let={
"a_coeff": Const(98),
"b_coeff": Const(56),
"k_val": Const(497),
"step": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"_inner_result": Floor(Div(Ref("k_val"), GCD(a=Ref("k_val"), b=Ref("step")))),
"_scale_k": Const(7... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 3 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T05:22:53.148136Z | {
"verified": true,
"answer": 6742,
"timestamp": "2026-02-08T05:22:53.149143Z"
} | b355ea | 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": 576
},
"timestamp": "2026-02-12T07:23:07.692Z",
"answer": 6742
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
6471fd | nt_count_coprime_and_v1_1520064083_4937 | Let $m = 14$ and let $d_0$ be the smallest divisor of $6125$ that is at least $2$. Let $k_1 = 8$ and define $$ k_2 = \sum_{k=1}^{d_0} \phi(k) \left\lfloor \frac{1}{k} \cdot \left| \left\{ n \in \mathbb{Z}^+ : 1 \leq n \leq 120,\ m \mid F_n \right\} \right| \right\rfloor, $$ where $F_n$ denotes the $n$th Fibonacci numbe... | 23,075 | graphs = [
Graph(
let={
"_m": Const(14),
"_n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(6125))))),
"upper": Const(86531),
"k1": Const(8),
"k2": Summation(var="k", star... | NT | null | COUNT | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE/K2",
"MIN_PRIME_FACTOR/K2"
] | 8bd614 | nt_count_coprime_and_v1 | null | 7 | 0 | [
"COUNT_FIB_DIVISIBLE",
"K2",
"MIN_PRIME_FACTOR"
] | 3 | 8.583 | 2026-02-08T06:31:15.305050Z | {
"verified": true,
"answer": 23075,
"timestamp": "2026-02-08T06:31:23.888331Z"
} | 236192 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 227,
"completion_tokens": 2356
},
"timestamp": "2026-02-13T01:01:32.013Z",
"answer": 23075
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K2",
"status": "ok_later"
},
{
"lemma": "MAX_PRIME_BELOW",
"st... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
adf92a | algebra_poly_eval_v1_601307018_7036 | Let $b = 5$. Compute
$$
-1 \cdot b^3 + \left|\left\{ (a, b_1) : 1 \le a \le 30,\, 1 \le b_1 \le 30,\, 64a^3 + 108a b_1^2 + 144a^2 b_1 + 27b_1^3 = 1225043 \right\}\right| \cdot b^2 + 7b + 10.
$$ | 120 | graphs = [
Graph(
let={
"_n": Const(10),
"b": Const(5),
"result": Sum(Mul(Const(-1), Pow(Ref("b"), Const(3))), Mul(CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b1")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(30)), Geq(Var("b1"), Cons... | ALG | null | COMPUTE | sympy | POLY3_COUNT | [
"POLY3_COUNT"
] | 355dbe | algebra_poly_eval_v1 | null | 6 | 0 | [
"POLY3_COUNT"
] | 1 | 0.008 | 2026-03-10T07:40:59.981682Z | {
"verified": true,
"answer": 120,
"timestamp": "2026-03-10T07:40:59.989922Z"
} | 23598a | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 225,
"completion_tokens": 1456
},
"timestamp": "2026-04-19T05:49:42.051Z",
"answer": 120
},
{
"i... | 1 | [
{
"lemma": "POLY3_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
e8db89 | comb_count_derangements_v1_784195855_3524 | Let $P$ be the set of all positive integers $p$ for which there exists a positive integer $q > p$ such that $pq = 9261000$ and $\gcd(p, q) = 1$. Let $N$ be the number of elements in $P$. Define $n$ to be the largest prime number at most $N$. Compute the number of derangements of $n$ elements, denoted $!n$. | 1,854 | graphs = [
Graph(
let={
"_n": Const(2),
"n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Va... | NT | COMB | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/MAX_PRIME_BELOW"
] | 2248fc | comb_count_derangements_v1 | null | 7 | 0 | [
"COPRIME_PAIRS",
"MAX_PRIME_BELOW"
] | 2 | 0.001 | 2026-02-08T06:28:24.880255Z | {
"verified": true,
"answer": 1854,
"timestamp": "2026-02-08T06:28:24.881735Z"
} | 800205 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 139,
"completion_tokens": 2049
},
"timestamp": "2026-02-13T00:40:58.002Z",
"answer": 1854
},
{... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"stat... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
5801b2 | comb_count_surjections_v1_784195855_5091 | Let $n = 7$ and $k = 5$. Define $r = k! \cdot S(n,k)$, where $S(n,k)$ is the number of ways to partition a set of $n$ elements into $k$ nonempty subsets. Let $T$ be the set of all integers $t$ such that $5 \leq t \leq 17$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 4$, $1 \leq b \leq 3$, and $t = ... | 5 | graphs = [
Graph(
let={
"n": Const(7),
"k": Const(5),
"result": Mul(Factorial(Ref("k")), Stirling2(n=Ref(name='n'), k=Ref(name='k'))),
"Q": Bell(Mod(value=Abs(arg=Ref(name='result')), modulus=CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var... | COMB | null | COUNT | sympy | COMB1 | [
"LIN_FORM"
] | 1ae498 | comb_count_surjections_v1 | bell_mod | 6 | 0 | [
"COMB1",
"LIN_FORM"
] | 2 | 0.009 | 2026-02-08T07:39:46.873815Z | {
"verified": true,
"answer": 5,
"timestamp": "2026-02-08T07:39:46.883295Z"
} | cea2c0 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 303,
"completion_tokens": 1247
},
"timestamp": "2026-02-24T08:20:04.766Z",
"answer": 5
},
{
"id":... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status... | {
"lo": -4.92,
"mid": -2.91,
"hi": -0.68
} | ||
adf8ff | modular_modexp_compute_v1_1520064083_1788 | Let $a = 2$. Let $e$ be the sum of all positive integers $n$ such that $1 \leq n \leq 1010$ and $n \equiv 0 \pmod{101}$. Let $m = 50000$. Compute $a^e \bmod m$, that is, the remainder when $a^e$ is divided by $m$. | 3,968 | graphs = [
Graph(
let={
"_n": Const(1010),
"a": Const(2),
"e": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_n")), Eq(Mod(value=Var("n"), modulus=Const(101)), Const(0))))),
"m": Const(50000),
"... | NT | null | COMPUTE | sympy | SUM_DIVISIBLE | [
"SUM_DIVISIBLE"
] | 02dbe3 | modular_modexp_compute_v1 | null | 4 | 0 | [
"SUM_DIVISIBLE"
] | 1 | 0.001 | 2026-02-08T04:16:29.353126Z | {
"verified": true,
"answer": 3968,
"timestamp": "2026-02-08T04:16:29.354284Z"
} | 7c16f5 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 196,
"completion_tokens": 3398
},
"timestamp": "2026-02-10T16:03:33.219Z",
"answer": 3968
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_DIVISIBLE",
"status": "... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
184fc7 | diophantine_fbi2_count_v1_865884756_2655 | Let $k$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 3600$. Find the number of integers $d$ such that $3 \leq d \leq 102$, $d$ divides $k$, $\frac{k}{d} \geq 2$, and $\frac{k}{d} \leq p$, where $p$ is the largest prime $n$ satisfying $2 \leq n \leq 101$. Compute t... | 13 | graphs = [
Graph(
let={
"_n": Const(2),
"k": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(3600)))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW",
"B3"
] | 78ed98 | diophantine_fbi2_count_v1 | null | 6 | 0 | [
"B3",
"MAX_PRIME_BELOW"
] | 2 | 0.01 | 2026-02-08T16:51:57.638696Z | {
"verified": true,
"answer": 13,
"timestamp": "2026-02-08T16:51:57.648834Z"
} | a867d4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 160,
"completion_tokens": 1256
},
"timestamp": "2026-02-17T14:35:10.989Z",
"answer": 13
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
03fc67 | comb_count_surjections_v1_1125832087_1328 | Let $T$ be the set of all integers $t$ such that $5 \leq t \leq 14$, and there exist positive integers $a$ and $b$ with $1 \leq a \leq 2$, $1 \leq b \leq 4$, and $t = 3a + 2b$. Let $n$ be the number of elements in $T$. Compute the value of $4! \cdot S(n, 4)$, where $S(n, 4)$ denotes the Stirling number of the second ki... | 40,824 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=2)), Geq(left=Var(name='b'), right=Const(value=1... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_count_surjections_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T03:41:25.151370Z | {
"verified": true,
"answer": 40824,
"timestamp": "2026-02-08T03:41:25.152809Z"
} | a89522 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 234,
"completion_tokens": 1365
},
"timestamp": "2026-02-10T15:24:06.883Z",
"answer": 40824
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
... | {
"lo": -4.92,
"mid": -2.9,
"hi": -0.7
} | ||
50cdb2 | diophantine_fbi2_min_v1_784195855_2693 | Let $n = 4$ and $k = 8$. Define $s$ to be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 81$.
Determine the smallest integer $d$ such that $n \leq d \leq s$, $d$ divides $k$, and $\frac{k}{d} \geq 2$. | 4 | graphs = [
Graph(
let={
"_n": Const(4),
"k": Const(8),
"upper": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(81)))), expr=... | NT | null | EXTREMUM | sympy | V1 | [
"V1",
"B3"
] | 07b21c | diophantine_fbi2_min_v1 | null | 4 | 0 | [
"B3",
"V1"
] | 2 | 0.009 | 2026-02-08T05:56:11.704338Z | {
"verified": true,
"answer": 4,
"timestamp": "2026-02-08T05:56:11.713120Z"
} | a8b459 | 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": 597
},
"timestamp": "2026-02-12T17:01:01.277Z",
"answer": 4
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K5",
"status": "same_pattern_wrong"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
6ccc2d | comb_count_derangements_v1_124444284_6301 | Let $n = 7$. Let $r = !n$, the $n$th subfactorial. Let $D$ be the set of all integers $d \geq 2$ that divide $537251$. Let $m$ be the smallest element of $D$. Compute $B_k$, where $k$ is the remainder when $|r|$ is divided by $m$. | 203 | graphs = [
Graph(
let={
"_n": Const(2),
"n": Const(7),
"result": Subfactorial(arg=Ref(name='n')),
"Q": Bell(Mod(value=Abs(arg=Ref(name='result')), modulus=MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"... | NT | COMB | COUNT | sympy | MAX_PRIME_BELOW | [
"MIN_PRIME_FACTOR"
] | 58d7e9 | comb_count_derangements_v1 | bell_mod | 6 | 0 | [
"MAX_PRIME_BELOW",
"MIN_PRIME_FACTOR"
] | 2 | 0.014 | 2026-02-08T08:16:55.100167Z | {
"verified": true,
"answer": 203,
"timestamp": "2026-02-08T08:16:55.113837Z"
} | 7fccfe | 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": 1167
},
"timestamp": "2026-02-13T16:32:29.904Z",
"answer": 203
},
{
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K15",
"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
} | ||
00c8d7 | nt_sum_divisors_mod_v1_1520064083_7277 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 396900$. Let $n$ be the minimum value of $x + y$ over all such pairs. Compute the remainder when the sum of all positive divisors of $n$ is divided by $10477$. | 4,368 | graphs = [
Graph(
let={
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(396900)))), expr=Sum(Var("x"), Var("y")))),
"M": Const(10477... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_divisors_mod_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.002 | 2026-02-08T08:52:55.478681Z | {
"verified": true,
"answer": 4368,
"timestamp": "2026-02-08T08:52:55.480236Z"
} | 2b652c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 115,
"completion_tokens": 2069
},
"timestamp": "2026-02-13T22:52:45.556Z",
"answer": 4368
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "n... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
5bc95a | comb_count_permutations_fixed_v1_2051736721_308 | Let $n$ be the sum of all positive integers at most $5$ that are divisible by $5$. Let $k = \sum_{k_1=1}^{2} \phi(k_1) \left\lfloor \frac{2}{k_1} \right\rfloor$, where $\phi$ denotes Euler's totient function. Compute $\binom{n}{k} \cdot !(n - k)$, where $!m$ denotes the number of derangements of $m$ elements. Take the ... | 34,373 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(11),
"n": SumOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(1)), Leq(Var("n1"), Const(5)), Eq(Mod(value=Var("n1"), modulus=Const(5)), Const(0))))),
"k": Summation(var="k1", start=C... | NT | COMB | COUNT | sympy | MIN_PRIME_FACTOR | [
"SUM_DIVISIBLE",
"K2"
] | a10886 | comb_count_permutations_fixed_v1 | null | 6 | 0 | [
"K2",
"MIN_PRIME_FACTOR",
"SUM_DIVISIBLE"
] | 3 | 0.028 | 2026-02-08T15:20:54.910251Z | {
"verified": true,
"answer": 34373,
"timestamp": "2026-02-08T15:20:54.937820Z"
} | c81350 | 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": 719
},
"timestamp": "2026-02-16T04:23:24.638Z",
"answer": 34373
},
{... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
200540 | algebra_quadratic_discriminant_v1_655260480_497 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 25$. Define $c$ to be the minimum value of $x + y$ as $(x, y)$ ranges over $S$. Compute the value of $(-9)^2 - 4 \cdot (-9) \cdot c$. | 441 | graphs = [
Graph(
let={
"_n": Const(4),
"a": Const(-9),
"b": Const(-9),
"c": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | algebra_quadratic_discriminant_v1 | null | 3 | 0 | [
"B3"
] | 1 | 0.003 | 2026-02-08T15:24:47.409534Z | {
"verified": true,
"answer": 441,
"timestamp": "2026-02-08T15:24:47.412645Z"
} | 1803b7 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 121,
"completion_tokens": 342
},
"timestamp": "2026-02-16T05:31:03.111Z",
"answer": 441
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
36488a | algebra_poly_eval_v1_1439011603_576 | Let $y = 25$. Define $\text{result}$ to be the value of $$6 \cdot 25^k - 6 \cdot 25 - 3,$$ where $k$ is the number of positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 12$, $\gcd(p, q) = 1$, and $p < q$. Let $Q = 33124 - \text{result}$. Find the value of $Q$. | 29,527 | graphs = [
Graph(
let={
"_n": Const(6),
"y": Const(25),
"result": Sum(Mul(Ref("_n"), Pow(Ref("y"), 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')), r... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | algebra_poly_eval_v1 | null | 3 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.003 | 2026-02-08T15:35:48.465827Z | {
"verified": true,
"answer": 29527,
"timestamp": "2026-02-08T15:35:48.469008Z"
} | 613340 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 172,
"completion_tokens": 387
},
"timestamp": "2026-02-16T06:11:37.043Z",
"answer": -60473
},
{
"id": 1... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}... | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
26d65a | comb_catalan_compute_v1_153355830_472 | Let $n$ be the number of integers $t$ with $10 \leq t \leq 34$ for which there exist positive integers $a$ and $b$ such that $1 \leq a \leq 3$, $1 \leq b \leq 4$, and $t = 6a + 4b$.
Let $C_n$ denote the $n$-th Catalan number, and let $c = 10572$. Define $Q$ to be the remainder when $c \cdot C_n$ is divided by $90611$.... | 75,354 | graphs = [
Graph(
let={
"_n": Const(90611),
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=3)), Geq(left=Va... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_catalan_compute_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.003 | 2026-02-08T03:07:30.973381Z | {
"verified": true,
"answer": 75354,
"timestamp": "2026-02-08T03:07:30.976468Z"
} | 5d5bfe | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 244,
"completion_tokens": 1934
},
"timestamp": "2026-02-10T12:54:49.281Z",
"answer": 75354
},
{
"... | 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_SUM",
... | {
"lo": -0.05,
"mid": 2.89,
"hi": 5.27
} | ||
51c53b | nt_count_gcd_equals_v1_865884756_231 | Let $A$ be the set of all positive integers $n \le 7744$ such that $\gcd(n, 293) = 293$. Let $r$ be the number of elements in $A$. Let $P$ be the set of all ordered pairs $(x,y)$ of positive integers such that $x + y = 164$. Let $m$ be the maximum value of $xy$ over all pairs in $P$. Compute $$\sum_{i=0}^{d-1} \left( \... | 6,738 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": Const(7744),
"k": Const(293),
"d": Const(293),
"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 | B1 | [
"B1"
] | 51a773 | nt_count_gcd_equals_v1 | digits_weighted_mod | 4 | 0 | [
"B1"
] | 1 | 0.755 | 2026-02-08T15:16:08.176673Z | {
"verified": true,
"answer": 6738,
"timestamp": "2026-02-08T15:16:08.931796Z"
} | d3d9a4 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 263,
"completion_tokens": 2984
},
"timestamp": "2026-02-10T05:52:41.962Z",
"answer": 6750
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
}
] | {
"lo": 3.24,
"mid": 5.68,
"hi": 8.81
} | ||
a97387 | nt_count_digit_sum_v1_865884756_426 | Let $S$ be the set of all positive integers $n$ such that $1 \le n \le 37$ and the sum of the digits of $n$ is odd. Let $T$ be the set of all positive integers $n_1$ such that $1 \le n_1 \le 126736$ and the sum of the digits of $n_1$ equals the number of elements in $S$. Let $U$ be the set of all positive integers $t$ ... | 57,262 | graphs = [
Graph(
let={
"_n": Const(63253),
"upper": Const(126736),
"target_sum": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(37)), Eq(Mod(value=DigitSum(Var("n")), modulus=Const(2)), Const(1))))),
"re... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM",
"L3B"
] | 047cdd | nt_count_digit_sum_v1 | negation_mod | 5 | 0 | [
"L3B",
"LIN_FORM"
] | 2 | 6.716 | 2026-02-08T15:21:35.482240Z | {
"verified": true,
"answer": 57262,
"timestamp": "2026-02-08T15:21:42.198482Z"
} | 66e88b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 229,
"completion_tokens": 5462
},
"timestamp": "2026-02-16T06:19:25.884Z",
"answer": 57262
},
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3B",
"status": "ok"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIF... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
f7d5eb | algebra_poly_eval_v1_1874849503_1264 | Let $m = 8$. Compute the value of
$$
4m^4 + 3m^{\sum_{k=1}^{2} \phi(k) \left\lfloor \frac{2}{k} \right\rfloor} - m^2 + 4m - 2.
$$ | 17,886 | graphs = [
Graph(
let={
"_n": Const(2),
"m": Const(8),
"result": Sum(Mul(Const(4), Pow(Ref("m"), Const(4))), Mul(Const(3), Pow(Ref("m"), Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(2), Var("k"))))))), Mul(Const(-1), Pow... | NT | null | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | algebra_poly_eval_v1 | null | 5 | 0 | [
"K2"
] | 1 | 0.003 | 2026-02-08T13:43:48.796731Z | {
"verified": true,
"answer": 17886,
"timestamp": "2026-02-08T13:43:48.800174Z"
} | 4765ea | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 177,
"completion_tokens": 565
},
"timestamp": "2026-02-10T02:55:19.496Z",
"answer": 17886
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
}
] | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
54bfc7 | modular_inverse_v1_1874849503_1616 | Let $a$ be the smallest divisor of $55595131$ that is at least $2$. Let $m = 577$ and $u = 576$. Determine the value of the smallest positive integer $x \le u$ such that $ax \equiv 1 \pmod{m}$. | 475 | graphs = [
Graph(
let={
"_n": Const(2),
"a": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(55595131))))),
"m": Const(577),
"upper": Const(576),
"result": MinOverSet(set=So... | NT | null | EXTREMUM | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | modular_inverse_v1 | null | 4 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.046 | 2026-02-08T14:00:14.997673Z | {
"verified": true,
"answer": 475,
"timestamp": "2026-02-08T14:00:15.043476Z"
} | 981f77 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 109,
"completion_tokens": 3619
},
"timestamp": "2026-02-15T23:07:36.384Z",
"answer": 475
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CON... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
671e92 | diophantine_fbi2_min_v1_1978505735_6234 | Let $c$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq = 2700$, $\gcd(p, q) = 1$, and $p < q$. Let $T$ be the set of integers $t$ with $21 \leq t \leq 2960$ that can be written as $5a + 7b + 9$ for some positive integers $a \leq 523$ and $b \leq 48$. Let $k$ be the nu... | 9,876 | graphs = [
Graph(
let={
"_m": Const(81),
"_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=2700)), Eq(left=GCD(a=Var(name='p'), b=Var(name... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/C2",
"LIN_FORM/C2"
] | 5accb4 | diophantine_fbi2_min_v1 | null | 6 | 0 | [
"C2",
"COPRIME_PAIRS",
"LIN_FORM"
] | 3 | 0.013 | 2026-02-08T19:30:54.995762Z | {
"verified": true,
"answer": 9876,
"timestamp": "2026-02-08T19:30:55.009210Z"
} | 462fb4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 239,
"completion_tokens": 6440
},
"timestamp": "2026-02-18T22:34:14.439Z",
"answer": 9876
},
{... | 1 | [
{
"lemma": "C2",
"status": "ok_later"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
175e86 | alg_qf_psd_min_v1_601307018_5591 | Let $A = \left|\{ v \geq 1 : v \leq 10676 \text{ and } v = 17a^2 + 16b^2 - 32ab \text{ for some integers } a, b \in [1,26] \}\right|$. Find the minimum value of $22590ab + 12801b^2 + 37650a^2$ over all ordered pairs $(a, b)$ of positive integers with $1 \leq a \leq A$ and $1 \leq b \leq 450$. | 73,041 | graphs = [
Graph(
let={
"_n": Const(22590),
"result": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), CountOverSet(set=SolutionsSet(var=Var("v"), condition=And(Geq(Var("v"), Const(1)), Leq(Var("... | ALG | null | COMPUTE | sympy | QF_PSD_DISTINCT | [
"QF_PSD_DISTINCT"
] | a8f9cb | alg_qf_psd_min_v1 | null | 5 | 0 | [
"QF_PSD_DISTINCT"
] | 1 | 0.37 | 2026-03-10T06:11:35.658820Z | {
"verified": true,
"answer": 73041,
"timestamp": "2026-03-10T06:11:36.028429Z"
} | c262f8 | 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": 2271
},
"timestamp": "2026-04-19T02:27:47.034Z",
"answer": 73041
},
{
... | 2 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_DISTINCT",
"status": "ok"
}
] | {
"lo": -10,
"mid": -5.89,
"hi": -1.79
} | ||
d984d7 | comb_count_surjections_v1_124444284_5351 | Let $k$ be the number of ordered pairs $(i, j)$ such that $i \in \{1, 2\}$ and $j \in \{1, 2\}$. Let $r = k! \cdot S(4, k)$, where $S(n, k)$ denotes the number of ways to partition a set of $n$ elements into $k$ nonempty unlabeled subsets. Compute the remainder when $51743 \cdot r$ is divided by 79734. | 45,822 | graphs = [
Graph(
let={
"_n": Const(51743),
"n": Const(4),
"k": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(2)), right=IntegerRange(start=Const(1), end=Const(2)))),
"result": Mul(Factorial(Ref("k")), Stirling2(n=Ref(name='n'),... | COMB | null | COUNT | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | comb_count_surjections_v1 | null | 4 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.001 | 2026-02-08T06:33:09.382037Z | {
"verified": true,
"answer": 45822,
"timestamp": "2026-02-08T06:33:09.383298Z"
} | cda146 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 219,
"completion_tokens": 843
},
"timestamp": "2026-02-24T06:24:31.350Z",
"answer": 45822
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
... | {
"lo": -3.84,
"mid": -1.69,
"hi": 1.09
} | ||
5ff0fd | comb_count_partitions_v1_1125832087_1143 | Let $n$ be the number of integers $t$ such that $8 \leq t \leq 57$ and
\[
t = 5a + 3b
\]
for some integers $a$ and $b$ with $1 \leq a \leq 3$ and $1 \leq b \leq 14$. Compute the number of integer partitions of $n$. | 53,174 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=3)), Geq(left=Var(name='b'), right=Const(value=1... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_count_partitions_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T03:33:44.714385Z | {
"verified": true,
"answer": 53174,
"timestamp": "2026-02-08T03:33:44.715973Z"
} | 51c77c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 198,
"completion_tokens": 32768
},
"timestamp": "2026-02-23T22:34:32.521Z",
"answer": null
},
{
... | 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": 1.97,
"mid": 4.36,
"hi": 6.69
} | ||
26cbce | nt_num_divisors_compute_v1_1918700295_4645 | Let $T$ be the set of all integers $t$ such that $23 \leq t \leq 77$ and
$$
t = 6a + 9b + 8
$$
for some integers $a$ and $b$ with $1 \leq a \leq 7$ and $1 \leq b \leq 3$. Let $n = |T|$. Compute the number of positive divisors of $n$. | 2 | 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=7)), Geq(left=Var(name='b'), right=Const(value=1... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_num_divisors_compute_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T09:29:38.006120Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-02-08T09:29:38.007112Z"
} | 35174c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 139,
"completion_tokens": 2172
},
"timestamp": "2026-02-14T04:34:29.980Z",
"answer": 2
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
... | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
f2f1f1 | lte_diff_endings_v1_1742523217_2419 | Let $a = 73$ and $b = 10$. Define $d = a - b$. Let $v$ be the largest integer such that $3^v$ divides $d$. Let $e = 10 - v$. Compute $3^e$. | 6,561 | graphs = [
Graph(
let={
"a_val": Const(73),
"b_val": Const(10),
"p_val": Const(3),
"T_val": Const(10),
"diff": Sub(Ref("a_val"), Ref("b_val")),
"vp_diff": MaxKDivides(target=Ref("diff"), base=Ref("p_val")),
"exp": Sub(Ref("T... | NT | null | COMPUTE | sympy | LTE_DIFF | [
"LTE_DIFF"
] | cf8260 | lte_diff_endings_v1 | null | 3 | null | [
"LTE_DIFF"
] | 1 | 0 | 2026-02-08T04:46:03.733811Z | {
"verified": true,
"answer": 6561,
"timestamp": "2026-02-08T04:46:03.734285Z"
} | df1f0b | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 152,
"completion_tokens": 171
},
"timestamp": "2026-02-18T13:12:11.238Z",
"answer": 6561
}
] | 2 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
ca4699 | comb_count_permutations_fixed_v1_153355830_1849 | Let $n = 8$. Let $k$ be the smallest divisor of $1225$ that is at least $2$. Define $D$ to be the number of derangements of $n - k$ elements, and let $C = \binom{n}{k} \cdot D$. Compute the remainder when $55339 \cdot C$ is divided by $71750$. | 27,468 | graphs = [
Graph(
let={
"_n": Const(71750),
"n": Const(8),
"k": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(1225))))),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=S... | NT | COMB | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | comb_count_permutations_fixed_v1 | null | 5 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.002 | 2026-02-08T06:39:16.349837Z | {
"verified": true,
"answer": 27468,
"timestamp": "2026-02-08T06:39:16.351561Z"
} | 264692 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 126,
"completion_tokens": 1287
},
"timestamp": "2026-02-13T04:28:13.906Z",
"answer": 27468
},
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V5",
"status": "... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
df096a | geo_count_lattice_triangle_v1_1520064083_7529 | Let $A$, $B$, and $C$ be the points $(0, 0)$, $(169, 81)$, and $(7, 100)$, respectively. The area of triangle $ABC$ is half of $|169 \cdot 100 - 7 \cdot 81|$. Let $I$ be twice the area of triangle $ABC$. Let $B$ be the number of lattice points on the boundary of triangle $ABC$, computed as the sum of the greatest commo... | 8,166 | graphs = [
Graph(
let={
"_n": Const(169),
"area_2x": Abs(arg=Sum(Mul(Const(value=169), Const(value=100)), Mul(Const(value=7), Sub(left=Const(value=0), right=Const(value=81))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=169)), b=Abs(arg=Const(value=81))), GCD(a=Abs(arg=Su... | ALG | NT | COUNT | sympy | C4 | [
"C4"
] | 08d162 | geo_count_lattice_triangle_v1 | null | 5 | 0 | [
"C4"
] | 1 | 0.004 | 2026-02-08T09:06:05.382747Z | {
"verified": true,
"answer": 8166,
"timestamp": "2026-02-08T09:06:05.386895Z"
} | 38431a | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 213,
"completion_tokens": 905
},
"timestamp": "2026-02-15T20:34:38.360Z",
"answer": 4081
},
{
"id": 11,
... | 1 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.34
} | ||
9986ff | nt_count_intersection_v1_655260480_1568 | Let $N = \sum_{d \mid 5000} \phi(d)$. Let $a$ be the smallest divisor of $5000567$ that is at least 2. Compute the number of positive integers $n \leq N$ such that $a$ divides $n$ and $\gcd(n, 6) = 1$. Let this count be $r$. Find the remainder when $44121 \cdot r$ is divided by $93598$. | 16,813 | graphs = [
Graph(
let={
"_n": Const(5000),
"N": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"a": MinOverSet(set=SolutionsSet(var=Var("d1"), condition=And(Geq(Var("d1"), Const(2)), Divides(divisor=Var("d1"), dividend=Const(5000567))))),
... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR",
"K3"
] | aa151e | nt_count_intersection_v1 | null | 5 | 0 | [
"K3",
"MIN_PRIME_FACTOR"
] | 2 | 0.176 | 2026-02-08T16:13:32.480516Z | {
"verified": true,
"answer": 16813,
"timestamp": "2026-02-08T16:13:32.656855Z"
} | 515378 | 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": 1825
},
"timestamp": "2026-02-16T22:50:41.730Z",
"answer": 16813
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
9a747e | lin_form_endings_v1_397696148_2513 | Let $a = 16$ and $b = 24$. Let $k = 2$ and let $L$ be the least common multiple of $a$ and $b$. Define $s = kL + a + b$. Compute the remainder when $18740 \cdot s$ is divided by $61175$. | 40,465 | graphs = [
Graph(
let={
"a_coeff": Const(16),
"b_coeff": Const(24),
"k_val": Const(2),
"lcm_node": LCM(a=Ref("a_coeff"), b=Ref("b_coeff")),
"_inner_result": Sum(Mul(Ref("k_val"), Ref("lcm_node")), Ref("a_coeff"), Ref("b_coeff")),
"_scal... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 2 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T13:22:37.190106Z | {
"verified": true,
"answer": 40465,
"timestamp": "2026-02-08T13:22:37.190802Z"
} | 5f3305 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 115,
"completion_tokens": 1799
},
"timestamp": "2026-02-15T14:40:17.870Z",
"answer": 40465
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
2c511f | diophantine_product_count_v1_1520064083_2886 | Let $k$ be the number of integers $t$ such that $21 \leq t \leq 756$ and there exist positive integers $a \leq 40$, $b \leq 33$ for which $t = 9a + 12b$. Let $u$ be the number of integers $t$ such that $12 \leq t \leq 209$ and there exist positive integers $a \leq 17$, $b \leq 18$ for which $t = 7a + 5b$. Let $R$ be th... | 20,868 | graphs = [
Graph(
let={
"_n": Const(40820),
"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=40)), Geq(left=V... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | diophantine_product_count_v1 | null | 7 | 0 | [
"LIN_FORM"
] | 1 | 0.016 | 2026-02-08T05:17:18.747853Z | {
"verified": true,
"answer": 20868,
"timestamp": "2026-02-08T05:17:18.763623Z"
} | fbd932 | 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": 6075
},
"timestamp": "2026-02-12T07:06:46.795Z",
"answer": 20868
},
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
}
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
9014c4 | comb_sum_binomial_row_v1_124444284_9305 | Let $n = 11$ and $m = 16$. Let $R = 2^m$. Let $p_{\text{max}}$ be the largest prime number less than or equal to $n$. Compute the $\left( R \bmod p_{\text{max}} \right)$-th Bell number. | 21,147 | graphs = [
Graph(
let={
"_n": Const(11),
"n": Const(16),
"result": Pow(Const(2), Ref("n")),
"Q": Bell(Mod(value=Abs(arg=Ref(name='result')), modulus=MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPr... | NT | COMB | SUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | 88ea9c | comb_sum_binomial_row_v1 | bell_mod | 6 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.002 | 2026-02-08T12:21:59.554359Z | {
"verified": true,
"answer": 21147,
"timestamp": "2026-02-08T12:21:59.555907Z"
} | 0b3a9c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 114,
"completion_tokens": 1815
},
"timestamp": "2026-02-15T00:43:36.332Z",
"answer": 21147
},
... | 1 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
ff7037 | modular_count_residue_v1_717093673_1490 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 144$. Let $m$ be the minimum value of $x + y$ as $(x, y)$ ranges over $S$. Determine the number of positive integers $n$ such that $1 \leq n \leq 61009$ and $n \equiv 23 \pmod{m}$. | 2,542 | graphs = [
Graph(
let={
"upper": Const(61009),
"m": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(144)))), expr=Sum(Var("x"), Var("y"))... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | modular_count_residue_v1 | null | 3 | 0 | [
"B3"
] | 1 | 2.732 | 2026-02-08T16:06:32.046119Z | {
"verified": true,
"answer": 2542,
"timestamp": "2026-02-08T16:06:34.777642Z"
} | 6b6172 | 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": 1162
},
"timestamp": "2026-02-16T21:57:25.160Z",
"answer": 2542
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
9ffa77 | algebra_quadratic_discriminant_v1_397696148_1590 | Let $N$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq = 1800$, $\gcd(p, q) = 1$, and $p < q$. Compute $(-9)^2 - (-3) \cdot 5 \cdot N$. | 141 | graphs = [
Graph(
let={
"_n": Const(2),
"a": Const(-3),
"b": Const(-9),
"c": Const(5),
"result": Sub(Pow(Ref("b"), Ref("_n")), Mul(CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), co... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | algebra_quadratic_discriminant_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.038 | 2026-02-08T12:39:30.475741Z | {
"verified": true,
"answer": 141,
"timestamp": "2026-02-08T12:39:30.513940Z"
} | 7bcc34 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 113,
"completion_tokens": 1166
},
"timestamp": "2026-02-15T03:08:33.656Z",
"answer": 141
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
c9d1cc | geo_count_lattice_rect_v1_48377204_2592 | Compute the number of lattice points $(x, y)$ such that $0 \leq x \leq 100$ and $0 \leq y \leq 278$.
Find the value of this number. | 28,179 | graphs = [
Graph(
let={
"a": Const(100),
"b": Const(278),
"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 | 2026-02-08T16:49:58.178003Z | {
"verified": true,
"answer": 28179,
"timestamp": "2026-02-08T16:49:58.179112Z"
} | 41ee0c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 88,
"completion_tokens": 676
},
"timestamp": "2026-02-24T22:00:09.031Z",
"answer": 28179
},
{
... | 2 | [] | {
"lo": -10,
"mid": -7.42,
"hi": -4.85
} | ||||
8a141f | antilemma_sum_equals_v1_1125832087_366 | Let $n = 51$. Define $x$ to be the number of ordered pairs $(i, j)$ of integers with $1 \le i \le 51$ and $1 \le j \le 51$ such that $i + j = n$. Let $c = 97034$. Compute the remainder when $c \cdot x$ is divided by $63835$. | 240 | graphs = [
Graph(
let={
"_n": Const(51),
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref("_n")), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(51)), right=IntegerRange(start=Const(1), end=Con... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 3 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.009 | 2026-02-08T03:02:25.131270Z | {
"verified": true,
"answer": 240,
"timestamp": "2026-02-08T03:02:25.140303Z"
} | 4825ba | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 192,
"completion_tokens": 914
},
"timestamp": "2026-02-23T21:22:22.676Z",
"answer": 240
},
{
"id"... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"stat... | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
e05ae2 | comb_count_partitions_v1_168721529_1116 | Let $n = 40$. Let $p = p(n)$ denote the number of integer partitions of $n$. Compute the value of $$ p + \phi(|p| + 1) + \tau(|p| + \phi(1)), $$ where $\phi$ denotes Euler's totient function and $\tau(m)$ denotes the number of positive divisors of $m$. | 74,678 | graphs = [
Graph(
let={
"n": Const(40),
"result": Partition(arg=Ref(name='n')),
"Q": Sum(Ref("result"), EulerPhi(n=Sum(Abs(arg=Ref(name='result')), Const(1))), NumDivisors(n=Sum(Abs(arg=Ref(name='result')), EulerPhi(n=Const(1))))),
},
goal=Ref("Q"),
)
... | NT | COMB | COUNT | sympy | ONE_PHI_1 | [
"ONE_PHI_1"
] | f6b5a5 | comb_count_partitions_v1 | null | 3 | 0 | [
"ONE_PHI_1"
] | 1 | 0.002 | 2026-02-08T13:28:16.005340Z | {
"verified": true,
"answer": 74678,
"timestamp": "2026-02-08T13:28:16.007155Z"
} | 6a2f49 | 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": 6183
},
"timestamp": "2026-02-09T13:50:34.853Z",
"answer": 74678
},
{
"... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "ONE_PHI_1",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -6.69,
"mid": -2.39,
"hi": 1.83
} | ||
ee26f8 | alg_qf_psd_sum_v1_1218484723_659 | Find the remainder when
$$
\sum_{\substack{a=1}}^{264} \sum_{\substack{b=1}}^{\min\{ x + y : x > 0, y > 0,\, xy = 17424 \}} \left(16a^2 - 32ab + 20b^2\right)
$$
is divided by $77133$. | 40,353 | graphs = [
Graph(
let={
"_n": Const(20),
"result": Mod(value=SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(264)), Geq(Var("b"), Const(1)), Leq(Var("b"), MinOverSet(set=MapOverSet(set=Sol... | ALG | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | alg_qf_psd_sum_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.11 | 2026-02-25T02:24:13.358607Z | {
"verified": true,
"answer": 40353,
"timestamp": "2026-02-25T02:24:13.468929Z"
} | 7cfe62 | 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": 2903
},
"timestamp": "2026-03-28T23:43:28.114Z",
"answer": 40353
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -0.93,
"mid": 2.04,
"hi": 4.6
} | ||
c5f5ce | comb_count_partitions_v1_717093673_1639 | Let $n$ be the minimum value of $x + y$ over all ordered pairs of positive integers $(x, y)$ such that $xy = 400$. Let $p(n)$ denote the number of integer partitions of $n$. Compute $50400 - p(n)$. | 13,062 | graphs = [
Graph(
let={
"_n": Const(50400),
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(400)))), expr=Sum(Var("x"), Var("y")))),... | COMB | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | comb_count_partitions_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.002 | 2026-02-08T16:13:22.289430Z | {
"verified": true,
"answer": 13062,
"timestamp": "2026-02-08T16:13:22.291237Z"
} | 425f8a | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 168,
"completion_tokens": 746
},
"timestamp": "2026-02-24T20:11:31.421Z",
"answer": 13062
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -2.4,
"mid": 1.57,
"hi": 5.75
} | ||
ca7f63 | comb_count_permutations_fixed_v1_151522320_1238 | Let $n = 6$. Consider the set of all pairs of positive integers $(x, y)$ such that $x + y = 4$. Let $k$ be the maximum value of $xy$ over all such pairs. Compute the value of $\binom{n}{k} \cdot !{(n - k)}$, where $!m$ denotes the number of derangements of $m$ elements. | 15 | graphs = [
Graph(
let={
"n": Const(6),
"k": 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(4)))), expr=Mul(Var("x"), Var("y")))),
... | COMB | null | COUNT | sympy | B1 | [
"B1"
] | 5b950e | comb_count_permutations_fixed_v1 | null | 5 | 0 | [
"B1"
] | 1 | 0.001 | 2026-02-08T03:51:26.761696Z | {
"verified": true,
"answer": 15,
"timestamp": "2026-02-08T03:51:26.762829Z"
} | 35c640 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 198,
"completion_tokens": 495
},
"timestamp": "2026-02-10T15:53:54.709Z",
"answer": 15
},
{
"id":... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
... | {
"lo": -9.23,
"mid": -6.18,
"hi": -4.06
} | ||
b8f06a | antilemma_k2_v1_784195855_6960 | Let $m = 185$. Define $n$ to be the sum of $\phi(d)$ over all positive divisors $d$ of $m$, where $\phi$ denotes Euler's totient function. Compute
$$
\sum_{k=1}^{185} \phi(k) \left\lfloor \frac{n}{k} \right\rfloor.
$$ | 17,205 | graphs = [
Graph(
let={
"_m": Const(185),
"_n": SumOverDivisors(n=Ref(name='_m'), var='d', expr=EulerPhi(n=Var(name='d'))),
"x": Summation(var="k", start=Div(Const(5), Const(5)), end=Const(185), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Ref("_n"), Var("k"))))),
},
... | NT | COMB | COMPUTE | sympy | IDENTITY_DIV_SELF | [
"IDENTITY_DIV_SELF",
"K3/K2",
"K2"
] | 8236d1 | antilemma_k2_v1 | null | 7 | 0 | [
"IDENTITY_DIV_SELF",
"K2",
"K3"
] | 3 | 0.001 | 2026-02-08T09:01:46.559788Z | {
"verified": true,
"answer": 17205,
"timestamp": "2026-02-08T09:01:46.560773Z"
} | bbb971 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 119,
"completion_tokens": 618
},
"timestamp": "2026-02-13T23:48:16.457Z",
"answer": 17205
},
{... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "IDENTITY_DIV_SELF",
"status": "ok"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
1f7f9d | nt_min_with_divisor_count_v1_1918700295_2028 | Let $n = 7$ and $U = 99856$. Let $m$ be the smallest positive integer such that $1 \leq m \leq U$ and the number of positive divisors of $m$ is exactly 9. Compute the value of
$$
\left( \sum_{k=1}^{7} \phi(k) \left\lfloor \frac{7}{k} \right\rfloor \right) \cdot m.
$$ | 1,008 | graphs = [
Graph(
let={
"_n": Const(7),
"upper": Const(99856),
"div_count": Const(9),
"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 | K2 | [
"K2"
] | 2e65cb | nt_min_with_divisor_count_v1 | affine_mod | 5 | 0 | [
"K2"
] | 1 | 5.23 | 2026-02-08T07:39:02.845336Z | {
"verified": true,
"answer": 1008,
"timestamp": "2026-02-08T07:39:08.075335Z"
} | afbe80 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 141,
"completion_tokens": 1191
},
"timestamp": "2026-02-13T11:31:14.434Z",
"answer": 1008
},
{... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
af1b33 | nt_count_digit_sum_v1_458359167_5736 | Let $\phi(n)$ denote Euler's totient function. Define $\text{target\_sum} = \sum_{d \mid 30} \phi(d)$. Let $\text{result}$ be the number of positive integers $n$ such that $1 \leq n \leq 126025$ and the sum of the decimal digits of $n$ is equal to $\text{target\_sum}$. Determine the value of $\text{result}$. | 3,587 | graphs = [
Graph(
let={
"_n": Const(30),
"upper": Const(126025),
"target_sum": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n")... | NT | null | COUNT | sympy | K3 | [
"K3"
] | 54c41e | nt_count_digit_sum_v1 | null | 5 | 0 | [
"K3"
] | 1 | 5.507 | 2026-02-08T12:40:06.347574Z | {
"verified": true,
"answer": 3587,
"timestamp": "2026-02-08T12:40:11.855016Z"
} | ee2c59 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 138,
"completion_tokens": 4145
},
"timestamp": "2026-02-15T03:56:39.942Z",
"answer": 3587
},
{... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": ... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
2d089c | comb_count_permutations_fixed_v1_1915831931_2684 | Let $n = \sum_{k=1}^{3} \phi(k) \cdot \left\lfloor \frac{3}{k} \right\rfloor$, where $\phi$ is Euler's totient function. Compute $\binom{n}{2} \cdot !(n-2)$, where $!m$ denotes the number of derangements of $m$ elements. | 135 | graphs = [
Graph(
let={
"_n": Const(3),
"n": Summation(var="k1", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k1")), Floor(Div(Const(3), Var("k1"))))),
"k": Const(2),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub(left=Ref(name='n... | NT | COMB | COUNT | sympy | K2 | [
"K2"
] | 6897ab | comb_count_permutations_fixed_v1 | null | 4 | 0 | [
"K2"
] | 1 | 0.005 | 2026-02-08T17:03:37.042413Z | {
"verified": true,
"answer": 135,
"timestamp": "2026-02-08T17:03:37.046937Z"
} | b93302 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 124,
"completion_tokens": 817
},
"timestamp": "2026-02-17T18:21:24.183Z",
"answer": 135
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
4905e8 | nt_count_digit_sum_v1_168721529_1499 | Let $n$ be a positive integer such that $1 \leq n \leq 29929$. Define the target sum as
$$
\sum_{k=1}^{6} \phi(k) \left\lfloor \frac{6}{k} \right\rfloor,
$$
where $\phi(k)$ denotes Euler's totient function. Compute the number of such integers $n$ for which the sum of the decimal digits of $n$ equals this target sum. | 1,885 | graphs = [
Graph(
let={
"_n": Const(6),
"upper": Const(29929),
"target_sum": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(6), Var("k"))))),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(... | NT | null | COUNT | sympy | K2 | [
"K2"
] | 6897ab | nt_count_digit_sum_v1 | null | 5 | 0 | [
"K2"
] | 1 | 1.184 | 2026-02-08T13:44:04.418248Z | {
"verified": true,
"answer": 1885,
"timestamp": "2026-02-08T13:44:05.602739Z"
} | 0fa65e | 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": 3384
},
"timestamp": "2026-02-11T07:57:57.823Z",
"answer": 1885
},
{
"... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -5.48,
"mid": 0.74,
"hi": 7.52
} | ||
052641 | antilemma_sum_equals_v1_717093673_626 | Let $m = 158$. Define $t$ to be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 158$. Let $S$ be the set of all ordered pairs $(i, j)$ with $1 \leq i \leq 77$ and $1 \leq j \leq 77$ such that $i + j = t$. Compute the remainder when $2 - |S|$ is divided by 71239. | 71,165 | graphs = [
Graph(
let={
"_m": Const(158),
"_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 | 0.006 | 2026-02-08T15:34:34.008165Z | {
"verified": true,
"answer": 71165,
"timestamp": "2026-02-08T15:34:34.013686Z"
} | 03aeee | 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": 711
},
"timestamp": "2026-02-24T17:59:04.088Z",
"answer": 71165
},
{
"... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7... | {
"lo": -2.4,
"mid": 1.57,
"hi": 5.75
} | ||
d4975a | antilemma_k2_v1_971394319_718 | Let $$x = \sum_{k=1}^{299} \phi(k) \left\lfloor \frac{1}{k} \sum_{d \mid 299} \phi(d) \right\rfloor,$$ where $\phi(n)$ denotes Euler's totient function. Compute the remainder when $$\left(x \bmod 199\right) + 1009 \cdot \left(x \bmod 499\right)$$ is divided by $60708$. | 18,070 | graphs = [
Graph(
let={
"_n": Const(499),
"x": Summation(var="k", start=Const(1), end=Const(299), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(SumOverDivisors(n=Const(value=299), var='d', expr=EulerPhi(n=Var(name='d'))), Var("k"))))),
"Q": Mod(value=Sum(Mod(value=Ref("x"), mo... | NT | COMB | COMPUTE | sympy | K3 | [
"K3/K2",
"K2"
] | c7f244 | antilemma_k2_v1 | null | 7 | 0 | [
"K2",
"K3"
] | 2 | 0.002 | 2026-02-08T13:16:19.801993Z | {
"verified": true,
"answer": 18070,
"timestamp": "2026-02-08T13:16:19.803835Z"
} | 6afbbe | 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": 1231
},
"timestamp": "2026-02-15T11:45:32.708Z",
"answer": 18070
},
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
e7c3da | lin_form_endings_v1_1520064083_7658 | Let $a = 24$ and $b = 30$. Let $k = 240$. Compute $\gcd(a, b)$, and let $d = \gcd(k, \gcd(a, b))$. Define $r = \left\lfloor \frac{k}{d} \right\rfloor$. Now compute $7380 \cdot r$, and let $x$ be the remainder when this value is divided by 59160. Find the value of $x$. | 58,560 | graphs = [
Graph(
let={
"a_coeff": Const(24),
"b_coeff": Const(30),
"k_val": Const(240),
"step": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"_inner_result": Floor(Div(Ref("k_val"), GCD(a=Ref("k_val"), b=Ref("step")))),
"_scale_k": Const(7... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 2 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T09:14:00.932816Z | {
"verified": true,
"answer": 58560,
"timestamp": "2026-02-08T09:14:00.933515Z"
} | a2b022 | 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": 439
},
"timestamp": "2026-02-14T01:41:00.917Z",
"answer": 58560
},
{... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"st... | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
ad9670 | antilemma_cartesian_v1_1978505735_2326 | Let $x$ be the number of ordered pairs $(i, j)$ such that $1 \le i \le 22$ and $1 \le j \le 38$. Compute the remainder when $44121 \cdot x$ is divided by $94604$. | 84,200 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(22)), right=IntegerRange(start=Const(1), end=Const(38)))),
"Q": Mod(value=Mul(Const(44121), Ref("x")), modulus=Const(94604)),
},
goal=Ref("Q"),
)
] | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | antilemma_cartesian_v1 | null | 2 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.001 | 2026-02-08T16:49:47.990471Z | {
"verified": true,
"answer": 84200,
"timestamp": "2026-02-08T16:49:47.991227Z"
} | 71d05e | 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": 762
},
"timestamp": "2026-02-17T12:39:51.174Z",
"answer": 84200
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"statu... | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||
b20fdb | comb_factorial_compute_v1_1915831931_2176 | Let $P$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 1323000$, $\gcd(p, q) = 1$, and $p < q$. Let $n$ be the number of elements in $P$. Compute $n!$. Let $c = 50400$. Determine the value of $c - n!$. | 10,080 | 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=1323000)), 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_factorial_compute_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.003 | 2026-02-08T16:39:23.266419Z | {
"verified": true,
"answer": 10080,
"timestamp": "2026-02-08T16:39:23.269521Z"
} | e6e286 | 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": 949
},
"timestamp": "2026-02-17T09:02:16.895Z",
"answer": 10080
},
{... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
fd8cdb | nt_count_divisible_and_v1_1470522791_1819 | Let $r$ be the number of positive integers $n$ at most $46740$ that are divisible by both $4$ and $6$. Let $c$ be the largest prime number at most $3002$. Compute the remainder when $\left( r \bmod 317 \right) + c \cdot \left( r \bmod 313 \right)$ is divided by $58487$. | 7,821 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": Const(46740),
"d1": Const(4),
"d2": Const(6),
"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=... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | 08a653 | nt_count_divisible_and_v1 | two_moduli | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 2.543 | 2026-02-08T14:00:01.347522Z | {
"verified": true,
"answer": 7821,
"timestamp": "2026-02-08T14:00:03.890839Z"
} | 90b567 | 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": 1119
},
"timestamp": "2026-02-15T23:43:12.647Z",
"answer": 7821
},
{... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8_SUM",
"statu... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
b1e12f | geo_count_lattice_rect_v1_655260480_2949 | Let $a = 128$ and $b = 445$. Define $R$ to be the set of all lattice points $(x, y)$ such that $0 \le x \le a$ and $0 \le y \le b$. Let $N$ be the number of elements in $R$. Compute the remainder when $128 - N$ is divided by $74827$. | 17,421 | graphs = [
Graph(
let={
"a": Const(128),
"b": Const(445),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"Q": Mod(value=Sub(Const(128), Ref("result")), modulus=Const(74827)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.002 | 2026-02-08T17:05:18.649148Z | {
"verified": true,
"answer": 17421,
"timestamp": "2026-02-08T17:05:18.651530Z"
} | 0dce5c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 128,
"completion_tokens": 511
},
"timestamp": "2026-02-17T19:34:14.622Z",
"answer": 17421
},
{... | 1 | [] | {
"lo": -5.64,
"mid": -3.17,
"hi": -0.81
} | ||||
69884f | nt_sum_totient_over_divisors_v1_168721529_569 | Let $m = 13$. Let $k_0$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 142884$. Let $n$ be the smallest positive integer such that the largest power of $13$ dividing $n!$ is at least $k_0$. Define $S = \sum_{d \mid n} \phi(d)$, where $\phi$ denotes Euler's totient function.... | 80,293 | graphs = [
Graph(
let={
"_m": Const(13),
"_n": Const(17412),
"n": MinOverSet(set=SolutionsSet(var=Var("n"), condition=Geq(MaxKDivides(target=Factorial(Var("n")), base=Ref("_m")), MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), conditio... | NT | null | COMPUTE | sympy | B3 | [
"B3/V5"
] | 2589a0 | nt_sum_totient_over_divisors_v1 | null | 7 | 0 | [
"B3",
"V5"
] | 2 | 0.004 | 2026-02-08T13:08:32.977995Z | {
"verified": true,
"answer": 80293,
"timestamp": "2026-02-08T13:08:32.981976Z"
} | e36ed0 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 242,
"completion_tokens": 4200
},
"timestamp": "2026-02-09T06:28:23.720Z",
"answer": 80293
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V5",
"status": "ok_later"
},
{
... | {
"lo": -1.99,
"mid": 2.14,
"hi": 6.33
} |
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