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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
c7c25e | nt_count_coprime_and_v1_2051736721_4283 | Let $k_1 = 8$. Let $p$ be a prime number such that $2 \leq p \leq 5$, and define $m$ to be the largest such prime. Define
$$
k_2 = \sum_{k=1}^{m} \phi(k) \left\lfloor \frac{5}{k} \right\rfloor,
$$
where $\phi$ denotes Euler's totient function.
Let $n_1$ be a positive integer such that $1 \leq n_1 \leq 46147$, $\gcd(n_... | 18,315 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": Const(46147),
"k1": Const(8),
"k2": Summation(var="k", start=Const(1), end=MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Const(5)), IsPrime(Var("n"))))), expr=Mu... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW/K2"
] | 7eb1ee | nt_count_coprime_and_v1 | null | 5 | 0 | [
"K2",
"MAX_PRIME_BELOW"
] | 2 | 4.577 | 2026-02-08T17:52:09.487534Z | {
"verified": true,
"answer": 18315,
"timestamp": "2026-02-08T17:52:14.064308Z"
} | 9b3ad8 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 223,
"completion_tokens": 1768
},
"timestamp": "2026-02-18T10:00:15.167Z",
"answer": 18315
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K2",
"status": "ok_later"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V3",
"stat... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
a3fbfa | comb_bell_compute_v1_124444284_2139 | Let $P$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 519750$, $\gcd(p, q) = 1$, and $p < q$. Let $N$ be the number of elements in $P$.
Let $T$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = N$. Let $s$ be the minimum value of $x +... | 4,140 | graphs = [
Graph(
let={
"_n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=519750)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(value=1... | NT | COMB | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/B3"
] | 3f0fb0 | comb_bell_compute_v1 | null | 7 | 0 | [
"B3",
"COPRIME_PAIRS"
] | 2 | 0.003 | 2026-02-08T04:20:45.614022Z | {
"verified": true,
"answer": 4140,
"timestamp": "2026-02-08T04:20:45.617080Z"
} | c17185 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 249,
"completion_tokens": 1623
},
"timestamp": "2026-02-10T16:32:44.239Z",
"answer": 4140
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
12b2cc | nt_min_coprime_above_v1_1125832087_760 | Let $\_n = 2$. Define $\text{start}$ to be the smallest integer $d \geq \_n$ that divides $1052651$. Let $\text{upper}$ be the number of ordered pairs $(i, j)$ such that $1 \leq i \leq 5$ and $1 \leq j \leq 223$. Let $\text{result}$ be the smallest integer $n$ such that $\text{start} < n \leq \text{upper}$ and $\gcd(n,... | 5,975 | graphs = [
Graph(
let={
"_n": Const(2),
"start": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(1052651))))),
"upper": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const... | NT | null | EXTREMUM | sympy | B3 | [
"B3",
"MIN_PRIME_FACTOR",
"COUNT_CARTESIAN"
] | fd9d9a | nt_min_coprime_above_v1 | negation_mod | 6 | 0 | [
"B3",
"COUNT_CARTESIAN",
"MIN_PRIME_FACTOR"
] | 3 | 0.026 | 2026-02-08T03:15:34.444588Z | {
"verified": true,
"answer": 5975,
"timestamp": "2026-02-08T03:15:34.470107Z"
} | e19805 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 322,
"completion_tokens": 1623
},
"timestamp": "2026-02-10T13:11:53.783Z",
"answer": 6981
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "MAX_... | {
"lo": 1.96,
"mid": 5.23,
"hi": 8.52
} | ||
f52bb2 | alg_linear_system_2x2_v1_1218484723_638 | Let $\det = 6 \cdot (-10) - 8 \cdot 5$, $M = 142977 \cdot (-10) - 184186 \cdot 5$, and $R = 6 \cdot 184186 - \left|\{ v : 20 \le v \le 1280,\ \text{there exist integers } a, b \text{ with } 1 \le a, b \le 8 \text{ such that } 20 \cdot a^2 = v \}\right| \cdot 142977$. Let $S = \frac{M}{\det} + \frac{R}{\det}$ and $Q = |... | 23,894 | graphs = [
Graph(
let={
"_n": Const(8),
"num_x": Sub(Mul(Const(142977), Const(-10)), Mul(Const(184186), Const(5))),
"num_y": Sub(Mul(Const(6), Const(184186)), Mul(CountOverSet(set=SolutionsSet(var=Var("v"), condition=And(Geq(Var("v"), Const(20)), Leq(Var("v"), Const(1280)... | ALG | null | COMPUTE | sympy | QF_PSD_DISTINCT | [
"QF_PSD_DISTINCT"
] | a8f9cb | alg_linear_system_2x2_v1 | null | 4 | 0 | [
"QF_PSD_DISTINCT"
] | 1 | 0.004 | 2026-02-25T02:22:54.948693Z | {
"verified": true,
"answer": 23894,
"timestamp": "2026-02-25T02:22:54.952949Z"
} | 8638fd | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 269,
"completion_tokens": 1064
},
"timestamp": "2026-03-28T23:32:56.292Z",
"answer": 23894
},
{
"... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_DISTINCT",
"status": "ok"
}
] | {
"lo": -4.31,
"mid": -1.92,
"hi": 0.62
} | ||
273052 | nt_min_coprime_above_v1_48377204_2006 | Let $S$ be the set of all integers $n$ such that $1 \leq n \leq 33285$ and
$$
n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{11}.
$$
Let $T$ be the set of all integers $n_1$ such that $n_1 > |S|$, $n_1 \leq 3409$, and $\gcd(n_1, 374) = 1$.
Compute the minimum element of $T$. | 3,027 | graphs = [
Graph(
let={
"start": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(33285)), Congruent(a=Var(name='n'), b=Floor(arg=Div(left=Var(name='n'), right=Const(value=2))), modulus=Const(value=11))))),
"upper": Const(3409),
... | NT | null | EXTREMUM | sympy | L3C | [
"L3C"
] | 73f8b0 | nt_min_coprime_above_v1 | null | 5 | 0 | [
"L3C"
] | 1 | 0.061 | 2026-02-08T16:33:01.256294Z | {
"verified": true,
"answer": 3027,
"timestamp": "2026-02-08T16:33:01.316897Z"
} | 7bdcc4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 158,
"completion_tokens": 1280
},
"timestamp": "2026-02-17T06:24:05.406Z",
"answer": 3027
},
{... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
edca53 | diophantine_fbi2_min_v1_1520064083_311 | Let $d$ be an integer such that $5 \le d \le 24$, $d$ divides $14$, and $\frac{14}{d} \ge 2$. Determine the value of the smallest such $d$. | 7 | graphs = [
Graph(
let={
"k": Const(14),
"a": Const(4),
"b": Const(1),
"upper": Const(24),
"result": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(5)), Leq(Var("d"), Ref("upper")), Divides(divisor=Var("d"), dividend=Ref... | NT | null | EXTREMUM | sympy | OMEGA_ONE | [
"OMEGA_ONE",
"LIN_FORM",
"WILSON"
] | a6aa9b | diophantine_fbi2_min_v1 | null | 3 | 0 | [
"LIN_FORM",
"OMEGA_ONE",
"WILSON"
] | 3 | 0.052 | 2026-02-08T03:14:37.507153Z | {
"verified": true,
"answer": 7,
"timestamp": "2026-02-08T03:14:37.559248Z"
} | ebc60c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 159,
"completion_tokens": 425
},
"timestamp": "2026-02-10T13:37:08.681Z",
"answer": 7
},
{
"id": ... | 1 | [
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "OMEGA_ONE",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},... | {
"lo": -9.14,
"mid": -6.05,
"hi": -3.74
} | ||
3cf431 | algebra_poly_eval_v1_865884756_3350 | Let $n = 8$ and $m = 24$. Let $S$ be the set of all integers $t$ such that $15 \leq t \leq 42$ and $t = 6a + 9b$ for some integers $a$ with $1 \leq a \leq 4$ and $b$ with $1 \leq b \leq 2$. Let $k$ be the number of elements in $S$. Compute the value of $8 \cdot 24^2 + k \cdot 24 - 7$, take its absolute value, find the ... | 4,140 | graphs = [
Graph(
let={
"_n": Const(8),
"n": Const(24),
"result": Sum(Mul(Ref("_n"), Pow(Ref("n"), Const(2))), Mul(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'), rig... | COMB | null | COMPUTE | sympy | K13 | [
"LIN_FORM"
] | 7b2633 | algebra_poly_eval_v1 | null | 5 | 0 | [
"K13",
"LIN_FORM"
] | 2 | 0.011 | 2026-02-08T17:19:10.999592Z | {
"verified": true,
"answer": 4140,
"timestamp": "2026-02-08T17:19:11.010171Z"
} | e7604c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 193,
"completion_tokens": 760
},
"timestamp": "2026-02-17T23:32:43.258Z",
"answer": 4140
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"sta... | {
"lo": -8,
"mid": -4.75,
"hi": -2.28
} | ||
8664e8 | geo_count_lattice_rect_v1_784195855_3393 | Compute the number of lattice points $(x, y)$ such that $0 \leq x \leq 30$ and $0 \leq y \leq 95$. Multiply this number by $79143$, and find the remainder when the result is divided by $76723$. | 66,681 | graphs = [
Graph(
let={
"a": Const(30),
"b": Const(95),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"Q": Mod(value=Mul(Const(79143), Ref("result")), modulus=Const(76723)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 4 | 0 | null | null | 0 | 2026-02-08T06:24:31.377575Z | {
"verified": true,
"answer": 66681,
"timestamp": "2026-02-08T06:24:31.377953Z"
} | 7a95e0 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 170,
"completion_tokens": 2564
},
"timestamp": "2026-02-24T06:10:44.173Z",
"answer": 66681
},
{
"... | 1 | [] | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||||
171182 | nt_sum_divisors_mod_v1_1978505735_6492 | Let $n$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $x \cdot y = 129600$. Let $\sigma$ be the sum of the positive divisors of $n$. Let $M = 11159$. Compute the remainder when $50917 \cdot \sigma$ is divided by $53068$. | 52,614 | graphs = [
Graph(
let={
"_n": Const(53068),
"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(129600)))), expr=Sum(Var("x"), Var("y"))... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_divisors_mod_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.004 | 2026-02-08T19:36:31.222090Z | {
"verified": true,
"answer": 52614,
"timestamp": "2026-02-08T19:36:31.225652Z"
} | 174a8a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 127,
"completion_tokens": 2244
},
"timestamp": "2026-02-18T23:01:04.849Z",
"answer": 52614
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
a3952d | nt_sum_gcd_range_mod_v1_865884756_2790 | Let $N$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 640000$. Let $S = \sum_{n=1}^{N} \gcd(n, 108)$. Compute the remainder when $S$ is divided by 11657. | 9,536 | 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(640000)))), expr=Sum(Var("x"), Var("y")))),
"k": Const(108),... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_gcd_range_mod_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.347 | 2026-02-08T16:56:13.506813Z | {
"verified": true,
"answer": 9536,
"timestamp": "2026-02-08T16:56:13.853342Z"
} | 2a518f | 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": 2189
},
"timestamp": "2026-02-17T16:10:32.151Z",
"answer": 9536
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
037087 | nt_sum_totient_over_divisors_v1_168721529_636 | Let $n = 64160$. Compute the sum of $\phi(d)$ over all positive divisors $d$ of $n$, where $\phi$ denotes Euler's totient function. | 64,160 | graphs = [
Graph(
let={
"n": Const(64160),
"result": SumOverDivisors(n=Ref(name='n'), var='d', expr=EulerPhi(n=Var(name='d'))),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/MOBIUS_SQUAREFREE",
"LTE_DIFF/MOBIUS_SQUAREFREE",
"LIN_FORM/MOBIUS_SQUAREFREE",
"WILSON"
] | b1680b | nt_sum_totient_over_divisors_v1 | null | 3 | 0 | [
"COPRIME_PAIRS",
"LIN_FORM",
"LTE_DIFF",
"MOBIUS_SQUAREFREE",
"WILSON"
] | 5 | 0.063 | 2026-02-08T13:10:13.377538Z | {
"verified": true,
"answer": 64160,
"timestamp": "2026-02-08T13:10:13.440604Z"
} | 92a0e0 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 153,
"completion_tokens": 491
},
"timestamp": "2026-02-09T07:15:27.747Z",
"answer": 64160
},
{
"i... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "ok"
... | {
"lo": -6.97,
"mid": -4.58,
"hi": -1.65
} | ||
0aa07a | comb_count_surjections_v1_124444284_1886 | Let $n = 5$ and $k = 5$. Define $S(n,k)$ to be the Stirling number of the second kind. Compute the value of $42^2 - k! \cdot S(n,k)$. | 1,644 | graphs = [
Graph(
let={
"n": Const(5),
"k": Const(5),
"result": Mul(Factorial(Ref("k")), Stirling2(n=Ref(name='n'), k=Ref(name='k'))),
"_c": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(42)), right=IntegerRange(start=Const(1), ... | COMB | null | COUNT | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 009729 | comb_count_surjections_v1 | negation_mod | 3 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.003 | 2026-02-08T04:11:55.089876Z | {
"verified": true,
"answer": 1644,
"timestamp": "2026-02-08T04:11:55.093032Z"
} | e28ed2 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 160,
"completion_tokens": 232
},
"timestamp": "2026-02-23T23:41:49.703Z",
"answer": 1644
},
{
"id... | 2 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SU... | {
"lo": -10,
"mid": -7.79,
"hi": -5.57
} | ||
d1b9e3 | sequence_lucas_compute_v1_458359167_1323 | Let $c = 2$ and $m = 2$. Define $N$ to be the largest prime number $n$ such that $n \ge m$ and $n$ is at most the number of positive integers $k$ with $1 \le k \le 156$ for which the sum of the digits of $k$ is divisible by $c$. Let $p$ be the number of prime numbers less than or equal to $N$ and at least 2. Compute th... | 24,476 | graphs = [
Graph(
let={
"_c": Const(2),
"_m": Const(2),
"_n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_m")), Leq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(156)), Eq(M... | NT | null | COMPUTE | sympy | L3B | [
"L3B/MAX_PRIME_BELOW/COUNT_PRIMES"
] | 5bb2ab | sequence_lucas_compute_v1 | null | 6 | 0 | [
"COUNT_PRIMES",
"L3B",
"MAX_PRIME_BELOW"
] | 3 | 0.002 | 2026-02-08T04:33:03.864294Z | {
"verified": true,
"answer": 24476,
"timestamp": "2026-02-08T04:33:03.866755Z"
} | 1dd1e9 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 222,
"completion_tokens": 3027
},
"timestamp": "2026-02-10T17:01:12.873Z",
"answer": 24476
},
{
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "ok_later"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3B",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
47b530 | antilemma_k2_v1_458359167_1436 | Let $S = \sum_{k=1}^{337} \phi(k) \left\lfloor \frac{337}{k} \right\rfloor$, where $\phi(k)$ denotes Euler's totient function. Compute $S$. | 56,953 | graphs = [
Graph(
let={
"x": Summation(var="k", start=Const(1), end=Const(337), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(337), Var("k"))))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | VIETA_SUM | [
"K2"
] | 6897ab | antilemma_k2_v1 | null | 5 | 0 | [
"K2",
"VIETA_SUM"
] | 2 | 0.005 | 2026-02-08T04:36:46.698919Z | {
"verified": true,
"answer": 56953,
"timestamp": "2026-02-08T04:36:46.704113Z"
} | 052d52 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 161,
"completion_tokens": 903
},
"timestamp": "2026-02-10T17:20:42.366Z",
"answer": 56953
},
{
"... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
ef7cd8 | lin_form_endings_v1_1978505735_4625 | Let $a = 105$, $b = 45$, and $k = 59$. Let $d = \gcd(a, b)$, and let $m = \left\lfloor \frac{k}{\gcd(k, d)} \right\rfloor$. Define $x$ to be the remainder when $16142 \cdot m$ is divided by $59374$. Find the value of $x$. | 2,394 | graphs = [
Graph(
let={
"a_coeff": Const(105),
"b_coeff": Const(45),
"k_val": Const(59),
"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(1... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 5 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T18:24:38.738535Z | {
"verified": true,
"answer": 2394,
"timestamp": "2026-02-08T18:24:38.739745Z"
} | c18ad0 | 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": 950
},
"timestamp": "2026-02-18T16:54:58.029Z",
"answer": 2394
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
a1ab11 | geo_count_lattice_rect_v1_1520064083_10244 | Let $a = 66$ and $b = 21$. Define $\text{result}$ to be the number of lattice points in the rectangle $[0, a] \times [0, b]$, including the boundaries. Compute $\text{result}$. | 1,474 | graphs = [
Graph(
let={
"a": Const(66),
"b": Const(21),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.001 | 2026-02-08T11:18:37.041179Z | {
"verified": true,
"answer": 1474,
"timestamp": "2026-02-08T11:18:37.041776Z"
} | 859793 | 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": 288
},
"timestamp": "2026-02-24T13:23:43.364Z",
"answer": 1474
},
{
"id... | 1 | [] | {
"lo": -9.23,
"mid": -6.18,
"hi": -4.06
} | ||||
d5f6a0 | comb_catalan_compute_v1_124444284_8218 | Let $T$ be the set of all integers $t$ with $7 \leq t \leq 30$ for which there exist positive integers $a$ and $b$ such that $1 \leq a \leq 2$, $1 \leq b \leq 10$, and $t = 5a + 2b$. Let $n$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2$ equals the number of elements in $T$. ... | 16,796 | graphs = [
Graph(
let={
"_n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=2)), Geq(left=Var(name='b'), right=Const(value=... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/COMB1"
] | 268a62 | comb_catalan_compute_v1 | null | 6 | 0 | [
"COMB1",
"LIN_FORM"
] | 2 | 0.002 | 2026-02-08T09:36:30.141218Z | {
"verified": true,
"answer": 16796,
"timestamp": "2026-02-08T09:36:30.143188Z"
} | ac0a81 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 241,
"completion_tokens": 1415
},
"timestamp": "2026-02-24T11:33:38.642Z",
"answer": 16796
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok_later"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status": "... | {
"lo": -5.97,
"mid": -3.97,
"hi": -1.93
} | ||
af1cec | modular_count_residue_v1_717093673_2050 | Let $m = \sum_{k=1}^{5} k$. Let $r = 13$ and $U = 49729$. Compute the number of positive integers $n$ such that $1 \leq n \leq U$ and $n \equiv r \pmod{m}$. Let this count be $C$. Find the value of $44121 \cdot C \bmod{89660}$. | 25,655 | graphs = [
Graph(
let={
"_n": Const(89660),
"upper": Const(49729),
"m": Summation(var="k", start=Const(1), end=Const(5), expr=Var("k")),
"r": Const(13),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Le... | NT | null | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | modular_count_residue_v1 | null | 3 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 2.52 | 2026-02-08T16:28:19.503763Z | {
"verified": true,
"answer": 25655,
"timestamp": "2026-02-08T16:28:22.023746Z"
} | 24ead0 | 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": 1457
},
"timestamp": "2026-02-17T05:37:43.466Z",
"answer": 25655
},
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
4d31e8 | alg_qf_psd_sum_v1_1218484723_6441 | Let $M = \min\{ 41a_1^2 + 16b_1^2 + 32a_1b_1 : a_1, b_1 \in \{1, 2, \dots, 8\} \}$. Find the remainder when $$\sum_{a=1}^{M} \sum_{b=1}^{89} \left(17a^2 - 28ab + 13b^2\right)$$ is divided by $99741$. | 6,396 | graphs = [
Graph(
let={
"_n": Const(2),
"result": Mod(value=SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a1"), Var("b1")]),... | ALG | null | COMPUTE | sympy | QF_PSD_MIN | [
"QF_PSD_MIN"
] | c66ce3 | alg_qf_psd_sum_v1 | null | 5 | 0 | [
"QF_PSD_MIN"
] | 1 | 0.021 | 2026-02-25T08:00:13.063668Z | {
"verified": true,
"answer": 6396,
"timestamp": "2026-02-25T08:00:13.084354Z"
} | 182543 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 220,
"completion_tokens": 2626
},
"timestamp": "2026-03-30T01:43:25.755Z",
"answer": 6396
},
{
"i... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_MIN",
"status": "ok"
}
] | {
"lo": -3.33,
"mid": 1.03,
"hi": 5.26
} | ||
98ecb3 | nt_count_divisible_and_v1_1248542787_153 | Let $t$ be an integer. Define $S$ as the set of all integers $t$ such that $7 \leq t \leq 22$ and there exist integers $a$ and $b$ satisfying $1 \leq a \leq 6$, $1 \leq b \leq 2$, and $t = 2a + 5b$. Let $d_1$ be the largest integer $k$ such that $11^k$ divides $|S|^{285311670611} - \phi(1)^{285311670611}$. Let $d_2 = 1... | 45,436 | graphs = [
Graph(
let={
"_n": Const(11),
"upper": Const(94968),
"d1": MaxKDivides(target=Sub(Pow(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))... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/LTE_DIFF",
"ONE_PHI_1"
] | da7f9f | nt_count_divisible_and_v1 | null | 7 | 0 | [
"LIN_FORM",
"LTE_DIFF",
"ONE_PHI_1"
] | 3 | 3.576 | 2026-02-08T02:58:25.170319Z | {
"verified": true,
"answer": 45436,
"timestamp": "2026-02-08T02:58:28.745991Z"
} | ee6647 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 320,
"completion_tokens": 7979
},
"timestamp": "2026-02-09T13:39:43.105Z",
"answer": 45436
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "ok_later"
},
{
"lemma": "MOD_ADD",
"status": "no"... | {
"lo": -6.49,
"mid": 0.51,
"hi": 7.52
} | ||
243588 | sequence_fibonacci_compute_v1_124444284_385 | Let $d$ be a positive divisor of 20677. Define $S$ to be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $p < q$, $\gcd(p, q) = 1$, and $pq = 18$. Let $m$ be the smallest integer $d$ such that $d \geq |S|$. Compute the remainder when $44121 \cdot F_m$ is divided by 95464, wh... | 50,281 | graphs = [
Graph(
let={
"_m": Const(44121),
"_n": Const(95464),
"n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(l... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/MIN_PRIME_FACTOR"
] | 52cee2 | sequence_fibonacci_compute_v1 | null | 6 | 0 | [
"COPRIME_PAIRS",
"MIN_PRIME_FACTOR"
] | 2 | 0.003 | 2026-02-08T03:14:43.235565Z | {
"verified": true,
"answer": 50281,
"timestamp": "2026-02-08T03:14:43.239041Z"
} | 559418 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 237,
"completion_tokens": 6886
},
"timestamp": "2026-02-09T16:52:26.425Z",
"answer": 49831
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok_later"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V5",
... | {
"lo": 1.71,
"mid": 5.04,
"hi": 8.38
} | ||
33ee3a | nt_max_prime_below_v1_168721529_208 | Let $S$ be the set of all positive integers $p$ such that there exists a positive integer $q$ satisfying $pq = 24$, $\gcd(p, q) = 1$, and $p < q$. Let $T$ be the set of all prime numbers $n$ such that $n \geq |S|$ and $n \leq 77841$. Determine the value of the largest element in $T$. | 77,839 | graphs = [
Graph(
let={
"upper": Const(77841),
"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 | 4.399 | 2026-02-08T12:54:16.792697Z | {
"verified": true,
"answer": 77839,
"timestamp": "2026-02-08T12:54:21.191474Z"
} | 4981e1 | CC BY 4.0 | [
{
"id": 4,
"model": "NousResearch/Hermes-4-405B",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 149,
"completion_tokens": 4575
},
"timestamp": "2026-02-09T14:30:04.657Z",
"answer": 77839
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -6.97,
"mid": -4.58,
"hi": -1.65
} | ||
b8ce0f | nt_count_primes_v1_2051736721_5214 | Let $s$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 400$. Let $c$ be the number of positive integers $n_1$ with $1 \le n_1 \le s$ such that $15$ divides the $n_1$-th Fibonacci number. Determine the value of the number of prime numbers $n$ such that $c \le n \le 1... | 1,900 | 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(400)))), expr=Sum(Var("x"), Var("y")))),
"upper": Const(163... | NT | null | COUNT | sympy | B3 | [
"B3/COUNT_FIB_DIVISIBLE"
] | 9b7a57 | nt_count_primes_v1 | null | 6 | 0 | [
"B3",
"COUNT_FIB_DIVISIBLE"
] | 2 | 0.358 | 2026-02-08T18:25:30.104562Z | {
"verified": true,
"answer": 1900,
"timestamp": "2026-02-08T18:25:30.462789Z"
} | 41bad4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 149,
"completion_tokens": 2461
},
"timestamp": "2026-02-18T16:47:11.613Z",
"answer": 1900
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok_later"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
2622c0 | alg_poly3_sum_v1_1218484723_6850 | Find the remainder when
$$
\sum_{a=1}^{327} \sum_{b=1}^{327} \left( 39a^2b + \sum_{k=1}^{5} k a b^2 - 63a^3 - 26b^3 \right)
$$
is divided by $75322$. | 15,874 | graphs = [
Graph(
let={
"_n": Const(5),
"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(327)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(327)))), expr=Sum(Mul(Const(... | ALG | null | COMPUTE | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | alg_poly3_sum_v1 | null | 4 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.229 | 2026-02-25T08:18:46.564856Z | {
"verified": true,
"answer": 15874,
"timestamp": "2026-02-25T08:18:46.793979Z"
} | 058db6 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 183,
"completion_tokens": 11407
},
"timestamp": "2026-03-30T02:50:28.882Z",
"answer": 15874
},
{
... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
}
] | {
"lo": 1.53,
"mid": 4.7,
"hi": 7.23
} | ||
f06aef | algebra_vieta_sum_v1_601307018_7153 | Let $M$ be the sum of all positive integers $x$ satisfying $x^2 - 9x + d = 0$, where $d$ is the largest positive divisor of $342$ such that $d^2 \leq 342$. Find the remainder when $44121 \cdot M$ is divided by $99191€. | 325 | graphs = [
Graph(
let={
"_n": Const(44121),
"result": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Const(2)), Mul(Const(-9), Var("x")), MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Divides(divisor=Var("d"), dividend=Cons... | NT | null | COMPUTE | sympy | POLY_ORBIT_HENSEL | [
"B3_CLOSEST"
] | 25e610 | algebra_vieta_sum_v1 | null | 4 | 0 | [
"B3_CLOSEST",
"POLY_ORBIT_HENSEL"
] | 2 | 0.393 | 2026-03-10T07:46:16.995883Z | {
"verified": true,
"answer": 325,
"timestamp": "2026-03-10T07:46:17.388510Z"
} | 4a9ccc | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 183,
"completion_tokens": 802
},
"timestamp": "2026-04-19T06:06:14.662Z",
"answer": 325
},
{
"id... | 1 | [
{
"lemma": "B3_CLOSEST",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
604965 | nt_count_coprime_v1_124444284_3530 | Let $r$ be the sum of all real numbers $x$ such that $x^2 - 17x - 4898 = 0$. Let $N$ be the number of positive integers $n$ less than or equal to $34969$ for which $\gcd(n, r) = 1$. Compute $N$. | 32,912 | graphs = [
Graph(
let={
"upper": Const(34969),
"k": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Const(2)), Mul(Const(-17), Var("x")), Const(-4898)), Const(0)))),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"),... | NT | null | COUNT | sympy | VIETA_SUM | [
"VIETA_SUM"
] | b33a7a | nt_count_coprime_v1 | null | 4 | 0 | [
"VIETA_SUM"
] | 1 | 5.504 | 2026-02-08T05:26:20.599617Z | {
"verified": true,
"answer": 32912,
"timestamp": "2026-02-08T05:26:26.103173Z"
} | 2d2b06 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 117,
"completion_tokens": 582
},
"timestamp": "2026-02-12T08:36:24.664Z",
"answer": 32912
},
{... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
},
{
"lemma": "VIETA_SUM",
"stat... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
275798 | modular_min_linear_v1_1248542787_299 | Let $\phi(n)$ denote Euler's totient function. Find the smallest nonnegative integer $x$ such that $20673x \equiv 14703 \pmod{38018}$ and $x \leq 38018$. Let this value be $r$. Determine the smallest positive integer $k$ such that the $k$th Fibonacci number is divisible by $|r| + 2$. | 31,644 | graphs = [
Graph(
let={
"a": Const(20673),
"b": Const(14703),
"m": Const(38018),
"result": MinOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), EulerPhi(n=Const(1))), Leq(Var("x"), Ref("m")), Eq(Mod(value=Mul(Ref("a"), Var("x")), modulus=Ref("... | NT | null | EXTREMUM | sympy | ONE_PHI_1 | [
"ONE_PHI_1"
] | f6b5a5 | modular_min_linear_v1 | null | 6 | 0 | [
"ONE_PHI_1"
] | 1 | 2.225 | 2026-02-08T03:03:03.936921Z | {
"verified": true,
"answer": 31644,
"timestamp": "2026-02-08T03:03:06.162196Z"
} | 0cf6c0 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 195,
"completion_tokens": 6316
},
"timestamp": "2026-02-09T14:57:16.373Z",
"answer": 31644
},
{
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "ONE_PHI_1",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
... | {
"lo": -6.49,
"mid": 0.51,
"hi": 7.52
} | ||
ba2d13 | nt_count_with_divisor_count_v1_2051736721_2748 | Let $n$ be a positive integer such that $1 \leq n \leq 27225$ and the number of positive divisors of $n$ is exactly 5. Let $A$ be the number of such integers $n$. Let $B$ be the smallest divisor of 35 that is at least 2. Compute $B - A$. | 0 | graphs = [
Graph(
let={
"upper": Const(27225),
"div_count": Const(5),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(NumDivisors(n=Var("n")), Ref("div_count"))))),
"_c": MinOverSet(s... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MIN_PRIME_FACTOR"
] | fd27b3 | nt_count_with_divisor_count_v1 | negation_mod | 3 | 0 | [
"MAX_PRIME_BELOW",
"MIN_PRIME_FACTOR"
] | 2 | 3.786 | 2026-02-08T16:53:12.047214Z | {
"verified": true,
"answer": 0,
"timestamp": "2026-02-08T16:53:15.832859Z"
} | 64575f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 120,
"completion_tokens": 672
},
"timestamp": "2026-02-17T14:47:10.594Z",
"answer": 0
},
{
... | 1 | [
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
07ea97 | modular_modexp_compute_v1_1742523217_3939 | Let $e$ be the number of integers $n$ with $1 \leq n \leq 1057$ such that the sum of the decimal digits of $n$ is odd. Compute the remainder when $41^e$ is divided by $17424$. | 17,321 | graphs = [
Graph(
let={
"_n": Const(2),
"a": Const(41),
"e": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(1057)), Eq(Mod(value=DigitSum(Var("n")), modulus=Ref("_n")), Const(1))))),
"m": Const(17424),
... | NT | null | COMPUTE | sympy | L3B | [
"L3B"
] | cc148f | modular_modexp_compute_v1 | null | 5 | 0 | [
"L3B"
] | 1 | 0.001 | 2026-02-08T06:09:23.104389Z | {
"verified": true,
"answer": 17321,
"timestamp": "2026-02-08T06:09:23.105361Z"
} | db7972 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 102,
"completion_tokens": 3896
},
"timestamp": "2026-02-12T20:09:32.464Z",
"answer": 17321
},
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "L3B",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V5",
"status": "n... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
b4a087_l | geo_count_lattice_rect_v1_784195855_7193 | Let $a = 349$ and $b = 105$. Define $R$ to be the number of lattice points in the rectangle $[0, a] \times [0, b]$, including the boundary. Let $r$ be the remainder when $|R|$ is divided by $11$. Compute the Bell number $B_r$, which counts the number of partitions of a set of $r$ elements. Find the value of $B_r$. | 1 | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 4 | 0 | null | null | 0.002 | 2026-02-08T09:08:25.147989Z | {
"verified": false,
"answer": 4140,
"timestamp": "2026-02-08T09:08:25.149540Z"
} | 10ea69 | b4a087 | legacy_text | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 206,
"completion_tokens": 1630
},
"timestamp": "2026-02-24T10:34:52.718Z",
"answer": 4140
},
{
"i... | 1 | [] | {
"lo": -3.84,
"mid": -1.67,
"hi": 1.32
} | |||
1da02c | alg_poly_preperiod_count_v1_601307018_576 | Let $N = (a^2 + a - 12) \bmod 31$, $M = (N^2 + N - 12) \bmod 31$, $R = (M^2 + M - 12) \bmod 31$, and $S = (R^2 + R - 12) \bmod 31$. Find the number of non-negative integers $a$ with $0 \leq a \leq 12523$ such that $S = N$, $M \neq N$, and $R \neq N$. | 4,848 | graphs = [
Graph(
let={
"p1": Mod(value=Sum(Pow(Var("a"), Const(2)), Var("a"), Const(-12)), modulus=Const(31)),
"p2": Mod(value=Sum(Pow(Ref("p1"), Const(2)), Ref("p1"), Const(-12)), modulus=Const(31)),
"p3": Mod(value=Sum(Pow(Ref("p2"), Const(2)), Ref("p2"), Const(-12)), ... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_preperiod_count_v1 | null | 6 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.042 | 2026-03-10T01:06:33.526138Z | {
"verified": true,
"answer": 4848,
"timestamp": "2026-03-10T01:06:33.568187Z"
} | b0b05e | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 232,
"completion_tokens": 9022
},
"timestamp": "2026-03-28T23:26:42.791Z",
"answer": 4848
},
{
"i... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 1.27,
"mid": 3.84,
"hi": 5.91
} | ||
64e7a6 | antilemma_k3_v1_2051736721_2999 | Let $n = 36998$. Compute the sum of $\phi(d)$ over all positive divisors $d$ of $n$, where $\phi$ denotes Euler's totient function. | 36,998 | graphs = [
Graph(
let={
"_n": Const(36998),
"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 | 2026-02-08T17:03:49.145362Z | {
"verified": true,
"answer": 36998,
"timestamp": "2026-02-08T17:03:49.146248Z"
} | 2f9907 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 100,
"completion_tokens": 1401
},
"timestamp": "2026-02-16T08:57:47.839Z",
"answer": 10720
},
{
"id": 11... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
e2bed7 | sequence_lucas_compute_v1_655260480_4849 | Let $m = 18$. Define $s = \sum_{d \mid m} \phi(d)$, where $\phi$ denotes Euler's totient function. Let $n$ be the largest positive divisor of 342 that is less than or equal to $s$. Let $L_n$ denote the $n$th Lucas number, defined by $L_1 = 1$, $L_2 = 3$, and $L_k = L_{k-1} + L_{k-2}$ for $k \geq 3$. Compute the remaind... | 45,417 | graphs = [
Graph(
let={
"_m": Const(18),
"_n": SumOverDivisors(n=Ref(name='_m'), var='d', expr=EulerPhi(n=Var(name='d'))),
"n": MaxOverSet(set=SolutionsSet(var=Var("d1"), condition=And(Geq(Var("d1"), Const(1)), Leq(Var("d1"), Ref("_n")), Divides(divisor=Var("d1"), dividen... | NT | null | COMPUTE | sympy | K3 | [
"K3/MAX_DIVISOR"
] | 43ff77 | sequence_lucas_compute_v1 | null | 4 | 0 | [
"K3",
"MAX_DIVISOR"
] | 2 | 0.002 | 2026-02-08T18:09:01.442610Z | {
"verified": true,
"answer": 45417,
"timestamp": "2026-02-08T18:09:01.444939Z"
} | a52776 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 179,
"completion_tokens": 2029
},
"timestamp": "2026-02-18T14:57:31.297Z",
"answer": 45417
},
... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok_later"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
b8b7bb | nt_sum_divisors_mod_v1_153355830_1142 | Let $n$ be the number of integers $t$ such that $7 \leq t \leq 372$ and $t = 3a + 4b$ for some positive integers $a \leq 120$ and $b \leq 3$. Let $M = 10861$. Compute the remainder when the sum of all positive divisors of $n$ is divided by $M$. | 1,170 | 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=120)), Geq(left=Var(name='b'), right=Const(value... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_sum_divisors_mod_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T04:25:02.117796Z | {
"verified": true,
"answer": 1170,
"timestamp": "2026-02-08T04:25:02.119740Z"
} | 6ef18a | 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": 1314
},
"timestamp": "2026-02-12T20:26:00.767Z",
"answer": 1170
},
{... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
09b956 | nt_euler_phi_compute_v1_124444284_713 | Let $m_0=67081$. Let $A$ be the set of all positive integers $p$ such that there exists a positive integer $q$ with $pq=24$, $\gcd(p,q)=1$, and $p<q$. Let $n_0$ be the number of elements in $A$.
Let $B$ be the set of all integers $d$ such that $d\ge n_0$ and $d$ divides $20677$, and let $n_1$ be the smallest element o... | 55,944 | graphs = [
Graph(
let={
"_m": Const(67081),
"_n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=24)), Eq(left=GCD(a=Var(name='p'), b=Var(nam... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/MIN_PRIME_FACTOR/EULER_TOTIENT_SUM",
"WILSON"
] | 9caf8d | nt_euler_phi_compute_v1 | null | 7 | 2 | [
"COPRIME_PAIRS",
"EULER_TOTIENT_SUM",
"MIN_PRIME_FACTOR",
"WILSON"
] | 4 | 0.004 | 2026-02-08T03:27:56.114481Z | {
"verified": true,
"answer": 55944,
"timestamp": "2026-02-08T03:27:56.118503Z"
} | 1b0558 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 323,
"completion_tokens": 1676
},
"timestamp": "2026-02-09T20:58:20.613Z",
"answer": 55944
},
{
"... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "EULER_TOTIENT_SUM",
"status": "ok_later"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok_later"
},
{
"lemma": "MOD_ADD",
... | {
"lo": -6.51,
"mid": -0.31,
"hi": 5.43
} | ||
f9392e_n | alg_qf_psd_count_v1_1419126231_1899 | A game designer assigns scores based on two player stats, $a$ and $b$, each ranging from 1 to 109. A combo is valid if the score expression $10a^2 - 10ab + 5b^2$ equals exactly 31450. How many valid stat combinations $(a, b)$ exist? | 10 | ALG | null | COUNT | sympy | K2 | [
"K2/V8"
] | c69745 | alg_qf_psd_count_v1 | null | 3 | null | [
"K2",
"V8"
] | 2 | 0.318 | 2026-02-25T11:27:42.698547Z | null | c3a712 | f9392e | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 179,
"completion_tokens": 23801
},
"timestamp": "2026-03-31T05:13:41.287Z",
"answer": 9
},
{
"i... | 1 | [
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8",
"status": "ok_later"
}
] | {
"lo": 1.5,
"mid": 4.69,
"hi": 7.23
} | |
85f636 | geo_count_lattice_triangle_v1_601307018_8316 | Let $R$ be the number of positive integers $v$ with $10 \leq v \leq \min\{ x + y : x,y > 0,\ xy = 1918225,\ x \leq y \}$ such that there exist integers $a,b$ with $1 \leq a,b \leq 11$ satisfying $25a^2 - 24ab + 9b^2 = v$. Let $S = |111 \cdot 128 + 49 \cdot (-64)|$. Let $$T = \gcd(R, 64) + \gcd(|49 - 111|, |128 - 64|) +... | 14,319 | graphs = [
Graph(
let={
"_c": Const(2),
"_m": Const(20),
"_n": CountOverSet(set=SolutionsSet(var=Var("v"), condition=And(Geq(Var("v"), Const(10)), Leq(Var("v"), MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(a... | GEOM | NT | COUNT | sympy | B3 | [
"B3/QF_PSD_DISTINCT/QF_PSD_MIN"
] | b70603 | geo_count_lattice_triangle_v1 | null | 7 | 0 | [
"B3",
"QF_PSD_DISTINCT",
"QF_PSD_MIN"
] | 3 | 0.022 | 2026-03-10T08:48:42.525261Z | {
"verified": true,
"answer": 14319,
"timestamp": "2026-03-10T08:48:42.547737Z"
} | 41928d | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 337,
"completion_tokens": 19191
},
"timestamp": "2026-04-19T08:50:09.980Z",
"answer": 14319
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "QF_PSD_DISTINCT",
"status": "ok_later"
},
{
"lemma": "QF_PSD_MIN",
"status": "ok_later"
}
] | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
c9fe6b | comb_count_derangements_v1_1915831931_1960 | Let $n$ be the largest prime number satisfying $2 \leq n \leq 7$. Compute the number of derangements of $n$ elements. | 1,854 | graphs = [
Graph(
let={
"_n": Const(2),
"n": MaxOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Ref("_n")), Leq(Var("n1"), Const(7)), IsPrime(Var("n1"))))),
"result": Subfactorial(arg=Ref(name='n')),
},
goal=Ref("result"),
)
] | NT | COMB | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | comb_count_derangements_v1 | null | 2 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.002 | 2026-02-08T16:33:10.025474Z | {
"verified": true,
"answer": 1854,
"timestamp": "2026-02-08T16:33:10.027680Z"
} | 099a7c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 79,
"completion_tokens": 1000
},
"timestamp": "2026-02-17T06:48:57.391Z",
"answer": 1854
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V3",
"status": ... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
05fef2 | geo_count_lattice_rect_v1_717093673_3631 | Let $a = 43$ and $b = 65$. Compute the number of lattice points in the rectangle $[0, a] \times [0, b]$, including the boundary.
Find the value of this number. | 2,904 | graphs = [
Graph(
let={
"a": Const(43),
"b": Const(65),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.001 | 2026-02-08T17:43:56.640227Z | {
"verified": true,
"answer": 2904,
"timestamp": "2026-02-08T17:43:56.641486Z"
} | 60098f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 95,
"completion_tokens": 469
},
"timestamp": "2026-02-24T22:58:25.578Z",
"answer": 2904
},
{
... | 1 | [] | {
"lo": -8.52,
"mid": -5.43,
"hi": -3.2
} | ||||
a9d57e | alg_poly4_min_v1_1218484723_729 | Find the minimum value of $15552a^3b + 27648ab^3 + 2916a^4 + 18432b^4 + 31104a^2b^2$ over all ordered pairs $(a, b)$ of positive integers with $1 \leq a \leq 169$ and $1 \leq b \leq B$, where $B = \max\{ xy : x > 0, y > 0, x + y = N \}$ and $N$ is the number of ordered pairs $(a_1, b_1)$ with $1 \leq a_1, b_1 \leq 30$ ... | 95,652 | graphs = [
Graph(
let={
"_n": Const(169),
"result": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Ref("_n")), Geq(Var("b"), Const(1)), Leq(Var("b"), MaxOverSet(set=MapOverSet(set=SolutionsSet(... | ALG | null | COMPUTE | sympy | POLY4_COUNT | [
"POLY4_COUNT/B1"
] | 9db650 | alg_poly4_min_v1 | null | 6 | 0 | [
"B1",
"POLY4_COUNT"
] | 2 | 0.117 | 2026-02-25T02:28:01.184319Z | {
"verified": true,
"answer": 95652,
"timestamp": "2026-02-25T02:28:01.301497Z"
} | d66d4a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 313,
"completion_tokens": 3943
},
"timestamp": "2026-03-10T01:14:14.275Z",
"answer": 95652
},
{
"... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "POLY4_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -2.78,
"mid": -0.24,
"hi": 2.7
} | ||
3f863f | diophantine_fbi2_count_v1_153355830_753 | Let $k = 420$. Let $T$ be the set of all integers $t$ such that $8 \leq t \leq 84$ and there exist positive integers $a$, $b$ with $1 \leq a \leq 9$, $1 \leq b \leq 13$, and $t = 5a + 3b$.\\
Let $D$ be the number of positive divisors $d$ of $k$ such that $6 \leq d \leq |T|$, $\frac{k}{d} \geq 3$, and $\frac{k}{d} \leq... | 47,159 | graphs = [
Graph(
let={
"_n": Const(3),
"k": Const(420),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(6)), Leq(Var("d"), CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(nam... | NT | null | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC",
"LIN_FORM"
] | 7209d0 | diophantine_fbi2_count_v1 | null | 4 | 0 | [
"LIN_FORM",
"SUM_ARITHMETIC"
] | 2 | 0.015 | 2026-02-08T04:09:49.937382Z | {
"verified": true,
"answer": 47159,
"timestamp": "2026-02-08T04:09:49.952441Z"
} | 9c2e38 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 281,
"completion_tokens": 4891
},
"timestamp": "2026-02-10T15:32:20.254Z",
"answer": 47159
},
{
... | 1 | [
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"le... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
dc7f18 | comb_catalan_compute_v1_548369836_291 | Let $n$ be the number of integers $t$ with $5 \leq t \leq 17$ for which there exist positive integers $a$ and $b$ such that $1 \leq a \leq 4$, $1 \leq b \leq 3$, and $t = 2a + 3b$. Compute the $n$-th Catalan number, defined by $$C_n = \frac{1}{n+1} \binom{2n}{n}.$$ | 58,786 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=4)), Geq(left=Var(name='b'), right=Const(value=1... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_catalan_compute_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.003 | 2026-02-08T02:51:28.086840Z | {
"verified": true,
"answer": 58786,
"timestamp": "2026-02-08T02:51:28.089627Z"
} | ef4ffa | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 226,
"completion_tokens": 1439
},
"timestamp": "2026-02-08T20:17:39.620Z",
"answer": 58786
},
{
"... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"s... | {
"lo": -1.87,
"mid": 0.05,
"hi": 1.73
} | ||
893c66 | nt_count_divisible_and_v1_2051736721_2619 | Let $d_1$ be the number of integers $t$ such that $5 \le t \le 12$ and there exist positive integers $a \le 3$, $b \le 2$ satisfying $t = 2a + 3b$. Let $d_2 = 9$. Determine the number of positive integers $n$ such that $1 \le n \le 22662$, $n$ is divisible by $d_1$, and $n$ is divisible by $d_2$. | 1,259 | graphs = [
Graph(
let={
"upper": Const(22662),
"d1": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=3)), Geq(lef... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_count_divisible_and_v1 | null | 3 | 0 | [
"LIN_FORM"
] | 1 | 6.965 | 2026-02-08T16:49:01.674958Z | {
"verified": true,
"answer": 1259,
"timestamp": "2026-02-08T16:49:08.639612Z"
} | 5cca6f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 158,
"completion_tokens": 816
},
"timestamp": "2026-02-17T12:04:40.987Z",
"answer": 1259
},
{
... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
4f9be9 | comb_count_partitions_v1_717093673_884 | Let $N = 94987$. Let $A$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 6$, $\gcd(p, q) = 1$, and $p < q$. Let $d_0$ be the smallest positive divisor of $N$ that is at least the number of elements in $A$. Compute the number of integer partitions of $d_0$. | 63,261 | graphs = [
Graph(
let={
"_n": Const(94987),
"n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name=... | NT | COMB | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/MIN_PRIME_FACTOR"
] | 52cee2 | comb_count_partitions_v1 | null | 5 | 0 | [
"COPRIME_PAIRS",
"MIN_PRIME_FACTOR"
] | 2 | 0.002 | 2026-02-08T15:44:41.360856Z | {
"verified": true,
"answer": 63261,
"timestamp": "2026-02-08T15:44:41.362659Z"
} | 9fc46d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 142,
"completion_tokens": 1250
},
"timestamp": "2026-02-16T12:11:06.651Z",
"answer": 63261
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
96af86 | antilemma_v1_legendre_1520064083_2622 | Compute the largest integer $x$ such that $7^x$ divides $54376!$. | 9,060 | graphs = [
Graph(
let={
"x": MaxKDivides(target=Factorial(Const(54376)), base=Const(7)),
},
goal=Ref("x"),
)
] | NT | null | COMPUTE | sympy | V1 | [
"V1"
] | dae96f | antilemma_v1_legendre | null | 5 | 0 | [
"V1"
] | 1 | 0 | 2026-02-08T04:53:28.766874Z | {
"verified": true,
"answer": 9060,
"timestamp": "2026-02-08T04:53:28.767221Z"
} | 6692dc | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 116,
"completion_tokens": 590
},
"timestamp": "2026-02-18T14:34:11.643Z",
"answer": 9060
}
] | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K5",
"status": "same_pattern_wrong"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"... | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
d8d16b | diophantine_fbi2_min_v1_971394319_2006 | Let $k = 14$. Define $T$ as the set of all integers $t$ such that $9 \leq t \leq 44$ and there exist integers $a$ and $b$ with $1 \leq a \leq 6$, $1 \leq b \leq 4$, and $t = 4a + 5b$. Let $\text{upper}$ be the number of elements in $T$. Find the smallest integer $d$ such that $6 \leq d \leq \text{upper}$, $d$ divides $... | 7 | graphs = [
Graph(
let={
"_n": Const(2),
"k": Const(14),
"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=... | NT | null | EXTREMUM | sympy | MIN_PRIME_FACTOR | [
"LIN_FORM",
"L3B"
] | f85b0e | diophantine_fbi2_min_v1 | null | 4 | 0 | [
"L3B",
"LIN_FORM",
"MIN_PRIME_FACTOR"
] | 3 | 0.126 | 2026-02-08T14:05:00.879075Z | {
"verified": true,
"answer": 7,
"timestamp": "2026-02-08T14:05:01.005503Z"
} | 207d8c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 185,
"completion_tokens": 2239
},
"timestamp": "2026-02-15T23:41:46.355Z",
"answer": 7
},
{
... | 1 | [
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3B",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"le... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
c91a34 | comb_count_permutations_fixed_v1_809748730_1678 | Let $n$ be the smallest integer $d \geq 2$ that divides 77. Compute $\binom{n}{0} \cdot !n$, where $!n$ denotes the number of derangements of $n$ elements. | 1,854 | graphs = [
Graph(
let={
"_n": Const(2),
"n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(77))))),
"k": Const(0),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub(le... | NT | COMB | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | comb_count_permutations_fixed_v1 | null | 3 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.002 | 2026-02-08T12:37:33.504552Z | {
"verified": true,
"answer": 1854,
"timestamp": "2026-02-08T12:37:33.506060Z"
} | 5c9de5 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 96,
"completion_tokens": 1314
},
"timestamp": "2026-02-15T02:56:36.232Z",
"answer": 1854
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
... | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
e36e78 | nt_count_with_divisor_count_v1_124444284_4202 | Let $ n = 84391 $ and $ u = 30976 $. Let $ d_0 $ be the smallest divisor of $ 1001 $ that is at least $ 2 $. Define $ c $ to be the number of positive integers $ n $ such that $ 1 \leq n \leq u $ and the number of positive divisors of $ n $ is equal to $ d_0 $. Compute the remainder when $ 44121 \times c $ is divided b... | 47,972 | graphs = [
Graph(
let={
"_n": Const(84391),
"upper": Const(30976),
"div_count": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(1001))))),
"result": CountOverSet(set=SolutionsSet(var=Var... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | nt_count_with_divisor_count_v1 | null | 3 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 2.223 | 2026-02-08T05:51:06.049926Z | {
"verified": true,
"answer": 47972,
"timestamp": "2026-02-08T05:51:08.273239Z"
} | c3e721 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 149,
"completion_tokens": 1049
},
"timestamp": "2026-02-12T15:28:07.923Z",
"answer": 47972
},
... | 1 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V8",
"status": "... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
65b6e6 | modular_min_linear_v1_1470522791_320 | Let $ m = 69069 $, $ a = 22961 $, and $ b = 30329 $. Let $ x $ be the smallest positive integer solution to the congruence $ ax \equiv b \pmod{m} $. Compute the value of
\[
353702 \cdot (|x| \bmod 97) + 329703 \cdot (x^2 + 1 \bmod 101) + 215534 \cdot \left(|x| + 1 \bmod d_0\right),
\]
where $ d_0 $ is the smallest divi... | 52,229 | graphs = [
Graph(
let={
"_n": Const(2),
"a": Const(22961),
"b": Const(30329),
"m": Const(69069),
"result": MinOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), Const(1)), Leq(Var("x"), Ref("m")), Eq(Mod(value=Mul(Ref("a"), Var("x")... | NT | null | EXTREMUM | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | b5b91a | modular_min_linear_v1 | crt_mix_3 | 6 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 3.067 | 2026-02-08T12:56:39.153611Z | {
"verified": true,
"answer": 52229,
"timestamp": "2026-02-08T12:56:42.220158Z"
} | 176b2b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 218,
"completion_tokens": 3736
},
"timestamp": "2026-02-15T07:34:24.384Z",
"answer": 52229
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
c3bb21 | nt_count_divisors_in_range_v1_548369836_335 | Let $n$ be the number of ordered pairs $(i, j)$ such that $1 \leq i \leq 28$ and $1 \leq j \leq 30$. Let $\mathcal{D}$ be the set of all positive divisors $d$ of $n$ satisfying $1 \leq d \leq 216$. Let $r$ be the number of elements in $\mathcal{D}$. Compute $\sum_{k=1}^{r} \phi(k)$, where $\phi$ denotes Euler's totient... | 270 | graphs = [
Graph(
let={
"n": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(28)), right=IntegerRange(start=Const(1), end=Const(30)))),
"a": Const(1),
"b": Const(216),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), conditio... | NT | null | COUNT | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | nt_count_divisors_in_range_v1 | null | 5 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.005 | 2026-02-08T02:52:09.807468Z | {
"verified": true,
"answer": 270,
"timestamp": "2026-02-08T02:52:09.812563Z"
} | c53f54 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 230,
"completion_tokens": 2242
},
"timestamp": "2026-02-23T17:55:30.007Z",
"answer": 270
},
{
"id... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": 0.15,
"mid": 1.94,
"hi": 3.63
} | ||
b9e62e | antilemma_sum_equals_v1_458359167_580 | Let $x$ be the number of ordered pairs $(i, j)$ of positive integers such that $i + j = 83$ and $1 \leq i, j \leq 82$. Compute the remainder when $44121 \cdot x$ is divided by $70612$. | 16,710 | graphs = [
Graph(
let={
"_n": Const(83),
"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(82)), 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 | 0.004 | 2026-02-08T03:25:56.026166Z | {
"verified": true,
"answer": 16710,
"timestamp": "2026-02-08T03:25:56.029702Z"
} | e77e80 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 172,
"completion_tokens": 736
},
"timestamp": "2026-02-10T14:21:24.458Z",
"answer": 16710
},
{
"i... | 1 | [
{
"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": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
99c0ef | nt_num_divisors_compute_v1_1439011603_1190 | Let $n = 29241$. Compute the number of positive divisors of $n$. | 15 | graphs = [
Graph(
let={
"n": Const(29241),
"result": NumDivisors(n=Ref("n")),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | COUNT_COPRIME_GRID | [
"LIN_FORM/B1"
] | b32639 | nt_num_divisors_compute_v1 | null | 2 | 0 | [
"B1",
"COUNT_COPRIME_GRID",
"LIN_FORM"
] | 3 | 0.062 | 2026-02-08T15:58:01.943770Z | {
"verified": true,
"answer": 15,
"timestamp": "2026-02-08T15:58:02.005275Z"
} | 281a57 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 65,
"completion_tokens": 491
},
"timestamp": "2026-02-16T16:51:06.221Z",
"answer": 15
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "n... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
d7f0a2 | antilemma_cartesian_v1_124444284_2905 | Let $x$ be the number of ordered pairs $(i,j)$ where $i$ is an integer from $1$ to $16$ and $j$ is an integer from $1$ to $24$. Compute the smallest positive integer $k$ such that the $k$-th Fibonacci number is divisible by $|x| + 2$. | 291 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(16)), right=IntegerRange(start=Const(1), end=Const(24)))),
"Q": FibonacciEntryPoint(modulus=Sum(Abs(arg=Ref(name='x')), Const(value=2))),
},
goal=Ref("Q"),
)... | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | antilemma_cartesian_v1 | null | 2 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.005 | 2026-02-08T05:04:10.953750Z | {
"verified": true,
"answer": 291,
"timestamp": "2026-02-08T05:04:10.959005Z"
} | 979d4a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 183,
"completion_tokens": 4920
},
"timestamp": "2026-02-24T02:35:48.696Z",
"answer": 291
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": 1.97,
"mid": 4.36,
"hi": 6.69
} | ||
56660a_n | comb_count_surjections_v1_1218484723_6832 | A software system assigns 6 distinct tasks to a set of identical servers, such that no server is idle and each task goes to exactly one server. Initially, a parameter $k$ is computed through a series of inclusion-exclusion-like sums: starting with $R = 4$, compute $c$ as the alternating sum of binomial coefficients $\s... | 720 | COMB | null | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING",
"ZERO_BINOM_0"
] | 38a409 | comb_count_surjections_v1 | null | 4 | null | [
"BINOMIAL_ALTERNATING",
"ZERO_BINOM_0"
] | 2 | 0.002 | 2026-02-25T08:18:23.112123Z | null | 874ab7 | 56660a | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 266,
"completion_tokens": 904
},
"timestamp": "2026-03-31T01:48:31.490Z",
"answer": 720
},
{
"id"... | 2 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V8_S... | {
"lo": -10,
"mid": -5.89,
"hi": -1.79
} | |
702eff | alg_sum_ap_v1_1218484723_6490 | Let $M$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 40$ such that
$$
13a^2 - 2ab + 2b^2 \le 10125.
$$
Let $T$ be the set of integers $t$ for which there exist integers $a, b$ with $1 \le a \le 1989$, $1 \le b \le 958$, $t = 2a + 3b$, and $5 \le t \le 6852$. Define
$$
R = \sum_{k=0}... | 14,232 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(40)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(40)), Leq(Sum(Mul(Const(-2), Var("a"), Var("b")), Mul(Co... | ALG | null | COMPUTE | sympy | QF_PSD_COUNT_LEQ | [
"QF_PSD_COUNT_LEQ/LIN_FORM"
] | 5171b8 | alg_sum_ap_v1 | null | 5 | 0 | [
"LIN_FORM",
"QF_PSD_COUNT_LEQ"
] | 2 | 0.016 | 2026-02-25T08:03:15.375390Z | {
"verified": true,
"answer": 14232,
"timestamp": "2026-02-25T08:03:15.391496Z"
} | 0c253b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 272,
"completion_tokens": 28190
},
"timestamp": "2026-03-30T01:58:18.459Z",
"answer": 14232
},
{
... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok_later"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
}
] | {
"lo": 3.81,
"mid": 6.33,
"hi": 9.49
} | ||
bfbb9e | algebra_quadratic_discriminant_v1_2051736721_3754 | Let $a = -1$, $b = 20$, and $c = -100$. Define $\Delta = b^2 - 4ac$. Let $n = 124$. Consider the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = n$. Let $P$ be the maximum value of $xy$ over all such pairs. Compute $\Delta^2 + \Delta + P$. | 3,844 | graphs = [
Graph(
let={
"_n": Const(124),
"a": Const(-1),
"b": Const(20),
"c": Const(-100),
"result": Sub(Pow(Ref("b"), Const(2)), Mul(Const(4), Ref("a"), Ref("c"))),
"_c": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[... | NT | null | COMPUTE | sympy | B1 | [
"B1"
] | bf138c | algebra_quadratic_discriminant_v1 | quadratic_mod | 4 | 0 | [
"B1"
] | 1 | 0.003 | 2026-02-08T17:31:00.009974Z | {
"verified": true,
"answer": 3844,
"timestamp": "2026-02-08T17:31:00.013139Z"
} | 75a6bc | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 152,
"completion_tokens": 250
},
"timestamp": "2026-02-16T09:46:46.793Z",
"answer": 3844
},
{
"id": 11,
... | 2 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
ecf284 | nt_sum_over_divisible_v1_153355830_1385 | Let $T$ be the set of all integers $t$ such that $26 \leq t \leq 143$ and $t = 4a + 7b + 15$ for some positive integers $a \leq 18$ and $b \leq 8$. Let $d$ be the largest positive divisor of $10300$ that does not exceed the number of elements in $T$. Compute the sum of all positive integers $n \leq 68644$ that are divi... | 29,627 | graphs = [
Graph(
let={
"_n": Const(10300),
"upper": Const(68644),
"divisor": MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Leq(Var("d"), CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(va... | NT | null | SUM | sympy | LIN_FORM | [
"LIN_FORM/MAX_DIVISOR"
] | 8c55ae | nt_sum_over_divisible_v1 | null | 5 | 0 | [
"LIN_FORM",
"MAX_DIVISOR"
] | 2 | 4.639 | 2026-02-08T06:22:25.962968Z | {
"verified": true,
"answer": 29627,
"timestamp": "2026-02-08T06:22:30.602212Z"
} | 361815 | 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": 4490
},
"timestamp": "2026-02-12T23:09:29.590Z",
"answer": 29627
},
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok_later"
},
{
"lemma": "MAX_VAL",
"statu... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
f264a3 | nt_count_divisors_in_range_v1_1742523217_2635 | Let $T$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 129600$. Define $n$ to be the minimum value of $x + y$ over all pairs $(x, y) \in T$. Let $S$ be the set of all positive divisors $d$ of $n$ such that $6 \leq d \leq 241$. Compute the remainder when $44121 \cdot |S|$ is divided by $51... | 39,304 | 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(129600)))), expr=Sum(Var("x"), Var("y")))),
"a": Const(6),
... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | nt_count_divisors_in_range_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.006 | 2026-02-08T04:53:35.813172Z | {
"verified": true,
"answer": 39304,
"timestamp": "2026-02-08T04:53:35.818929Z"
} | 84f358 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 219,
"completion_tokens": 2459
},
"timestamp": "2026-02-11T22:20:22.317Z",
"answer": 39304
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
ab292d | nt_count_divisible_v1_397696148_188 | Let $n = 15539$ and $U = 43681$. For each integer $k$, define $c_k = (-1)^k \binom{3}{k}$. Let $T$ be the set of all ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 6$. Let $s$ be the number of elements in $T$, and let $\sigma = \sum_{k=0}^{s} c_k$. Determine the number of integers $m$ such t... | 1,876 | graphs = [
Graph(
let={
"_n": Const(15539),
"upper": Const(43681),
"divisor": Const(20),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(value=Var("n"), modulus=Ref("divisor")), S... | COMB | null | COUNT | sympy | COMB1 | [
"COMB1/BINOMIAL_ALTERNATING"
] | e72f96 | nt_count_divisible_v1 | null | 5 | 0 | [
"BINOMIAL_ALTERNATING",
"COMB1"
] | 2 | 5.567 | 2026-02-08T11:21:20.882398Z | {
"verified": true,
"answer": 1876,
"timestamp": "2026-02-08T11:21:26.448940Z"
} | 1d15d3 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 282,
"completion_tokens": 8510
},
"timestamp": "2026-02-24T13:31:30.963Z",
"answer": 1876
},
{
"i... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
81fd94 | nt_sum_totient_over_divisors_v1_1439011603_590 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 1175056$. Let $n$ be the minimum value of $x + y$ as $(x, y)$ ranges over $S$. Compute $$\sum_{d \mid n} \phi(d).$$ | 2,168 | graphs = [
Graph(
let={
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(1175056)))), expr=Sum(Var("x"), Var("y")))),
"result": SumOv... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_totient_over_divisors_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.002 | 2026-02-08T15:36:05.594989Z | {
"verified": true,
"answer": 2168,
"timestamp": "2026-02-08T15:36:05.597049Z"
} | 9a7217 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 115,
"completion_tokens": 2620
},
"timestamp": "2026-02-16T10:11:26.267Z",
"answer": 2168
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
b9f670 | modular_min_modexp_v1_1520064083_963 | Let $a = 2$, $b = 312$, and $m = 773$. Define $N$ to be the number of ordered pairs $(i, j)$ such that $1 \leq i \leq 4$ and $1 \leq j \leq 193$. Determine the smallest positive integer $x$ such that $1 \leq x \leq N$ and $$a^x \equiv b \pmod{m}.$$ | 611 | graphs = [
Graph(
let={
"a": Const(2),
"b": Const(312),
"m": Const(773),
"upper": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(4)), right=IntegerRange(start=Const(1), end=Const(193)))),
"result": MinOverSet(set=Solu... | NT | null | EXTREMUM | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | modular_min_modexp_v1 | null | 7 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.09 | 2026-02-08T03:41:34.275922Z | {
"verified": true,
"answer": 611,
"timestamp": "2026-02-08T03:41:34.365717Z"
} | 8c4495 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 210,
"completion_tokens": 5456
},
"timestamp": "2026-02-10T15:34:48.844Z",
"answer": 611
},
{
"id... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8",
"status": "n... | {
"lo": -3.53,
"mid": 1.02,
"hi": 5.49
} | ||
1c94ef | comb_sum_binomial_row_v1_548369836_419 | Let $m=3$. Consider all ordered pairs $(x_1,x_2)$ of positive integers such that $x_1$ and $x_2$ are both odd and
$$x_1+x_2=4.$$
Let $n_0$ be the number of such ordered pairs.
Let $n_2=0$ and
$$s=\sum_{k=0}^{n_2}(-1)^k\binom{n_2}{k}.$$
Let $a=1$ and $b=ms$, and define
$$n_1=a+b.$$
Let
$$c=\sum_{k=\binom{8}{8}-1}^{n_1... | 65,536 | graphs = [
Graph(
let={
"_m": Const(3),
"_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")), Co... | COMB | null | SUM | sympy | COMB1 | [
"COMB1/COUNT_CARTESIAN/BINOMIAL_ALTERNATING",
"ZERO_BINOM_N"
] | c51063 | comb_sum_binomial_row_v1 | null | 4 | 2 | [
"BINOMIAL_ALTERNATING",
"COMB1",
"COUNT_CARTESIAN",
"ZERO_BINOM_N"
] | 4 | 0.003 | 2026-02-08T02:54:15.659920Z | {
"verified": true,
"answer": 65536,
"timestamp": "2026-02-08T02:54:15.663136Z"
} | 12cdee | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 337,
"completion_tokens": 938
},
"timestamp": "2026-02-08T20:27:02.062Z",
"answer": 65536
},
{
"i... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok_later"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "CO... | {
"lo": -5.97,
"mid": -3.96,
"hi": -1.98
} | ||
1ce729 | alg_qf_psd_count_leq_v1_1419126231_1018 | Find the number of ordered triples $(a, b, c)$ of integers with $1 \le a, b, c \le 12$ such that $$
-588ac + 882c^2 + \left|\left\{ (a_1, b_1) \in \mathbb{Z}^2 : 1 \le a_1, b_1 \le 40,\ -2a_1b_1 + 41b_1^2 + 2a_1^2 \le 52688 \right\}\right| \cdot b^2 + 1862a^2 -1372bc + 2744ab \le 91091.
$$ | 272 | graphs = [
Graph(
let={
"_n": Const(2),
"result": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b"), Var("c")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(12)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(12)), Geq(Var("c"), Const(1)), Leq(Var("c"... | ALG | null | COUNT | sympy | QF_PSD_COUNT_LEQ | [
"QF_PSD_COUNT_LEQ"
] | 009d0f | alg_qf_psd_count_leq_v1 | null | 5 | 0 | [
"QF_PSD_COUNT_LEQ"
] | 1 | 0.017 | 2026-02-25T10:31:39.012584Z | {
"verified": true,
"answer": 272,
"timestamp": "2026-02-25T10:31:39.029837Z"
} | 4d7d16 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 260,
"completion_tokens": 32768
},
"timestamp": "2026-03-30T11:11:27.667Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
}
] | {
"lo": 3.8,
"mid": 6.33,
"hi": 9.49
} | ||
aa9277 | nt_count_divisors_in_range_v1_124444284_4546 | Let $P$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 396900$. Let $n$ be the minimum value of $x + y$ as $(x, y)$ ranges over $P$. Let $A$ be the set of all positive divisors $d$ of $n$ such that $5 \leq d \leq 147$. Let $a$ be the number of elements in $A$. Let $B$ be the set of all in... | 215 | 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")))),
"a": Const(5),
... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM",
"B3"
] | ad075d | nt_count_divisors_in_range_v1 | negation_mod | 6 | 0 | [
"B3",
"LIN_FORM"
] | 2 | 0.007 | 2026-02-08T06:05:09.536075Z | {
"verified": true,
"answer": 215,
"timestamp": "2026-02-08T06:05:09.542626Z"
} | 20d717 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 235,
"completion_tokens": 4332
},
"timestamp": "2026-02-12T19:09:56.425Z",
"answer": 215
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
4b25d7 | comb_count_permutations_fixed_v1_865884756_309 | Consider the Cartesian product of the integer intervals $\{1,2,3\}$ and $\{1,2,3\}$. Let $N$ be the number of ordered pairs in this product.
Let $n_{2}=0$ and define
$$c=\sum_{k=\binom{16}{0}-1}^{n_{2}} (-1)^{k}\binom{n_{2}}{k}.$$
Let $n_{1}=0$ and define
$$e=\sum_{k=0}^{n_{1}} (-1)^{k}\binom{n_{1}}{k}.$$
Let
$$n=N\c... | 86,703 | graphs = [
Graph(
let={
"_m": Const(89273),
"_n": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(3)), right=IntegerRange(start=Const(1), end=Const(3)))),
"n2": Const(0),
"c": Summation(var="k1", start=Sub(Binom(n=Const(16), k=Con... | COMB | null | COUNT | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN/COMB1/BINOMIAL_ALTERNATING",
"LIN_FORM/COMB1",
"ZERO_BINOM_0"
] | 0fdb62 | comb_count_permutations_fixed_v1 | null | 6 | 2 | [
"BINOMIAL_ALTERNATING",
"COMB1",
"COUNT_CARTESIAN",
"LIN_FORM",
"ZERO_BINOM_0"
] | 5 | 0.006 | 2026-02-08T15:18:34.745605Z | {
"verified": true,
"answer": 86703,
"timestamp": "2026-02-08T15:18:34.751435Z"
} | b7db2f | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 440,
"completion_tokens": 3196
},
"timestamp": "2026-02-24T20:21:34.393Z",
"answer": 86703
},
{
"... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok_later"
},
{
"lemma": "COMB1",
"status": "ok_later"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
... | {
"lo": -2.43,
"mid": 1.2,
"hi": 4.84
} | ||
bb0dc7 | diophantine_fbi2_min_v1_1742523217_630 | Let $k = 27$, $a = 4$, $b = 2$, and $u = 37$. Find the smallest positive integer $d$ such that $d \geq 5$, $d \leq u$, $d$ divides $k$, and $\frac{k}{d} \geq 3$. Compute the value of $d$. | 9 | graphs = [
Graph(
let={
"k": Const(27),
"a": Const(4),
"b": Const(2),
"upper": Const(37),
"result": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(5)), Leq(Var("d"), Ref("upper")), Divides(divisor=Var("d"), dividend=Ref... | NT | null | EXTREMUM | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC",
"COPRIME_PAIRS"
] | ac053f | diophantine_fbi2_min_v1 | null | 2 | 0 | [
"COPRIME_PAIRS",
"SUM_ARITHMETIC"
] | 2 | 0.025 | 2026-02-08T03:09:19.426168Z | {
"verified": true,
"answer": 9,
"timestamp": "2026-02-08T03:09:19.451597Z"
} | 6e08de | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 188,
"completion_tokens": 208
},
"timestamp": "2026-02-09T20:30:16.664Z",
"answer": 9
},
{
"id": ... | 2 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
... | {
"lo": -10,
"mid": -7.73,
"hi": -5.46
} | ||
dc8493 | diophantine_fbi2_count_v1_397696148_2444 | Let $k = 1260$. Consider the set of integers $d$ such that $4 \leq d \leq 203$, $d$ divides $k$, and $2 \leq \frac{k}{d} \leq 201$. Let $r$ be the number of such integers $d$.
Compute the sum $\sum_{n=1}^{|r|} \tau(n)$, where $\tau(n)$ denotes the number of positive divisors of $n$. | 84 | 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 | MAX_PRIME_BELOW | [
"ONE_PHI_2",
"C2"
] | d7864f | diophantine_fbi2_count_v1 | null | 4 | 0 | [
"C2",
"MAX_PRIME_BELOW",
"ONE_PHI_2"
] | 3 | 0.097 | 2026-02-08T13:20:06.036440Z | {
"verified": true,
"answer": 84,
"timestamp": "2026-02-08T13:20:06.133055Z"
} | ec3804 | 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": 3300
},
"timestamp": "2026-02-15T14:34:17.781Z",
"answer": 84
},
{
... | 1 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"s... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
f5c4d0 | nt_count_divisible_v1_1918700295_3795 | Let $n$ be a positive integer such that $1 \leq n \leq 49729$. Let $d$ be the number of integers $t$ with $7 \leq t \leq 39$ for which there exist integers $a$ and $b$ such that $1 \leq a \leq 7$, $1 \leq b \leq 5$, and $t = 2a + 5b$. Suppose that $n$ satisfies
$$
n \equiv \sum_{k=0}^{7} (-1)^k \binom{7}{k} \pmod{d}.
$... | 1,714 | graphs = [
Graph(
let={
"_n": Const(7),
"upper": Const(49729),
"divisor": 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'... | COMB | null | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING",
"LIN_FORM"
] | 10f694 | nt_count_divisible_v1 | null | 5 | 0 | [
"BINOMIAL_ALTERNATING",
"LIN_FORM"
] | 2 | 1.601 | 2026-02-08T08:57:22.302032Z | {
"verified": true,
"answer": 1714,
"timestamp": "2026-02-08T08:57:23.902561Z"
} | 99cb7d | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 259,
"completion_tokens": 2084
},
"timestamp": "2026-02-24T10:12:47.286Z",
"answer": 1714
},
{
"i... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
688392 | nt_count_divisors_in_range_v1_717093673_1711 | Let $n = 7560$, $a = 29$, and $b = 365$. Determine the number of positive divisors $d$ of $n$ such that $a \leq d \leq b$. Let this number be $k$. Compute $k + 2^{k \bmod 15} \bmod 82900$. | 31 | graphs = [
Graph(
let={
"n": Const(7560),
"a": Const(29),
"b": Const(365),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Divides(divisor=Var("d"), dividend=Ref("n")), Geq(Var("d"), Ref("a")), Leq(Var("d"), Ref("b"))))),
"Q": S... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_count_divisors_in_range_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.05 | 2026-02-08T16:16:21.541119Z | {
"verified": true,
"answer": 31,
"timestamp": "2026-02-08T16:16:21.591353Z"
} | 1e3eb0 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 120,
"completion_tokens": 3527
},
"timestamp": "2026-02-17T00:45:18.431Z",
"answer": 31
},
{
... | 1 | [
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
985719 | nt_count_coprime_and_v1_784195855_959 | Let $N = 80880$. Find the number of positive integers $n$ such that $1 \leq n \leq N$, $\gcd(n, 4) = 1$, and $\gcd(n, 9) = 1$. Let $c$ be the largest prime number less than or equal to $26$. Compute the remainder when $c$ minus the number of such integers $n$ is divided by $58613$. | 31,676 | graphs = [
Graph(
let={
"_n": Const(26),
"upper": Const(80880),
"k1": Const(4),
"k2": Const(9),
"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("k1")... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | 2ed1de | nt_count_coprime_and_v1 | negation_mod | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 12.795 | 2026-02-08T04:43:24.687473Z | {
"verified": true,
"answer": 31676,
"timestamp": "2026-02-08T04:43:37.482947Z"
} | 45c28b | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 205,
"completion_tokens": 877
},
"timestamp": "2026-02-11T21:59:05.837Z",
"answer": 31676
},
{
"... | 1 | [
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
553824 | nt_count_gcd_equals_v1_1915831931_184 | Let $k$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 16129$. Let $S$ be the set of positive integers $n$ from 1 to 10201, inclusive, such that $\gcd(n, k) = 2$. Compute the number of elements in $S$, and then find the remainder when this number is divided by 73831... | 5,060 | graphs = [
Graph(
let={
"_n": Const(73831),
"upper": Const(10201),
"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(16129... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | nt_count_gcd_equals_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.811 | 2026-02-08T15:13:13.382803Z | {
"verified": true,
"answer": 5060,
"timestamp": "2026-02-08T15:13:14.193410Z"
} | d37b30 | 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": 966
},
"timestamp": "2026-02-16T02:00:48.867Z",
"answer": 5060
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
698461 | nt_count_intersection_v1_898971024_1766 | Let $P$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 6250000$. Let $N$ be the minimum value of $x + y$ as $(x, y)$ ranges over $P$. Determine the number of positive integers $n$ such that $1 \leq n \leq N$, $5$ divides $n$, and $\gcd(n, 6) = 1$. | 333 | graphs = [
Graph(
let={
"N": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(6250000)))), expr=Sum(Var("x"), Var("y")))),
"a": Const(5),
... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | nt_count_intersection_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.576 | 2026-02-08T16:19:00.965517Z | {
"verified": true,
"answer": 333,
"timestamp": "2026-02-08T16:19:01.541849Z"
} | ff9b4d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 140,
"completion_tokens": 1797
},
"timestamp": "2026-02-17T01:24:06.978Z",
"answer": 333
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
5260e5 | algebra_quadratic_discriminant_v1_1218484723_2154 | Let $R$ be the number of integers $v$ with $0 \le v \le 1274$ such that $26d^2 + 26x^2 - 52dx = v$ for some integers $d, x$ with $1 \le d, x \le 8$. Let $D = R^2 - 64$. Compute $2\cdot[D > 0] + [D = 0]$, where $[\cdot]$ is the Iverson bracket. | 1 | graphs = [
Graph(
let={
"_n": Const(2),
"a": Const(-1),
"b": CountOverSet(set=SolutionsSet(var=Var("v"), condition=And(Geq(Var("v"), Const(0)), Leq(Var("v"), Const(1274)), Exists(var=Tuple(elements=[Var(name='a'), Var(name='b')]), condition=And(Geq(left=Var(name='a'), rig... | ALG | null | COMPUTE | sympy | QF_PSD_DISTINCT | [
"QF_PSD_DISTINCT"
] | a8f9cb | algebra_quadratic_discriminant_v1 | null | 2 | 0 | [
"QF_PSD_DISTINCT"
] | 1 | 0.05 | 2026-02-25T03:55:16.744621Z | {
"verified": true,
"answer": 1,
"timestamp": "2026-02-25T03:55:16.794215Z"
} | 19846c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 218,
"completion_tokens": 797
},
"timestamp": "2026-03-29T03:17:20.777Z",
"answer": 1
},
{
"id": ... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_DISTINCT",
"status": "ok"
}
] | {
"lo": -2.45,
"mid": 1.37,
"hi": 5.29
} | ||
d82f5e | comb_count_derangements_v1_1915831931_3085 | Let $n$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p < q$, $\gcd(p, q) = 1$, and $pq = 52920$. Let $!n$ denote the number of derangements of $n$ objects. Compute the value of $!n$. | 14,833 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=52920)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(value=1))... | NT | COMB | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_count_derangements_v1 | null | 6 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.002 | 2026-02-08T17:21:20.057284Z | {
"verified": true,
"answer": 14833,
"timestamp": "2026-02-08T17:21:20.059711Z"
} | ad52bc | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 120,
"completion_tokens": 2126
},
"timestamp": "2026-02-18T01:07:18.441Z",
"answer": 14833
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V1",
"status... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
f0c313 | alg_poly4_count_v1_601307018_9044 | Find the number of ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 434$ such that $337 \cdot b^4 = 122221116432$. | 434 | graphs = [
Graph(
let={
"result": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(434)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(434)), Eq(Mul(Const(337), Pow(Var("b"), Const(4))), Const(122221116432))))),
... | ALG | null | COUNT | sympy | POLY_ORBIT_LEGENDRE | [
"POLY_ORBIT_LEGENDRE"
] | 7c2be8 | alg_poly4_count_v1 | null | 3 | null | [
"POLY_ORBIT_LEGENDRE"
] | 1 | 10.892 | 2026-03-10T09:27:44.255069Z | {
"verified": true,
"answer": 434,
"timestamp": "2026-03-10T09:27:55.146634Z"
} | 781952 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 154,
"completion_tokens": 1948
},
"timestamp": "2026-04-19T10:31:10.760Z",
"answer": 434
},
{
"i... | 1 | [
{
"lemma": "POLY_ORBIT_LEGENDRE",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
f77394 | modular_product_range_v1_601307018_9834 | Let $N = \prod_{i=16}^{104} i$. Find the remainder when $N$ is divided by $11423$. | 7,539 | graphs = [
Graph(
let={
"prod": MathProduct(expr=Var("i"), var="i", start=Const(16), end=Const(104)),
"result": Mod(value=Ref("prod"), modulus=Const(11423)),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | POLY_ORBIT_HENSEL | [
"POLY_ORBIT_HENSEL/POLY3_MIN",
"QUADRATIC_INEQ"
] | d182a9 | modular_product_range_v1 | null | 4 | 0 | [
"POLY3_MIN",
"POLY_ORBIT_HENSEL",
"QUADRATIC_INEQ"
] | 3 | 0.086 | 2026-03-10T10:13:58.392902Z | {
"verified": true,
"answer": 7539,
"timestamp": "2026-03-10T10:13:58.479163Z"
} | 85c99e | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 139,
"completion_tokens": 9086
},
"timestamp": "2026-04-19T12:13:02.239Z",
"answer": 7539
},
{
"... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY3_MIN",
"status": "ok_later"
},
{
"lemma": "POLY_ORBIT_HENSEL",
"stat... | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
acabb6 | alg_poly4_sum_v1_1419126231_1468 | Let $M$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 40$ such that $17a^2 - 8ab + 16b^2 \le 22633$. Find the remainder when
$$
\sum_{\substack{a_1=1 \\ b_1=1}}^{100} \left( \min_{\substack{a_2=1 \\ b_2=1}}^{26} \left( 26a_2^2 + 41b_2^2 + 30a_2b_2 \right) \cdot a_1^4 - 1280a_1b_1^3 +... | 10,115 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(40)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(40)), Leq(Sum(Mul(Const(-8), Var("a"), Var("b")), Mul(Co... | ALG | null | COMPUTE | sympy | QF_PSD_COUNT_LEQ | [
"QF_PSD_COUNT_LEQ/QF_PSD_MIN"
] | 7f6761 | alg_poly4_sum_v1 | null | 6 | 0 | [
"QF_PSD_COUNT_LEQ",
"QF_PSD_MIN"
] | 2 | 0.041 | 2026-02-25T10:56:05.498920Z | {
"verified": true,
"answer": 10115,
"timestamp": "2026-02-25T10:56:05.540304Z"
} | 3dc0fb | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 309,
"completion_tokens": 17683
},
"timestamp": "2026-03-30T12:44:11.131Z",
"answer": 10115
},
{
... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
},
{
"lemma": "QF_PSD_MIN",
"status": "ok_later"
}
] | {
"lo": 1.5,
"mid": 4.69,
"hi": 7.23
} | ||
7d8dbd | comb_count_partitions_v1_1520064083_6253 | Let $n$ be the number of ordered pairs $(i,j)$ of positive integers such that $1 \leq i \leq 6$, $1 \leq j \leq 10$, and $\gcd(i,j) = 1$. Compute the number of integer partitions of $n$. | 26,015 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(GCD(a=Var("i"), b=Var("j")), Const(1)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(6)), right=IntegerRange(start=Const(1), end=Const(10))))),
"re... | NT | COMB | COUNT | sympy | COUNT_COPRIME_GRID | [
"COUNT_COPRIME_GRID"
] | 20ec03 | comb_count_partitions_v1 | null | 5 | 0 | [
"COUNT_COPRIME_GRID"
] | 1 | 0.001 | 2026-02-08T07:58:37.089475Z | {
"verified": true,
"answer": 26015,
"timestamp": "2026-02-08T07:58:37.090242Z"
} | c70c12 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 106,
"completion_tokens": 1280
},
"timestamp": "2026-02-13T13:56:23.001Z",
"answer": 26015
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "V5",
"status": "n... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
0db94a | modular_mod_compute_v1_2051736721_5318 | Let $a = -20449$. Consider the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 6718464$. Let $m$ be the minimum value of $x + y$ over all such pairs. Define $r$ to be the remainder when $a$ is divided by $m$, so that $0 \leq r < m$ and $r \equiv a \pmod{m}$. Let $Q$ be the smallest positive integ... | 153 | graphs = [
Graph(
let={
"a": Const(-20449),
"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(6718464)))), expr=Sum(Var("x"), Var("y")... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | modular_mod_compute_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.003 | 2026-02-08T18:29:38.880970Z | {
"verified": true,
"answer": 153,
"timestamp": "2026-02-08T18:29:38.884252Z"
} | 9a632d | 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": 2707
},
"timestamp": "2026-02-18T17:23:59.974Z",
"answer": 153
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
d3be1e | nt_count_intersection_v1_397696148_964 | Let $ a $ be the number of ordered pairs of positive integers $ (i, j) $ such that $ i + j = 7 $, $ 1 \leq i \leq 5 $, and $ 1 \leq j \leq 6 $. Let $ b = 12 $. Determine the number of positive integers $ n \leq 50000 $ such that $ a $ divides $ n $ and $ \gcd(n, b) = 1 $. | 3,333 | graphs = [
Graph(
let={
"_n": Const(7),
"N": Const(50000),
"a": 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(5)), right=Integer... | NT | null | COUNT | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | nt_count_intersection_v1 | null | 4 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 2.917 | 2026-02-08T11:58:18.904818Z | {
"verified": true,
"answer": 3333,
"timestamp": "2026-02-08T11:58:21.822130Z"
} | ea7bd1 | 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": 1318
},
"timestamp": "2026-02-14T23:43:24.464Z",
"answer": 3333
},
{... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
485997 | algebra_poly_eval_v1_784195855_8235 | Let $c = 19$. Let $m$ be the smallest divisor of 6125 that is at least 2. Let $n$ be the largest prime number not exceeding $c$. Let $b$ be the largest prime number not exceeding $n$. Compute the value of $9b^3 + m b^2 - 8b - 1$. | 63,383 | graphs = [
Graph(
let={
"_c": Const(19),
"_m": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(6125))))),
"_n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(V... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/MAX_PRIME_BELOW",
"MAX_PRIME_BELOW/MAX_PRIME_BELOW"
] | f15075 | algebra_poly_eval_v1 | null | 4 | 0 | [
"MAX_PRIME_BELOW",
"MIN_PRIME_FACTOR"
] | 2 | 0.006 | 2026-02-08T15:58:03.985255Z | {
"verified": true,
"answer": 63383,
"timestamp": "2026-02-08T15:58:03.991238Z"
} | 318b32 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 123,
"completion_tokens": 621
},
"timestamp": "2026-02-16T17:44:35.602Z",
"answer": 63383
},
{... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MIN_PRIME_FACTOR"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
ba19a7_n | alg_telescope_v1_1419126231_346 | A rectangular garden has area $724201$ square meters, with side lengths $x$ and $y$ in meters, both positive integers. The architect wants to minimize the perimeter, so they choose the pair $(x, y)$ that minimizes $x + y$. Let $s$ be this minimal sum. A fountain is placed along a walkway with $s + 1$ tiles numbered $0$... | 3,013 | ALG | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | alg_telescope_v1 | null | 4 | null | [
"B3"
] | 1 | 0.138 | 2026-02-25T09:51:30.007845Z | null | 985489 | ba19a7 | narrative | 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": 9592
},
"timestamp": "2026-03-31T03:34:29.005Z",
"answer": 3013
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | |
d168bd | comb_count_derangements_v1_124444284_3517 | Let $m = 11$ and $n = 2$. Define $d_{\text{min}}$ to be the smallest integer $d \geq n$ that divides $77077$. Let $D = !d_{\text{min}}$, the number of derangements of $d_{\text{min}}$ elements. Let $P_{\text{max}}$ be the largest prime number $p$ such that $2 \leq p \leq m$. Compute the remainder when $D$ is divided by... | 203 | graphs = [
Graph(
let={
"_m": Const(11),
"_n": Const(2),
"n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(77077))))),
"result": Subfactorial(arg=Ref(name='n')),
"Q": Bel... | NT | COMB | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW",
"MIN_PRIME_FACTOR"
] | 114c7a | comb_count_derangements_v1 | bell_mod | 4 | 0 | [
"MAX_PRIME_BELOW",
"MIN_PRIME_FACTOR"
] | 2 | 0.002 | 2026-02-08T05:26:09.201004Z | {
"verified": true,
"answer": 203,
"timestamp": "2026-02-08T05:26:09.202690Z"
} | bef374 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 176,
"completion_tokens": 1351
},
"timestamp": "2026-02-12T08:34:29.283Z",
"answer": 203
},
{
... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
e4f8c5 | nt_count_intersection_v1_1439011603_1444 | Let $N$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 6250000$. Let $b$ be the minimum value of $x_1 + y_1$ over all pairs of positive integers $(x_1, y_1)$ such that $x_1 y_1 = 121$. Compute the number of positive integers $n \leq N$ such that $n$ is divisible by 3 and $\... | 757 | graphs = [
Graph(
let={
"N": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(6250000)))), expr=Sum(Var("x"), Var("y")))),
"a": Const(3),
... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | nt_count_intersection_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.24 | 2026-02-08T16:06:07.349577Z | {
"verified": true,
"answer": 757,
"timestamp": "2026-02-08T16:06:07.590070Z"
} | efefba | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 161,
"completion_tokens": 1778
},
"timestamp": "2026-02-16T21:25:55.100Z",
"answer": 757
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
a783a2 | nt_count_with_divisor_count_v1_458359167_1230 | Let $n$ range over the integers from $2$ to $12$. Among these values, let $d$ be the largest prime $n$. Let $N = 12544$. Compute the number of positive integers $n$ such that $1 \leq n \leq N$ and the number of positive divisors of $n$ is equal to $d$. | 1 | graphs = [
Graph(
let={
"_n": Const(12),
"upper": Const(12544),
"div_count": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), ... | NT | null | COUNT | sympy | LIN_FORM | [
"MAX_PRIME_BELOW"
] | dc3ad3 | nt_count_with_divisor_count_v1 | null | 4 | 0 | [
"LIN_FORM",
"MAX_PRIME_BELOW"
] | 2 | 2.419 | 2026-02-08T04:30:11.373979Z | {
"verified": true,
"answer": 1,
"timestamp": "2026-02-08T04:30:13.792664Z"
} | 1a7aed | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 188,
"completion_tokens": 932
},
"timestamp": "2026-02-10T16:54:09.423Z",
"answer": 1
},
{
"id":... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -8.32,
"mid": -5.11,
"hi": -2.37
} | ||
1220a9 | nt_max_prime_below_v1_1742523217_1390 | Let $d$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq = 6$, $\gcd(p,q) = 1$, and $p < q$. Compute the largest prime number $n$ such that $d \leq n \leq 44100$. | 44,089 | graphs = [
Graph(
let={
"upper": Const(44100),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), V... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_max_prime_below_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 1.06 | 2026-02-08T03:41:59.315162Z | {
"verified": true,
"answer": 44089,
"timestamp": "2026-02-08T03:42:00.375491Z"
} | 6e4ce3 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 180,
"completion_tokens": 2761
},
"timestamp": "2026-02-10T14:57:05.851Z",
"answer": 44089
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
695503 | sequence_lucas_compute_v1_153355830_1016 | Let $ n $ be the sum $ \sum_{k=1}^{6} k $. Define $ a = L_n $, where $ L_n $ denotes the $ n $th Lucas number. Compute the value of
$$
a + \phi(|a| + 1) + \tau(|a| + 1),
$$
where $ \phi(n) $ denotes Euler's totient function and $ \tau(n) $ denotes the number of positive divisors of $ n $. | 40,324 | graphs = [
Graph(
let={
"_n": Const(6),
"n": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Var("k")),
"result": Lucas(arg=Ref(name='n')),
"Q": Sum(Ref("result"), EulerPhi(n=Sum(Abs(arg=Ref(name='result')), Const(1))), NumDivisors(n=Sum(Abs(arg=Ref(nam... | NT | null | COMPUTE | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | sequence_lucas_compute_v1 | null | 3 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.002 | 2026-02-08T04:21:17.178638Z | {
"verified": true,
"answer": 40324,
"timestamp": "2026-02-08T04:21:17.180372Z"
} | 8eff8d | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 211,
"completion_tokens": 1766
},
"timestamp": "2026-02-10T16:12:00.464Z",
"answer": 40324
},
{
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V8_SUM",
"status... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
261bb7 | modular_count_residue_v1_1978505735_3330 | Let $r$ be the minimum value of $x + y$ over all ordered pairs of positive integers $(x, y)$ such that $xy = 4$. Let $m = 18$. Find the number of positive integers $n$ such that $1 \le n \le 33489$ and $n \equiv r \pmod{m}$. Compute the remainder when $44121$ times this number is divided by $77186$. | 60,463 | graphs = [
Graph(
let={
"_n": Const(77186),
"upper": Const(33489),
"m": Const(18),
"r": 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(... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | modular_count_residue_v1 | null | 3 | 0 | [
"B3"
] | 1 | 1.114 | 2026-02-08T17:34:05.125377Z | {
"verified": true,
"answer": 60463,
"timestamp": "2026-02-08T17:34:06.238995Z"
} | bf3170 | 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": 1695
},
"timestamp": "2026-02-18T04:42:01.067Z",
"answer": 60463
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status":... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
51f63a | alg_qf_psd_sum_v1_1218484723_6345 | Consider all ordered quadruples $(a,b,c,d)$ of positive integers satisfying
\[1 \le a \le 25, \quad 1 \le b \le 25,\]
\[1 \le c \le \min\bigl\{-6a1 \cdot b1 + b1^{2} + 34 \cdot a1^{2} : (a1, b1),\, 1 \le a1 \le 14,\, 1 \le b1 \le 14 \bigr\},\]
\[1 \le d \le \left|\bigl\{ (a2, b2) : 1 \le a2 \le 30,\, 1 \le b2 \le 30,\,... | 67,172 | graphs = [
Graph(
let={
"_c": Const(16),
"_m": Const(15),
"_n": Const(25),
"result": Mod(value=SumOverSet(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"), Ref("_n... | ALG | null | COMPUTE | sympy | QF_PSD_ORBIT | [
"QF_PSD_ORBIT",
"POLY4_COUNT",
"QF_PSD_MIN"
] | 588cb2 | alg_qf_psd_sum_v1 | null | 7 | 0 | [
"POLY4_COUNT",
"QF_PSD_MIN",
"QF_PSD_ORBIT"
] | 3 | 1.864 | 2026-02-25T07:53:40.681601Z | {
"verified": true,
"answer": 67172,
"timestamp": "2026-02-25T07:53:42.545355Z"
} | f0d845 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 527,
"completion_tokens": 14879
},
"timestamp": "2026-03-30T01:16:37.668Z",
"answer": 67284
},
{
... | 1 | [
{
"lemma": "POLY4_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_MIN",
"status": "ok"
},
{
"lemma": "QF_PSD_ORBIT",
"status": "ok"
}
] | {
"lo": 1.53,
"mid": 4.7,
"hi": 7.23
} | ||
d9e0f8 | comb_count_permutations_fixed_v1_1218484723_5470 | Let $D_n$ denote the number of derangements of $n$ elements. Let $M = \sum_{k=1}^{2} k$, $k = \sum_{j=1}^{M} j$, and $n = 9$. Compute $66666 - \binom{n}{k} \cdot D_{n-k}$. | 66,498 | graphs = [
Graph(
let={
"_n": Summation(var="k1", start=Const(1), end=Const(2), expr=Var("k1")),
"n": Const(9),
"k": Summation(var="k2", start=Const(1), end=Ref("_n"), expr=Var("k2")),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub(left=Ref(... | COMB | null | COUNT | sympy | POLY_ORBIT_LEGENDRE | [
"SUM_ARITHMETIC/SUM_ARITHMETIC"
] | 2a57af | comb_count_permutations_fixed_v1 | null | 3 | 0 | [
"POLY_ORBIT_LEGENDRE",
"SUM_ARITHMETIC"
] | 2 | 0.269 | 2026-02-25T07:01:05.523169Z | {
"verified": true,
"answer": 66498,
"timestamp": "2026-02-25T07:01:05.791713Z"
} | 942d35 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 185,
"completion_tokens": 790
},
"timestamp": "2026-03-29T21:14:51.832Z",
"answer": 66498
},
{
"i... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V8",
"... | {
"lo": -10,
"mid": -6.24,
"hi": -2.48
} | ||
6b0124 | comb_count_derangements_v1_784195855_5985 | Let $n$ be the number of positive integers $k$ such that $1 \leq k \leq 21$ and the $k$-th Fibonacci number is divisible by $2$. Compute the subfactorial of $n$, denoted $!n$, which is the number of derangements of $n$ elements. | 1,854 | graphs = [
Graph(
let={
"_n": Const(2),
"n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(21)), Divides(divisor=Ref("_n"), dividend=Fibonacci(arg=Var(name='n')))))),
"result": Subfactorial(arg=Ref(name='n')),
... | NT | COMB | COUNT | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE"
] | 66de3c | comb_count_derangements_v1 | null | 4 | 0 | [
"COUNT_FIB_DIVISIBLE"
] | 1 | 0.001 | 2026-02-08T08:15:02.019352Z | {
"verified": true,
"answer": 1854,
"timestamp": "2026-02-08T08:15:02.020089Z"
} | d14852 | 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": 775
},
"timestamp": "2026-02-13T15:57:48.170Z",
"answer": 1854
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
8b0392 | lin_form_endings_v1_124444284_4874 | Let $a = 30$, $b = 18$, $A = 46$, and $B = 18$. Let $g = \gcd(a,b)$, $a' = \left\lfloor \frac{a}{g} \right\rfloor$, and $b' = \left\lfloor \frac{b}{g} \right\rfloor$. Define $T$ to be a set whose size is $a' \cdot A + b' \cdot B - a' \cdot b'$. The total number of elements in a certain structure is $a \cdot A + b \cdot... | 1,388 | graphs = [
Graph(
let={
"a_coeff": Const(30),
"b_coeff": Const(18),
"A_val": Const(46),
"B_val": Const(18),
"g_step": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"ap_node": Floor(Div(Ref("a_coeff"), Ref("g_step"))),
"bp_node": ... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 4 | null | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T06:16:36.710440Z | {
"verified": true,
"answer": 1388,
"timestamp": "2026-02-08T06:16:36.712196Z"
} | 57d81c | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 214,
"completion_tokens": 451
},
"timestamp": "2026-02-15T17:23:53.990Z",
"answer": 1387
},
{
"id": 11,... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
cab665 | antilemma_k3_v1_124444284_3575 | Let $n = 44062$. Define $x = \sum_{d \mid n} \phi(d)$, where the sum is taken over all positive divisors $d$ of $n$. Compute the value of the Bell number $B_{|x| \bmod 11}$. | 877 | graphs = [
Graph(
let={
"_n": Const(44062),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Bell(Mod(value=Abs(arg=Ref(name='x')), modulus=Const(11))),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K13 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 4 | 0 | [
"K13",
"K3"
] | 2 | 0.007 | 2026-02-08T05:27:44.058555Z | {
"verified": true,
"answer": 877,
"timestamp": "2026-02-08T05:27:44.065860Z"
} | aa73ce | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 106,
"completion_tokens": 495
},
"timestamp": "2026-02-12T09:35:50.945Z",
"answer": 877
},
{
... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
7d81ef | lin_form_endings_v1_971394319_1700 | Compute the value of $ \left\lfloor \frac{20}{\gcd(20, 16)} \right\rfloor $. Multiply this value by $15001$, then find the remainder when the result is divided by $90980$. | 75,005 | graphs = [
Graph(
let={
"a_coeff": Const(20),
"b_coeff": Const(16),
"_inner_result": Floor(Div(Const(20), GCD(a=Ref("a_coeff"), b=Ref("b_coeff")))),
"_scale_k": Const(15001),
"_scaled": Mul(Ref("_scale_k"), Ref("_inner_result")),
"_mod_... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 3 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T13:51:57.853469Z | {
"verified": true,
"answer": 75005,
"timestamp": "2026-02-08T13:51:57.854035Z"
} | 4d1cfa | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 117,
"completion_tokens": 307
},
"timestamp": "2026-02-16T05:07:44.919Z",
"answer": 75005
},
{
"id": 11,
... | 2 | [
{
"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": -10,
"mid": -7.27,
"hi": -4.54
} | ||
3cc7a7 | diophantine_fbi2_min_v1_784195855_3972 | Let $k = 96$, $a = 2$, $b = 3$, and $\text{upper} = 106$. Consider the set of all integers $d$ such that $d \geq 3$, $d \leq \text{upper}$, $d$ divides $k$, and $\frac{k}{d} \geq 4$. Let $r$ be the minimum value of $d$ in this set. Compute $r$. | 3 | graphs = [
Graph(
let={
"k": Const(96),
"a": Const(2),
"b": Const(3),
"upper": Const(106),
"result": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(3)), Leq(Var("d"), Ref("upper")), Divides(divisor=Var("d"), dividend=Re... | NT | null | EXTREMUM | sympy | K2 | [
"B3"
] | 0cd20d | diophantine_fbi2_min_v1 | null | 2 | 0 | [
"B3",
"K2"
] | 2 | 0.123 | 2026-02-08T06:43:44.790694Z | {
"verified": true,
"answer": 3,
"timestamp": "2026-02-08T06:43:44.913691Z"
} | 2fb6b4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 142,
"completion_tokens": 728
},
"timestamp": "2026-02-13T03:48:09.716Z",
"answer": 3
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
1e06fa | nt_sum_divisors_compute_v1_124444284_805 | Let $n = 21787$. Define $\sigma(n)$ to be the sum of all positive divisors of $n$. Let $c$ be the largest integer such that $7^c$ divides $11634!$. Compute the remainder when $c - \sigma(n)$ is divided by $58441$. | 38,589 | graphs = [
Graph(
let={
"_n": Const(58441),
"n": Const(21787),
"result": SumDivisors(n=Ref("n")),
"_c": MaxKDivides(target=Factorial(Const(11634)), base=Const(7)),
"Q": Mod(value=Sub(Ref("_c"), Ref("result")), modulus=Ref("_n")),
},
... | NT | null | COMPUTE | sympy | C3 | [
"V1"
] | 574795 | nt_sum_divisors_compute_v1 | negation_mod | 5 | 0 | [
"C3",
"V1"
] | 2 | 0.017 | 2026-02-08T03:31:51.352016Z | {
"verified": true,
"answer": 38589,
"timestamp": "2026-02-08T03:31:51.369137Z"
} | deac17 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 175,
"completion_tokens": 3704
},
"timestamp": "2026-02-09T22:19:49.568Z",
"answer": 38589
},
{
"... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K5",
"status": "same_pattern_wrong"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V1",
"status": ... | {
"lo": -6.51,
"mid": -0.31,
"hi": 5.43
} | ||
bb21c2 | comb_count_partitions_v1_1978505735_2480 | Let $ n $ be the number of integers $ t $ with $ 11 \le t \le 68 $ for which there exist positive integers $ a $ and $ b $, with $ 1 \le a \le 10 $ and $ 1 \le b \le 4 $, such that $ t = 4a + 7b $. Let $ \text{result} $ be the number of integer partitions of $ n $. Let $ Q = \sum_{i=0}^{d-1} d_i (i+1)^2 + 32768 $, wher... | 33,002 | graphs = [
Graph(
let={
"_n": Const(2),
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=10)), Geq(left=Var(n... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_count_partitions_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.004 | 2026-02-08T16:54:54.093453Z | {
"verified": true,
"answer": 33002,
"timestamp": "2026-02-08T16:54:54.097215Z"
} | 0211bd | 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": 2107
},
"timestamp": "2026-02-17T15:52:55.982Z",
"answer": 33002
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"st... | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||
a18d4e | comb_bell_compute_v1_865884756_2430 | Let $N = 33344$. Define $n$ to be the number of nonnegative integers $j$ such that $0 \leq j \leq N$ and $\binom{33344}{j}$ is odd. Compute the Bell number $B_n$, which counts the number of partitions of a set of $n$ elements. | 4,140 | graphs = [
Graph(
let={
"_n": Const(33344),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Ref("_n")), Eq(Mod(value=Binom(n=Const(33344), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')),
"r... | COMB | null | COMPUTE | sympy | V8 | [
"V8"
] | 86348e | comb_bell_compute_v1 | null | 7 | 0 | [
"V8"
] | 1 | 0.002 | 2026-02-08T16:46:26.973228Z | {
"verified": true,
"answer": 4140,
"timestamp": "2026-02-08T16:46:26.975700Z"
} | 4a1703 | 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": 998
},
"timestamp": "2026-02-17T11:10:10.928Z",
"answer": 4140
},
{
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
}
] | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||
e51748 | algebra_poly_eval_v1_1742523217_1666 | Let $a$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 121$. Compute $a^2 + 4a$. | 572 | graphs = [
Graph(
let={
"_n": Const(121),
"a": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_n")))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | algebra_poly_eval_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.001 | 2026-02-08T04:06:00.041882Z | {
"verified": true,
"answer": 572,
"timestamp": "2026-02-08T04:06:00.043324Z"
} | adc614 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 153,
"completion_tokens": 254
},
"timestamp": "2026-02-10T15:17:40.177Z",
"answer": 572
},
{
"id... | 2 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.73,
"hi": -5.46
} | ||
878f2a | nt_count_divisible_v1_1978505735_1776 | Let $$d = \sum_{k=1}^{6} \varphi(k) \left\lfloor \frac{6}{k} \right\rfloor,$$ where $\varphi$ denotes Euler's totient function. Find the number of positive integers $n \leq 31684$ such that $n$ is divisible by $d$. Then, compute the smallest positive integer $k$ such that the $k$-th Fibonacci number is divisible by thi... | 150 | graphs = [
Graph(
let={
"_n": Const(6),
"upper": Const(31684),
"divisor": 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(Geq... | NT | null | COUNT | sympy | K2 | [
"K2"
] | 6897ab | nt_count_divisible_v1 | null | 6 | 0 | [
"K2"
] | 1 | 6.256 | 2026-02-08T16:23:42.376556Z | {
"verified": true,
"answer": 150,
"timestamp": "2026-02-08T16:23:48.632883Z"
} | 4f64f9 | 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": 2063
},
"timestamp": "2026-02-17T02:29:39.418Z",
"answer": 150
},
{
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} |
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