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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
fdfd07 | antilemma_k2_v1_124444284_1948 | Let $N=320$. For each integer $k$ with $1\le k\le 320$ and each integer $j$ with $1\le j\le 6$, consider the product $\varphi(k)\left\lfloor\dfrac{N}{k}\right\rfloor$, where $\varphi$ is Euler's totient function. Let
$$A=\sum_{k=1}^{320}\sum_{j=1}^{6} \varphi(k)\left\lfloor\frac{N}{k}\right\rfloor.$$
Let
$$B=\sum_{k=1... | 51,360 | graphs = [
Graph(
let={
"_c": Const(8),
"_m": Const(6),
"_n": Const(320),
"x": Div(Mul(Ref("_m"), SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("k"), Var("_j")]), condition=Const(1), domain=CartesianProduct(left=IntegerRange(start=Const(1)... | NT | COMB | COMPUTE | sympy | K13 | [
"K2/SUM_INDEPENDENT",
"K2"
] | 5e8371 | antilemma_k2_v1 | null | 8 | 0 | [
"K13",
"K2",
"SUM_INDEPENDENT"
] | 3 | 0.003 | 2026-02-08T04:13:05.306018Z | {
"verified": true,
"answer": 51360,
"timestamp": "2026-02-08T04:13:05.308760Z"
} | 0f6332 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 285,
"completion_tokens": 1634
},
"timestamp": "2026-02-11T23:35:46.225Z",
"answer": 51360
},
{
"... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "SUM_INDEPENDENT",
"status": "ok_later"
},
{
"... | {
"lo": -3.86,
"mid": -1.04,
"hi": 1.59
} | ||
9e3334 | comb_count_permutations_fixed_v1_655260480_990 | Let $ n $ be the minimum value of $ x + y $ over all pairs of positive integers $ (x, y) $ such that $ xy = 9 $. Let $ k = \sum_{k_1=1}^{2} \phi(k_1) \left\lfloor \frac{2}{k_1} \right\rfloor $. Compute $ \binom{n}{k} \cdot !(n - k) $, where $ !m $ denotes the number of derangements of $ m $ elements. | 40 | graphs = [
Graph(
let={
"_n": Const(9),
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_n")))), expr=Sum(Var("x"), Var("y")))),
... | NT | COMB | COUNT | sympy | B3 | [
"B3",
"K2"
] | f1ea07 | comb_count_permutations_fixed_v1 | null | 6 | 0 | [
"B3",
"K2"
] | 2 | 0.002 | 2026-02-08T15:51:33.459981Z | {
"verified": true,
"answer": 40,
"timestamp": "2026-02-08T15:51:33.462397Z"
} | 37e97e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 156,
"completion_tokens": 805
},
"timestamp": "2026-02-16T15:03:57.795Z",
"answer": 40
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
c50ada | nt_count_with_divisor_count_v1_124444284_1974 | Let $n = 6$. Consider the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = n$. Let $P$ be the set of all values of $xy$ for such pairs. Let $d$ be the maximum element of $P$. Determine the number of positive integers $m \leq 34225$ such that the number of positive divisors of $m$ is equal to $d... | 56 | graphs = [
Graph(
let={
"_n": Const(6),
"upper": Const(34225),
"div_count": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Ref("_n... | NT | null | COUNT | sympy | EULER_TOTIENT_SUM | [
"B1"
] | 5b950e | nt_count_with_divisor_count_v1 | null | 5 | 0 | [
"B1",
"EULER_TOTIENT_SUM"
] | 2 | 5.089 | 2026-02-08T04:13:42.191147Z | {
"verified": true,
"answer": 56,
"timestamp": "2026-02-08T04:13:47.279692Z"
} | 9e4c65 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 204,
"completion_tokens": 2563
},
"timestamp": "2026-02-10T15:57:54.728Z",
"answer": 56
},
{
"id... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
dc0662 | comb_factorial_compute_v1_458359167_0 | Let $m = 6$. Let $p$ and $q$ be positive integers such that $pq = 36$, $\gcd(p, q) = 1$, and $p < q$. Let $S$ be the set of all such $p$. Define $n_0$ to be the number of elements in $S$. Let $T$ be the set of all positive integers $n$ such that $n \geq n_0$, $n$ is prime, and $n \leq \max\{xy \mid x, y \in \mathbb{Z}^... | 5,040 | graphs = [
Graph(
let={
"_m": Const(6),
"_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=36)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/MAX_PRIME_BELOW",
"B1/MAX_PRIME_BELOW"
] | efa041 | comb_factorial_compute_v1 | null | 4 | 0 | [
"B1",
"COPRIME_PAIRS",
"MAX_PRIME_BELOW"
] | 3 | 0.013 | 2026-02-08T02:56:44.271852Z | {
"verified": true,
"answer": 5040,
"timestamp": "2026-02-08T02:56:44.284537Z"
} | 154eb5 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 270,
"completion_tokens": 1128
},
"timestamp": "2026-02-08T19:57:45.519Z",
"answer": 5040
},
{
"i... | 2 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{... | {
"lo": -10,
"mid": -7.73,
"hi": -5.46
} | ||
68f2ee | geo_count_lattice_rect_v1_349078426_963 | Compute the number of lattice points in the rectangle $[0, 333] \times [0, 187]$, including the boundary. | 62,792 | graphs = [
Graph(
let={
"a": Const(333),
"b": Const(187),
"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 | 2026-02-08T13:21:12.915795Z | {
"verified": true,
"answer": 62792,
"timestamp": "2026-02-08T13:21:12.916535Z"
} | 5e3f1d | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 139,
"completion_tokens": 281
},
"timestamp": "2026-02-24T17:50:39.343Z",
"answer": 62792
},
{
"i... | 1 | [] | {
"lo": -3.84,
"mid": -1.67,
"hi": 1.32
} | ||||
9a4588 | nt_max_prime_below_v1_1520064083_8234 | Let $c$ be the number of positive integers $p$ such that there exists a positive integer $q > p$ with $pq = 216$ and $\gcd(p, q) = 1$. Define $S$ to be the set of prime numbers $n$ such that $n \geq c$ and $n \leq 74529$. Let $r$ be the largest element of $S$. Compute the remainder when $36856 \cdot r$ is divided by 77... | 50,934 | graphs = [
Graph(
let={
"upper": Const(74529),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), V... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_max_prime_below_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 2.092 | 2026-02-08T10:05:42.348669Z | {
"verified": true,
"answer": 50934,
"timestamp": "2026-02-08T10:05:44.440590Z"
} | 903130 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 151,
"completion_tokens": 4485
},
"timestamp": "2026-02-14T06:23:29.795Z",
"answer": 50934
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
156971 | nt_count_divisors_in_range_v1_1248542787_596 | Let $n = 110880$, $a = 85$, and let $b$ be the largest prime number less than or equal to the number of positive integers $t$ with $21 \leq t \leq 1357$ that can be written in the form $5a' + 4b' + 12$ for positive integers $a' \leq 129$ and $b' \leq 175$. Compute the number of positive divisors $d$ of $n$ such that $8... | 63 | graphs = [
Graph(
let={
"_n": Const(2),
"n": Const(110880),
"a": Const(85),
"b": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), con... | NT | null | COUNT | sympy | B3 | [
"LIN_FORM/MAX_PRIME_BELOW"
] | 47006e | nt_count_divisors_in_range_v1 | null | 6 | 0 | [
"B3",
"LIN_FORM",
"MAX_PRIME_BELOW"
] | 3 | 0.119 | 2026-02-08T03:15:15.279210Z | {
"verified": true,
"answer": 63,
"timestamp": "2026-02-08T03:15:15.398692Z"
} | 8b93cf | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 230,
"completion_tokens": 7490
},
"timestamp": "2026-02-09T18:52:46.519Z",
"answer": 63
},
{
"id... | 1 | [
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}... | {
"lo": -3.49,
"mid": 1.84,
"hi": 7.55
} | ||
038bb9 | alg_qf_psd_sum_v1_1218484723_3490 | Let $S$ be the sum over all ordered triples $(a, b, c)$ with $1 \leq a \leq 19$, $1 \leq b \leq 19$, and $1 \leq c \leq N$, where $$N = \left|\left\{ (a_1, b_1) : 1 \leq a_1, b_1 \leq 40,\ 384a_1 b_1^2 + 128a_1^3 + 128b_1^3 + 384a_1^2 b_1 = 1024000 \right\}\right|,$$ of the expression $$-24bc + 10ac + 6c^2 + 4ab + 51b^... | 78,188 | graphs = [
Graph(
let={
"_n": Const(51),
"result": Mod(value=SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b"), Var("c")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(19)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(19)), Geq(Var("c")... | ALG | null | COMPUTE | sympy | POLY3_COUNT | [
"POLY3_COUNT"
] | 355dbe | alg_qf_psd_sum_v1 | null | 5 | 0 | [
"POLY3_COUNT"
] | 1 | 0.026 | 2026-02-25T05:09:44.392005Z | {
"verified": true,
"answer": 78188,
"timestamp": "2026-02-25T05:09:44.418219Z"
} | d21be8 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 301,
"completion_tokens": 3044
},
"timestamp": "2026-03-29T10:33:36.916Z",
"answer": 78188
},
{
"... | 1 | [
{
"lemma": "POLY3_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -2.45,
"mid": 1.37,
"hi": 5.29
} | ||
dd4875_n | alg_poly4_sum_v1_1218484723_852 | A signal processor evaluates energy levels across a grid of frequencies $a$ and amplitudes $b$. The frequency $a$ ranges from $1$ to the smallest prime factor of $1195154041$, and amplitude $b$ ranges from $1$ to $181$. The energy at each point is $81a^4 + 324a^3b + 486a^2b^2 + 324ab^3 + 97b^4$. What is the total energ... | 20,041 | ALG | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | alg_poly4_sum_v1 | null | 5 | null | [
"MIN_PRIME_FACTOR"
] | 1 | 0.079 | 2026-02-25T02:33:51.681133Z | null | de69b3 | dd4875 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 217,
"completion_tokens": 8597
},
"timestamp": "2026-03-30T16:05:57.641Z",
"answer": 19214
},
{
... | 1 | [
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 1.5,
"mid": 4.69,
"hi": 7.23
} | |
cd904d | antilemma_sum_factor_cartesian_v1_153355830_143 | Let $S$ be the set of all ordered pairs $(i,j)$ of integers with $1 \leq i \leq 19$ and $1 \leq j \leq 19$. For each such pair, compute $\gcd(7, 11)$, and then compute the sum $$\sum_{d \mid \gcd(7,11)} \mu(d),$$ where $\mu$ denotes the M\"obius function. Let $T$ be the subset of $S$ consisting of all pairs $(i,j)$ for... | 36,100 | graphs = [
Graph(
let={
"x": SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=SumOverDivisors(n=GCD(a=Const(value=7), b=Const(value=11)), var='d', expr=MoebiusMu(n=Var(name='d'))), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(1... | NT | null | COMPUTE | sympy | SUM_FACTOR_CARTESIAN | [
"SUM_FACTOR_CARTESIAN",
"MOBIUS_COPRIME"
] | 1428b5 | antilemma_sum_factor_cartesian_v1 | null | 4 | 0 | [
"MOBIUS_COPRIME",
"SUM_FACTOR_CARTESIAN"
] | 2 | 0.001 | 2026-02-08T02:54:49.727647Z | {
"verified": true,
"answer": 36100,
"timestamp": "2026-02-08T02:54:49.728550Z"
} | cbb0ce | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 270,
"completion_tokens": 559
},
"timestamp": "2026-02-08T23:30:36.533Z",
"answer": 36100
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok"
},
{
"lemma": "SUM_FACTOR_CARTESIAN",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
... | {
"lo": -6.49,
"mid": 0.51,
"hi": 7.52
} | ||
66e16d_n | alg_qf_psd_count_v1_601307018_1217 | An engineering team is testing combinations of three design parameters $a$, $b$, and $c$, each an integer between $1$ and $41$ inclusive. The total performance score of a configuration $(a, b, c)$ is given by
$$15a^{2} + 18ab + D \cdot c^{2} + 81b^{2} + E \cdot ac + 138bc,$$
where $D$ is the minimum possible value of $... | 10 | graphs = [
Graph(
let={
"_d": Const(18),
"_c": Const(2),
"_m": Const(81897),
"_n": Const(81),
"result": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b"), Var("c")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(41)... | NT | null | COUNT | sympy | COUNT_FIB_DIVISIBLE | [
"B3_CLOSEST/MAX_PRIME_BELOW/QF_PSD_DISTINCT",
"B3_DIFF"
] | ccfc7d | alg_qf_psd_count_v1 | null | 7 | null | [
"B3_CLOSEST",
"B3_DIFF",
"COUNT_FIB_DIVISIBLE",
"MAX_PRIME_BELOW",
"QF_PSD_DISTINCT"
] | 5 | 1.264 | 2026-03-10T01:53:40.000337Z | null | 73c2b0 | 66e16d | narrative | CC BY 4.0 | [
{
"id": 36,
"model": "qwen2.5:3b-32k",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 365,
"completion_tokens": 1010
},
"timestamp": "2026-04-23T15:07:43.013Z",
"answer": 10
}
] | 2 | [
{
"lemma": "B3_CLOSEST",
"status": "ok"
},
{
"lemma": "B3_DIFF",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma":... | {
"lo": -10,
"mid": -5.89,
"hi": -1.79
} |
a62736 | nt_sum_totient_over_divisors_v1_458359167_76 | Let $n$ be the number of integers $t$ such that $20 \leq t \leq 12034$ and there exist positive integers $a \leq 158$ and $b \leq 1637$ for which $t = 14a + 6b$. Compute the sum of $\phi(d)$ over all positive divisors $d$ of $n$. | 5,996 | 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=158)), Geq(left=Var(name='b'), right=Const(value... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_sum_totient_over_divisors_v1 | null | 7 | 0 | [
"LIN_FORM"
] | 1 | 0.006 | 2026-02-08T02:59:16.274532Z | {
"verified": true,
"answer": 5996,
"timestamp": "2026-02-08T02:59:16.280472Z"
} | da9cba | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 193,
"completion_tokens": 1206
},
"timestamp": "2026-02-10T12:01:36.754Z",
"answer": 6008
},
{
... | 0 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
}
] | {
"lo": 4.62,
"mid": 6.54,
"hi": 9.53
} | ||
676a8e | geo_visible_lattice_v1_809748730_1418 | Let $n = 64$. Define a visible lattice point $(x,y)$ to be a point with integer coordinates such that $1 \leq x, y \leq n$ and $\gcd(x,y) = 1$. Let $v$ be the number of visible lattice points. Find the remainder when $37652 \cdot v$ is divided by $50843$. | 23,193 | graphs = [
Graph(
let={
"n": Const(64),
"result": VisibleLatticePoints(n=Ref(name='n')),
"_c": Const(37652),
"Q": Mod(value=Mul(Ref("_c"), Ref("result")), modulus=Const(50843)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 3 | 0 | null | null | 0.422 | 2026-02-08T12:25:28.570843Z | {
"verified": true,
"answer": 23193,
"timestamp": "2026-02-08T12:25:28.993163Z"
} | ca9f1e | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 190,
"completion_tokens": 32768
},
"timestamp": "2026-02-24T15:45:36.009Z",
"answer": null
},
{
... | 1 | [] | {
"lo": 3.25,
"mid": 5.68,
"hi": 8.81
} | ||||
b76fae | modular_inverse_v1_1874849503_716 | Let $N = 1184$. Compute the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = N$. Let $m$ be this number. Find the smallest positive integer $x$ such that $224x \equiv 1 \pmod{593}$ and $1 \leq x \leq m$. | 548 | graphs = [
Graph(
let={
"_n": Const(1184),
"a": Const(224),
"m": Const(593),
"upper": 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... | NT | null | EXTREMUM | sympy | COMB1 | [
"COMB1"
] | 567f58 | modular_inverse_v1 | null | 5 | 0 | [
"COMB1"
] | 1 | 0.044 | 2026-02-08T13:16:02.322992Z | {
"verified": true,
"answer": 548,
"timestamp": "2026-02-08T13:16:02.366908Z"
} | 46015c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 194,
"completion_tokens": 1493
},
"timestamp": "2026-02-09T20:11:35.985Z",
"answer": 548
},
{
"id... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
e29b71 | comb_count_surjections_v1_865884756_4872 | Define $T_1$ to be the set of all integers $t$ such that there exist integers $a$ and $b$ satisfying $1 \leq a \leq 2$, $1 \leq b \leq 5$, $7 \leq t \leq 20$, and $t = 5a + 2b$. Let $m$ be the number of elements in $T_1$. Let $S$ be the set of all ordered pairs $(i, j)$ of integers with $1 \leq i \leq 8$ and $1 \leq j ... | 15,120 | 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 | COUNT | sympy | LIN_FORM | [
"LIN_FORM/COUNT_SUM_EQUALS"
] | 8a3f7a | comb_count_surjections_v1 | null | 5 | 0 | [
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 2 | 0.063 | 2026-02-08T18:13:47.649410Z | {
"verified": true,
"answer": 15120,
"timestamp": "2026-02-08T18:13:47.711935Z"
} | a9755c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 327,
"completion_tokens": 1402
},
"timestamp": "2026-02-18T15:48:00.559Z",
"answer": 15120
},
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok_later"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"le... | {
"lo": -3.12,
"mid": 1.47,
"hi": 6.57
} | ||
86911a | comb_binomial_compute_v1_124444284_669 | Let $n = 15$. Let $k$ be the largest prime number such that $2 \leq k \leq 8$. Define $r = \binom{n}{k}$. Compute $$r + \varphi(|r| + 1) + \tau(|r| + 1),$$ where $\varphi(m)$ denotes the number of positive integers less than or equal to $m$ that are relatively prime to $m$, and $\tau(m)$ denotes the number of positive ... | 9,657 | graphs = [
Graph(
let={
"n": Const(15),
"k": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(8)), IsPrime(Var("n"))))),
"result": Binom(n=Ref("n"), k=Ref("k")),
"Q": Sum(Ref("result"), EulerPhi(n=Sum(Abs(arg... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | comb_binomial_compute_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.002 | 2026-02-08T03:26:39.506798Z | {
"verified": true,
"answer": 9657,
"timestamp": "2026-02-08T03:26:39.508325Z"
} | 598ac9 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 222,
"completion_tokens": 1385
},
"timestamp": "2026-02-09T20:29:24.967Z",
"answer": 9657
},
{
"i... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
cbef1e | geo_count_lattice_triangle_v1_1520064083_876 | Let $A$ be the area of the triangle with vertices at $(0,0)$, $(180,23)$, and $(60,111)$, multiplied by $2$. Let $B$ be the sum of the greatest common divisors of the absolute differences of the coordinates along each side of the triangle, that is,
$$
B = \gcd(180, 23) + \gcd(|60 - 180|, |111 - 23|) + \gcd(60, 111).
$$... | 64,703 | graphs = [
Graph(
let={
"area_2x": Abs(arg=Sum(Mul(Const(value=180), Const(value=111)), Mul(Const(value=60), Sub(left=Const(value=0), right=Const(value=23))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=180)), b=Abs(arg=Const(value=23))), GCD(a=Abs(arg=Sub(left=Const(value=60), right... | ALG | NT | COUNT | sympy | [] | geo_count_lattice_triangle_v1 | null | 3 | 0 | null | null | 0.002 | 2026-02-08T03:38:52.201087Z | {
"verified": true,
"answer": 64703,
"timestamp": "2026-02-08T03:38:52.203474Z"
} | f8c3e9 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 256,
"completion_tokens": 2311
},
"timestamp": "2026-02-10T15:16:01.449Z",
"answer": 64703
},
{
"... | 1 | [] | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||||
5c3afa | nt_sum_divisors_range_v1_655260480_3845 | Let $n = 94367$. Consider the set of all ordered pairs $(a, b)$ of positive integers such that $1 \le a \le 74$ and $1 \le b \le 74$. The number of such pairs is $74 \times 74 = 5476$. Let $S$ be the set of positive integers from $1$ to $5476$. Compute the sum of the number of positive divisors of each integer in $S$. ... | 89,218 | graphs = [
Graph(
let={
"_n": Const(94367),
"upper": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(74)), right=IntegerRange(start=Const(1), end=Const(74)))),
"result": SumOverSet(set=MapOverSet(set=SolutionsSet(var=Var("n"), condition=And(G... | NT | null | SUM | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | nt_sum_divisors_range_v1 | null | 4 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.234 | 2026-02-08T17:34:38.577740Z | {
"verified": true,
"answer": 89218,
"timestamp": "2026-02-08T17:34:38.811737Z"
} | b25844 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 180,
"completion_tokens": 4279
},
"timestamp": "2026-02-18T04:16:57.380Z",
"answer": 89218
},
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
79aac4 | antilemma_sum_equals_v1_458359167_2851 | Let $d = 17902$. Let $m$ be the number of ordered pairs $(i,j)$ of positive integers such that $i + j = 81$, $1 \le i \le 79$, and $1 \le j \le 80$. Let $n$ be the number of ordered pairs $(i,j)$ of positive integers such that $i + j = m$, $1 \le i \le 79$, and $1 \le j \le 79$. Let $x$ be the number of ordered pairs $... | 70,931 | graphs = [
Graph(
let={
"_d": Const(17902),
"_m": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(81)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(79)), right=IntegerRange(start=Const(1), end... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS/COMB1/COUNT_SUM_EQUALS",
"COMB1",
"COUNT_SUM_EQUALS"
] | 45fb03 | antilemma_sum_equals_v1 | affine_mod | 4 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS"
] | 2 | 0.011 | 2026-02-08T06:48:13.121181Z | {
"verified": true,
"answer": 70931,
"timestamp": "2026-02-08T06:48:13.132268Z"
} | fe1c6d | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 314,
"completion_tokens": 1515
},
"timestamp": "2026-02-24T07:05:01.787Z",
"answer": 70831
},
{
... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"statu... | {
"lo": -0.06,
"mid": 2.89,
"hi": 5.27
} | ||
d34ca4 | nt_min_crt_v1_1978505735_1116 | Let $m$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq = 24$, $\gcd(p, q) = 1$, and $p < q$. Let $a$ be the largest prime number $n$ such that $m \leq n \leq 3$. Let $b = 7$ and $k = 9$. Find the smallest positive integer $n_1$ such that $1 \leq n_1 \leq 63$, $n_1 \eq... | 52 | graphs = [
Graph(
let={
"_n": Const(3),
"m": Const(7),
"k": Const(9),
"a": 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'), ... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"COPRIME_PAIRS/MAX_PRIME_BELOW"
] | 2248fc | nt_min_crt_v1 | null | 6 | 0 | [
"COPRIME_PAIRS",
"LIN_FORM",
"MAX_PRIME_BELOW"
] | 3 | 0.049 | 2026-02-08T15:49:58.246742Z | {
"verified": true,
"answer": 52,
"timestamp": "2026-02-08T15:49:58.295380Z"
} | 6f8218 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 183,
"completion_tokens": 1130
},
"timestamp": "2026-02-16T14:45:25.341Z",
"answer": 52
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
}... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
235bfe | sequence_lucas_compute_v1_865884756_3875 | Let $m = 28$. Define $n_1$ to be the largest prime number less than or equal to $m$.
Let $n$ be the number of ordered pairs $(i, j)$ of positive integers such that $1 \leq i \leq 21$, $1 \leq j \leq 21$, and $i + j = n_1$.
The Lucas sequence is defined by $L_1 = 1$, $L_2 = 3$, and $L_k = L_{k-1} + L_{k-2}$ for $k \... | 15,127 | graphs = [
Graph(
let={
"_m": Const(28),
"_n": MaxOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(2)), Leq(Var("n1"), Ref("_m")), IsPrime(Var("n1"))))),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Su... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW/COUNT_SUM_EQUALS"
] | 06c6d1 | sequence_lucas_compute_v1 | null | 3 | 0 | [
"COUNT_SUM_EQUALS",
"MAX_PRIME_BELOW"
] | 2 | 0.062 | 2026-02-08T17:38:15.077868Z | {
"verified": true,
"answer": 15127,
"timestamp": "2026-02-08T17:38:15.139706Z"
} | d47c1e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 180,
"completion_tokens": 774
},
"timestamp": "2026-02-18T05:28:20.640Z",
"answer": 15127
},
{... | 1 | [
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok_later"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONS... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
a02dd4_l | modular_modexp_compute_v1_1520064083_571 | Let $a = 29$. Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 12250000$. Define $e$ to be the minimum value of $x + y$ as $(x, y)$ ranges over $S$. Let $m = 53824$. Compute the remainder when $a^e$ is divided by $m$. | 1 | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | modular_modexp_compute_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.001 | 2026-02-08T03:28:39.653505Z | {
"verified": false,
"answer": 21025,
"timestamp": "2026-02-08T03:28:39.654635Z"
} | 035ddd | a02dd4 | 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": 195,
"completion_tokens": 1819
},
"timestamp": "2026-02-10T14:36:40.646Z",
"answer": 21025
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | |
2401aa | algebra_poly_eval_v1_458359167_5085 | Let $k$ be the largest prime number less than or equal to 6. Let $d_{\text{min}}$ be the smallest divisor of 245 that is at least 2. Define
$$
\text{result} = d_{\text{min}} \cdot k^4 + 10k^3 - 9k^2 + k - 8.
$$
Find the remainder when $44121 \cdot \text{result}$ is divided by 80242. | 18,027 | graphs = [
Graph(
let={
"_m": Const(6),
"_n": Const(2),
"k": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_m")), IsPrime(Var("n"))))),
"result": Sum(Mul(MinOverSet(set=SolutionsSet(var=Var("d"), condition=... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR",
"MAX_PRIME_BELOW"
] | 9f9e96 | algebra_poly_eval_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW",
"MIN_PRIME_FACTOR"
] | 2 | 0.003 | 2026-02-08T12:16:18.453673Z | {
"verified": true,
"answer": 18027,
"timestamp": "2026-02-08T12:16:18.456653Z"
} | 9bda2e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 145,
"completion_tokens": 990
},
"timestamp": "2026-02-14T23:20:05.378Z",
"answer": 18027
},
{... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
4a7342 | comb_catalan_compute_v1_548369836_373 | Let $n$ be the number of ordered triples $(x_1, x_2, x_3)$ of positive odd integers such that $x_1 + x_2 + x_3 = 9$. Let $c = 10035$. Compute the remainder when $c \cdot C_n$ is divided by $50233$, where $C_n$ denotes the $n$-th Catalan number. | 16,145 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2"), Var("x3")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsPositive(arg=Var(name='x3')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), IsOdd(arg=Var(name... | COMB | null | COMPUTE | sympy | COMB1 | [
"COMB1"
] | 567f58 | comb_catalan_compute_v1 | null | 5 | 0 | [
"COMB1"
] | 1 | 0.002 | 2026-02-08T02:53:31.229896Z | {
"verified": true,
"answer": 16145,
"timestamp": "2026-02-08T02:53:31.231627Z"
} | e150f4 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 202,
"completion_tokens": 3618
},
"timestamp": "2026-02-08T20:26:02.009Z",
"answer": 16145
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
... | {
"lo": -0.15,
"mid": 1.46,
"hi": 2.88
} | ||
31e3ae | comb_bell_compute_v1_1918700295_1749 | Let $p$ and $q$ be positive integers such that $p \cdot q = 26460$, $\gcd(p, q) = 1$, and $p < q$. Let $n$ be the number of such integers $p$. Let $B_n$ denote the $n$-th Bell number, which counts the number of partitions of an $n$-element set. Compute the remainder when $44121 \cdot B_n$ is divided by $99097$. | 25,169 | graphs = [
Graph(
let={
"_n": Const(99097),
"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=26460)), Eq(left=GCD(a=Var(name='p'), b=Var(n... | NT | COMB | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_bell_compute_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.002 | 2026-02-08T05:59:22.955644Z | {
"verified": true,
"answer": 25169,
"timestamp": "2026-02-08T05:59:22.957742Z"
} | b217b4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 146,
"completion_tokens": 2273
},
"timestamp": "2026-02-12T17:49:53.080Z",
"answer": 25169
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
b5a73c | nt_count_divisible_and_v1_1978505735_6680 | Let $S$ be the set of all integers $n$ such that $1 \leq n \leq 70668$, $n$ is divisible by 6, and $n$ is divisible by the number of elements in the set $\{1,2,3\} \times \{1,2,3\}$. Let $c$ be the number of integers $t$ with $5 \leq t \leq 17$ for which there exist positive integers $a \leq 3$ and $b \leq 4$ such that... | 1,881 | graphs = [
Graph(
let={
"upper": Const(70668),
"d1": Const(6),
"d2": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(3)), right=IntegerRange(start=Const(1), end=Const(3)))),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), co... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM",
"COUNT_CARTESIAN"
] | 6e491f | nt_count_divisible_and_v1 | bell_mod | 5 | 0 | [
"COUNT_CARTESIAN",
"LIN_FORM"
] | 2 | 2.249 | 2026-02-08T19:44:36.017542Z | {
"verified": true,
"answer": 1881,
"timestamp": "2026-02-08T19:44:38.266794Z"
} | e70d66 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 196,
"completion_tokens": 1937
},
"timestamp": "2026-02-18T23:24:31.159Z",
"answer": 1881
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_F... | {
"lo": -3.12,
"mid": 1.47,
"hi": 6.57
} | ||
cb0d1b | sequence_count_fib_divisible_v1_1978505735_3871 | Let $N = 3548$. Let $A$ be the set of all positive integers $n$ such that $1 \leq n \leq N$ and $3$ divides the $n$-th Fibonacci number. Let $k$ be the number of elements in $A$. Let $B$ be the set of all integers $t$ such that $7 \leq t \leq 30$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 4$, $1 ... | 29 | graphs = [
Graph(
let={
"_n": Const(3548),
"upper": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_n")), Divides(divisor=Const(3), dividend=Fibonacci(arg=Var(name='n')))))),
"d": CountOverSet(set=SolutionsSet(var=Var... | NT | null | COUNT | sympy | K3 | [
"COUNT_FIB_DIVISIBLE",
"LIN_FORM"
] | 0f3003 | sequence_count_fib_divisible_v1 | null | 6 | 0 | [
"COUNT_FIB_DIVISIBLE",
"K3",
"LIN_FORM"
] | 3 | 0.078 | 2026-02-08T17:54:32.840966Z | {
"verified": true,
"answer": 29,
"timestamp": "2026-02-08T17:54:32.919348Z"
} | f5d5df | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 242,
"completion_tokens": 1611
},
"timestamp": "2026-02-18T09:51:07.313Z",
"answer": 29
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
cb55ac | geo_count_lattice_rect_v1_784195855_3107 | Let $ a = 128 $ and $ b = 258 $. The number of lattice points $ (x, y) $ such that $ 0 \leq x \leq a $ and $ 0 \leq y \leq b $ is denoted by $ L $. Compute the remainder when $ 75931 \cdot L $ is divided by $ 93222 $. | 80,355 | graphs = [
Graph(
let={
"a": Const(128),
"b": Const(258),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"Q": Mod(value=Mul(Const(75931), Ref("result")), modulus=Const(93222)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0 | 2026-02-08T06:13:59.307642Z | {
"verified": true,
"answer": 80355,
"timestamp": "2026-02-08T06:13:59.308130Z"
} | 471f28 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 192,
"completion_tokens": 6679
},
"timestamp": "2026-02-24T05:43:45.566Z",
"answer": 80355
},
{
"... | 1 | [] | {
"lo": -0.06,
"mid": 2.89,
"hi": 5.27
} | ||||
17d037 | nt_count_intersection_v1_349078426_1325 | Let $N = 20000$ and $a = 11$. Let $b$ be the sum $\sum_{k=1}^{3} k$. Determine the number of positive integers $n$ such that $1 \leq n \leq N$, $a$ divides $n$, and $\gcd(n, b) = 1$. | 606 | graphs = [
Graph(
let={
"N": Const(20000),
"a": Const(11),
"b": Summation(var="k", start=Const(1), end=Const(3), expr=Var("k")),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("N")), Divides(divis... | NT | null | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | nt_count_intersection_v1 | null | 4 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.665 | 2026-02-08T13:33:30.772351Z | {
"verified": true,
"answer": 606,
"timestamp": "2026-02-08T13:33:31.437712Z"
} | 2e2900 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 118,
"completion_tokens": 787
},
"timestamp": "2026-02-15T17:50:53.888Z",
"answer": 606
},
{
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
196db6_l | geo_count_lattice_rect_v1_1742523217_1997 | Let $a = 64$ and $b = 14$. Define $R$ to be the number of lattice points in the rectangle $[0, a] \times [0, b]$. Compute the remainder when $$\sum_{n=1}^{R} \phi(n)$$ is divided by $79267$. | 0 | GEOM | null | COUNT | sympy | IDENTITY_DIV_SELF | [
"IDENTITY_DIV_SELF"
] | b48fad | geo_count_lattice_rect_v1 | null | 5 | 0 | [
"IDENTITY_DIV_SELF"
] | 1 | 0.02 | 2026-02-08T04:23:07.606947Z | {
"verified": false,
"answer": 51363,
"timestamp": "2026-02-08T04:23:07.627183Z"
} | ddec20 | 196db6 | legacy_text | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 178,
"completion_tokens": 32768
},
"timestamp": "2026-02-24T00:31:43.462Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "IDENTITY_DIV_SELF",
"status": "ok"
}
] | {
"lo": 3.43,
"mid": 5.73,
"hi": 8.84
} | |
c4fccc | lin_form_endings_v1_677425708_1640 | Let $a = 16$ and $b = 56$. Let $\ell = \text{lcm}(a, b)$. Define $$s = 18397 \cdot (1 \cdot \ell + a + b).$$ Compute the remainder when $s$ is divided by $55043$. | 27,425 | graphs = [
Graph(
let={
"a_coeff": Const(16),
"b_coeff": Const(56),
"k_val": Const(1),
"lcm_node": LCM(a=Ref("a_coeff"), b=Ref("b_coeff")),
"_inner_result": Sum(Mul(Ref("k_val"), Ref("lcm_node")), Ref("a_coeff"), Ref("b_coeff")),
"_scal... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 2 | null | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T04:21:10.409377Z | {
"verified": true,
"answer": 27425,
"timestamp": "2026-02-08T04:21:10.411011Z"
} | fa0b0e | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 176,
"completion_tokens": 666
},
"timestamp": "2026-02-09T22:45:08.324Z",
"answer": 27425
},
{
"i... | 1 | [
{
"lemma": "C2",
"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",
"status": "no... | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
9bf9cc | sequence_fibonacci_compute_v1_1520064083_2972 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = 20$. Let $P$ be the set of products $xy$ for all $(x, y) \in S$. Let $m$ be the maximum value in $P$. Now, let $T$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = m$. Let $s$ be the minimum value of $x... | 6,765 | graphs = [
Graph(
let={
"_m": Const(20),
"_n": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Ref("_m")))), expr=Mul(Var("x"), Var("y")))),
... | NT | null | COMPUTE | sympy | B1 | [
"B1/B3"
] | 80b49d | sequence_fibonacci_compute_v1 | null | 5 | 0 | [
"B1",
"B3"
] | 2 | 0.003 | 2026-02-08T05:21:33.525280Z | {
"verified": true,
"answer": 6765,
"timestamp": "2026-02-08T05:21:33.528454Z"
} | 8bbc00 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 230,
"completion_tokens": 866
},
"timestamp": "2026-02-12T07:09:19.944Z",
"answer": 6765
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
2af9bb | algebra_quadratic_discriminant_v1_124444284_5709 | Let $m = 4$. Define $n$ to be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = m$. Let $a = 2$, $b = -16$, and let $c$ be the largest integer $k$ such that $3^k \leq 11413298$. Compute $b^2 - nac$. Find the value of this result. | 144 | graphs = [
Graph(
let={
"_m": Const(4),
"_n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_m")))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"B3/MAX_VAL"
] | 2438e8 | algebra_quadratic_discriminant_v1 | null | 4 | 0 | [
"B3",
"COPRIME_PAIRS",
"MAX_VAL"
] | 3 | 0.028 | 2026-02-08T06:46:53.791144Z | {
"verified": true,
"answer": 144,
"timestamp": "2026-02-08T06:46:53.818771Z"
} | ea50d7 | 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": 561
},
"timestamp": "2026-02-13T05:01:25.300Z",
"answer": 144
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "ok_later"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemm... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
809281 | comb_count_permutations_fixed_v1_1439011603_1056 | Let $k$ be the number of integers $t$ such that $5 \leq t \leq 14$ and there exist integers $a$ and $b$ with $1 \leq a \leq 4$, $1 \leq b \leq 2$, and $t = 2a + 3b$. Let $n = 11$. Define $N = \binom{n}{k} \cdot !(n - k)$, where $!m$ denotes the number of derangements of $m$ elements. Compute $N$. | 330 | graphs = [
Graph(
let={
"n": Const(11),
"k": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=4)), Geq(left=Var(na... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_count_permutations_fixed_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.003 | 2026-02-08T15:52:48.520359Z | {
"verified": true,
"answer": 330,
"timestamp": "2026-02-08T15:52:48.523535Z"
} | f1f2f8 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 233,
"completion_tokens": 768
},
"timestamp": "2026-02-24T18:55:00.378Z",
"answer": 330
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"st... | {
"lo": -6.4,
"mid": -4.13,
"hi": -2.01
} | ||
217a9f | antilemma_v7_kummer_1742523217_38 | Let $n = 3$. Let $A$ be the set of all positive integers $k$ such that $1 \leq k \leq 115$ and $k$ is divisible by $115$. Let $N$ be the sum of all elements in $A$. Compute the largest integer $x$ such that $n^x$ divides $\binom{N}{46}$. | 2 | graphs = [
Graph(
let={
"_n": Const(3),
"x": MaxKDivides(target=Binom(n=SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(115)), Eq(Mod(value=Var("n"), modulus=Const(115)), Const(0))))), k=Const(46)), base=Ref("_n")),
},
... | NT | null | COMPUTE | sympy | SUM_DIVISIBLE | [
"SUM_DIVISIBLE/V7",
"V7"
] | 3b997e | antilemma_v7_kummer | null | 5 | null | [
"SUM_DIVISIBLE",
"V7"
] | 2 | 0.035 | 2026-02-08T02:50:44.481730Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-02-08T02:50:44.516792Z"
} | 338b5a | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 197,
"completion_tokens": 1792
},
"timestamp": "2026-02-09T12:44:17.652Z",
"answer": 2
},
{
"id":... | 2 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "SUM_DIVISIBLE",
"status": "ok"
},
{
... | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
5859d6 | alg_sum_powers_v1_1218484723_7449 | Let $M$ be the number of positive integers $k$ with $1 \leq k \leq 1743$ such that $7 \mid k$. Find the remainder when $\sum_{k=1}^{M} k^2$ is divided by the number of integers $t$ in the range $10 \leq t \leq 16150$ that can be expressed as $t = 4a + 6b$ for some integers $a, b$ with $1 \leq a \leq 3796$, $1 \leq b \l... | 4,896 | graphs = [
Graph(
let={
"_m": Const(7),
"_n": CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(1)), Leq(Var("k"), Const(1743)), Divides(divisor=Ref("_m"), dividend=Var("k"))), domain='positive_integers')),
"result": Mod(value=Summation(var="k1... | NT | null | COMPUTE | sympy | C2 | [
"C2/LIN_FORM"
] | 79042e | alg_sum_powers_v1 | null | 4 | 0 | [
"C2",
"LIN_FORM"
] | 2 | 0.016 | 2026-02-25T08:52:52.278744Z | {
"verified": true,
"answer": 4896,
"timestamp": "2026-02-25T08:52:52.295234Z"
} | f26493 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 238,
"completion_tokens": 8764
},
"timestamp": "2026-03-30T04:37:10.272Z",
"answer": 4896
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok_later"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": ... | {
"lo": 1.53,
"mid": 4.7,
"hi": 7.23
} | ||
bf2bef_n | geo_count_lattice_rect_v1_1218484723_41 | A rectangular garden is laid out on a grid with corners at $(0,0)$ and $(21,57)$. Each plant is placed at a lattice point within or on the boundary of the rectangle. How many plants are in the garden? Compute the remainder when $44121$ times this number is divided by $52301$. | 22,520 | GEOM | GEOM | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 2 | null | null | null | 0.001 | 2026-02-25T01:44:35.358144Z | null | 0c1aa8 | bf2bef | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 177,
"completion_tokens": 2785
},
"timestamp": "2026-03-30T14:41:29.420Z",
"answer": 22520
},
{
"... | 1 | [] | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | |||
3e3973 | comb_factorial_compute_v1_168721529_1431 | Let $m = 43$. Define $n_0$ to be the largest integer $k$ such that $43^k$ divides $m^2$. Let $n$ be the smallest positive divisor of $91091$ that is at least $n_0$. Let $r = 45293 \cdot n!$. Find the remainder when $r$ is divided by $82071$. | 37,269 | graphs = [
Graph(
let={
"_m": Const(43),
"_n": MaxKDivides(target=Pow(Ref("_m"), Const(2)), base=Const(43)),
"n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(91091))))),
"result": F... | NT | null | COMPUTE | sympy | K14 | [
"K14/MIN_PRIME_FACTOR"
] | cab2ed | comb_factorial_compute_v1 | null | 3 | 0 | [
"K14",
"MIN_PRIME_FACTOR"
] | 2 | 0.005 | 2026-02-08T13:41:57.749293Z | {
"verified": true,
"answer": 37269,
"timestamp": "2026-02-08T13:41:57.754202Z"
} | f93ea9 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 194,
"completion_tokens": 3117
},
"timestamp": "2026-02-09T17:02:30.413Z",
"answer": 37269
},
{
"... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok_later"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
... | {
"lo": -6.5,
"mid": -0.2,
"hi": 6.11
} | ||
33df4c | nt_lcm_compute_v1_124444284_1600 | Let $a$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 550564$. Let $b$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 122500$. Compute the least common multiple of $a$ and $b$. | 37,100 | graphs = [
Graph(
let={
"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")), Const(550564)))), expr=Sum(Var("x"), Var("y")))),
"b": MinOverSet(... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_lcm_compute_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.002 | 2026-02-08T04:01:56.236727Z | {
"verified": true,
"answer": 37100,
"timestamp": "2026-02-08T04:01:56.239104Z"
} | 185f3c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 191,
"completion_tokens": 1326
},
"timestamp": "2026-02-11T15:48:04.455Z",
"answer": 37100
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
c38a68 | antilemma_k2_v1_1439011603_3041 | Let $m = 3$ and $c = 1 + 2 + 3 + 4 + 5$. Let $r_1$ and $r_2$ be the roots of the quadratic equation $x^2 - 358x + 11016 = 0$, and let $n = r_1 + r_2$. Define
$$
x = \frac{m}{c} \sum_{k=1}^{358} \sum_{j=1}^{5} \phi(k) \left\lfloor \frac{n}{k} \right\rfloor,
$$
where $\phi(k)$ denotes Euler's totient function. Let $a = |... | 91,997 | graphs = [
Graph(
let={
"_m": Const(3),
"_c": Summation(var="k", start=Const(1), end=Const(5), expr=Var("k")),
"_n": SumOverSet(set=SolutionsSet(var=Var("x1"), condition=Eq(Sum(Pow(Var("x1"), Const(2)), Mul(Const(-358), Var("x1")), Const(11016)), Const(0)))),
... | NT | COMB | COMPUTE | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC/SUM_INDEPENDENT",
"VIETA_SUM/K2",
"K2"
] | aaa84c | antilemma_k2_v1 | null | 6 | 0 | [
"K2",
"SUM_ARITHMETIC",
"SUM_INDEPENDENT",
"VIETA_SUM"
] | 4 | 0.005 | 2026-02-08T17:10:50.175262Z | {
"verified": true,
"answer": 91997,
"timestamp": "2026-02-08T17:10:50.179955Z"
} | 66cbd1 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 220,
"completion_tokens": 2000
},
"timestamp": "2026-02-17T22:00:45.884Z",
"answer": 91997
},
... | 1 | [
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "SUM_INDEPENDENT",
"status": "ok_later"... | {
"lo": 2.52,
"mid": 6.26,
"hi": 10
} | ||
8a63ba_l | modular_modexp_compute_v1_151522320_1351 | Let $a = 29$. Let $e$ be the maximum value of $xy$ over all pairs of positive integers $(x, y)$ such that $x + y = 48$. Compute the remainder when $a^e$ is divided by $70000$. | 1 | NT | null | COMPUTE | sympy | B1 | [
"B1"
] | 5b950e | modular_modexp_compute_v1 | null | 4 | 0 | [
"B1"
] | 1 | 0.001 | 2026-02-08T03:53:30.654387Z | {
"verified": false,
"answer": 62721,
"timestamp": "2026-02-08T03:53:30.655877Z"
} | 1bf298 | 8a63ba | 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": 166,
"completion_tokens": 4957
},
"timestamp": "2026-02-10T16:20:29.026Z",
"answer": 62721
},
{
"... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
... | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | |
6a2837 | comb_count_surjections_v1_601307018_5054 | Let $a$ be an integer with $0 \le a \le 30$. Define:
\begin{align*}
M &= a^{15} \bmod 31, \\
R &= (2a^4 + 4a^3 + 2a - 3) \bmod 31, \\
S &= R^{15} \bmod 31, \\
T &= (2R^4 + 4R^3 + 2R - 3) \bmod 31, \\
K &= T^{15} \bmod 31, \\
L &= M + S + K, \\
P &= (2T^4 + 4T^3 + 2T - 3) \bmod 31.
\end{align*}
Let $k$ be the number of ... | 1,806 | graphs = [
Graph(
let={
"_n": Const(4),
"n": Const(7),
"k": CountOverSet(set=SolutionsSet(var=Var("a"), condition=And(Geq(Var("a"), Const(0)), Leq(Var("a"), Const(30)), Eq(Ref("_po_p3"), Var("a")), Neq(Ref("_po_p1"), Var("a")), Neq(Ref("_po_p2"), Var("a")), Congruent(a=Re... | COMB | NT | COUNT | sympy | POLY_ORBIT_HENSEL | [
"POLY_ORBIT_LEGENDRE"
] | 7c2be8 | comb_count_surjections_v1 | null | 6 | 0 | [
"POLY_ORBIT_HENSEL",
"POLY_ORBIT_LEGENDRE"
] | 2 | 3.236 | 2026-03-10T05:42:46.643160Z | {
"verified": true,
"answer": 1806,
"timestamp": "2026-03-10T05:42:49.878876Z"
} | b85b9c | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 358,
"completion_tokens": 8736
},
"timestamp": "2026-04-19T01:08:51.202Z",
"answer": 1806
},
{
"... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "POLY_ORBIT_LEGENDRE",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SU... | {
"lo": 2.12,
"mid": 5.37,
"hi": 8.63
} | ||
8dcd2b | geo_count_lattice_rect_v1_1742523217_3212 | Let $a = 240$ and $b = 124$. Define $L$ to be the number of lattice points in the rectangle $[0, a] \times [0, b]$, including the boundary. Let $Q$ be the remainder when $42261 \cdot L$ is divided by 72998. Compute $Q$. | 27,505 | graphs = [
Graph(
let={
"a": Const(240),
"b": Const(124),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"Q": Mod(value=Mul(Const(42261), Ref("result")), modulus=Const(72998)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.007 | 2026-02-08T05:43:19.011321Z | {
"verified": true,
"answer": 27505,
"timestamp": "2026-02-08T05:43:19.018705Z"
} | e31957 | 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": 1935
},
"timestamp": "2026-02-24T04:23:09.828Z",
"answer": 27505
},
{
"... | 1 | [] | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||||
74a12d | comb_catalan_compute_v1_865884756_1957 | Let $n$ be the number of integers $t$ such that $21 \leq t \leq 33$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 3$, $1 \leq b \leq 4$, and $t = 3a + 2b + 16$. Define $\text{result} = C_n$, where $C_n$ is the $n$-th Catalan number. Find the value of $\text{result}$. | 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=3)), 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 | 0.002 | 2026-02-08T16:24:46.132428Z | {
"verified": true,
"answer": 58786,
"timestamp": "2026-02-08T16:24:46.134652Z"
} | 8c8453 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 224,
"completion_tokens": 1078
},
"timestamp": "2026-02-24T20:59:47.974Z",
"answer": 58786
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -2.4,
"mid": 1.57,
"hi": 5.75
} | ||
0fe4ac | antilemma_sum_equals_v1_1742523217_5065 | Let $m = 75$. Let $n$ be the number of ordered pairs $(i, j)$ of integers with $1 \le i \le 74$ and $1 \le j \le 75$ such that $i + j = m$. Let $x$ be the number of ordered pairs $(i, j)$ of integers with $1 \le i \le 72$ and $1 \le j \le 73$ such that $i + j = n$. Let $Q$ be the number of integers $t$ with $7 \le t \l... | 3,064 | graphs = [
Graph(
let={
"_m": Const(75),
"_n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref("_m")), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(74)), right=IntegerRange(start=Const(1), end=Co... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS/LIN_FORM/COUNT_SUM_EQUALS",
"LIN_FORM",
"COUNT_SUM_EQUALS"
] | 502df3 | antilemma_sum_equals_v1 | negation_mod | 5 | 0 | [
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 2 | 0.012 | 2026-02-08T10:46:05.366324Z | {
"verified": true,
"answer": 3064,
"timestamp": "2026-02-08T10:46:05.378667Z"
} | 1cf49c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 280,
"completion_tokens": 24562
},
"timestamp": "2026-02-24T12:22:07.581Z",
"answer": 3064
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status... | {
"lo": 1.15,
"mid": 4.18,
"hi": 6.61
} | ||
88bbd0 | alg_poly_orbit_count_v1_1218484723_5891 | For each non-negative integer $a$ with $0 \leq a \leq 2293$, define the sequence $N = a^3 \bmod 31$, $M = N^3 \bmod 31$, $R = M^3 \bmod 31$, $S = R^3 \bmod 31$. Find the number of values of $a$ such that $S = a$, but $N \ne a$, $M \ne a$, and $R \ne a$. | 592 | graphs = [
Graph(
let={
"p1": Mod(value=Pow(Var("a"), Const(3)), modulus=Const(31)),
"p2": Mod(value=Pow(Ref("p1"), Const(3)), modulus=Const(31)),
"p3": Mod(value=Pow(Ref("p2"), Const(3)), modulus=Const(31)),
"p4": Mod(value=Pow(Ref("p3"), Const(3)), modulus=C... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_orbit_count_v1 | null | 6 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.01 | 2026-02-25T07:28:22.231698Z | {
"verified": true,
"answer": 592,
"timestamp": "2026-02-25T07:28:22.241469Z"
} | 6666a9 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 219,
"completion_tokens": 2952
},
"timestamp": "2026-03-29T23:16:14.733Z",
"answer": 8
},
{
"i... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 3.81,
"mid": 6.33,
"hi": 9.49
} | ||
cd389d | geo_count_lattice_rect_v1_1978505735_3281 | Let $a = 377$ and $b = 199$. Compute the number of lattice points in the rectangle $[0, a] \times [0, b]$, including the boundary. Let $r$ be this number. Let $c = 57481$. Find the remainder when $c \cdot r$ is divided by $62892$. | 40,860 | graphs = [
Graph(
let={
"a": Const(377),
"b": Const(199),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"_c": Const(57481),
"Q": Mod(value=Mul(Ref("_c"), Ref("result")), modulus=Const(62892)),
},
goal=Ref("Q"),
... | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.004 | 2026-02-08T17:32:28.875861Z | {
"verified": true,
"answer": 40860,
"timestamp": "2026-02-08T17:32:28.880342Z"
} | c50cc1 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 121,
"completion_tokens": 1191
},
"timestamp": "2026-02-18T03:46:35.456Z",
"answer": 40860
},
... | 1 | [] | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||||
2e7e4b | nt_min_with_divisor_count_v1_349078426_259 | Determine the value of the smallest positive integer $n$ such that $n \leq 2704$ and $n$ has exactly 6 positive divisors. | 12 | graphs = [
Graph(
let={
"upper": Const(2704),
"div_count": Const(6),
"result": MinOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(NumDivisors(n=Var("n")), Ref("div_count"))))),
},
goal=Ref("resu... | NT | null | EXTREMUM | sympy | B3 | [
"MOBIUS_COPRIME"
] | ac54ac | nt_min_with_divisor_count_v1 | null | 3 | 0 | [
"B3",
"MOBIUS_COPRIME"
] | 2 | 23.143 | 2026-02-08T12:54:07.338358Z | {
"verified": true,
"answer": 12,
"timestamp": "2026-02-08T12:54:30.481366Z"
} | e463b4 | 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": 878
},
"timestamp": "2026-02-15T07:15:03.280Z",
"answer": 12
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"stat... | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
f72682 | modular_mod_compute_v1_1978505735_497 | Let $ a = -74529 $ and $ m = 30625 $. Define $ r $ to be the remainder when $ a $ is divided by $ m $, so $ 0 \leq r < m $. Let $ T $ be the set of all ordered pairs $ (x, y) $ of positive integers such that $ xy = 6002500 $. Define $ s $ to be the minimum value of $ x + y $ over all such pairs $ (x, y) \in T $. Comput... | 48,634 | graphs = [
Graph(
let={
"a": Const(-74529),
"m": Const(30625),
"result": Mod(value=Ref("a"), modulus=Ref("m")),
"Q": Mod(value=Sub(MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')),... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | fc629c | modular_mod_compute_v1 | negation_mod | 4 | 0 | [
"B3"
] | 1 | 0.002 | 2026-02-08T15:24:36.629292Z | {
"verified": true,
"answer": 48634,
"timestamp": "2026-02-08T15:24:36.631733Z"
} | ae3537 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 168,
"completion_tokens": 1967
},
"timestamp": "2026-02-16T05:46:12.538Z",
"answer": 48634
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
a077b1 | sequence_lucas_compute_v1_971394319_1207 | Let $p$ be a positive integer. Define $c$ to be the number of such $p$ for which there exists a positive integer $q$ satisfying $p \cdot q = 108$, $\gcd(p, q) = 1$, and $p < q$. Let $d$ be the smallest integer at least $c$ that divides 18588623. Compute the $d$th Lucas number.
Find the value of this Lucas number. | 64,079 | 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=108)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(value=1)),... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/MIN_PRIME_FACTOR"
] | 52cee2 | sequence_lucas_compute_v1 | null | 5 | 0 | [
"COPRIME_PAIRS",
"MIN_PRIME_FACTOR"
] | 2 | 0.003 | 2026-02-08T13:31:45.553469Z | {
"verified": true,
"answer": 64079,
"timestamp": "2026-02-08T13:31:45.556967Z"
} | 9dbf99 | 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": 3999
},
"timestamp": "2026-02-15T17:41:22.542Z",
"answer": 64079
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok_later"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
9dd3a3 | nt_count_divisible_v1_1742523217_346 | Let $T$ be the set of all integers $t$ with $14 \leq t \leq 48$ such that there exist positive integers $a$ and $b$ satisfying $1 \leq a \leq 4$, $1 \leq b \leq 3$, and $t = 6a + 8b$. Let $\text{divisor}$ be the number of elements in $T$. Let $\text{upper} = 89253$. Determine the number of positive integers $n \leq \te... | 7,437 | graphs = [
Graph(
let={
"upper": Const(89253),
"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'), right=Const(value=4)), Ge... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_count_divisible_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 3.157 | 2026-02-08T02:59:09.381425Z | {
"verified": true,
"answer": 7437,
"timestamp": "2026-02-08T02:59:12.538417Z"
} | 22fea0 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 244,
"completion_tokens": 859
},
"timestamp": "2026-02-09T16:45:35.367Z",
"answer": 7437
},
{
"id... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
... | {
"lo": -5.55,
"mid": -3.02,
"hi": 0.3
} | ||
f815a9 | comb_sum_binomial_row_v1_1218484723_398 | Find the number $n$ of ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 30$ satisfying $$384a^2b + 128a^3 + 128b^3 + 384ab^2 = 15059072,$$ and compute $2^n$. | 4,096 | graphs = [
Graph(
let={
"_n": Const(30),
"n": CountOverSet(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"), Const(30)), Eq(Sum(Mul(Const(384), Pow(Var("a"), Const(2)), Va... | COMB | null | SUM | sympy | POLY3_COUNT | [
"POLY3_COUNT"
] | 355dbe | comb_sum_binomial_row_v1 | null | 3 | 0 | [
"POLY3_COUNT"
] | 1 | 0.003 | 2026-02-25T02:05:56.050630Z | {
"verified": true,
"answer": 4096,
"timestamp": "2026-02-25T02:05:56.053211Z"
} | a39b4b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 179,
"completion_tokens": 862
},
"timestamp": "2026-03-28T22:30:31.073Z",
"answer": 4096
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "POLY3_COUNT",
"status": "ok"
},
{
"lemma": "V8_SUM",
... | {
"lo": -2.78,
"mid": -0.24,
"hi": 2.7
} | ||
422021 | diophantine_product_count_v1_1520064083_824 | Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 396900$. Define $k$ to be the minimum value of $x + y$ over all such pairs. Let $T$ be the set of all positive integers $x$ such that $1 \le x \le 71$, $x$ divides $k$, and $\frac{k}{x} \le 71$. Compute the remainder when $44121 \cdot ... | 51,908 | graphs = [
Graph(
let={
"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(396900)))), expr=Sum(Var("x"), Var("y")))),
"upper": Const(7... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | diophantine_product_count_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.006 | 2026-02-08T03:37:29.376097Z | {
"verified": true,
"answer": 51908,
"timestamp": "2026-02-08T03:37:29.382054Z"
} | d09dbe | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 223,
"completion_tokens": 2729
},
"timestamp": "2026-02-10T13:55:18.088Z",
"answer": 51908
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
987b97 | diophantine_fbi2_count_v1_1978505735_3054 | Let $\_n$ be the number of integers $t$ with $9 \leq t \leq 88$ such that there exist positive integers $a$ and $b$ with $1 \leq a \leq 7$, $1 \leq b \leq 12$, and $t = 4a + 5b$. Let $k$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 129600$. Compute the number of i... | 12 | graphs = [
Graph(
let={
"_m": Const(3),
"_n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=7)), Geq(left=Var(n... | NT | null | COUNT | sympy | SUM_DIVISIBLE | [
"LIN_FORM/B3"
] | 05313e | diophantine_fbi2_count_v1 | null | 6 | 0 | [
"B3",
"LIN_FORM",
"SUM_DIVISIBLE"
] | 3 | 0.026 | 2026-02-08T17:18:59.335999Z | {
"verified": true,
"answer": 12,
"timestamp": "2026-02-08T17:18:59.361714Z"
} | 805ad4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 198,
"completion_tokens": 5640
},
"timestamp": "2026-02-18T00:36:11.870Z",
"answer": 12
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
f2261b | nt_lcm_compute_v1_677425708_3030 | Let $a$ be the sum of all positive integers $n$ such that $n \leq 470$ and $n$ is divisible by $47$. Let $b = 592$, and let $\ell$ be the least common multiple of $a$ and $b$. Compute the remainder when $44121 \cdot \ell$ is divided by $94450$. | 60,570 | graphs = [
Graph(
let={
"_n": Const(470),
"a": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_n")), Eq(Mod(value=Var("n"), modulus=Const(47)), Const(0))))),
"b": Const(592),
"result": LCM(a=Ref("a"), b=Ref(... | NT | null | COMPUTE | sympy | SUM_DIVISIBLE | [
"SUM_DIVISIBLE"
] | 02dbe3 | nt_lcm_compute_v1 | null | 4 | 0 | [
"SUM_DIVISIBLE"
] | 1 | 0.001 | 2026-02-08T05:26:31.516291Z | {
"verified": true,
"answer": 60570,
"timestamp": "2026-02-08T05:26:31.517528Z"
} | eabbf7 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 124,
"completion_tokens": 7290
},
"timestamp": "2026-02-12T08:56:40.995Z",
"answer": 60570
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "SUM_DIVISIBLE",
"status": "ok"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
a9e517 | modular_modexp_compute_v1_601307018_7343 | Let $N$ be the maximum value of $xy$ over all ordered pairs $(x, y)$ of positive integers such that $x + y = 40$. Let $e = \sum_{k=0}^{9} 2^k$ and $R = 19^e \bmod 13225$. Find the remainder when $N - R$ is divided by $90513$. | 88,729 | graphs = [
Graph(
let={
"_n": Const(2),
"a": Const(19),
"e": Summation(var="k", start=Const(0), end=Const(9), expr=Pow(Ref("_n"), Var("k"))),
"m": Const(13225),
"result": ModExp(base=Ref("a"), exp=Ref("e"), mod=Ref("m")),
"_c": MaxOverS... | NT | null | COMPUTE | sympy | B1 | [
"B1",
"SUM_GEOM"
] | d0261a | modular_modexp_compute_v1 | negation_mod | 4 | 0 | [
"B1",
"SUM_GEOM"
] | 2 | 0.005 | 2026-03-10T07:55:56.008953Z | {
"verified": true,
"answer": 88729,
"timestamp": "2026-03-10T07:55:56.013675Z"
} | fe6fb2 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 193,
"completion_tokens": 2290
},
"timestamp": "2026-04-19T06:29:16.617Z",
"answer": 88729
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
... | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
31b155 | diophantine_fbi2_count_v1_784195855_3855 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 32400$. Define $n_0$ to be the minimum value of $x + y$ over all pairs $(x, y) \in S$. Let $k$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = n_0$. Compute the number of positive integers $... | 13 | graphs = [
Graph(
let={
"_m": Const(173),
"_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(32400)))), expr=Sum(Var("x"), Var("y"))))... | NT | null | COUNT | sympy | V8 | [
"B3/COMB1"
] | e26f7e | diophantine_fbi2_count_v1 | null | 6 | 0 | [
"B3",
"COMB1",
"V8"
] | 3 | 0.033 | 2026-02-08T06:40:31.240596Z | {
"verified": true,
"answer": 13,
"timestamp": "2026-02-08T06:40:31.274064Z"
} | c467cb | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 187,
"completion_tokens": 1686
},
"timestamp": "2026-02-13T03:06:17.610Z",
"answer": 13
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COMB1",
"status": "ok_later"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
70faa2 | comb_count_surjections_v1_1820931509_468 | Let $T$ be the set of all ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 14$. Let $s$ be the number of elements in $T$. Let $U$ be the set of all ordered triples $(x_1, x_2, x_3)$ of positive odd integers such that $x_1 + x_2 + x_3 = s$. Let $n$ be the number of elements in $U$. Compute $3! ... | 3,493 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2"), Var("x3")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsPositive(arg=Var(name='x3')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), IsOdd(arg=Var(name... | COMB | NT | COUNT | sympy | COMB1 | [
"COMB1/COMB1"
] | b2c526 | comb_count_surjections_v1 | null | 6 | 0 | [
"COMB1"
] | 1 | 0.002 | 2026-02-08T11:38:33.075305Z | {
"verified": true,
"answer": 3493,
"timestamp": "2026-02-08T11:38:33.077270Z"
} | 295ccf | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 284,
"completion_tokens": 14304
},
"timestamp": "2026-02-24T14:35:57.541Z",
"answer": 3493
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
aa235b | diophantine_sum_product_min_v1_655260480_927 | Let $s$ be the number of positive integers $p$ such that there exists a positive integer $q$ with $pq = 72$, $\gcd(p, q) = 1$, and $p < q$. Let $S$ be the largest prime number $n$ such that $s \leq n \leq 30$. Let $P = 120$. Determine the value of $x$ such that $1 \leq x \leq 28$ and $x(S - x) = P$. | 5 | graphs = [
Graph(
let={
"_n": Const(30),
"S": 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'), Var(name='q'... | NT | null | EXTREMUM | sympy | MAX_DIVISOR | [
"COPRIME_PAIRS/MAX_PRIME_BELOW"
] | 2248fc | diophantine_sum_product_min_v1 | null | 6 | 0 | [
"COPRIME_PAIRS",
"MAX_DIVISOR",
"MAX_PRIME_BELOW"
] | 3 | 0.027 | 2026-02-08T15:45:42.849316Z | {
"verified": true,
"answer": 5,
"timestamp": "2026-02-08T15:45:42.876655Z"
} | eafc11 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 153,
"completion_tokens": 3196
},
"timestamp": "2026-02-16T12:57:47.580Z",
"answer": 5
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MOD_SUB",
"status": "no"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
5e50e1 | nt_count_coprime_and_v1_349078426_1600 | Let $k_1 = 8$ and define $k_2 = \sum_{k=1}^{5} \phi(k) \left\lfloor \frac{5}{k} \right\rfloor$. Determine the number of positive integers $n$ such that $1 \leq n \leq 55095$, $\gcd(n, k_1) = 1$, and $\gcd(n, k_2) = 1$. | 14,692 | graphs = [
Graph(
let={
"upper": Const(55095),
"k1": Const(8),
"k2": Summation(var="k", start=Const(1), end=Const(5), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(5), Var("k"))))),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("... | NT | null | COUNT | sympy | K2 | [
"K2"
] | 6897ab | nt_count_coprime_and_v1 | null | 4 | 0 | [
"K2"
] | 1 | 6.94 | 2026-02-08T13:44:37.744004Z | {
"verified": true,
"answer": 14692,
"timestamp": "2026-02-08T13:44:44.683597Z"
} | 6b05d7 | 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": 1705
},
"timestamp": "2026-02-15T20:06:13.628Z",
"answer": 14692
},
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
e67dd1_l | algebra_quadratic_discriminant_v1_1520064083_9417 | Let $a = 1$, $b = -8$, and $c = 16$. Define the discriminant $D = b^2 - 4ac$. Let $\alpha = 1$ if $D > 0$, and $0$ otherwise. Let $\beta = 1$ if $D = \sum_{k=0}^{4} (-1)^k \binom{4}{k}$, and $0$ otherwise. Compute $50289(2\alpha + \beta)$. | 0 | COMB | null | COMPUTE | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING"
] | c21569 | algebra_quadratic_discriminant_v1 | null | 4 | 0 | [
"BINOMIAL_ALTERNATING"
] | 1 | 0.002 | 2026-02-08T10:44:03.344733Z | {
"verified": false,
"answer": 50289,
"timestamp": "2026-02-08T10:44:03.346520Z"
} | b43a81 | e67dd1 | 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": 217,
"completion_tokens": 488
},
"timestamp": "2026-02-24T12:17:59.253Z",
"answer": 50289
},
{
"i... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "... | {
"lo": -4.92,
"mid": -2.91,
"hi": -0.68
} | |
ef2c35 | sequence_lucas_compute_v1_2051736721_3705 | Let $n = 20$, $a = 4$, and $b = 2$. Let $L$ be the $n$-th Lucas number. Let $T$ be the set of all ordered pairs of positive integers $(x_1, y_1)$ such that $x_1 \cdot y_1 = 8836$. Let $s_{\min}$ be the minimum value of $x_1 + y_1$ over all such pairs. Now, let $P$ be the set of all products $x \cdot y$ where $x$ and $y... | 35,031 | graphs = [
Graph(
let={
"_m": Const(4),
"_n": Const(2),
"n": Const(20),
"result": Lucas(arg=Ref(name='n')),
"Q": Mod(value=Sum(Pow(Ref("result"), Ref("_n")), Mul(Ref("_m"), Ref("result")), MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elemen... | NT | null | COMPUTE | sympy | B3 | [
"B3/B1"
] | fc7512 | sequence_lucas_compute_v1 | quadratic_mod | 6 | 0 | [
"B1",
"B3"
] | 2 | 0.003 | 2026-02-08T17:29:18.074999Z | {
"verified": true,
"answer": 35031,
"timestamp": "2026-02-08T17:29:18.077898Z"
} | 1f5ad5 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 221,
"completion_tokens": 1604
},
"timestamp": "2026-02-18T03:02:21.577Z",
"answer": 35031
},
... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"l... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
3bc3d8 | modular_inverse_v1_2051736721_1283 | Let $a$ be the sum of $\phi(d)$ over all positive divisors $d$ of $1271$. Let $m = 1399$ and let $\text{upper} = 1398$. Define $\text{result}$ to be the smallest positive integer $x$ such that $1 \leq x \leq \text{upper}$ and $a \cdot x \equiv 1 \pmod{m}$. Find the value of $\text{result}$. | 776 | graphs = [
Graph(
let={
"a": SumOverDivisors(n=Const(value=1271), var='d', expr=EulerPhi(n=Var(name='d'))),
"m": Const(1399),
"upper": Const(1398),
"result": MinOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), Const(1)), Leq(Var("x"), Ref("up... | NT | null | EXTREMUM | sympy | B3 | [
"K3"
] | 54c41e | modular_inverse_v1 | null | 5 | 0 | [
"B3",
"K3"
] | 2 | 0.104 | 2026-02-08T15:55:57.774441Z | {
"verified": true,
"answer": 776,
"timestamp": "2026-02-08T15:55:57.878677Z"
} | 402995 | 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": 5280
},
"timestamp": "2026-02-16T18:14:10.355Z",
"answer": 776
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "n... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
a642da | modular_modexp_compute_v1_601307018_9178 | Let $e$ be the number of non-negative integers $j$ with $0 \le j \le 32631$ such that $\binom{32631}{j} \bmod 2 = 1$. Compute $3^e \bmod 28561$. | 17,078 | graphs = [
Graph(
let={
"_n": Const(32631),
"a": Const(3),
"e": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(32631)), Eq(Mod(value=Binom(n=Ref("_n"), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_... | NT | null | COMPUTE | sympy | V8 | [
"V8"
] | 86348e | modular_modexp_compute_v1 | null | 7 | 0 | [
"V8"
] | 1 | 0.003 | 2026-03-10T09:34:26.483065Z | {
"verified": true,
"answer": 17078,
"timestamp": "2026-03-10T09:34:26.485874Z"
} | e61a00 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 168,
"completion_tokens": 5553
},
"timestamp": "2026-04-19T10:47:41.926Z",
"answer": 17078
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
},
{
"lemma": "V8_SUM",
... | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
007ec9 | antilemma_sum_equals_v1_717093673_2869 | Let $n = 64$. Consider the set of all ordered pairs $(i,j)$ of integers such that $1 \leq i \leq 63$, $1 \leq j \leq 64$, and $i + j = n$. Compute the number of such ordered pairs. | 63 | graphs = [
Graph(
let={
"_n": Const(64),
"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(63)), right=IntegerRange(start=Const(1), end=Con... | COMB | GEOM | COMPUTE | sympy | COMB1 | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 2 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS"
] | 2 | 0.025 | 2026-02-08T17:14:33.895051Z | {
"verified": true,
"answer": 63,
"timestamp": "2026-02-08T17:14:33.920138Z"
} | 8fef6b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 105,
"completion_tokens": 1184
},
"timestamp": "2026-02-24T22:22:26.058Z",
"answer": 63
},
{
... | 2 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
... | {
"lo": -10,
"mid": -7.42,
"hi": -4.85
} | ||
18421c | comb_sum_binomial_row_v1_1218484723_1428 | Let $k = \left|\{ (a_1, b_1) : 1 \leq a_1, b_1 \leq 35,\, a_1 \leq b_1,\, 32a_1^2 - 64a_1b_1 + 32b_1^2 = 11552 \}\right|$. Find the number $n$ of ordered pairs $(a,b)$ of positive integers with $1 \leq a, b \leq 25$ such that $b^2 - 8ab + k a^2 = 49$, then compute $2^n$. | 2,048 | graphs = [
Graph(
let={
"_m": Const(32),
"_n": Const(25),
"n": CountOverSet(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"), Const(25)), Eq(Sum(Pow(Var("b"), ... | COMB | null | SUM | sympy | POLY_ORBIT_COUNT | [
"QF_PSD_ORBIT/QF_PSD_COUNT"
] | 0d9357 | comb_sum_binomial_row_v1 | null | 6 | 0 | [
"POLY_ORBIT_COUNT",
"QF_PSD_COUNT",
"QF_PSD_ORBIT"
] | 3 | 0.124 | 2026-02-25T03:08:49.213404Z | {
"verified": true,
"answer": 2048,
"timestamp": "2026-02-25T03:08:49.337809Z"
} | 454353 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 248,
"completion_tokens": 1290
},
"timestamp": "2026-03-10T07:07:19.672Z",
"answer": 2048
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT",
"status": "ok_later"
},
{
"lemma": "QF_PSD_ORBIT",
"status": "ok"
},
{
"lemma": "V8",
"st... | {
"lo": -2.47,
"mid": 1.2,
"hi": 4.81
} | ||
869c58_n | algebra_poly_eval_v1_1218484723_1403 | A solar panel array is to be arranged as a rectangle with area $21883684$ square meters, using only whole meter dimensions. The layout that minimizes the perimeter uses side lengths $x$ and $y$. Let $S = x + y$. A power efficiency factor $M$ is computed as $7 \cdot 9^4 + 3 \cdot 9^3 - 5 \cdot 9^2 + 2 \cdot 9 + 4$. What... | 62,940 | ALG | null | COMPUTE | sympy | B3 | [
"B3"
] | e0298c | algebra_poly_eval_v1 | affine_mod | 4 | null | [
"B3"
] | 1 | 0.004 | 2026-02-25T03:08:18.751978Z | null | 92ceb3 | 869c58 | narrative | 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": 9161
},
"timestamp": "2026-03-30T16:47:36.839Z",
"answer": 62940
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | |
b583be | nt_count_digit_sum_v1_1125832087_138 | Let $S$ be the set of all positive integers $n$ such that $1 \leq n \leq 99999$ and the sum of the digits of $n$ is $15$. Let $c = 59559$. Compute the remainder when $c \cdot |S|$ is divided by $82810$. | 49,974 | graphs = [
Graph(
let={
"upper": Const(99999),
"target_sum": Const(15),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), EulerPhi(n=Const(2))), Leq(Var("n"), Ref("upper")), Eq(DigitSum(Var("n")), Ref("target_sum"))))),
"_c": Co... | NT | null | COUNT | sympy | ONE_PHI_2 | [
"ONE_PHI_2"
] | e19278 | nt_count_digit_sum_v1 | null | 4 | 0 | [
"ONE_PHI_2"
] | 1 | 3.583 | 2026-02-08T02:52:52.678461Z | {
"verified": true,
"answer": 49974,
"timestamp": "2026-02-08T02:52:56.261525Z"
} | 21338e | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 172,
"completion_tokens": 686
},
"timestamp": "2026-02-17T15:47:20.867Z",
"answer": 65
}
] | 0 | [
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "ONE_PHI_2",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -6.48,
"mid": 1.54,
"hi": 9.56
} | ||
e89de9 | antilemma_sum_equals_v1_677425708_797 | Let $n = 97$. Compute the number of ordered pairs $(i, j)$ of positive integers such that $1 \leq i \leq 96$, $1 \leq j \leq 97$, and $i + j = n$. Let $x$ be this number. Compute the remainder when $44121 \cdot x$ is divided by $88279$. | 86,503 | graphs = [
Graph(
let={
"_n": Const(97),
"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(96)), right=IntegerRange(start=Const(1), end=Con... | COMB | GEOM | COMPUTE | sympy | COMB1 | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 3 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS"
] | 2 | 0.023 | 2026-02-08T03:44:27.154145Z | {
"verified": true,
"answer": 86503,
"timestamp": "2026-02-08T03:44:27.177281Z"
} | 33092d | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 196,
"completion_tokens": 1400
},
"timestamp": "2026-02-09T12:26:23.323Z",
"answer": 86503
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V8_SU... | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
4fb899 | antilemma_sum_equals_v1_124444284_2193 | Let $n = 93$. Compute the number of ordered pairs $(i, j)$ of positive integers such that $i + j = n$ and $1 \leq i, j \leq 92$. | 92 | graphs = [
Graph(
let={
"_n": Const(93),
"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(92)), 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 | 0.109 | 2026-02-08T04:30:36.488751Z | {
"verified": true,
"answer": 92,
"timestamp": "2026-02-08T04:30:36.597843Z"
} | 69bf20 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 155,
"completion_tokens": 457
},
"timestamp": "2026-02-24T00:55:51.518Z",
"answer": 92
},
{
"id":... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status"... | {
"lo": -5.97,
"mid": -3.96,
"hi": -1.93
} | ||
f63ea5 | lin_form_endings_v1_1978505735_4037 | Let $a = 27$ and $b = 63$. Define $\ell = \text{lcm}(a, b)$ and $s = 3\ell + a + b$. Let $x$ be the remainder when $10475 \cdot s$ is divided by $74067$. Find the value of $x$. | 67,911 | graphs = [
Graph(
let={
"a_coeff": Const(27),
"b_coeff": Const(63),
"k_val": Const(3),
"lcm_node": LCM(a=Ref("a_coeff"), b=Ref("b_coeff")),
"_inner_result": Sum(Mul(Ref("k_val"), Ref("lcm_node")), Ref("a_coeff"), Ref("b_coeff")),
"_scal... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 3 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T17:59:07.193760Z | {
"verified": true,
"answer": 67911,
"timestamp": "2026-02-08T17:59:07.194910Z"
} | f56820 | 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": 972
},
"timestamp": "2026-02-18T10:45:42.350Z",
"answer": 67911
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"statu... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
144c52 | comb_catalan_compute_v1_1520064083_5547 | Let $n$ be the number of ordered triples $(x_1, x_2, x_3)$ of positive odd integers such that $x_1 + x_2 + x_3 = 9$. Let $C_n$ denote the $n$-th Catalan number. Compute the remainder when $14303 \cdot C_n$ is divided by $74871$. | 47,020 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2"), Var("x3")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsPositive(arg=Var(name='x3')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), IsOdd(arg=Var(name... | COMB | null | COMPUTE | sympy | COMB1 | [
"COMB1"
] | 567f58 | comb_catalan_compute_v1 | null | 4 | 0 | [
"COMB1"
] | 1 | 0.002 | 2026-02-08T07:26:21.036432Z | {
"verified": true,
"answer": 47020,
"timestamp": "2026-02-08T07:26:21.038206Z"
} | dfa5bf | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 191,
"completion_tokens": 2413
},
"timestamp": "2026-02-24T08:04:16.493Z",
"answer": 47020
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V8_SUM",
"s... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
0f7c56 | antilemma_v8_lucas_151522320_101 | Let $x$ be the number of nonnegative integers $j$ such that $0 \le j \le 64427$ and
$$
\binom{64427}{j} \equiv 1 \pmod{2}.
$$
Compute $x$. | 4,096 | graphs = [
Graph(
let={
"_n": Const(2),
"x": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(64427)), Eq(Mod(value=Binom(n=Const(64427), k=Var("j")), modulus=Ref("_n")), Const(1))), domain='nonnegative_integers')),
},
... | NT | COMB | COMPUTE | sympy | V8 | [
"V8"
] | 86348e | antilemma_v8_lucas | null | 6 | 0 | [
"V8"
] | 1 | 0.001 | 2026-02-08T02:58:16.521857Z | {
"verified": true,
"answer": 4096,
"timestamp": "2026-02-08T02:58:16.522765Z"
} | c13a8b | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 171,
"completion_tokens": 1297
},
"timestamp": "2026-02-08T23:03:09.155Z",
"answer": 4096
},
{
"... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -6.49,
"mid": 0.51,
"hi": 7.52
} | ||
236883 | geo_count_lattice_triangle_v1_1978505735_4473 | Let the area of a triangle with vertices at $ (0,0) $, $ (120,128) $, and $ (81,113) $ be $ A $. Define $ B = 2A $. Let $ L $ be the number of lattice points on the boundary of this triangle. Compute the remainder when $ 44121 \cdot \frac{B + 2 - L}{2} $ is divided by $ 78235 $. | 19,716 | graphs = [
Graph(
let={
"_n": Const(113),
"area_2x": Abs(arg=Sum(Mul(Const(value=120), Const(value=113)), Mul(Const(value=81), Sub(left=Const(value=0), right=Const(value=128))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=120)), b=Abs(arg=Const(value=128))), GCD(a=Abs(arg... | ALG | NT | COUNT | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | geo_count_lattice_triangle_v1 | null | 5 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.011 | 2026-02-08T18:15:56.197843Z | {
"verified": true,
"answer": 19716,
"timestamp": "2026-02-08T18:15:56.208857Z"
} | 82b23e | 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": 3036
},
"timestamp": "2026-02-18T15:38:26.574Z",
"answer": 19716
},
... | 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_SUM",
"status"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
5884f8 | lte_diff_endings_v1_677425708_327 | Let $a = 37$ and $b = 9$. Let $p = 2$ and $K = 6$. Define $d_1$ to be the largest integer $k$ such that $p^k$ divides $a - b$, and define $d_2$ to be the largest integer $k$ such that $p^k$ divides $a + b$. Let $t = K + 1 - d_1 - d_2$, and let $p^t$ and $p^{t+1}$ be the corresponding powers of $p$. Let $N = 2671855$. T... | 83,495 | graphs = [
Graph(
let={
"a_val": Const(37),
"b_val": Const(9),
"p_val": Const(2),
"K_val": Const(6),
"N_val": Const(2671855),
"ab_diff": Sub(Ref("a_val"), Ref("b_val")),
"vp_diff": MaxKDivides(target=Ref("ab_diff"), base=Ref... | NT | null | COMPUTE | sympy | LTE_DIFF | [
"LTE_DIFF"
] | cf8260 | lte_diff_endings_v1 | null | 7 | null | [
"LTE_DIFF"
] | 1 | 0.001 | 2026-02-08T03:13:22.647788Z | {
"verified": true,
"answer": 83495,
"timestamp": "2026-02-08T03:13:22.648573Z"
} | ef835d | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 369,
"completion_tokens": 1560
},
"timestamp": "2026-02-08T20:27:39.582Z",
"answer": 83495
},
{
"... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_SUB",
"statu... | {
"lo": -6.51,
"mid": -0.31,
"hi": 5.43
} | ||
d47fd9 | comb_count_partitions_v1_2051736721_678 | Let $n$ be the number of positive integers less than or equal to $101$ that are relatively prime to $20$. Compute the number of integer partitions of $n$. | 44,583 | graphs = [
Graph(
let={
"_n": Const(101),
"n": CountOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(1)), Leq(Var("n1"), Ref("_n")), Eq(GCD(a=Var("n1"), b=Const(20)), Const(1))))),
"result": Partition(arg=Ref(name='n')),
},
goal=R... | NT | COMB | COUNT | sympy | C4 | [
"C4"
] | 08d162 | comb_count_partitions_v1 | null | 6 | 0 | [
"C4"
] | 1 | 0.002 | 2026-02-08T15:37:36.814328Z | {
"verified": true,
"answer": 44583,
"timestamp": "2026-02-08T15:37:36.816754Z"
} | 34372f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 83,
"completion_tokens": 2314
},
"timestamp": "2026-02-16T10:00:36.490Z",
"answer": 44583
},
{... | 1 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
751d14 | geo_visible_lattice_v1_2080023795_188 | Let $n = 144$. A visible lattice point $(x,y)$ is a point with positive integer coordinates such that $1 \le x, y \le n$ and $\gcd(x,y) = 1$. Let $V$ be the number of visible lattice points in this range. Compute the remainder when $44121 \cdot V$ is divided by 80350. | 14,889 | graphs = [
Graph(
let={
"n": Const(144),
"result": VisibleLatticePoints(n=Ref(name='n')),
"Q": Mod(value=Mul(Const(44121), Ref("result")), modulus=Const(80350)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 4 | 0 | null | null | 1.111 | 2026-02-08T11:35:19.701505Z | {
"verified": true,
"answer": 14889,
"timestamp": "2026-02-08T11:35:20.812780Z"
} | 0eaae2 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 194,
"completion_tokens": 6684
},
"timestamp": "2026-02-08T20:50:36.687Z",
"answer": 14889
},
{
"... | 1 | [] | {
"lo": 1.36,
"mid": 4.2,
"hi": 6.62
} | ||||
c20f1c | sequence_fibonacci_compute_v1_601307018_2454 | Let $F_n$ denote the $n$-th Fibonacci number. Let $R$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \leq a, b \leq 30$ such that $$
2b^2 - 2ab + 13a^2 \leq \left|\{ t : \text{there exist integers } a, b \text{ with } 1 \leq a \leq 943,\ 1 \leq b \leq 135 \text{ such that } t = 3a + 4b + 15,\ 22 \... | 28,657 | graphs = [
Graph(
let={
"_c": Const(30),
"_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(30)), Geq(Var("b"), Const(1)), Leq(Var("b"), Ref("_c")), Leq(Sum(Mul(Const(2),... | ALG | null | COMPUTE | sympy | K3 | [
"LIN_FORM/QF_PSD_COUNT_LEQ/QF_PSD_DISTINCT"
] | 19090f | sequence_fibonacci_compute_v1 | null | 8 | 0 | [
"K3",
"LIN_FORM",
"QF_PSD_COUNT_LEQ",
"QF_PSD_DISTINCT"
] | 4 | 0.045 | 2026-03-10T03:11:06.939817Z | {
"verified": true,
"answer": 28657,
"timestamp": "2026-03-10T03:11:06.984966Z"
} | d4f213 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 345,
"completion_tokens": 6314
},
"timestamp": "2026-04-18T22:48:51.602Z",
"answer": 28657
},
{
... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok_later"
},
{
"lemma": "QF_PSD_DISTINCT",
"status": "ok_later"
}
] | {
"lo": -3.31,
"mid": 1.32,
"hi": 5.87
} | ||
361cb0 | comb_count_derangements_v1_1742523217_3202 | Let $n$ be the largest prime number less than or equal to 10. Compute the remainder when $44121 \cdot !n$ is divided by $76024$, where $!n$ denotes the number of derangements of $n$ elements. | 74,534 | graphs = [
Graph(
let={
"_n": Const(44121),
"n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(10)), IsPrime(Var("n"))))),
"result": Subfactorial(arg=Ref(name='n')),
"Q": Mod(value=Mul(Ref("_n"), Ref("resu... | NT | COMB | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | comb_count_derangements_v1 | null | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.001 | 2026-02-08T05:42:59.647887Z | {
"verified": true,
"answer": 74534,
"timestamp": "2026-02-08T05:42:59.649035Z"
} | db7d3e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 100,
"completion_tokens": 1297
},
"timestamp": "2026-02-12T12:37:04.252Z",
"answer": 74534
},
... | 1 | [
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
00323a | comb_count_surjections_v1_1742523217_5348 | Let $n$ be the number of ordered pairs $(i, j)$ of positive integers such that $i + j = 8$, $1 \leq i \leq 7$, and $1 \leq j \leq 8$. Let $k = 3$. Define $S(n, k)$ as the Stirling number of the second kind, and let $r = k! \cdot S(n, k)$. Compute the remainder when $30922 \cdot r$ is divided by $56111$. | 14,687 | graphs = [
Graph(
let={
"_n": Const(30922),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(8)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(7)), right=IntegerRange(start=Const(1), end=Co... | COMB | null | COUNT | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | comb_count_surjections_v1 | null | 4 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.011 | 2026-02-08T10:56:05.239469Z | {
"verified": true,
"answer": 14687,
"timestamp": "2026-02-08T10:56:05.250891Z"
} | e3cec7 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 222,
"completion_tokens": 1495
},
"timestamp": "2026-02-24T12:35:02.843Z",
"answer": 14687
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V8",
... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
62e498 | sequence_lucas_compute_v1_784195855_9220 | Let $n$ be the number of positive integers $k$ such that $1 \leq k \leq 1782$ and $99$ divides $k$. Compute the $n$-th Lucas number. | 5,778 | graphs = [
Graph(
let={
"_n": Const(99),
"n": CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(1)), Leq(Var("k"), Const(1782)), Divides(divisor=Ref("_n"), dividend=Var("k"))), domain='positive_integers')),
"result": Lucas(arg=Ref(name='n')),
... | NT | null | COMPUTE | sympy | C2 | [
"C2"
] | 9685eb | sequence_lucas_compute_v1 | null | 4 | 0 | [
"C2"
] | 1 | 0.001 | 2026-02-08T16:39:08.775357Z | {
"verified": true,
"answer": 5778,
"timestamp": "2026-02-08T16:39:08.776818Z"
} | c04527 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 90,
"completion_tokens": 751
},
"timestamp": "2026-02-17T09:20:14.965Z",
"answer": 5778
},
{
... | 1 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
d4cc44 | algebra_poly_eval_v1_1125832087_2324 | Let $a = 11$. Compute the value of
$$
11^4 + 4 \cdot 11^3 + 6 \cdot 11^2 - 11 + \max\{n \mid n \in \{2,3\} \text{ and } n \text{ is prime}\}.
$$ | 20,683 | graphs = [
Graph(
let={
"_n": Const(3),
"a": Const(11),
"result": Sum(Pow(Ref("a"), Const(4)), Mul(Const(4), Pow(Ref("a"), Ref("_n"))), Mul(Const(6), Pow(Ref("a"), Const(2))), Mul(Const(-1), Ref("a")), MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), ... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | algebra_poly_eval_v1 | null | 2 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.004 | 2026-02-08T04:32:24.568413Z | {
"verified": true,
"answer": 20683,
"timestamp": "2026-02-08T04:32:24.571968Z"
} | a891fe | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 182,
"completion_tokens": 374
},
"timestamp": "2026-02-10T17:05:23.967Z",
"answer": 20683
},
{
"... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
e5f72a | diophantine_fbi2_min_v1_865884756_6693 | Let $k = 32$. Define $S$ to be the set of all integers $d$ such that $3 \leq d \leq 42$, $d$ divides $32$, and $\frac{32}{d} \geq 4$. Compute the minimum value of $d$ in $S$. | 4 | graphs = [
Graph(
let={
"k": Const(32),
"a": Const(2),
"b": Const(3),
"upper": Const(42),
"result": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(3)), Leq(Var("d"), Ref("upper")), Divides(divisor=Var("d"), dividend=Ref... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"L3C"
] | 73f8b0 | diophantine_fbi2_min_v1 | null | 2 | 0 | [
"COPRIME_PAIRS",
"L3C"
] | 2 | 0.075 | 2026-02-08T19:21:21.563654Z | {
"verified": true,
"answer": 4,
"timestamp": "2026-02-08T19:21:21.638365Z"
} | 308c24 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 112,
"completion_tokens": 912
},
"timestamp": "2026-02-18T22:03:42.685Z",
"answer": 4
},
{
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
8acf15 | lin_form_endings_v1_784195855_3477 | Let $T$ be the set of all integers $t$ with $18 \leq t \leq 630$ for which there exist positive integers $a$ and $b$ such that $1 \leq a \leq 28$, $1 \leq b \leq 37$, and $t = 4a + 14b$. Let $r$ be the number of elements in $T$. Compute the remainder when $19236 \cdot r$ is divided by $75458$. | 55,228 | graphs = [
Graph(
let={
"_inner_result": 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=28)), Geq(left=Var(name='b'), right=... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 6 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T06:27:33.240793Z | {
"verified": true,
"answer": 55228,
"timestamp": "2026-02-08T06:27:33.242280Z"
} | ebd8e1 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 219,
"completion_tokens": 5905
},
"timestamp": "2026-02-24T06:12:44.890Z",
"answer": 19728
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no... | {
"lo": 1.97,
"mid": 4.36,
"hi": 6.69
} | ||
2bab1c | diophantine_product_count_v1_1520064083_9202 | Let $k$ be the number of integers $t$ in the range $5 \le t \le 246$ for which there exist positive integers $a$ and $b$ with $1 \le a \le 9$, $1 \le b \le 76$, and $t = 2a + 3b$. Let $u$ be the number of integers $t$ in the range $7 \le t \le 185$ for which there exist positive integers $a$ and $b$ with $1 \le a \le 1... | 18 | graphs = [
Graph(
let={
"k": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=9)), Geq(left=Var(name='b'), right=Const(value=1... | NT | null | COUNT | sympy | C5 | [
"LIN_FORM"
] | 7b2633 | diophantine_product_count_v1 | null | 6 | 0 | [
"C5",
"LIN_FORM"
] | 2 | 0.033 | 2026-02-08T10:35:46.428364Z | {
"verified": true,
"answer": 18,
"timestamp": "2026-02-08T10:35:46.461360Z"
} | c5065f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 227,
"completion_tokens": 7324
},
"timestamp": "2026-02-14T07:56:58.349Z",
"answer": 18
},
{
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
91fab2_n | alg_poly3_min_v1_1218484723_1456 | A factory produces components using two settings: $a$ (precision level, 1 to 454) and $b$ (batch size). The cost function is $34552a^3 - 111060a^2b + 92550ab^2$. The maximum batch size $b$ is limited to the number of multiples of 34 between 1 and 15436. What is the minimum possible cost? | 16,042 | ALG | null | COMPUTE | sympy | POLY_ORBIT_HENSEL | [
"C2"
] | 9685eb | alg_poly3_min_v1 | null | 5 | null | [
"C2",
"POLY_ORBIT_HENSEL"
] | 2 | 1.048 | 2026-02-25T03:10:04.087727Z | null | 133fc0 | 91fab2 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 197,
"completion_tokens": 3933
},
"timestamp": "2026-03-30T16:52:58.717Z",
"answer": 16042
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
... | {
"lo": 1.5,
"mid": 4.69,
"hi": 7.23
} | |
7b45c9 | nt_min_coprime_above_v1_124444284_6591 | Let $S$ be the set of nonnegative integers $j$ such that $0 \leq j \leq 32311$ and $\binom{32311}{j}$ is odd. Let $s$ be the number of elements in $S$. Let $T$ be the set of integers $n$ such that $s < n \leq 2260$ and $\gcd(n, 202) = 1$. Let $m$ be the minimum element of $T$. Compute $m + \varphi(|m| + 1) + \tau(|m| +... | 2,861 | graphs = [
Graph(
let={
"start": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(32311)), Eq(Mod(value=Binom(n=Const(32311), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')),
"upper": Const(2260),
... | NT | null | EXTREMUM | sympy | V8 | [
"V8"
] | 86348e | nt_min_coprime_above_v1 | null | 7 | 0 | [
"V8"
] | 1 | 0.02 | 2026-02-08T08:32:55.466048Z | {
"verified": true,
"answer": 2861,
"timestamp": "2026-02-08T08:32:55.486287Z"
} | d1aa74 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 190,
"completion_tokens": 2690
},
"timestamp": "2026-02-13T19:24:08.404Z",
"answer": 2861
},
{... | 1 | [
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
23e9ad | comb_catalan_compute_v1_458359167_202 | Let $n$ be the number of elements in the Cartesian product of the sets $\{1, 2\}$ and $\{1, 2, 3, 4, 5\}$. Define the sequence $C_n$ by the recurrence
$$
C_0 = 1, \quad C_{n+1} = \sum_{i=0}^n C_i C_{n-i},
$$
which gives the $n$th Catalan number. Compute $C_n$. | 16,796 | graphs = [
Graph(
let={
"n": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(2)), right=IntegerRange(start=Const(1), end=Const(5)))),
"result": Catalan(Ref("n")),
},
goal=Ref("result"),
)
] | COMB | null | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | comb_catalan_compute_v1 | null | 2 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.002 | 2026-02-08T03:04:12.834305Z | {
"verified": true,
"answer": 16796,
"timestamp": "2026-02-08T03:04:12.835823Z"
} | cd40da | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 216,
"completion_tokens": 490
},
"timestamp": "2026-02-10T12:32:31.124Z",
"answer": 16796
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V8",
... | {
"lo": -5.97,
"mid": -3.96,
"hi": -1.93
} | ||
689ff3 | nt_count_with_divisor_count_v1_50713871_28 | Let $n$ be a positive integer. Define $A$ to be the number of positive integers $n \leq 50176$ such that $n$ has exactly $3$ positive divisors.
Let $s = \sum_{d \mid \gcd(p, 7)} \mu(d)$, where $p$ is the number of primes $q$ satisfying $2 \leq q \leq 11$, and $\mu$ denotes the M\"obius function.
Compute $$\sum_{n = s... | 712 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": Const(50176),
"div_count": Const(3),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(NumDivisors(n=Var("n")), Ref("div_count"))))),
... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"COUNT_PRIMES/MOBIUS_COPRIME"
] | 8a4ab7 | nt_count_with_divisor_count_v1 | sum_totient | 6 | 0 | [
"COUNT_PRIMES",
"MAX_PRIME_BELOW",
"MOBIUS_COPRIME"
] | 3 | 4.911 | 2026-02-08T02:43:36.582250Z | {
"verified": true,
"answer": 712,
"timestamp": "2026-02-08T02:43:41.493196Z"
} | 5dc354 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 253,
"completion_tokens": 3598
},
"timestamp": "2026-02-08T19:45:09.031Z",
"answer": 712
},
{
"id... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok_later"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V1",
"sta... | {
"lo": -4.6,
"mid": 0.19,
"hi": 4.77
} | ||
6f0588 | nt_min_phi_inverse_v1_2051736721_3 | Let $k$ be the number of integers $t$ with $5 \leq t \leq 18$ for which there exist positive integers $a$ and $b$ such that $1 \leq a \leq 6$, $1 \leq b \leq 2$, and $t = 2a + 3b$. Determine the smallest positive integer $n$, with $1 \leq n \leq 50$, such that $\phi(n) = k$, where $\phi(n)$ denotes the number of positi... | 13 | graphs = [
Graph(
let={
"upper": Const(50),
"k": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=6)), Geq(left=Va... | NT | null | EXTREMUM | sympy | B3 | [
"LIN_FORM"
] | 7b2633 | nt_min_phi_inverse_v1 | null | 6 | 0 | [
"B3",
"LIN_FORM"
] | 2 | 0.033 | 2026-02-08T15:07:08.574444Z | {
"verified": true,
"answer": 13,
"timestamp": "2026-02-08T15:07:08.607445Z"
} | fe4983 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 172,
"completion_tokens": 1140
},
"timestamp": "2026-02-16T01:02:20.589Z",
"answer": 13
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
1c4421 | modular_min_linear_v1_1918700295_2087 | Let $a = 15861$ and $m = 25964$. Let $b$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 8236900$. Determine the smallest positive integer $x$ such that $1 \leq x \leq m$ and $$ ax \equiv b \pmod{m}. $$ Let $r$ denote this value of $x$. Compute $$ r + \left( t^{r \bm... | 13,236 | graphs = [
Graph(
let={
"_n": Const(14),
"a": Const(15861),
"b": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(8236900)))),... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS",
"B3"
] | e09b60 | modular_min_linear_v1 | mod_exp | 7 | 0 | [
"B3",
"COPRIME_PAIRS"
] | 2 | 1.086 | 2026-02-08T07:40:54.103977Z | {
"verified": true,
"answer": 13236,
"timestamp": "2026-02-08T07:40:55.190466Z"
} | 1663ae | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 219,
"completion_tokens": 2985
},
"timestamp": "2026-02-13T11:52:27.379Z",
"answer": 13236
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
ddeeda | geo_count_lattice_triangle_v1_655260480_2902 | Let $A$ be the area of a triangle with vertices at $(0,0)$, $(120,169)$, and $(300,324)$. The value $2A$ is given by
$$
|120 \cdot 324 - 300 \cdot 169|.
$$
Let $B$ be the number of lattice points on the boundary of this triangle, computed using the formula
$$
B = \gcd(120, 169) + \gcd(180, 324 - \sum_{d\mid 169} \phi(d... | 60,242 | graphs = [
Graph(
let={
"_n": Const(324),
"area_2x": Abs(arg=Sum(Mul(Const(value=120), Ref(name='_n')), Mul(Const(value=300), Sub(left=Const(value=0), right=Const(value=169))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=120)), b=Abs(arg=Const(value=169))), GCD(a=Abs(arg=... | NT | null | COUNT | sympy | K3 | [
"K3"
] | 54c41e | geo_count_lattice_triangle_v1 | null | 6 | 0 | [
"K3"
] | 1 | 0.008 | 2026-02-08T17:03:30.904743Z | {
"verified": true,
"answer": 60242,
"timestamp": "2026-02-08T17:03:30.912489Z"
} | d2948a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 214,
"completion_tokens": 2508
},
"timestamp": "2026-02-17T18:15:53.326Z",
"answer": 60242
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
09b00a | comb_count_permutations_fixed_v1_1978505735_7946 | Let $P$ be the maximum value of $xy$ over all ordered pairs $(x, y)$ of positive integers such that $x + y = 10$.
Let $s$ be the minimum value of $x_1 + y_1$ over all ordered pairs $(x_1, y_1)$ of positive integers such that $x_1 y_1 = P$.
Compute $\binom{s}{7} \cdot !(s - 7)$, where $!m$ denotes the number of derang... | 240 | graphs = [
Graph(
let={
"_n": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Const(10)))), expr=Mul(Var("x"), Var("y")))),
"n": MinOverSet(set... | COMB | null | COUNT | sympy | B1 | [
"B1/B3"
] | 80b49d | comb_count_permutations_fixed_v1 | null | 5 | 0 | [
"B1",
"B3"
] | 2 | 0.002 | 2026-02-08T20:35:41.017975Z | {
"verified": true,
"answer": 240,
"timestamp": "2026-02-08T20:35:41.020444Z"
} | a28135 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 160,
"completion_tokens": 1036
},
"timestamp": "2026-02-19T00:43:59.186Z",
"answer": 240
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
... | {
"lo": -7.92,
"mid": -4.6,
"hi": -1.84
} | ||
fa150f | comb_factorial_compute_v1_1978505735_5997 | Let $P$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 18$, $\gcd(p, q) = 1$, and $p < q$. Let $\_n$ be the number of elements in $P$. Let $n$ be the smallest divisor of $637637$ that is at least $\_n$. Compute $n!$. | 5,040 | 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=18)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(value=1)), ... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/MIN_PRIME_FACTOR"
] | 52cee2 | comb_factorial_compute_v1 | null | 5 | 0 | [
"COPRIME_PAIRS",
"MIN_PRIME_FACTOR"
] | 2 | 0.002 | 2026-02-08T19:22:04.894179Z | {
"verified": true,
"answer": 5040,
"timestamp": "2026-02-08T19:22:04.895796Z"
} | b2c66b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 135,
"completion_tokens": 1566
},
"timestamp": "2026-02-18T22:05:20.987Z",
"answer": 5040
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok_later"
},
{
"lemma": "MOD_ADD",
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
51cbbe | antilemma_sum_equals_v1_124444284_8797 | Let $x$ be the number of ordered pairs $(i, j)$ of integers such that $1 \leq i \leq 6$, $1 \leq j \leq 6$, and $i + j = 8$. Compute $15546 \cdot x$. Determine the value of this product. | 77,730 | graphs = [
Graph(
let={
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(8)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(6)), right=IntegerRange(start=Const(1), end=Const(6))))),
"Q": Mul... | COMB | GEOM | COMPUTE | sympy | COMB1 | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 2 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS"
] | 2 | 0.038 | 2026-02-08T11:54:38.913371Z | {
"verified": true,
"answer": 77730,
"timestamp": "2026-02-08T11:54:38.951247Z"
} | e8884c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 178,
"completion_tokens": 301
},
"timestamp": "2026-02-24T14:59:55.297Z",
"answer": 77730
},
{
"i... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SU... | {
"lo": -7.18,
"mid": -5,
"hi": -3.01
} | ||
4a65ff | alg_sym_quad_system_v1_1218484723_7293 | Let $S$ be the set of integers $t$ for which there exist integers $a, b$ with $1 \le a \le 40$ and $1 \le b \le 2752$ such that
$$t = 5a + 2b + 19, \quad 26 \le t \le 5723.$$
Let $N = |S|$. Consider all ordered triples $(a, b, c)$ of positive integers satisfying
$$a^2 + b^2 + c^2 = ab + bc + ca, \qquad 6a + 4b + 3c = N... | 1,202 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(4),
"result": Mod(value=SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b"), Var("c")]), condition=And(Eq(Sum(Pow(Var("a"), Const(2)), Pow(Var("b"), Const(2)), Pow(Var("c"), Const(2))), Sum(... | ALG | null | COMPUTE | sympy | SUM_ARITHMETIC | [
"LIN_FORM",
"L3B"
] | f85b0e | alg_sym_quad_system_v1 | null | 7 | 0 | [
"L3B",
"LIN_FORM",
"SUM_ARITHMETIC"
] | 3 | 0.106 | 2026-02-25T08:43:48.743168Z | {
"verified": true,
"answer": 1202,
"timestamp": "2026-02-25T08:43:48.848730Z"
} | 39178e | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 354,
"completion_tokens": 32768
},
"timestamp": "2026-03-30T03:48:00.329Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "L3B",
"status": "ok"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 1.53,
"mid": 4.7,
"hi": 7.23
} | ||
ea4e56 | algebra_poly_eval_v1_1742523217_1620 | Let $n$ be a positive integer. Define $S$ as the set of all integers $n$ such that $1 \leq n \leq 51$ and the sum of the decimal digits of $n$ is even. Let $y = 24$. Compute
$$
\frac{|55y^3 + 20y^2 + 23y + 42 + |S| \cdot y^4|}{126}.
$$ | 71,959 | graphs = [
Graph(
let={
"_n": Const(4),
"y": Const(24),
"result": Div(Sum(Mul(CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(51)), Eq(Mod(value=DigitSum(Var("n")), modulus=Const(2)), Const(0))))), Pow(Ref("y"), Ref("... | NT | null | COMPUTE | sympy | L3B | [
"L3B"
] | cc148f | algebra_poly_eval_v1 | null | 4 | 0 | [
"L3B"
] | 1 | 0.002 | 2026-02-08T04:05:16.046670Z | {
"verified": true,
"answer": 71959,
"timestamp": "2026-02-08T04:05:16.048700Z"
} | fc4a29 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 206,
"completion_tokens": 1685
},
"timestamp": "2026-02-10T15:16:51.546Z",
"answer": 71959
},
{
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3B",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
f89113 | sequence_count_fib_divisible_v1_1978505735_6914 | Let $u$ be the number of integers $n$ with $1 \leq n \leq 4395$ such that $n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{7}$. Let $r$ be the number of integers $n_1$ with $1 \leq n_1 \leq u$ such that the Fibonacci number $F_{n_1}$ is divisible by $12$. Compute the sum $$\sum_{n_2=1}^{r} \tau(n_2),$$ where $\ta... | 217 | graphs = [
Graph(
let={
"upper": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(4395)), Congruent(a=Var(name='n'), b=Floor(arg=Div(left=Var(name='n'), right=Const(value=2))), modulus=Const(value=7))))),
"d": Const(12),
... | NT | null | COUNT | sympy | L3C | [
"L3C"
] | 73f8b0 | sequence_count_fib_divisible_v1 | null | 6 | 0 | [
"L3C"
] | 1 | 0.027 | 2026-02-08T19:53:46.140535Z | {
"verified": true,
"answer": 217,
"timestamp": "2026-02-08T19:53:46.167914Z"
} | 1c716d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 181,
"completion_tokens": 2776
},
"timestamp": "2026-02-18T23:41:57.054Z",
"answer": 217
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
}... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
cad53f | nt_min_phi_inverse_v1_124444284_5415 | Let $N = 625$. Consider the set of all ordered pairs $(x, y)$ of positive integers such that $xy = N$. Let $U$ be the minimum value of $x + y$ over all such pairs. Let $K$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 36$. Let $n_0$ be the smallest positive integer... | 58 | graphs = [
Graph(
let={
"_n": Const(625),
"upper": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_n")))), expr=Sum(Var("x"), Var("y"))))... | NT | null | EXTREMUM | sympy | B3 | [
"B3"
] | 0cd20d | nt_min_phi_inverse_v1 | null | 7 | 0 | [
"B3"
] | 1 | 0.01 | 2026-02-08T06:34:51.362035Z | {
"verified": true,
"answer": 58,
"timestamp": "2026-02-08T06:34:51.372023Z"
} | 4f8bf0 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 192,
"completion_tokens": 1885
},
"timestamp": "2026-02-13T02:16:12.684Z",
"answer": 58
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
dd3fdf | nt_max_prime_below_v1_865884756_162 | Let $ A $ be the set of all positive integers $ p $ such that there exists a positive integer $ q $ with $ p < q $, $ \gcd(p, q) = 1 $, and $ pq = 18 $. Let $ m $ be the number of elements in $ A $. Let $ B $ be the set of all prime numbers $ n $ such that $ m \leq n \leq 11321 $. Let $ r $ be the largest element of $ ... | 25,879 | graphs = [
Graph(
let={
"upper": Const(11321),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), V... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_max_prime_below_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.545 | 2026-02-08T15:13:46.678102Z | {
"verified": true,
"answer": 25879,
"timestamp": "2026-02-08T15:13:47.222782Z"
} | f29e3e | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 233,
"completion_tokens": 2570
},
"timestamp": "2026-02-11T11:05:11.075Z",
"answer": 25879
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": 0.22,
"hi": 7.52
} |
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