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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
2bdd2e_n | alg_sym_quad_system_v1_1218484723_3037 | A logistics company assigns three types of containers—A, B, and C—to shipments. Each container type has a volume equal to its label number cubed. The total squared volume satisfies $a^2 + b^2 + c^2 = ab + bc + ca$, and the weighted load $4a + 5b + 9c$ must match the number of distinct shipment weights possible using co... | 288 | ALG | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | alg_sym_quad_system_v1 | null | 7 | null | [
"LIN_FORM"
] | 1 | 0.417 | 2026-02-25T04:47:49.670941Z | null | d06427 | 2bdd2e | narrative | 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": 3254
},
"timestamp": "2026-03-30T19:24:17.298Z",
"answer": 288
},
{
"id... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | |
567183 | nt_count_coprime_and_v1_1978505735_1908 | Let $n$ be a positive integer such that $1 \leq n \leq 3679$ and $n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{5}$. Let $N$ be the number of such integers $n$. Let $k_1$ be the smallest divisor of $N$ that is at least 2, and let $k_2 = 7$. Compute the number of positive integers $n_1$ such that $1 \leq n_1 \le... | 16,001 | graphs = [
Graph(
let={
"_n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(3679)), Congruent(a=Var(name='n'), b=Floor(arg=Div(left=Var(name='n'), right=Const(value=2))), modulus=Const(value=5))))),
"upper": Const(28001),
... | NT | null | COUNT | sympy | L3C | [
"L3C/MIN_PRIME_FACTOR"
] | eb2a9a | nt_count_coprime_and_v1 | null | 6 | 0 | [
"L3C",
"MIN_PRIME_FACTOR"
] | 2 | 4.101 | 2026-02-08T16:31:19.762867Z | {
"verified": true,
"answer": 16001,
"timestamp": "2026-02-08T16:31:23.863400Z"
} | fbec86 | 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": 1298
},
"timestamp": "2026-02-17T05:02:27.545Z",
"answer": 16001
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MIN_PRIME_FAC... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
67bde7 | comb_count_permutations_fixed_v1_655260480_90 | Let $n$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq = 22050$, $\gcd(p, q) = 1$, and $p < q$. Let $k = 5$. Define $r = \binom{n}{k} \cdot !(n - k)$, where $!(n - k)$ denotes the number of derangements of $n - k$ elements. Determine the value of $Q$, the smallest pos... | 36 | 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=22050)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(value=1))... | NT | COMB | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_count_permutations_fixed_v1 | null | 6 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.001 | 2026-02-08T15:10:36.327855Z | {
"verified": true,
"answer": 36,
"timestamp": "2026-02-08T15:10:36.329181Z"
} | dfe771 | 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": 3057
},
"timestamp": "2026-02-16T00:30:17.902Z",
"answer": 36
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V3",
"st... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
04c649 | antilemma_sum_equals_v1_971394319_1242 | Let $x$ be the number of ordered pairs $(i, j)$ of positive integers such that $i + j = 17$, $1 \le i \le 15$, and $1 \le j \le 15$. Compute $\sum_{n=1}^{x} \phi(n)$, where $\phi$ denotes Euler's totient function. | 64 | graphs = [
Graph(
let={
"_n": Const(17),
"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(15)), right=IntegerRange(start=Const(1), end=Con... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 4 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.012 | 2026-02-08T13:32:29.264207Z | {
"verified": true,
"answer": 64,
"timestamp": "2026-02-08T13:32:29.276545Z"
} | 38f8a5 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 185,
"completion_tokens": 584
},
"timestamp": "2026-02-24T18:38:21.606Z",
"answer": 64
},
{
"id":... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"stat... | {
"lo": -3.84,
"mid": -1.67,
"hi": 1.32
} | ||
d0e1a0 | nt_max_prime_below_v1_655260480_1302 | Let $k_{\text{max}}$ be the largest nonnegative integer $k$ such that $7^k \leq 133$. Find the largest prime number $n$ such that $k_{\text{max}} \leq n \leq 11025$. | 11,003 | graphs = [
Graph(
let={
"_n": Const(133),
"upper": Const(11025),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), MaxOverSet(set=SolutionsSet(var=Var("k"), condition=Leq(Pow(Const(7), Var("k")), Ref("_n"))))), Leq(Var("n"), Ref("upper")), Is... | NT | null | EXTREMUM | sympy | MAX_VAL | [
"MAX_VAL"
] | 1da621 | nt_max_prime_below_v1 | null | 3 | 0 | [
"MAX_VAL"
] | 1 | 0.266 | 2026-02-08T16:04:01.261406Z | {
"verified": true,
"answer": 11003,
"timestamp": "2026-02-08T16:04:01.527644Z"
} | 99a273 | 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": 2812
},
"timestamp": "2026-02-16T20:26:24.205Z",
"answer": 11003
},
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K16",
"status": "same_pattern_wrong"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
8a6c5a | nt_count_coprime_v1_124444284_1855 | Let $n$ range over the positive integers from 1 to 64 inclusive. Define $k$ to be the number of such $n$ for which $\gcd(n, 15) = 1$. Now let $n$ range over the positive integers from 1 to 33489 inclusive. Define $S$ to be the set of such $n$ for which $\gcd(n, k) = 1$. Compute the remainder when $44121$ multiplied by ... | 75,316 | graphs = [
Graph(
let={
"_n": Const(15),
"upper": Const(33489),
"k": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(64)), Eq(GCD(a=Var("n"), b=Ref("_n")), Const(1))))),
"result": CountOverSet(set=Solution... | NT | null | COUNT | sympy | C4 | [
"C4"
] | 08d162 | nt_count_coprime_v1 | null | 4 | 0 | [
"C4"
] | 1 | 9.977 | 2026-02-08T04:11:07.846303Z | {
"verified": true,
"answer": 75316,
"timestamp": "2026-02-08T04:11:17.823145Z"
} | c84d13 | 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": 2512
},
"timestamp": "2026-02-10T15:41:46.588Z",
"answer": 75316
},
{
... | 1 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
ee4cc3 | nt_num_divisors_compute_v1_1978505735_4243 | Let $n$ be the largest prime number satisfying $2 \leq n \leq 9$. Compute the number of positive divisors of $n$. | 2 | graphs = [
Graph(
let={
"_n": Const(2),
"n": MaxOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Ref("_n")), Leq(Var("n1"), Const(9)), IsPrime(Var("n1"))))),
"result": NumDivisors(n=Ref("n")),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | nt_num_divisors_compute_v1 | null | 2 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.002 | 2026-02-08T18:07:32.938597Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-02-08T18:07:32.940989Z"
} | b29097 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 86,
"completion_tokens": 263
},
"timestamp": "2026-02-16T12:07:56.434Z",
"answer": 2
},
{
"id": 11,
"m... | 2 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
... | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
6b43f0 | comb_catalan_compute_v1_1440796553_252 | Let $n$ be the number of ordered pairs of positive integers $(i, j)$ such that $i + j = 12$, $1 \leq i \leq 11$, and $1 \leq j \leq 11$. Let $C_n$ denote the $n$-th Catalan number. Compute the smallest positive integer $k$ such that the $k$-th Fibonacci number is divisible by $|C_n| + 2$. | 840 | graphs = [
Graph(
let={
"_n": Const(12),
"n": 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(11)), right=IntegerRange(start=Const(1), end=Con... | COMB | NT | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | comb_catalan_compute_v1 | null | 6 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.017 | 2026-02-08T11:40:48.755899Z | {
"verified": true,
"answer": 840,
"timestamp": "2026-02-08T11:40:48.772411Z"
} | 155d55 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 209,
"completion_tokens": 32768
},
"timestamp": "2026-02-24T14:34:01.220Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status":... | {
"lo": 1.15,
"mid": 4.18,
"hi": 6.61
} | ||
f38e48 | nt_sum_divisors_mod_v1_784195855_6563 | Let $d_{\text{max}}$ be the largest positive divisor of $57161160$ that is at most $7560$. Let $n$ be the number of positive integers $j$ such that $j^5 \leq 24694996986777600000$. Define $\sigma(n)$ to be the sum of all positive divisors of $n$. Find the remainder when $\sigma(n)$ is divided by $11173$. | 6,454 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(1)), Leq(Var("j"), MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Leq(Var("d"), Const(7560)), Divides(divisor=Var("d"), dividend=Const(57161160)))))), Leq(... | NT | null | COMPUTE | sympy | MAX_DIVISOR | [
"MAX_DIVISOR/C3"
] | 602348 | nt_sum_divisors_mod_v1 | null | 5 | 0 | [
"C3",
"MAX_DIVISOR"
] | 2 | 0.002 | 2026-02-08T08:43:34.117825Z | {
"verified": true,
"answer": 6454,
"timestamp": "2026-02-08T08:43:34.120121Z"
} | 66c33c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 136,
"completion_tokens": 3801
},
"timestamp": "2026-02-13T21:04:11.614Z",
"answer": 6454
},
{... | 1 | [
{
"lemma": "C3",
"status": "ok_later"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"st... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
55403a | comb_count_derangements_v1_397696148_389 | Let $n$ be the largest positive integer $k$ such that $2^k \leq 224$. Define $D_n$ to be the number of derangements of $n$ objects. Let $Q = 15376 - D_n$. Compute $Q$. | 13,522 | graphs = [
Graph(
let={
"_n": Const(2),
"n": MaxOverSet(set=SolutionsSet(var=Var("k"), condition=Leq(Pow(Ref("_n"), Var("k")), Const(224)))),
"result": Subfactorial(arg=Ref(name='n')),
"_c": Const(15376),
"Q": Sub(Ref("_c"), Ref("result")),
... | COMB | null | COUNT | sympy | MAX_VAL | [
"MAX_VAL"
] | 1da621 | comb_count_derangements_v1 | null | 4 | 0 | [
"MAX_VAL"
] | 1 | 0.001 | 2026-02-08T11:27:49.546939Z | {
"verified": true,
"answer": 13522,
"timestamp": "2026-02-08T11:27:49.547926Z"
} | a89c18 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 167,
"completion_tokens": 1163
},
"timestamp": "2026-02-24T13:53:54.886Z",
"answer": 13522
},
{
"... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "same_pattern_wrong"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
... | {
"lo": -3.84,
"mid": -1.67,
"hi": 1.32
} | ||
f2534f | nt_count_intersection_v1_168721529_213 | Let $a = 7$. Let $b$ be the number of integers $t$ such that $18 \leq t \leq 64$ and there exist integers $a'$ and $b'$ with $1 \leq a' \leq 9$, $1 \leq b' \leq 2$, and $t = 4a' + 14b'$. Define $N = 20000$. Let $S$ be the set of all positive integers $n \leq N$ such that $a$ divides $n$ and $\gcd(n, b) = 1$. Compute th... | 953 | graphs = [
Graph(
let={
"_n": Const(65123),
"N": Const(20000),
"a": Const(7),
"b": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), ... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_count_intersection_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.791 | 2026-02-08T12:54:21.259411Z | {
"verified": true,
"answer": 953,
"timestamp": "2026-02-08T12:54:22.050861Z"
} | 076530 | 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": 1824
},
"timestamp": "2026-02-09T02:32:40.102Z",
"answer": 953
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
}
] | {
"lo": -5.3,
"mid": -2.04,
"hi": 1.84
} | ||
de1589 | antilemma_sum_factor_cartesian_v1_168721529_417 | Let $n$ be the smallest positive integer such that $2$ divides $n!$ at least once. Compute $\phi(n)$, where $\phi$ denotes Euler's totient function. Now consider all ordered pairs $(i, j)$ where $i$ ranges from $1$ to $5$ and $j$ ranges from $1$ to $10$. For each such pair, compute the product $i \cdot j$. Let $T$ be t... | 825 | graphs = [
Graph(
let={
"_n": Const(2),
"x": SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=EulerPhi(n=MinOverSet(set=SolutionsSet(var=Var("n"), condition=Geq(MaxKDivides(target=Factorial(Var("n")), base=Ref("_n")), Const(1)), domain='Z... | NT | null | COMPUTE | sympy | V5 | [
"V5/ONE_PHI_2/SUM_FACTOR_CARTESIAN",
"SUM_FACTOR_CARTESIAN"
] | 3b83f7 | antilemma_sum_factor_cartesian_v1 | null | 4 | 0 | [
"ONE_PHI_2",
"SUM_FACTOR_CARTESIAN",
"V5"
] | 3 | 0.002 | 2026-02-08T13:02:39.302798Z | {
"verified": true,
"answer": 825,
"timestamp": "2026-02-08T13:02:39.304596Z"
} | 312731 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 227,
"completion_tokens": 4159
},
"timestamp": "2026-02-09T04:48:55.312Z",
"answer": 543
},
{
... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "ONE_PHI_2",
"status": "ok_later"
... | {
"lo": 3.68,
"mid": 6.58,
"hi": 10
} | ||
eee00a | comb_binomial_compute_v1_865884756_158 | Let $n = 12$ and let $k$ be the largest prime number satisfying $2 \leq k \leq 5$. Compute $\binom{n}{k}$. | 792 | graphs = [
Graph(
let={
"_n": Const(2),
"n": Const(12),
"k": MaxOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Ref("_n")), Leq(Var("n1"), Const(5)), IsPrime(Var("n1"))))),
"result": Binom(n=Ref("n"), k=Ref("k")),
},
goal=R... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | comb_binomial_compute_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.001 | 2026-02-08T15:12:56.525866Z | {
"verified": true,
"answer": 792,
"timestamp": "2026-02-08T15:12:56.527214Z"
} | 699130 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 150,
"completion_tokens": 303
},
"timestamp": "2026-02-10T04:50:47.715Z",
"answer": 792
},
{
"id"... | 2 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
}
] | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
819c1c | comb_sum_binomial_row_v1_124444284_10339 | Let $t = \sum_{k=0}^{1} (-1)^k \binom{1}{k}$. Let $n_1 = \binom{8}{0} - 1$, and let $w = \sum_{k=0}^{n_1} (-1)^k \binom{n_1}{k}$. Let $P$ be the set of all ordered pairs $(i, j)$ of positive integers such that $1 \leq i \leq 12$, $1 \leq j \leq 12$, and $i + j = 14$. Let $n$ be the product of the number of elements in ... | 2,048 | graphs = [
Graph(
let={
"_n": Const(8),
"n2": Const(1),
"t": Summation(var="k", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n2"), k=Var("k")))),
"n1": Sub(Binom(n=Ref("_n"), k=Const(0)), Const(1)),
"w": Summation(... | COMB | null | SUM | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS/BINOMIAL_ALTERNATING",
"ZERO_BINOM_0"
] | a56205 | comb_sum_binomial_row_v1 | null | 4 | 2 | [
"BINOMIAL_ALTERNATING",
"COUNT_SUM_EQUALS",
"ZERO_BINOM_0"
] | 3 | 0.017 | 2026-02-08T12:59:10.384655Z | {
"verified": true,
"answer": 2048,
"timestamp": "2026-02-08T12:59:10.401636Z"
} | 918d6b | 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": 760
},
"timestamp": "2026-02-24T17:05:02.851Z",
"answer": 2048
},
{
"id... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemm... | {
"lo": -4.92,
"mid": -2.91,
"hi": -0.68
} | ||
4ca9cc | antilemma_product_of_sums_v1_1520064083_248 | Let $T$ be the set of all integers $t$ such that $21 \leq t \leq 90$ and $t = 12a + 9b$ for some integers $a$ and $b$ with $1 \leq a \leq 3$ and $1 \leq b \leq 6$. Let $m$ be the number of elements in $T$. Let $S_1 = \sum_{k=1}^{m} k$. Let $S_2$ be the sum of the first components $k$ over all ordered pairs $(k, j)$ in ... | 16,919 | graphs = [
Graph(
let={
"_m": Const(92179),
"_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=V... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/PRODUCT_OF_SUMS/SUM_ARITHMETIC"
] | bfe99e | antilemma_product_of_sums_v1 | null | 6 | 0 | [
"LIN_FORM",
"PRODUCT_OF_SUMS",
"SUM_ARITHMETIC"
] | 3 | 0.003 | 2026-02-08T03:08:59.023274Z | {
"verified": true,
"answer": 16919,
"timestamp": "2026-02-08T03:08:59.025853Z"
} | 05d010 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 290,
"completion_tokens": 1006
},
"timestamp": "2026-02-17T21:11:10.594Z",
"answer": 48000
}
] | 0 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "PRODUCT_OF_SUMS",
"status": "ok_later"
},
{
"lemma": "SUM_A... | {
"lo": -6.48,
"mid": 1.54,
"hi": 9.56
} | ||
614281 | nt_min_with_divisor_count_v1_1918700295_1363 | Let $U$ be the largest prime number at most $1818$. Define $c$ to be the number of unordered pairs of coprime positive integers $p$ and $q$ such that $p < q$ and $p \cdot q = 264600$. Let $r$ be the smallest positive integer $n$ such that $1 \le n \le U$ and the number of positive divisors of $n$ is equal to $c$. Let $... | 43 | graphs = [
Graph(
let={
"upper": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(1818)), IsPrime(Var("n"))))),
"div_count": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(nam... | NT | null | EXTREMUM | sympy | MIN_PRIME_FACTOR | [
"MAX_PRIME_BELOW",
"COPRIME_PAIRS"
] | 05d703 | nt_min_with_divisor_count_v1 | null | 7 | 0 | [
"COPRIME_PAIRS",
"MAX_PRIME_BELOW",
"MIN_PRIME_FACTOR"
] | 3 | 21.304 | 2026-02-08T05:48:06.747902Z | {
"verified": true,
"answer": 43,
"timestamp": "2026-02-08T05:48:28.051759Z"
} | 2bf5eb | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 237,
"completion_tokens": 1684
},
"timestamp": "2026-02-12T14:17:56.648Z",
"answer": 43
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"sta... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
01c4ee | geo_count_lattice_rect_v1_1419126231_409 | Let $M$ be the number of lattice points $(x,y)$ with $0 \le x \le 100$ and $0 \le y \le 35$. Find the remainder when $5163 \cdot M$ is divided by $60095$. | 23,028 | graphs = [
Graph(
let={
"a": Const(100),
"b": Const(35),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"_c": Const(5163),
"Q": Mod(value=Mul(Ref("_c"), Ref("result")), modulus=Const(60095)),
},
goal=Ref("Q"),
)
... | GEOM | GEOM | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 2 | 0 | null | null | 0.001 | 2026-02-25T09:56:13.640053Z | {
"verified": true,
"answer": 23028,
"timestamp": "2026-02-25T09:56:13.640853Z"
} | 1d1e41 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 165,
"completion_tokens": 819
},
"timestamp": "2026-03-30T08:22:55.595Z",
"answer": 23028
},
{
"i... | 1 | [] | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | ||||
5e0b05 | lte_diff_endings_v1_1742523217_387 | Let $a = 1253$ and $b = 3$. For each positive integer $k$, define $d_k = a^k - b^k$. Let $L_1 = \mathrm{lcm}(d_5, d_7)$, $L_2 = \mathrm{lcm}(L_1, d_{11})$, and $L_3 = \mathrm{lcm}(L_2, d_{25})$. Let $e$ be the largest integer such that $5^e$ divides $L_3$. Compute the remainder when $17916 \cdot e$ is divided by $90610... | 16,886 | graphs = [
Graph(
let={
"a_val": Const(1253),
"b_val": Const(3),
"p_val": Const(5),
"ap_5": Pow(Ref("a_val"), Const(5)),
"bp_5": Pow(Ref("b_val"), Const(5)),
"d_5": Sub(Ref("ap_5"), Ref("bp_5")),
"ap_7": Pow(Ref("a_val"), Co... | NT | null | COMPUTE | sympy | LTE_DIFF | [
"LTE_DIFF"
] | cf8260 | lte_diff_endings_v1 | null | 5 | null | [
"LTE_DIFF"
] | 1 | 0.002 | 2026-02-08T03:00:46.067661Z | {
"verified": true,
"answer": 16886,
"timestamp": "2026-02-08T03:00:46.069231Z"
} | c411f2 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 247,
"completion_tokens": 490
},
"timestamp": "2026-02-09T17:18:48.809Z",
"answer": 16886
},
{
"i... | 1 | [
{
"lemma": "LTE_DIFF",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -6.51,
"mid": -0.31,
"hi": 5.43
} | ||
101f29 | diophantine_product_count_v1_717093673_3991 | Let $k$ be the number of positive integers $n$ with $1 \leq n \leq 1439$ such that $\gcd(n, 6) = 1$. Determine the number of positive integers $x$ such that $1 \leq x \leq 303$, $x$ divides $k$, and $\frac{k}{x} \leq 303$. Compute this number. | 22 | graphs = [
Graph(
let={
"k": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(1439)), Eq(GCD(a=Var("n"), b=Const(6)), Const(1))))),
"upper": Const(303),
"result": CountOverSet(set=SolutionsSet(var=Var("x"), condition=A... | NT | null | COUNT | sympy | C4 | [
"C4"
] | 08d162 | diophantine_product_count_v1 | null | 6 | 0 | [
"C4"
] | 1 | 0.023 | 2026-02-08T17:59:18.702331Z | {
"verified": true,
"answer": 22,
"timestamp": "2026-02-08T17:59:18.725663Z"
} | c1570a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 129,
"completion_tokens": 1002
},
"timestamp": "2026-02-18T10:59:00.262Z",
"answer": 22
},
{
... | 1 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
2464f2_n | geo_count_lattice_triangle_v1_1218484723_1133 | Three satellites are positioned along a line at coordinates $0$, $89$, and $111$, with a relay station at $103$. The total signal interference $M$ is computed as $|111 \cdot 103 - 89^2|$. The network redundancy $R$ is the sum of GCDs of pairwise distances: $\gcd(111,89)$, $\gcd(22,14)$, and $\gcd(89,103)$. The effectiv... | 51,675 | GEOM | null | COUNT | sympy | [] | geo_count_lattice_triangle_v1 | null | 4 | null | null | null | 0.003 | 2026-02-25T02:52:39.842826Z | null | cae542 | 2464f2 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 246,
"completion_tokens": 2051
},
"timestamp": "2026-03-30T16:23:24.170Z",
"answer": 51675
},
{
"... | 1 | [] | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | |||
79aaf4 | sequence_lucas_compute_v1_1978505735_4673 | Let $n$ be the sum of all real solutions $x$ to the equation $x^2 - 22x - 6279 = 0$. Let $L_n$ denote the $n$-th Lucas number. Let $c$ be the minimum value of $x_1 + y$ over all ordered pairs $(x_1, y)$ of positive integers such that $x_1 y = 9000000$. Let $s$ be the sum of the digits of $L_n$, where each digit in posi... | 6,276 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(2),
"n": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Ref("_m")), Mul(Const(-22), Var("x")), Const(-6279)), Const(0)))),
"result": Lucas(arg=Ref(name='n')),
"_c": MinOv... | NT | null | COMPUTE | sympy | B3 | [
"B3",
"VIETA_SUM"
] | 7da6e0 | sequence_lucas_compute_v1 | digits_weighted_mod | 6 | 0 | [
"B3",
"VIETA_SUM"
] | 2 | 0.004 | 2026-02-08T18:25:55.977533Z | {
"verified": true,
"answer": 6276,
"timestamp": "2026-02-08T18:25:55.981923Z"
} | 6d20be | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 189,
"completion_tokens": 2752
},
"timestamp": "2026-02-18T17:04:26.351Z",
"answer": 6276
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
cbc76b | geo_count_lattice_rect_v1_717093673_2651 | Let $a = 48$ and $b = 21$. Define the rectangle with vertices at $(0,0)$, $(a,0)$, $(0,b)$, and $(a,b)$. Compute the number of lattice points (points with integer coordinates) that lie inside or on the boundary of this rectangle. | 1,078 | graphs = [
Graph(
let={
"a": Const(48),
"b": Const(21),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.004 | 2026-02-08T17:02:11.339769Z | {
"verified": true,
"answer": 1078,
"timestamp": "2026-02-08T17:02:11.343424Z"
} | 26d9eb | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 109,
"completion_tokens": 448
},
"timestamp": "2026-02-17T17:06:33.208Z",
"answer": 1078
},
{
... | 1 | [] | {
"lo": -8,
"mid": -4.75,
"hi": -2.28
} | ||||
a71832 | nt_count_coprime_and_v1_124444284_271 | Let $k_1 = 3$ and let $k_2$ be the largest prime number between $2$ and $11$, inclusive. Compute the number of positive integers $n \leq 45919$ such that $\gcd(n, k_1) = 1$ and $\gcd(n, k_2) = 1$. | 27,830 | graphs = [
Graph(
let={
"upper": Const(45919),
"k1": Const(3),
"k2": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(11)), IsPrime(Var("n"))))),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), conditio... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | nt_count_coprime_and_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 5.508 | 2026-02-08T03:07:35.349906Z | {
"verified": true,
"answer": 27830,
"timestamp": "2026-02-08T03:07:40.857622Z"
} | 41d355 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 185,
"completion_tokens": 959
},
"timestamp": "2026-02-09T15:29:32.115Z",
"answer": 27830
},
{
"i... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no... | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
d41236 | algebra_quadratic_discriminant_v1_717093673_2006 | Let $a = -8$, $b = -6$, and $c = 3$. Define the discriminant $D = b^2 - 4ac$. Let $r$ be the value of $2$ if $D > 0$, $1$ if $D = 0$, and $0$ otherwise. Compute $44121 \cdot r$. | 88,242 | graphs = [
Graph(
let={
"a": Const(-8),
"b": Const(-6),
"c": Const(3),
"D": Sub(Pow(Ref("b"), Const(2)), Mul(Const(4), Ref("a"), Ref("c"))),
"result": Sum(Mul(Const(2), Iverson(condition=Gt(Ref("D"), Const(0)))), Iverson(condition=Eq(Ref("D"), Cons... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | algebra_quadratic_discriminant_v1 | null | 2 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.017 | 2026-02-08T16:27:06.524181Z | {
"verified": true,
"answer": 88242,
"timestamp": "2026-02-08T16:27:06.541420Z"
} | 97b87a | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 136,
"completion_tokens": 138
},
"timestamp": "2026-02-16T07:23:16.392Z",
"answer": 88242
},
{
"id": 11,
... | 2 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
... | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
a41be2 | antilemma_k2_v1_1520064083_7757 | Let $S$ be the set of all ordered pairs $(k, j)$ with $1 \leq k \leq 294$ and $1 \leq j \leq 10$. Define
$$
x = \frac{2}{20} \sum_{(k,j) \in S} \phi(k) \left\lfloor \frac{294}{k} \right\rfloor.
$$
Let $A$ be the sum of $d_i (i+1)^2$ over all digits $d_i$ of $|x|$, where $d_0$ is the units digit, $d_1$ the tens digit, a... | 10,204 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(2),
"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), end=Const(294)), right=Integ... | NT | COMB | COMPUTE | sympy | VIETA_SUM | [
"VIETA_SUM",
"SUM_INDEPENDENT/K2",
"K2"
] | aa9f52 | antilemma_k2_v1 | digits_weighted_mod | 6 | 0 | [
"K2",
"SUM_INDEPENDENT",
"VIETA_SUM"
] | 3 | 0.005 | 2026-02-08T09:17:24.358772Z | {
"verified": true,
"answer": 10204,
"timestamp": "2026-02-08T09:17:24.363977Z"
} | 5c9c84 | 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": 1036
},
"timestamp": "2026-02-14T02:11:54.518Z",
"answer": 10204
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "SUM_INDEPENDENT",
"status": "ok"
},
... | {
"lo": -5.14,
"mid": 0.3,
"hi": 6.27
} | ||
de2cdf | alg_poly3_min_v1_601307018_6535 | Find the remainder when $$\min\left\{ 83a^3 - 195a^2b + 177ab^2 + 7c^3 + 48abc - 24a^2c - 57b^3 - 24b^2c + 12bc^2 - 12ac^2 \mid 1 \le a, b \le 27,\ 1 \le c \le \left|\left\{ (a_1,b_1) \in [1,40]^2 : 17a_1^4 + 68a_1^3b_1 + 68a_1b_1^3 + 17b_1^4 + \left|\{ n \in [1,253] : \gcd(n,10)=1 \}\right| a_1^2b_1^2 = 10449152 \righ... | 17,284 | graphs = [
Graph(
let={
"_m": Const(55553),
"_n": Const(3),
"result": Mod(value=MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b"), Var("c")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(27)), Geq(Var("b"), Const(1)), Leq(Var... | NT | null | COMPUTE | sympy | QF_PSD_DISTINCT | [
"C4/POLY4_COUNT"
] | 8b27cc | alg_poly3_min_v1 | null | 7 | 0 | [
"C4",
"POLY4_COUNT",
"QF_PSD_DISTINCT"
] | 3 | 0.246 | 2026-03-10T07:10:10.022720Z | {
"verified": true,
"answer": 17284,
"timestamp": "2026-03-10T07:10:10.268412Z"
} | 110b4a | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 321,
"completion_tokens": 8932
},
"timestamp": "2026-04-19T04:41:37.689Z",
"answer": 17284
},
{
... | 1 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "POLY4_COUNT",
"status": "ok_later"
},
{
"lemma": "V5",
"status": "no... | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
1d2d94_n | alg_poly4_count_v1_1218484723_3120 | Two players choose integers $a$ and $b$ from $1$ to $279$, respectively. A score is computed using the formula $-1088ab^3 + \left(\sum x\right)a^2b^2 - 1088a^3b + 272a^4 + 272b^4$, where the sum is over roots $x$ of $x^2 - 1632x - 164065 = 0$. How many pairs yield a score of exactly $1281663656192$? | 34 | ALG | null | COUNT | sympy | VIETA_SUM | [
"VIETA_SUM"
] | b33a7a | alg_poly4_count_v1 | null | 6 | null | [
"VIETA_SUM"
] | 1 | 0.386 | 2026-02-25T04:51:08.951488Z | null | c629b5 | 1d2d94 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 223,
"completion_tokens": 32768
},
"timestamp": "2026-03-30T19:38:47.401Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "VIETA_SUM",
"status": "ok"
}
] | {
"lo": 1.5,
"mid": 4.69,
"hi": 7.23
} | |
7eda69 | comb_factorial_compute_v1_1520064083_4864 | Let $n$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p < q$, $\gcd(p, q) = 1$, and $pq = 264600$. Compute the value of $n!$. | 40,320 | 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=264600)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(value=1)... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_factorial_compute_v1 | null | 6 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.001 | 2026-02-08T06:27:57.029997Z | {
"verified": true,
"answer": 40320,
"timestamp": "2026-02-08T06:27:57.031402Z"
} | 30d764 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 103,
"completion_tokens": 1222
},
"timestamp": "2026-02-13T00:23:31.021Z",
"answer": 40320
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
6f628e | nt_count_intersection_v1_124444284_8442 | Let $N = 20000$ and $a = 7$. Let $b$ be the number of integers $t$ such that $5 \leq t \leq 12$ and there exist integers $a'$ and $b'$ with $1 \leq a' \leq 3$, $1 \leq b' \leq 2$, and $t = 2a' + 3b'$. Compute the number of positive integers $n \leq N$ such that $a$ divides $n$ and $\gcd(n, b) = 1$. Let this count be $c... | 4,606 | graphs = [
Graph(
let={
"_n": Const(40377),
"N": Const(20000),
"a": Const(7),
"b": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), ... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_count_intersection_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.754 | 2026-02-08T09:42:37.654521Z | {
"verified": true,
"answer": 4606,
"timestamp": "2026-02-08T09:42:38.408075Z"
} | c89201 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 193,
"completion_tokens": 1911
},
"timestamp": "2026-02-14T05:43:35.580Z",
"answer": 4606
},
{... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
83bb42 | diophantine_fbi2_count_v1_784195855_2795 | Let $k = 240$. Determine the number of integers $d$ such that $2 \leq d \leq 65$, $d$ divides $k$, and $4 \leq \frac{k}{d} \leq 67$. Let $r$ denote this number.
Let $s$ be the number of positive integers $p$ such that there exists a positive integer $q$ with $p < q$, $\gcd(p, q) = 1$, and $p \cdot q = 108$.
Compute t... | 96 | graphs = [
Graph(
let={
"k": Const(240),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Leq(Var("d"), Const(65)), Divides(divisor=Var("d"), dividend=Ref("k")), Geq(Div(Ref("k"), Var("d")), Const(4)), Leq(Div(Ref("k"), Var("d")), Const(67)... | NT | null | COUNT | sympy | SUM_DIVISIBLE | [
"SUM_DIVISIBLE",
"COPRIME_PAIRS"
] | 5bee1f | diophantine_fbi2_count_v1 | digits_weighted_mod | 5 | 0 | [
"COPRIME_PAIRS",
"SUM_DIVISIBLE"
] | 2 | 0.011 | 2026-02-08T06:02:57.843034Z | {
"verified": true,
"answer": 96,
"timestamp": "2026-02-08T06:02:57.853737Z"
} | fca7e4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 284,
"completion_tokens": 1952
},
"timestamp": "2026-02-12T18:48:15.042Z",
"answer": 96
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "SUM_DIVISIBLE",
"statu... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
be4837 | diophantine_fbi2_min_v1_48377204_2838 | Let $k$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 36$. Let $d$ be an integer satisfying $3 \leq d \leq 22$, $d \mid k$, and $\frac{k}{d} \geq 4$. Determine the minimum such $d$. Multiply this $d$ by 19823 and compute the result. | 59,469 | graphs = [
Graph(
let={
"_n": Const(19823),
"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(36)))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | EXTREMUM | sympy | B3 | [
"B3"
] | 0cd20d | diophantine_fbi2_min_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.006 | 2026-02-08T17:01:24.159152Z | {
"verified": true,
"answer": 59469,
"timestamp": "2026-02-08T17:01:24.164903Z"
} | 7420e7 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 155,
"completion_tokens": 518
},
"timestamp": "2026-02-16T08:56:53.443Z",
"answer": 59469
},
{
"id": 11,
... | 2 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
b85f71 | comb_count_derangements_v1_1978505735_5078 | Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 254100$, $\gcd(p, q) = 1$, and $p < q$. Let $n$ be the minimum value of $x + y$ where $x$ and $y$ are positive integers such that $xy = |S|$. Compute the number of derangements of $n$ elements. | 14,833 | graphs = [
Graph(
let={
"_n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=254100)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(value=1... | NT | COMB | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/B3"
] | 3f0fb0 | comb_count_derangements_v1 | null | 6 | 0 | [
"B3",
"COPRIME_PAIRS"
] | 2 | 0.004 | 2026-02-08T18:45:33.529367Z | {
"verified": true,
"answer": 14833,
"timestamp": "2026-02-08T18:45:33.533326Z"
} | 759c59 | 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": 2656
},
"timestamp": "2026-02-18T19:12:29.581Z",
"answer": 14833
},
... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
d6e558 | comb_catalan_compute_v1_1978505735_6772 | 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 4$, $1 \leq b \leq 3$, and $t = 2a + 3b + 16$. Compute the $n$th Catalan number. | 58,786 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=4)), Geq(left=Var(name='b'), right=Const(value=1... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_catalan_compute_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T19:47:05.797584Z | {
"verified": true,
"answer": 58786,
"timestamp": "2026-02-08T19:47:05.799874Z"
} | 119b6f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 128,
"completion_tokens": 1491
},
"timestamp": "2026-02-18T23:32:25.759Z",
"answer": 58786
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.92,
"mid": -4.6,
"hi": -1.84
} | ||
b68bcd | algebra_poly_eval_v1_1978505735_1357 | Let $t = 21$. Let $k$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq = 72$, $\gcd(p, q) = 1$, and $p < q$. Define
$$
\text{result} = 7 \cdot t^k - 6t + 8.
$$
Compute the remainder when $44121 \cdot \text{result}$ is divided by $85367$. Find the value of this remainder... | 42,271 | graphs = [
Graph(
let={
"t": Const(21),
"result": Sum(Mul(Const(7), Pow(Ref("t"), 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=72)), Eq(lef... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | algebra_poly_eval_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.004 | 2026-02-08T16:06:15.533675Z | {
"verified": true,
"answer": 42271,
"timestamp": "2026-02-08T16:06:15.537689Z"
} | 1577d1 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 152,
"completion_tokens": 1499
},
"timestamp": "2026-02-16T20:56:35.515Z",
"answer": 42271
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
a318dc | comb_factorial_compute_v1_151522320_1023 | Let $m = 2$. Let $n$ be the largest prime number such that $m \leq n \leq 8$. Define $n$ to be the sum of $\phi(d)$ over all positive divisors $d$ of this largest prime. Compute $n!$. | 5,040 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_m")), Leq(Var("n"), Const(8)), IsPrime(Var("n"))))),
"n": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"res... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW/K3"
] | 6b6e89 | comb_factorial_compute_v1 | null | 4 | 0 | [
"K3",
"MAX_PRIME_BELOW"
] | 2 | 0.002 | 2026-02-08T03:42:40.212874Z | {
"verified": true,
"answer": 5040,
"timestamp": "2026-02-08T03:42:40.214495Z"
} | 5f6842 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 171,
"completion_tokens": 605
},
"timestamp": "2026-02-10T15:32:31.157Z",
"answer": 5040
},
{
"id... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K3",
"status": "ok_later"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"... | {
"lo": -10,
"mid": -7.73,
"hi": -5.46
} | ||
0ee81b | comb_count_permutations_fixed_v1_458359167_222 | Let $n$ be the largest prime number satisfying $2 \leq n \leq 9$. Let $k = 1$. Compute the value of $\binom{n}{k} \cdot !(n - k)$, where $!m$ denotes the number of derangements of $m$ elements. | 1,855 | graphs = [
Graph(
let={
"_n": Const(2),
"n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Const(9)), IsPrime(Var("n"))))),
"k": Const(1),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub(left=... | NT | COMB | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | comb_count_permutations_fixed_v1 | null | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.004 | 2026-02-08T03:05:09.239368Z | {
"verified": true,
"answer": 1855,
"timestamp": "2026-02-08T03:05:09.243150Z"
} | 1b1638 | 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": 635
},
"timestamp": "2026-02-10T13:17:38.589Z",
"answer": 1855
},
{
"id... | 1 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
e6b542 | alg_poly3_sum_v1_601307018_10208 | Compute the remainder when $$\sum_{\substack{1 \leq a, b, c \leq 49}} \left( -12a^2c -15b^3 -34c^3 + \left|\left\{ (a_1, b_1) : 1 \leq a_1 \leq 25,\ 1 \leq b_1 \leq N,\ -52a_1b_1 + 26a_1^2 + 26b_1^2 = 26 \right\}\right| \cdot a^3 + 18ab^2 -21b^2c -60abc -66ac^2 -108a^2b -3bc^2 \right)$$ is divided by $59164$, where $N ... | 58,527 | graphs = [
Graph(
let={
"_m": Const(26),
"_n": Const(2),
"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(49)), Geq(Var("b"), Const(1)), Leq(Var("b... | ALG | null | COMPUTE | sympy | QF_PSD_DISTINCT | [
"QF_PSD_DISTINCT/QF_PSD_COUNT"
] | a6a878 | alg_poly3_sum_v1 | null | 6 | 0 | [
"QF_PSD_COUNT",
"QF_PSD_DISTINCT"
] | 2 | 0.486 | 2026-03-10T10:44:25.633340Z | {
"verified": true,
"answer": 58527,
"timestamp": "2026-03-10T10:44:26.119308Z"
} | ede9de | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 368,
"completion_tokens": 6875
},
"timestamp": "2026-04-19T13:11:42.300Z",
"answer": 58527
},
{
... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT",
"status": "ok_later"
},
{
"lemma": "QF_PSD_DISTINCT",
"status": "ok"
}
] | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
e07e49 | nt_sum_gcd_range_mod_v1_124444284_4560 | Let $N$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 705600$. Let $k = 600$ and define $\text{sum} = \sum_{n=1}^{N} \gcd(n, k)$. Given $M = 11839$, compute the remainder when $\text{sum}$ is divided by $M$. | 6,081 | graphs = [
Graph(
let={
"N": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(705600)))), expr=Sum(Var("x"), Var("y")))),
"k": Const(600),... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_gcd_range_mod_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.08 | 2026-02-08T06:05:12.947131Z | {
"verified": true,
"answer": 6081,
"timestamp": "2026-02-08T06:05:13.027198Z"
} | 65765d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 134,
"completion_tokens": 4127
},
"timestamp": "2026-02-12T19:10:45.521Z",
"answer": 6081
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
ec4c85 | nt_count_coprime_and_v1_1742523217_435 | Let $k_1 = 4$ and let $k_2$ be the largest integer $k$ such that $43^k$ divides $1849 \times 271818611107$. Determine the number of positive integers $n$ not exceeding 55305 that are relatively prime to both $k_1$ and $k_2$. | 18,435 | graphs = [
Graph(
let={
"upper": Const(55305),
"k1": Const(4),
"k2": MaxKDivides(target=Mul(Const(1849), Const(271818611107)), base=Const(43)),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("uppe... | NT | null | COUNT | sympy | K13 | [
"K13"
] | 8d970a | nt_count_coprime_and_v1 | null | 5 | 0 | [
"K13"
] | 1 | 7.095 | 2026-02-08T03:01:55.796618Z | {
"verified": true,
"answer": 18435,
"timestamp": "2026-02-08T03:02:02.891613Z"
} | cba2c1 | 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": 3460
},
"timestamp": "2026-02-09T17:55:28.332Z",
"answer": 18435
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K13",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": 1.69,
"mid": 5.03,
"hi": 8.38
} | ||
4e0872 | comb_bell_compute_v1_784195855_1610 | Let $S$ be the set of all positive integers $t$ such that $15 \leq t \leq 45$ and there exist positive integers $a$, $b$ with $1 \leq a \leq 3$, $1 \leq b \leq 3$, and $t = 6a + 9b$. Let $n = |S| \cdot \left(\sum_{k=0}^{0} (-1)^k \binom{0}{k}\right)^2$. Compute the Bell number $B_n$. | 21,147 | graphs = [
Graph(
let={
"n2": Const(0),
"h": Summation(var="k", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n2"), k=Var("k")))),
"n1": Const(0),
"t": Summation(var="k", start=Const(0), end=Ref("n1"), expr=Mul(Pow(Const(-1), V... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/BINOMIAL_ALTERNATING"
] | bebeab | comb_bell_compute_v1 | null | 3 | 2 | [
"BINOMIAL_ALTERNATING",
"LIN_FORM"
] | 2 | 0.002 | 2026-02-08T05:10:22.978670Z | {
"verified": true,
"answer": 21147,
"timestamp": "2026-02-08T05:10:22.980541Z"
} | c181d4 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 231,
"completion_tokens": 862
},
"timestamp": "2026-02-24T02:52:00.281Z",
"answer": 21147
},
{
"i... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8... | {
"lo": -4.93,
"mid": -2.91,
"hi": -0.71
} | ||
b55c50 | nt_sum_totient_over_divisors_v1_168721529_1735 | Let $n$ be the number of positive integers less than or equal to $13915$ whose digit sum leaves a remainder of $1$ when divided by $2$. Compute the multiplicative order of $2$ modulo $2\left|\sum_{d \mid n} \phi(d)\right| + 3$. | 1,120 | graphs = [
Graph(
let={
"_n": Const(2),
"n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(13915)), Eq(Mod(value=DigitSum(Var("n")), modulus=Ref("_n")), Const(1))))),
"result": SumOverDivisors(n=Ref(name='n'), var='... | NT | null | COMPUTE | sympy | L3B | [
"L3B"
] | cc148f | nt_sum_totient_over_divisors_v1 | null | 7 | 0 | [
"L3B"
] | 1 | 0.005 | 2026-02-08T13:54:01.377988Z | {
"verified": true,
"answer": 1120,
"timestamp": "2026-02-08T13:54:01.383297Z"
} | d29bb0 | 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": 4363
},
"timestamp": "2026-02-09T20:57:05.183Z",
"answer": 1120
},
{
"i... | 1 | [
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3B",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -6.5,
"mid": -0.2,
"hi": 6.11
} | ||
4f5573 | comb_count_derangements_v1_601307018_6410 | Let $D_n$ denote the number of derangements of $n$ elements. Define the sequence $R = a^3 \bmod 4913$, $S = R^3 \bmod 4913$, $T = S^3 \bmod m$, $K = T^3 \bmod 4913$, where $m$ is the number of integers $t$ in $[7, 4923]$ that can be expressed as $t = 2a + 5b$ for integers $a, b$ with $1 \le a \le 984$, $1 \le b \le 591... | 14,833 | graphs = [
Graph(
let={
"_m": Const(4912),
"_n": Const(3),
"n": CountOverSet(set=SolutionsSet(var=Var("a"), condition=And(Geq(Var("a"), Const(0)), Leq(Var("a"), Ref("_m")), Eq(Ref("_po_p4"), Var("a")), Neq(Ref("_po_p1"), Var("a")), Neq(Ref("_po_p2"), Var("a")), Neq(Ref("_... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/POLY_ORBIT_HENSEL"
] | 007af8 | comb_count_derangements_v1 | null | 7 | 0 | [
"LIN_FORM",
"POLY_ORBIT_HENSEL"
] | 2 | 0.006 | 2026-03-10T07:05:06.574380Z | {
"verified": true,
"answer": 14833,
"timestamp": "2026-03-10T07:05:06.580355Z"
} | 34cfe8 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 296,
"completion_tokens": 8276
},
"timestamp": "2026-04-19T04:19:12.159Z",
"answer": 14833
},
{
... | 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": "POLY_ORBIT_HENS... | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
4d05c3 | nt_count_divisible_and_v1_1520064083_1156 | Compute the number of integers $n$ such that $1 \leq n \leq 84144$, $n$ is divisible by 8, and $n$ is divisible by 12. | 3,506 | graphs = [
Graph(
let={
"upper": Const(84144),
"d1": Const(8),
"d2": Const(12),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), EulerPhi(n=Const(2))), Leq(Var("n"), Ref("upper")), Eq(Mod(value=Var("n"), modulus=Ref("d1")), Con... | NT | null | COUNT | sympy | ONE_PHI_2 | [
"ONE_PHI_2"
] | e19278 | nt_count_divisible_and_v1 | null | 3 | 0 | [
"ONE_PHI_2"
] | 1 | 2.813 | 2026-02-08T03:48:47.318266Z | {
"verified": true,
"answer": 3506,
"timestamp": "2026-02-08T03:48:50.131312Z"
} | a71517 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 139,
"completion_tokens": 423
},
"timestamp": "2026-02-18T06:19:30.465Z",
"answer": 3506
}
] | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "ONE_PHI_2",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
3a7bdb_l | algebra_quadratic_discriminant_v1_798873815_166 | Let $a = -1$, $b = 20$, and $c = -100$. Let $k$ be the largest integer such that $5^k$ divides $\binom{910}{364}$. Define $D = b^2 - 4ac \cdot k$. Let $\alpha = 1$ if $D > 0$, and $0$ otherwise. Let $\beta = 1$ if $D = 0$, and $0$ otherwise. Compute the value of $|2\alpha + \beta|$. | 0 | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"V7"
] | 0672d4 | algebra_quadratic_discriminant_v1 | null | 6 | 0 | [
"COPRIME_PAIRS",
"V7"
] | 2 | 0.012 | 2026-02-08T02:29:55.411728Z | {
"verified": false,
"answer": 1,
"timestamp": "2026-02-08T02:29:55.424053Z"
} | d7ad9f | 3a7bdb | legacy_text | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 229,
"completion_tokens": 1182
},
"timestamp": "2026-02-08T19:06:38.303Z",
"answer": 0
},
{
"id... | 1 | [
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "V7",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": 4.26,
"mid": 6.42,
"hi": 9.47
} | |
5dc044 | lin_form_endings_v1_677425708_419 | Let $a = 45$ and $b = 63$. Define $d = \gcd(a, b)$ and $k = 141$. Let $n = \left\lfloor \frac{k}{\gcd(k, d)} \right\rfloor$. Compute the remainder when $19349 \cdot n$ is divided by $75750$. | 403 | graphs = [
Graph(
let={
"a_coeff": Const(45),
"b_coeff": Const(63),
"k_val": Const(141),
"step": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"_inner_result": Floor(Div(Ref("k_val"), GCD(a=Ref("k_val"), b=Ref("step")))),
"_scale_k": Const(1... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 3 | null | [
"LIN_FORM"
] | 1 | 0 | 2026-02-08T03:31:59.130443Z | {
"verified": true,
"answer": 403,
"timestamp": "2026-02-08T03:31:59.130899Z"
} | 1d3217 | 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": 692
},
"timestamp": "2026-02-08T20:33:54.934Z",
"answer": 403
},
{
"id"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
58a9c1 | diophantine_product_count_v1_865884756_3970 | Let $T$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 9216$. Define $s$ to be the minimum value of $x + y$ as $(x, y)$ ranges over $T$.
Let $k$ be the sum of all positive integers $n$ such that $1 \leq n \leq s$, $n$ is divisible by 48, and $n$ divides 9216.
Let $u = 223$. Define $D$ t... | 128 | graphs = [
Graph(
let={
"_n": Const(9216),
"k": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(... | NT | null | COUNT | sympy | B3 | [
"B3/SUM_DIVISIBLE"
] | 138b1a | diophantine_product_count_v1 | null | 6 | 0 | [
"B3",
"SUM_DIVISIBLE"
] | 2 | 0.011 | 2026-02-08T17:40:53.512155Z | {
"verified": true,
"answer": 128,
"timestamp": "2026-02-08T17:40:53.523304Z"
} | 06727d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 233,
"completion_tokens": 2159
},
"timestamp": "2026-02-18T06:37:59.722Z",
"answer": 128
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "SUM_DIVISIBLE",
"status": "ok_later"
},
{
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
f76406 | algebra_quadratic_discriminant_v1_1742523217_1251 | Let $a = 10$, $b = -10$, and $c = -7$. Let $D = b^2 - 4ac$. Define $\alpha = 1$ if $D > 0$, and $0$ otherwise. Define $\beta = 1$ if $D = 0$, and $0$ otherwise. Let $r = 2\alpha + \beta$. Compute the smallest positive integer $k$ such that the $k$-th Fibonacci number is divisible by $r + 2$. | 6 | graphs = [
Graph(
let={
"a": Const(10),
"b": Const(-10),
"c": Const(-7),
"D": Sub(Pow(Ref("b"), Const(2)), Mul(Const(4), Ref("a"), Ref("c"))),
"result": Sum(Mul(Const(2), Iverson(condition=Gt(Ref("D"), Const(0)))), Iverson(condition=Eq(Ref("D"), Co... | NT | null | COMPUTE | sympy | SUM_DIVISIBLE | [
"SUM_DIVISIBLE/SUM_ARITHMETIC",
"MOBIUS_COPRIME"
] | b498df | algebra_quadratic_discriminant_v1 | null | 2 | 0 | [
"MOBIUS_COPRIME",
"SUM_ARITHMETIC",
"SUM_DIVISIBLE"
] | 3 | 0.021 | 2026-02-08T03:35:05.797378Z | {
"verified": true,
"answer": 6,
"timestamp": "2026-02-08T03:35:05.818415Z"
} | d15b38 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 221,
"completion_tokens": 758
},
"timestamp": "2026-02-10T05:42:30.724Z",
"answer": 6
},
{
"id": ... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "o... | {
"lo": -5.55,
"mid": -3.02,
"hi": 0.31
} | ||
dc3bda | diophantine_product_count_v1_655260480_210 | Let $n = 2$. Define $k$ to be the number of positive integers $j$ such that $1 \le j \le 420$ and $j^n \le 176400$. Let $s$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 29929$. Define $\text{upper}$ to be the minimum value of $x + y$ over all pairs $(x, y) \in s$. Let $T$ be the set of ... | 22 | graphs = [
Graph(
let={
"_n": Const(2),
"k": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(1)), Leq(Var("j"), Const(420)), Leq(Pow(Var("j"), Ref("_n")), Const(176400))), domain='positive_integers')),
"upper": MinOverSet(set=MapOverSet(set=S... | NT | null | COUNT | sympy | B3 | [
"B3",
"C3"
] | 5d1796 | diophantine_product_count_v1 | null | 6 | 0 | [
"B3",
"C3"
] | 2 | 0.023 | 2026-02-08T15:18:08.210434Z | {
"verified": true,
"answer": 22,
"timestamp": "2026-02-08T15:18:08.233910Z"
} | a4e58a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 213,
"completion_tokens": 1610
},
"timestamp": "2026-02-16T02:56:44.256Z",
"answer": 22
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C3",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemm... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
1f0c45 | comb_count_surjections_v1_677425708_370 | Let $k$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 8$. Let $n = 5$. Define $S = k! \cdot S(n, k)$, where $S(n, k)$ denotes the Stirling number of the second kind. Compute $29578 \cdot S$ modulo 80831. | 66,423 | graphs = [
Graph(
let={
"_n": Const(80831),
"n": Const(5),
"k": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq... | COMB | null | COUNT | sympy | COMB1 | [
"COMB1"
] | 567f58 | comb_count_surjections_v1 | null | 5 | 0 | [
"COMB1"
] | 1 | 0.002 | 2026-02-08T03:14:37.885643Z | {
"verified": true,
"answer": 66423,
"timestamp": "2026-02-08T03:14:37.887484Z"
} | c4235d | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 204,
"completion_tokens": 1934
},
"timestamp": "2026-02-08T20:29:19.168Z",
"answer": 66423
},
{
"... | 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": -0.05,
"mid": 2.89,
"hi": 5.27
} | ||
ed2e0f | nt_sum_divisors_compute_v1_349078426_1643 | Let $P$ be the set of all positive integers $p$ such that there exists a positive integer $q$ with $p < q$, $pq = 6$, and $\gcd(p, q) = 1$. Let $N$ be the number of elements in $P$. Let $\sigma(n)$ denote the sum of the positive divisors of $n$. Define $S$ to be the sum of all real solutions $x$ to the equation $x^N - ... | 1,420 | 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=6)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(value=1)), L... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/VIETA_SUM"
] | ea2fe2 | nt_sum_divisors_compute_v1 | negation_mod | 7 | 0 | [
"COPRIME_PAIRS",
"VIETA_SUM"
] | 2 | 0.003 | 2026-02-08T13:49:04.445241Z | {
"verified": true,
"answer": 1420,
"timestamp": "2026-02-08T13:49:04.448403Z"
} | 329f27 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 178,
"completion_tokens": 794
},
"timestamp": "2026-02-15T20:48:18.771Z",
"answer": 1420
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "VIETA_... | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
5b1b25 | antilemma_k3_v1_1742523217_1686 | Let $n = 50471$. Compute the sum of $\phi(d)$ over all positive divisors $d$ of $n$, where $\phi$ denotes Euler's totient function. | 50,471 | graphs = [
Graph(
let={
"_n": Const(50471),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 4 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T04:06:26.978530Z | {
"verified": true,
"answer": 50471,
"timestamp": "2026-02-08T04:06:26.979143Z"
} | aea2f8 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 149,
"completion_tokens": 438
},
"timestamp": "2026-02-10T15:18:12.689Z",
"answer": 50471
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.33
} | ||
eec7cb | nt_count_gcd_equals_v1_1742523217_5615 | Let $k$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 8464$. Let $s$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 17909824$, and let $d$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of posit... | 54 | graphs = [
Graph(
let={
"_n": Const(8464),
"upper": Const(10080),
"k": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_n"))))... | NT | null | COUNT | sympy | B3 | [
"B3/B3"
] | 8ffef9 | nt_count_gcd_equals_v1 | null | 7 | 0 | [
"B3"
] | 1 | 3.195 | 2026-02-08T11:05:58.312226Z | {
"verified": true,
"answer": 54,
"timestamp": "2026-02-08T11:06:01.507072Z"
} | 4d2d27 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 184,
"completion_tokens": 1431
},
"timestamp": "2026-02-14T10:26:39.644Z",
"answer": 54
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
e93b76 | sequence_fibonacci_compute_v1_898971024_87 | Let $n$ be the number of integers $t$ with $18 \leq t \leq 47$ for which there exist positive integers $a \leq 4$ and $b \leq 6$ such that $t = 3a + 4b + 11$. Let $F_n$ denote the $n$th Fibonacci number, where $F_1 = F_2 = 1$ and $F_k = F_{k-1} + F_{k-2}$ for $k \geq 3$. Find the remainder when $26671 \cdot F_n$ is div... | 7,392 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=4)), Geq(left=Var(name='b'), right=Const(value=1... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | sequence_fibonacci_compute_v1 | null | 3 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T15:10:52.443334Z | {
"verified": true,
"answer": 7392,
"timestamp": "2026-02-08T15:10:52.445428Z"
} | 3c6280 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 179,
"completion_tokens": 3002
},
"timestamp": "2026-02-16T01:02:47.275Z",
"answer": 7392
},
{... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
f450b1 | nt_lcm_compute_v1_655260480_250 | Let $a$ be the number of ordered pairs $(i, j)$ of positive integers with $1 \leq i \leq 35$ and $1 \leq j \leq 56$ such that $\gcd(i, j) = 1$. Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 147456$. For each such pair, compute $x + y$. Let $b$ be the minimum value of $x + y$ over... | 14,592 | graphs = [
Graph(
let={
"a": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(GCD(a=Var("i"), b=Var("j")), Const(1)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(35)), right=IntegerRange(start=Const(1), end=Const(56))))),
"b... | NT | null | COMPUTE | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_COPRIME_GRID",
"B3"
] | a8b7cb | nt_lcm_compute_v1 | null | 6 | 0 | [
"B3",
"COUNT_COPRIME_GRID",
"COUNT_FIB_DIVISIBLE"
] | 3 | 0.008 | 2026-02-08T15:19:23.407674Z | {
"verified": true,
"answer": 14592,
"timestamp": "2026-02-08T15:19:23.415606Z"
} | caf4c5 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 170,
"completion_tokens": 5508
},
"timestamp": "2026-02-16T03:25:46.384Z",
"answer": 14592
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "n... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
5456ce | modular_mod_compute_v1_655260480_4225 | Consider the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 3600$. For each such pair, compute $x + y$. Let $S$ be the set of all such sums. Define $n$ to be the minimum value in $S$.
Let $m = \sum_{k=1}^{n} k$ and let $a = -8192$. Compute the remainder when $a$ is divided by $m$, and denote thi... | 95,739 | graphs = [
Graph(
let={
"_m": Const(76418),
"_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(3600)))), expr=Sum(Var("x"), Var("y")))... | NT | null | COMPUTE | sympy | B3 | [
"B3/SUM_ARITHMETIC"
] | b6a880 | modular_mod_compute_v1 | null | 4 | 0 | [
"B3",
"SUM_ARITHMETIC"
] | 2 | 0.003 | 2026-02-08T17:48:39.516910Z | {
"verified": true,
"answer": 95739,
"timestamp": "2026-02-08T17:48:39.519554Z"
} | a14bb8 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 178,
"completion_tokens": 2232
},
"timestamp": "2026-02-18T08:44:50.701Z",
"answer": 95739
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
727891 | geo_count_lattice_triangle_v1_124444284_5151 | Let $A$ be the set of all ordered pairs $(i, j)$ of integers with $1 \leq i \leq 200$ and $1 \leq j \leq 200$ such that $i + j = 201$. Let $\text{area}_{2x} = \left| 196 \cdot |A| - 233 \cdot 200 \right|$. Define the boundary length as
$$
\gcd(200, 200) + \gcd(|233 - 200|, |196 - 200|) + \gcd(233, 196).
$$
Let $\text{r... | 3,600 | graphs = [
Graph(
let={
"_n": Const(201),
"area_2x": Abs(arg=Sum(Mul(CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var(name='i'), Var(name='j')]), condition=Eq(left=Sum(Var(name='i'), Var(name='j')), right=Ref(name='_n')), domain=CartesianProduct(left=IntegerRange(start=Const(val... | ALG | NT | COUNT | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | geo_count_lattice_triangle_v1 | null | 6 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.005 | 2026-02-08T06:25:17.626526Z | {
"verified": true,
"answer": 3600,
"timestamp": "2026-02-08T06:25:17.631574Z"
} | 86c9c8 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 209,
"completion_tokens": 715
},
"timestamp": "2026-02-12T23:42:55.301Z",
"answer": 3600
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
f8c8c3 | nt_max_prime_below_v1_1125832087_769 | Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 108$, $\gcd(p, q) = 1$, and $p < q$. Let $c$ be the number of elements in $S$. Let $T$ be the set of all prime numbers $n$ such that $n \geq c$ and $n \leq 76729$. Determine the value of the largest element in ... | 76,717 | graphs = [
Graph(
let={
"upper": Const(76729),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), V... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_max_prime_below_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 1.92 | 2026-02-08T03:16:37.549177Z | {
"verified": true,
"answer": 76717,
"timestamp": "2026-02-08T03:16:39.469520Z"
} | fd923c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 216,
"completion_tokens": 5691
},
"timestamp": "2026-02-10T13:47:28.094Z",
"answer": 76721
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": 1.71,
"mid": 5.04,
"hi": 8.38
} | ||
3db7c6 | modular_mod_compute_v1_397696148_1909 | Let $T$ be the set of all integers $t$ such that $7 \leq t \leq 74$ and there exist integers $a$, $b$ with $1 \leq a \leq 6$, $1 \leq b \leq 22$, and $t = 5a + 2b$. Let $s$ be the number of elements in $T$. Let $M$ be the maximum value of $xy$ over all pairs of positive integers $(x, y)$ such that $x + y = s$. Let $r$ ... | 31,812 | graphs = [
Graph(
let={
"_n": Const(81266),
"a": Const(77028),
"m": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), CountOverSet(se... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/B1"
] | b32639 | modular_mod_compute_v1 | null | 5 | 0 | [
"B1",
"LIN_FORM"
] | 2 | 0.004 | 2026-02-08T12:50:30.012796Z | {
"verified": true,
"answer": 31812,
"timestamp": "2026-02-08T12:50:30.016307Z"
} | 40dabc | 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": 3257
},
"timestamp": "2026-02-15T06:36:10.172Z",
"answer": 31812
},
... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lem... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
ad8d50 | comb_catalan_compute_v1_1520064083_7349 | Let $C_{10}$ denote the 10th Catalan number. Compute the remainder when the Bell number $B_k$ is divided by 50647, where $k$ is the remainder when $|C_{10}|$ is divided by 11. | 14,681 | graphs = [
Graph(
let={
"n": Const(10),
"result": Catalan(Ref("n")),
"Q": Mod(value=Bell(Mod(value=Abs(arg=Ref(name='result')), modulus=Const(11))), modulus=Const(50647)),
},
goal=Ref("Q"),
)
] | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 1ae498 | comb_catalan_compute_v1 | bell_mod | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.011 | 2026-02-08T08:58:50.507807Z | {
"verified": true,
"answer": 14681,
"timestamp": "2026-02-08T08:58:50.519057Z"
} | 776eb1 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 164,
"completion_tokens": 851
},
"timestamp": "2026-02-24T10:16:26.642Z",
"answer": 14781
},
{
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
394076 | algebra_quadratic_discriminant_v1_458359167_4873 | Let $a = -1$, $b = 0$, and $c = 4$. Define $\Delta = b^2 - 4ac$. Let $d_{\text{min}}$ be the smallest integer $d \geq 2$ that divides 1859. Compute the value of the Bell number $B_n$, where $n$ is the remainder when $|\Delta|$ is divided by $d_{\text{min}}$. Determine the value of this Bell number. | 52 | graphs = [
Graph(
let={
"a": Const(-1),
"b": Const(0),
"c": Const(4),
"result": Sub(Pow(Ref("b"), Const(2)), Mul(Const(4), Ref("a"), Ref("c"))),
"Q": Bell(Mod(value=Abs(arg=Ref(name='result')), modulus=MinOverSet(set=SolutionsSet(var=Var("d"), cond... | NT | COMB | COMPUTE | sympy | B1 | [
"MIN_PRIME_FACTOR"
] | 58d7e9 | algebra_quadratic_discriminant_v1 | bell_mod | 3 | 0 | [
"B1",
"MIN_PRIME_FACTOR"
] | 2 | 0.043 | 2026-02-08T12:06:45.165004Z | {
"verified": true,
"answer": 52,
"timestamp": "2026-02-08T12:06:45.207614Z"
} | 4262cb | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 147,
"completion_tokens": 928
},
"timestamp": "2026-02-14T22:17:56.959Z",
"answer": 52
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "o... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
4c08d7 | comb_count_partitions_v1_1742523217_3879 | Let $T$ be the set of all positive integers $t$ for which there exist positive integers $a$ and $b$ such that $1 \leq a \leq 10$, $1 \leq b \leq 8$, $10 \leq t \leq 92$, and $t = 6a + 4b$. Let $n$ be the number of elements in $T$. Compute the number of integer partitions of $n$. | 37,338 | 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=10)), Geq(left=Var(name='b'), right=Const(value=... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_count_partitions_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T06:07:20.202370Z | {
"verified": true,
"answer": 37338,
"timestamp": "2026-02-08T06:07:20.203368Z"
} | c34066 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 210,
"completion_tokens": 2643
},
"timestamp": "2026-02-24T05:24:39.954Z",
"answer": 37338
},
{
"... | 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": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
a4ea3b | diophantine_product_count_v1_971394319_1179 | Let $k = 720$. Let $\mathcal{S}$ be the set of all ordered pairs $(i,j)$ of integers with $1 \leq i \leq 8$ and $1 \leq j \leq 60$ such that $\gcd(i,j) = 1$. Define $u$ to be the number of elements in $\mathcal{S}$. Let $\mathcal{T}$ be the set of all positive integers $x$ such that $1 \leq x \leq u$, $x$ divides $k$, ... | 48 | graphs = [
Graph(
let={
"k": Const(720),
"upper": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(GCD(a=Var("i"), b=Var("j")), Const(1)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(8)), right=IntegerRange(start=Const(1), e... | NT | null | COUNT | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_COPRIME_GRID"
] | 20ec03 | diophantine_product_count_v1 | null | 6 | 0 | [
"COUNT_COPRIME_GRID",
"COUNT_FIB_DIVISIBLE"
] | 2 | 0.087 | 2026-02-08T13:31:33.563967Z | {
"verified": true,
"answer": 48,
"timestamp": "2026-02-08T13:31:33.650994Z"
} | e4f545 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 222,
"completion_tokens": 1860
},
"timestamp": "2026-02-15T16:43:05.462Z",
"answer": 48
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V1",
... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
a10f8b | diophantine_fbi2_count_v1_1080341949_273 | Let $k = 720$, $m = 128$, and $n = 5$. Let $P$ be the set of all prime numbers from 2 to 135, inclusive. Let $D$ be the set of all positive integers $d$ such that $n \leq d \leq \max(P)$, $d$ divides $k$, and $2 \leq k/d \leq m$. Let $c$ be the number of elements in $D$. Compute
$$
\sum_{i=1}^{c} \phi(i),
$$
where $\ph... | 128 | graphs = [
Graph(
let={
"_m": Const(128),
"_n": Const(5),
"k": Const(720),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Leq(Var("d"), MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2... | NT | null | COUNT | sympy | LIN_FORM | [
"MAX_PRIME_BELOW",
"COPRIME_PAIRS"
] | 05d703 | diophantine_fbi2_count_v1 | null | 6 | 0 | [
"COPRIME_PAIRS",
"LIN_FORM",
"MAX_PRIME_BELOW"
] | 3 | 0.085 | 2026-02-08T13:22:04.535324Z | {
"verified": true,
"answer": 128,
"timestamp": "2026-02-08T13:22:04.620575Z"
} | 460231 | 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": 2562
},
"timestamp": "2026-02-15T14:46:21.713Z",
"answer": 128
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
}... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
368502 | nt_count_divisible_and_v1_784195855_1651 | Let $d_1 = \sum_{k=1}^{3} k$ and $d_2 = 9$. Let $u = 13554$. Define $S$ to be the set of all positive integers $n$ such that $1 \leq n \leq u$, $n$ is divisible by $d_1$, and $n$ is divisible by $d_2$. Let $r$ be the number of elements in $S$.
Compute the remainder when $44121 \cdot r$ is divided by 91937. | 33,856 | graphs = [
Graph(
let={
"_n": Const(3),
"upper": Const(13554),
"d1": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Var("k")),
"d2": Const(9),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(... | NT | null | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | nt_count_divisible_and_v1 | null | 3 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.975 | 2026-02-08T05:12:04.341514Z | {
"verified": true,
"answer": 33856,
"timestamp": "2026-02-08T05:12:05.316239Z"
} | dadc99 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 228,
"completion_tokens": 859
},
"timestamp": "2026-02-11T23:03:02.881Z",
"answer": 33856
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
263e3d | modular_mod_compute_v1_1978505735_343 | Let $ m $ be the maximum value of $ xy $ over all pairs of positive integers $ (x, y) $ such that $ x + y = 192 $. Compute the remainder when $ -21904 $ is divided by $ m $. | 5,744 | graphs = [
Graph(
let={
"_n": Const(192),
"a": Const(-21904),
"m": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Ref("_n")))), ex... | NT | null | COMPUTE | sympy | B1 | [
"B1"
] | 5b950e | modular_mod_compute_v1 | null | 4 | 0 | [
"B1"
] | 1 | 0.002 | 2026-02-08T15:19:54.925963Z | {
"verified": true,
"answer": 5744,
"timestamp": "2026-02-08T15:19:54.927853Z"
} | 0e18b6 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 97,
"completion_tokens": 702
},
"timestamp": "2026-02-16T04:31:28.178Z",
"answer": 5744
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
e5b72a | nt_euler_phi_compute_v1_1520064083_2588 | Let $n = 71289$. Define $A = \phi(n)$ and $B$ as the number of positive integers $k$ at most $9997$ such that $\gcd(k, 12) = 1$. Compute the remainder when $A^2 + 16A + B$ is divided by $77020$. | 69,669 | graphs = [
Graph(
let={
"_n": Const(2),
"n": Const(71289),
"result": EulerPhi(n=Ref("n")),
"_c": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(9997)), Eq(GCD(a=Var("n"), b=Const(12)), Const(1))))),
... | NT | null | COMPUTE | sympy | C4 | [
"C4"
] | 40da2d | nt_euler_phi_compute_v1 | quadratic_mod | 5 | 0 | [
"C4"
] | 1 | 0.002 | 2026-02-08T04:52:37.134226Z | {
"verified": true,
"answer": 69669,
"timestamp": "2026-02-08T04:52:37.136377Z"
} | 195e47 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 181,
"completion_tokens": 2519
},
"timestamp": "2026-02-11T22:24:03.024Z",
"answer": 69669
},
{
... | 1 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
3ea891 | nt_min_coprime_above_v1_677425708_457 | Let $n$ be a positive integer. Define $\mathcal{S}$ as the set of all integers $n$ such that $1 \leq n \leq 581$, $7$ divides $n$, and $$\gcd\left(n, \, \text{the number of integers } m \text{ with } 1 \leq m \leq 225 \text{ and } 10 \mid F_m\right) = 1,$$ where $F_m$ denotes the $m$-th Fibonacci number. Let $M$ be the... | 61,507 | graphs = [
Graph(
let={
"_n": Const(7),
"start": Const(61504),
"upper": Const(61559),
"modulus": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(581)), Divides(divisor=Ref("_n"), dividend=Var("n")), Eq(GCD... | NT | null | EXTREMUM | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE/C5",
"MOBIUS_COPRIME"
] | 336b0b | nt_min_coprime_above_v1 | null | 7 | 0 | [
"C5",
"COUNT_FIB_DIVISIBLE",
"MOBIUS_COPRIME"
] | 3 | 0.01 | 2026-02-08T03:33:15.405289Z | {
"verified": true,
"answer": 61507,
"timestamp": "2026-02-08T03:33:15.415516Z"
} | 9e3103 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 317,
"completion_tokens": 3216
},
"timestamp": "2026-02-08T20:36:01.345Z",
"answer": 61507
},
{
"... | 1 | [
{
"lemma": "C5",
"status": "ok_later"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"st... | {
"lo": -6.51,
"mid": -0.31,
"hi": 5.43
} | ||
8991cf | algebra_quadratic_discriminant_v1_1520064083_8542 | Let $P$ be the set of all positive integers $p$ such that there exists a positive integer $q$ with $p < q$, $pq = 12$, and $\gcd(p, q) = 1$. Let $m$ be the number of elements in $P$.
Let $D = (-2)^m - 4(-1)(-1)$.
Compute the value of $2 \cdot [D > 0] + [D = 0]$, where $[\cdot]$ denotes the Iverson bracket (1 if the c... | 1 | graphs = [
Graph(
let={
"_n": Const(2),
"a": Const(-1),
"b": Const(-2),
"c": Const(-1),
"D": Sub(Pow(Ref("b"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=... | NT | null | COMPUTE | sympy | LIN_FORM | [
"COPRIME_PAIRS"
] | 2bb3aa | algebra_quadratic_discriminant_v1 | null | 5 | 0 | [
"COPRIME_PAIRS",
"LIN_FORM"
] | 2 | 0.027 | 2026-02-08T10:15:02.307864Z | {
"verified": true,
"answer": 1,
"timestamp": "2026-02-08T10:15:02.334557Z"
} | 860640 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 186,
"completion_tokens": 359
},
"timestamp": "2026-02-15T20:51:46.999Z",
"answer": 1
},
{
"id": 11,
"... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.71,
"hi": -5.43
} | ||
505bb8 | antilemma_coprime_grid_v1_124444284_836 | Let $m=17$ and $n_0=2$. Let $S$ be the set of all positive integers $n$ such that $n\ge n_0$, $n$ is prime, and $n\le L$, where $L$ is the smallest positive integer with the following property: if $F$ is the greatest integer $k$ such that $7^k$ divides $n!$, then $F\ge 3$. Let $p$ be the maximum element of $S$.
Let
$$... | 3,588 | graphs = [
Graph(
let={
"_m": Const(17),
"_n": Const(2),
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(GCD(a=Var("i"), b=Var("j")), SumOverDivisors(n=GCD(a=Ref(name='_m'), b=MaxOverSet(set=SolutionsSet(var=Var(name='n'), conditi... | NT | null | COMPUTE | sympy | V5 | [
"V5/MAX_PRIME_BELOW/MOBIUS_COPRIME/COUNT_COPRIME_GRID",
"COUNT_COPRIME_GRID"
] | ffc62d | antilemma_coprime_grid_v1 | null | 7 | 0 | [
"COUNT_COPRIME_GRID",
"MAX_PRIME_BELOW",
"MOBIUS_COPRIME",
"V5"
] | 4 | 0.002 | 2026-02-08T03:32:54.353244Z | {
"verified": true,
"answer": 3588,
"timestamp": "2026-02-08T03:32:54.355208Z"
} | 3867f4 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 326,
"completion_tokens": 3803
},
"timestamp": "2026-02-09T06:29:42.191Z",
"answer": 3588
},
{
"... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MOBIUS_COPR... | {
"lo": -6.49,
"mid": 0.51,
"hi": 7.52
} | ||
866aa1 | geo_visible_lattice_v1_655260480_2339 | Let $n = 88$. A lattice point $(x, y)$ is said to be visible from the origin if $\gcd(x, y) = 1$. Let $V$ be the number of visible lattice points $(x, y)$ with $1 \leq x, y \leq n$. Compute the remainder when $96350 \cdot V$ is divided by $50253$. | 20,516 | graphs = [
Graph(
let={
"n": Const(88),
"result": VisibleLatticePoints(n=Ref(name='n')),
"Q": Mod(value=Mul(Const(96350), Ref("result")), modulus=Const(50253)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 3 | 0 | null | null | 1.491 | 2026-02-08T16:41:01.061691Z | {
"verified": true,
"answer": 20516,
"timestamp": "2026-02-08T16:41:02.552769Z"
} | 2621ef | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 127,
"completion_tokens": 5450
},
"timestamp": "2026-02-17T09:31:40.100Z",
"answer": 20516
},
... | 1 | [] | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||||
b4ba90 | sequence_count_fib_divisible_v1_809748730_71 | Let $n = 478$. Define $\phi$ to be Euler's totient function. Let $S$ be the set of all positive divisors of $n$. Define $\text{upper} = \sum_{d \mid n} \phi(d)$.
Let $F_k$ denote the $k$-th Fibonacci number, where $F_1 = 1$, $F_2 = 1$, and $F_k = F_{k-1} + F_{k-2}$ for $k \geq 3$. Let $T$ be the set of all positive in... | 119 | graphs = [
Graph(
let={
"_n": Const(478),
"upper": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"d": Const(3),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper"... | NT | null | COUNT | sympy | K3 | [
"K3"
] | 54c41e | sequence_count_fib_divisible_v1 | null | 6 | 0 | [
"K3"
] | 1 | 0.073 | 2026-02-08T11:18:54.634397Z | {
"verified": true,
"answer": 119,
"timestamp": "2026-02-08T11:18:54.707084Z"
} | 2c1079 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 203,
"completion_tokens": 970
},
"timestamp": "2026-02-14T11:38:08.076Z",
"answer": 119
},
{
... | 1 | [
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
7b9ce2 | nt_sum_totient_over_divisors_v1_677425708_2630 | Let $n$ be the minimum value of $x + y$ where $x$ and $y$ are positive integers such that $xy = 9114361$. Compute the sum of $\phi(d)$ over all positive divisors $d$ of $n$. | 6,038 | graphs = [
Graph(
let={
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(9114361)))), expr=Sum(Var("x"), Var("y")))),
"result": SumOv... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_totient_over_divisors_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.005 | 2026-02-08T05:09:53.174883Z | {
"verified": true,
"answer": 6038,
"timestamp": "2026-02-08T05:09:53.180353Z"
} | 920236 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 165,
"completion_tokens": 946
},
"timestamp": "2026-02-11T22:58:36.505Z",
"answer": 6038
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
08230b | alg_qf_psd_min_v1_601307018_736 | Let $A = \left|\{ t : \text{there exist integers } a, b \text{ with } 1 \leq a \leq 11, 1 \leq b \leq 5 \text{ such that } t = 10a + 14b,\ 24 \leq t \leq 180 \}\right|$ and $B = \sum_{k=1}^{10} \varphi(k) \cdot \left\lfloor \frac{10}{k} \right\rfloor$. Find the minimum value of $30400a^2 + 10944b^2$ over all ordered pa... | 41,344 | graphs = [
Graph(
let={
"_n": Const(30400),
"result": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Ex... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM",
"K2"
] | b46b5e | alg_qf_psd_min_v1 | null | 5 | 0 | [
"K2",
"LIN_FORM"
] | 2 | 0.017 | 2026-03-10T01:23:00.139513Z | {
"verified": true,
"answer": 41344,
"timestamp": "2026-03-10T01:23:00.156350Z"
} | 6c612b | 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": 2942
},
"timestamp": "2026-03-28T23:57:12.721Z",
"answer": 41344
},
{
"... | 2 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma"... | {
"lo": -10,
"mid": -6.42,
"hi": -2.84
} | ||
1565c9 | antilemma_coprime_grid_v1_677425708_459 | Let $\mathcal{P}$ be the set of all ordered pairs $(i,j)$ of positive integers such that $1 \leq i \leq 41$, $1 \leq j \leq 75$, and $\gcd(i,j) = 1$. Let $x$ be the number of elements in $\mathcal{P}$. Let $d_{\text{min}}$ be the smallest integer $d \geq 2$ that divides $537251$. Compute the value of the Bell number $B... | 5 | graphs = [
Graph(
let={
"_n": Const(2),
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(GCD(a=Var("i"), b=Var("j")), Const(1)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(41)), right=IntegerRange(start=Const(1), end=C... | NT | COMB | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR",
"COUNT_COPRIME_GRID"
] | 4dd972 | antilemma_coprime_grid_v1 | bell_mod | 6 | 0 | [
"COUNT_COPRIME_GRID",
"MIN_PRIME_FACTOR"
] | 2 | 0.001 | 2026-02-08T03:33:15.444213Z | {
"verified": true,
"answer": 5,
"timestamp": "2026-02-08T03:33:15.445267Z"
} | 08c9d0 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 236,
"completion_tokens": 3361
},
"timestamp": "2026-02-10T04:11:29.229Z",
"answer": 5
},
{
"id"... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
... | {
"lo": -6.49,
"mid": 0.51,
"hi": 7.52
} | ||
b8d991_n | geo_visible_lattice_v1_1218484723_675 | A game board is a square grid with side length $n$, where $n = \sum_{k=1}^{10} \varphi(k) \lfloor 10/k \rfloor$. A token can be placed on a grid point $(x, y)$ only if $\gcd(x, y) = 1$. How many such valid positions are there on the board? | 1,879 | GEOM | GEOM | COUNT | sympy | K2 | [
"K2"
] | 6897ab | geo_visible_lattice_v1 | null | 3 | null | [
"K2"
] | 1 | 0.06 | 2026-02-25T02:24:50.109919Z | null | 943a24 | b8d991 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 189,
"completion_tokens": 28191
},
"timestamp": "2026-03-30T15:45:43.735Z",
"answer": 1879
},
{
"... | 1 | [
{
"lemma": "K2",
"status": "ok"
}
] | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | |
3639f0 | antilemma_k2_v1_1125832087_1030 | Let $S$ be the set of all real numbers $x$ such that $x^2 - 214x + 5049 = 0$. Let $m = \sum_{k=1}^{N} \phi(k) \left\lfloor \frac{214}{k} \right\rfloor$, where $N$ is the sum of all elements in $S$. Compute the remainder when $55137 \cdot m$ is divided by $86234$. | 10,779 | graphs = [
Graph(
let={
"_m": Const(55137),
"_n": Const(214),
"x": Summation(var="k", start=Const(1), end=SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Const(2)), Mul(Const(-214), Var("x")), Const(5049)), Const(0)))), expr=Mul(EulerPhi(n=Var("k"... | NT | COMB | COMPUTE | sympy | VIETA_SUM | [
"VIETA_SUM/K2",
"K2"
] | 6be084 | antilemma_k2_v1 | null | 6 | 0 | [
"K2",
"VIETA_SUM"
] | 2 | 0.001 | 2026-02-08T03:28:00.433536Z | {
"verified": true,
"answer": 10779,
"timestamp": "2026-02-08T03:28:00.435010Z"
} | 59f1f2 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 210,
"completion_tokens": 6307
},
"timestamp": "2026-02-10T14:30:20.110Z",
"answer": 10779
},
{
"... | 1 | [
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
},
{
"lemma": "VIETA_SU... | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
786b39_l | nt_sum_divisors_mod_v1_1116507919_208 | Let $n$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 14400$. Let $\sigma$ be the sum of the positive divisors of $n$. Compute the remainder when $44121 \cdot \sigma$ is divided by $85439$. | 44,121 | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_divisors_mod_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.001 | 2026-02-08T02:27:55.679154Z | {
"verified": false,
"answer": 17448,
"timestamp": "2026-02-08T02:27:55.680439Z"
} | c21697 | 786b39 | 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": 185,
"completion_tokens": 2598
},
"timestamp": "2026-02-08T19:13:22.996Z",
"answer": 17448
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
... | {
"lo": -0.94,
"mid": 0.82,
"hi": 2.35
} | |
f77b5b | diophantine_sum_product_min_v1_1874849503_48 | Let $N = 23903$. Let $S$ be the number of integers $t$ with $20 \leq t \leq 96$ for which there exist integers $a$ and $b$ such that $1 \leq a \leq 3$, $1 \leq b \leq 9$, and $t = 14a + 6b$. Let $P = 72$. Find the smallest positive integer $x \leq 26$ such that $x(S - x) = P$. Compute $N$ multiplied by this value of $x... | 71,709 | graphs = [
Graph(
let={
"_n": Const(23903),
"S": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=3)), Geq(left=Va... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | diophantine_sum_product_min_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.006 | 2026-02-08T12:46:31.865631Z | {
"verified": true,
"answer": 71709,
"timestamp": "2026-02-08T12:46:31.872071Z"
} | 899763 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 236,
"completion_tokens": 2191
},
"timestamp": "2026-02-10T02:08:54.520Z",
"answer": 71709
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.45,
"hi": 6.36
} | ||
aef821 | comb_bell_compute_v1_1218484723_976 | Let $n$ be the number of integers $t$ such that $t = 3a + 2b$ for some integers $a, b$ with $1 \leq a \leq 3$, $1 \leq b \leq 3$, and $5 \leq t \leq 15$. Let $M = B_n$, where $B_n$ denotes the $n$-th Bell number. Compute $48400 - M$. | 27,253 | graphs = [
Graph(
let={
"_n": Const(48400),
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=3)), Geq(left=Va... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_bell_compute_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-25T02:40:52.017508Z | {
"verified": true,
"answer": 27253,
"timestamp": "2026-02-25T02:40:52.019315Z"
} | e0d648 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 210,
"completion_tokens": 822
},
"timestamp": "2026-03-10T03:21:24.648Z",
"answer": 27253
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -6.52,
"mid": -3.37,
"hi": -0.99
} | ||
b3dbeb | diophantine_fbi2_min_v1_168721529_191 | Let $m = 5$. Let $n$ be the largest integer such that $7^n$ divides $343^{34}$. Define $K$ as the set of all integers $t$ such that $23 \leq t \leq 130$ and there exist positive integers $a, b$ with $1 \leq a \leq 12$, $1 \leq b \leq 11$, and $t = 7a + 3b + 13$. Let $k$ be the number of elements in $K$.
Let $u$ be th... | 2 | graphs = [
Graph(
let={
"_m": Const(5),
"_n": MaxKDivides(target=Pow(Const(343), Const(34)), base=Const(7)),
"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'), righ... | NT | null | EXTREMUM | sympy | COUNT_SUM_EQUALS | [
"K14/V5",
"LIN_FORM"
] | e3d8a9 | diophantine_fbi2_min_v1 | null | 7 | 0 | [
"COUNT_SUM_EQUALS",
"K14",
"LIN_FORM",
"V5"
] | 4 | 0.152 | 2026-02-08T12:54:05.245876Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-02-08T12:54:05.398238Z"
} | dd6c2d | CC BY 4.0 | [
{
"id": 4,
"model": "NousResearch/Hermes-4-405B",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 254,
"completion_tokens": 673
},
"timestamp": "2026-02-09T14:19:20.875Z",
"answer": 2
},
{
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
... | {
"lo": -6.69,
"mid": -2.39,
"hi": 1.85
} | ||
f68429 | diophantine_fbi2_count_v1_1742523217_1746 | Let $m=4$ and $n=4$.
Consider all ordered pairs $(x,y)$ of positive integers such that $xy=32400$, and let $k$ be the minimum possible value of $x+y$ over all such pairs.
Let $T$ be the number of integers $t$ for which there exist integers $a$ and $b$ satisfying $1\le a\le 217$, $1\le b\le 781$, $27\le t\le 17703$, a... | 12 | graphs = [
Graph(
let={
"_m": Const(4),
"_n": Const(4),
"k": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(32400)))), expr=... | NT | null | COUNT | sympy | B3 | [
"LIN_FORM/COUNT_FIB_DIVISIBLE/B3"
] | cb7aba | diophantine_fbi2_count_v1 | null | 8 | 0 | [
"B3",
"COUNT_FIB_DIVISIBLE",
"LIN_FORM"
] | 3 | 0.086 | 2026-02-08T04:12:50.830515Z | {
"verified": true,
"answer": 12,
"timestamp": "2026-02-08T04:12:50.916044Z"
} | c2ace3 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 375,
"completion_tokens": 3329
},
"timestamp": "2026-02-10T15:50:49.892Z",
"answer": 12
},
{
"id... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok_later"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_SUB",
"s... | {
"lo": -0.04,
"mid": 2.43,
"hi": 4.79
} | ||
76e26a | geo_count_lattice_rect_v1_677425708_976 | Let $a = 66$ and $b = 128$. Define $r$ to be the number of lattice points $(x, y)$ with $0 \leq x \leq 66$ and $0 \leq y \leq 128$. Let $Q$ be the remainder when $44121 \cdot r$ is divided by $55774$. Compute the value of $Q$. | 10,965 | graphs = [
Graph(
let={
"a": Const(66),
"b": Const(128),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"Q": Mod(value=Mul(Const(44121), Ref("result")), modulus=Const(55774)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.001 | 2026-02-08T03:54:44.550169Z | {
"verified": true,
"answer": 10965,
"timestamp": "2026-02-08T03:54:44.550973Z"
} | 4b9471 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 200,
"completion_tokens": 3106
},
"timestamp": "2026-02-09T14:32:58.144Z",
"answer": 10965
},
{
"... | 1 | [] | {
"lo": -0.05,
"mid": 2.89,
"hi": 5.27
} | ||||
101d16 | nt_lcm_compute_v1_168721529_1654 | Let $a$ be the number of positive integers $n$ with $1 \le n \le 15428$ such that $n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{7}$. Let $b = 2949$, and let $r$ be the least common multiple of $a$ and $b$. Compute the remainder when $57183 \cdot r$ is divided by $83669$. | 82,161 | graphs = [
Graph(
let={
"_n": Const(83669),
"a": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(15428)), Congruent(a=Var(name='n'), b=Floor(arg=Div(left=Var(name='n'), right=Const(value=2))), modulus=Const(value=7))))),
... | NT | null | COMPUTE | sympy | L3C | [
"L3C"
] | 73f8b0 | nt_lcm_compute_v1 | null | 5 | 0 | [
"L3C"
] | 1 | 0.001 | 2026-02-08T13:49:34.141386Z | {
"verified": true,
"answer": 82161,
"timestamp": "2026-02-08T13:49:34.142772Z"
} | 3ab65c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 211,
"completion_tokens": 6415
},
"timestamp": "2026-02-09T19:56:48.710Z",
"answer": 42529
},
{
... | 1 | [
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
... | {
"lo": 1.69,
"mid": 5.03,
"hi": 8.38
} | ||
f10416 | comb_binomial_compute_v1_1978505735_5643 | Let $k$ be the smallest divisor of $4235$ that is at least $2$. Compute $\binom{12}{k}$. | 792 | graphs = [
Graph(
let={
"_n": Const(2),
"n": Const(12),
"k": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(4235))))),
"result": Binom(n=Ref("n"), k=Ref("k")),
},
goal=... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | comb_binomial_compute_v1 | null | 3 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.001 | 2026-02-08T19:08:24.875261Z | {
"verified": true,
"answer": 792,
"timestamp": "2026-02-08T19:08:24.876193Z"
} | dc79e8 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 88,
"completion_tokens": 498
},
"timestamp": "2026-02-16T18:34:20.030Z",
"answer": 792
},
{
"id": 11,
... | 2 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
2fca2f | comb_count_derangements_v1_124444284_4767 | Let $n$ be the number of nonnegative integers $j$ such that $0 \leq j \leq 33028$ and $\binom{33028}{j}$ is odd. Compute the subfactorial of $n$. | 14,833 | graphs = [
Graph(
let={
"_n": Const(33028),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Ref("_n")), Eq(Mod(value=Binom(n=Const(33028), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')),
"r... | COMB | null | COUNT | sympy | V8 | [
"V8"
] | 86348e | comb_count_derangements_v1 | null | 7 | 0 | [
"V8"
] | 1 | 0.002 | 2026-02-08T06:13:06.685380Z | {
"verified": true,
"answer": 14833,
"timestamp": "2026-02-08T06:13:06.686905Z"
} | 09665f | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 161,
"completion_tokens": 1607
},
"timestamp": "2026-02-24T05:39:33.693Z",
"answer": 14833
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
}
] | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
6a1412 | nt_max_prime_below_v1_1918700295_2573 | Let $T$ be the set of all positive integers $t$ such that $14 \leq t \leq 8912$ and $t = 8a + 6b$ for some positive integers $a \leq 811$ and $b \leq 404$. Let $n = |T|$. Let $M$ be the largest prime number at most $13924$. Let $c$ be the number of positive integers $j \leq n$ such that $j^3 \leq 87765160384$. Compute ... | 78,794 | graphs = [
Graph(
let={
"_m": Const(88271),
"_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=811)), Geq(left... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM/C3"
] | 0b75f5 | nt_max_prime_below_v1 | negation_mod | 6 | 0 | [
"C3",
"LIN_FORM"
] | 2 | 0.312 | 2026-02-08T07:59:56.869226Z | {
"verified": true,
"answer": 78794,
"timestamp": "2026-02-08T07:59:57.180958Z"
} | 5c02c7 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 174,
"completion_tokens": 8099
},
"timestamp": "2026-02-13T13:55:01.796Z",
"answer": 78794
},
... | 1 | [
{
"lemma": "C3",
"status": "ok_later"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
d265fc | nt_count_digit_sum_v1_458359167_5558 | Let $A$ be the set of positive integers $n \leq 69999$ such that $n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{7}$. Let $a$ be the number of elements in $A$. Compute the number of positive integers $n \leq a$ such that the sum of the digits of $n$ is $23$. Let this count be $b$. Find the remainder when $36859 ... | 18,048 | graphs = [
Graph(
let={
"_n": Const(69999),
"upper": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_n")), Congruent(a=Var(name='n'), b=Floor(arg=Div(left=Var(name='n'), right=Const(value=2))), modulus=Const(value=7))))),
... | NT | null | COUNT | sympy | L3C | [
"L3C"
] | 73f8b0 | nt_count_digit_sum_v1 | null | 6 | 0 | [
"L3C"
] | 1 | 0.87 | 2026-02-08T12:35:44.483713Z | {
"verified": true,
"answer": 18048,
"timestamp": "2026-02-08T12:35:45.353473Z"
} | f5bb1f | 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": 2416
},
"timestamp": "2026-02-15T02:33:07.293Z",
"answer": 18048
},
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": ... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
136225 | nt_num_divisors_compute_v1_124444284_3759 | Let $n = 26896$. Compute the number of positive divisors of $n$. | 15 | graphs = [
Graph(
let={
"n": Const(26896),
"result": NumDivisors(n=Ref("n")),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | V5 | [
"MIN_PRIME_FACTOR"
] | bc3776 | nt_num_divisors_compute_v1 | null | 2 | 0 | [
"MIN_PRIME_FACTOR",
"V5"
] | 2 | 0.008 | 2026-02-08T05:35:16.379726Z | {
"verified": true,
"answer": 15,
"timestamp": "2026-02-08T05:35:16.387910Z"
} | 07873a | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 77,
"completion_tokens": 301
},
"timestamp": "2026-02-11T22:54:36.963Z",
"answer": 45
},
{
"id": 11,
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
d4c81e | modular_inverse_v1_1520064083_1361 | Let $a = 141$ and $m = 461$. Let $u$ be the number of ordered pairs $(i, j)$ with $1 \le i \le 20$ and $1 \le j \le 23$. Determine the smallest positive integer $x$ such that $1 \le x \le u$ and $a \cdot x \equiv 1 \pmod{m}$. Find the remainder when $44121$ multiplied by this value of $x$ is divided by $74990$. | 16,706 | graphs = [
Graph(
let={
"a": Const(141),
"m": Const(461),
"upper": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(20)), right=IntegerRange(start=Const(1), end=Const(23)))),
"result": MinOverSet(set=SolutionsSet(var=Var("x"), cond... | NT | null | EXTREMUM | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | modular_inverse_v1 | null | 5 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.022 | 2026-02-08T03:56:39.205634Z | {
"verified": true,
"answer": 16706,
"timestamp": "2026-02-08T03:56:39.227183Z"
} | 37f8d3 | 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": 1114
},
"timestamp": "2026-02-10T16:12:58.250Z",
"answer": 16706
},
{
"... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
}
] | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
55c53d | comb_count_partitions_v1_1520064083_4447 | Let $n$ be the number of positive integers at most $80$ whose digit sum is even. Determine the number of integer partitions of $n$. | 37,338 | graphs = [
Graph(
let={
"_n": Const(80),
"n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_n")), Eq(Mod(value=DigitSum(Var("n")), modulus=Const(2)), Const(0))))),
"result": Partition(arg=Ref(name='n')),
},
... | COMB | null | COUNT | sympy | L3B | [
"L3B"
] | cc148f | comb_count_partitions_v1 | null | 5 | 0 | [
"L3B"
] | 1 | 0.001 | 2026-02-08T06:16:26.627426Z | {
"verified": true,
"answer": 37338,
"timestamp": "2026-02-08T06:16:26.628368Z"
} | fe3e41 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 141,
"completion_tokens": 1251
},
"timestamp": "2026-02-24T05:46:48.127Z",
"answer": 37338
},
{
"... | 1 | [
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "L3B",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
5cd6f1 | nt_sum_divisors_mod_v1_168721529_1296 | Let $n$ be the number of integers $t$ such that $9 \leq t \leq 1694$ and there exist integers $a$ and $b$ with $1 \leq a \leq 218$, $1 \leq b \leq 84$, and $t = 7a + 2b$. Let $\sigma$ be the sum of all positive divisors of $n$. Let $M = 11621$. Compute the remainder when $\sigma$ is divided by $M$. | 5,952 | 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=218)), Geq(left=Var(name='b'), right=Const(value... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_sum_divisors_mod_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.003 | 2026-02-08T13:33:54.024107Z | {
"verified": true,
"answer": 5952,
"timestamp": "2026-02-08T13:33:54.026633Z"
} | e86e0d | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 226,
"completion_tokens": 6145
},
"timestamp": "2026-02-09T15:21:36.510Z",
"answer": 5952
},
{
"i... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status... | {
"lo": -1.95,
"mid": 2.14,
"hi": 6.33
} | ||
a054d9 | diophantine_fbi2_min_v1_717093673_3164 | Let $k$ be the number of integers $t$ such that $20 \leq t \leq 292$ and there exist positive integers $a \leq 17$, $b \leq 9$ satisfying $t = 14a + 6b$. Let $u$ be the number of integers $t_1$ such that $31 \leq t_1 \leq 469$ and there exist positive integers $a \leq 45$, $b \leq 3$ satisfying $t_1 = 9a + 21b + 1$. Le... | 8,269 | graphs = [
Graph(
let={
"_m": Const(4),
"_n": Const(53084),
"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=... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | diophantine_fbi2_min_v1 | null | 7 | 0 | [
"LIN_FORM"
] | 1 | 0.016 | 2026-02-08T17:24:49.216839Z | {
"verified": true,
"answer": 8269,
"timestamp": "2026-02-08T17:24:49.232603Z"
} | 4971f6 | 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": 6148
},
"timestamp": "2026-02-18T01:26:55.750Z",
"answer": 8269
},
{... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
21a358 | antilemma_v7_kummer_168721529_199 | Let $c=85264$.
Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy=212521$. Let $T$ be the set of all values of $x+y$ as $(x,y)$ ranges over $S$, and let $m$ be the minimum element of $T$.
Let $U$ be the set of all integers $n$ such that $1\le n\le 11529$ and
$$n\equiv \left\lfloor\frac... | 85,254 | graphs = [
Graph(
let={
"_c": Const(85264),
"_m": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(212521)))), expr=Sum(Var("x"), Var("y")... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/V7",
"B3/L3C/V7",
"V7"
] | f331cf | antilemma_v7_kummer | null | 8 | 0 | [
"B3",
"COPRIME_PAIRS",
"L3C",
"V7"
] | 4 | 0.005 | 2026-02-08T12:54:12.001801Z | {
"verified": true,
"answer": 85254,
"timestamp": "2026-02-08T12:54:12.006873Z"
} | a72568 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 363,
"completion_tokens": 2346
},
"timestamp": "2026-02-09T02:26:14.200Z",
"answer": 85254
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3C",
"status": ... | {
"lo": -1.99,
"mid": 2.14,
"hi": 6.33
} | ||
91f4dd | diophantine_fbi2_min_v1_1742523217_3 | Let $u$ be the number of ordered pairs $(i,j)$ of positive integers with $1 \leq i \leq 4$, $1 \leq j \leq 8$, and $\gcd(i,j) = 1$. Let $d$ be the smallest integer such that $d \geq 2$, $d \leq u$, $d$ divides $12$, and $\frac{12}{d} \geq 6$. Compute the smallest positive integer $k$ such that the $k$-th Fibonacci numb... | 6 | graphs = [
Graph(
let={
"_n": Const(2),
"k": Const(12),
"upper": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(GCD(a=Var("i"), b=Var("j")), Const(1)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(4)), right=Int... | NT | null | EXTREMUM | sympy | COUNT_SUM_EQUALS | [
"COUNT_COPRIME_GRID",
"MIN_PRIME_FACTOR"
] | d38484 | diophantine_fbi2_min_v1 | null | 5 | 0 | [
"COUNT_COPRIME_GRID",
"COUNT_SUM_EQUALS",
"MIN_PRIME_FACTOR"
] | 3 | 0.069 | 2026-02-08T02:50:17.374636Z | {
"verified": true,
"answer": 6,
"timestamp": "2026-02-08T02:50:17.443327Z"
} | 9be8d9 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 242,
"completion_tokens": 1253
},
"timestamp": "2026-02-08T19:52:34.920Z",
"answer": 6
},
{
"id":... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"... | {
"lo": -4.35,
"mid": -2.1,
"hi": 0.02
} | ||
405bc9 | modular_modexp_compute_v1_601307018_2732 | Let $a$ be the largest prime $n$ with $2 \le n \le 40$. Let $e$ be the largest positive integer $d$ such that $d^2 \le 4970614$ and $d \mid 4970614$. Define $R = a^e \bmod 89401$. Find the remainder when $44121R$ is divided by $89279$. | 65,133 | graphs = [
Graph(
let={
"_m": Const(40),
"_n": Const(89279),
"a": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_m")), IsPrime(Var("n"))))),
"e": MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW",
"B3_CLOSEST"
] | 8a13ed | modular_modexp_compute_v1 | null | 4 | 0 | [
"B3_CLOSEST",
"MAX_PRIME_BELOW"
] | 2 | 0.005 | 2026-03-10T03:23:41.023575Z | {
"verified": true,
"answer": 65133,
"timestamp": "2026-03-10T03:23:41.028128Z"
} | 209847 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 197,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T06:24:57.845Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "B3_CLOSEST",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
},
{
... | {
"lo": 1.23,
"mid": 4.27,
"hi": 6.7
} | ||
7e44c4 | nt_count_with_divisor_count_v1_2051736721_5341 | Let $d_{\text{max}}$ be the largest positive divisor of $35295337$ that is at most $5929$. Determine the number of positive integers $n \leq d_{\text{max}}$ that have exactly $11$ positive divisors. Multiply this count by $78205$ and compute the result. | 78,205 | graphs = [
Graph(
let={
"_n": Const(5929),
"upper": MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Leq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(35295337))))),
"div_count": Const(11),
"result": CountOverSe... | NT | null | COUNT | sympy | MAX_DIVISOR | [
"MAX_DIVISOR"
] | 51757e | nt_count_with_divisor_count_v1 | null | 5 | 0 | [
"MAX_DIVISOR"
] | 1 | 3.293 | 2026-02-08T18:30:21.817862Z | {
"verified": true,
"answer": 78205,
"timestamp": "2026-02-08T18:30:25.110662Z"
} | 993991 | 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": 6867
},
"timestamp": "2026-02-18T17:34:43.872Z",
"answer": 78205
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
"lemma": "V8",
"status... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
e7deb4 | comb_binomial_compute_v1_784195855_1072 | Let $n = 13$ and let $k$ be the smallest divisor of $1001$ that is at least $2$. Compute the remainder when $60503 \cdot \binom{n}{k}$ is divided by $62320$. | 60,348 | graphs = [
Graph(
let={
"_n": Const(1001),
"n": Const(13),
"k": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Ref("_n"))))),
"result": Binom(n=Ref("n"), k=Ref("k")),
"Q": Mod(val... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | comb_binomial_compute_v1 | null | 3 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.002 | 2026-02-08T04:49:34.163126Z | {
"verified": true,
"answer": 60348,
"timestamp": "2026-02-08T04:49:34.165162Z"
} | b7c1ce | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 163,
"completion_tokens": 1210
},
"timestamp": "2026-02-11T22:14:47.952Z",
"answer": 60348
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V3",
"status": "no... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
d64b7f_n | alg_poly3_min_v1_1218484723_170 | An engineer evaluates energy outputs modeled by the expression $-133a^3 - 96ab^2 + 64b^3 + 48a^2b$ for integer configurations $a$ and $b$ between $1$ and $238$. The system records the minimum possible output. What is this minimum value modulo $86369$? | 29,953 | ALG | null | COMPUTE | sympy | QF_PSD_COUNT_LEQ | [
"QF_PSD_COUNT_LEQ/QF_PSD_DISTINCT",
"K3/POLY_ORBIT_HENSEL"
] | 066493 | alg_poly3_min_v1 | null | 3 | null | [
"K3",
"POLY_ORBIT_HENSEL",
"QF_PSD_COUNT_LEQ",
"QF_PSD_DISTINCT"
] | 4 | 0.328 | 2026-02-25T01:51:53.939714Z | null | cceb94 | d64b7f | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 182,
"completion_tokens": 7188
},
"timestamp": "2026-03-30T15:05:46.391Z",
"answer": 29953
},
{
"... | 1 | [
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "POLY_ORBIT_HENSEL",
"status": "ok_later"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
},
{
"lemma": "QF_PSD_DISTINCT",
"status": "ok_later"
}
] | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | |
a0f645 | diophantine_fbi2_min_v1_124444284_8204 | Let $d_1$ be the smallest positive integer $d$ such that $d \geq 2$, $d \leq 43$, $d$ divides 33, and $\frac{33}{d} \geq 3$. Let $d_2$ be the smallest prime divisor of 1517. Compute $d_1^2 + 4d_1 + d_2$. | 58 | graphs = [
Graph(
let={
"_n": Const(2),
"k": Const(33),
"upper": Const(43),
"result": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Leq(Var("d"), Ref("upper")), Divides(divisor=Var("d"), dividend=Ref("k")), Geq(Div(Ref("k"),... | NT | null | EXTREMUM | sympy | C4 | [
"MIN_PRIME_FACTOR"
] | 76121b | diophantine_fbi2_min_v1 | quadratic_mod | 4 | 0 | [
"C4",
"MIN_PRIME_FACTOR"
] | 2 | 0.054 | 2026-02-08T09:36:06.935574Z | {
"verified": true,
"answer": 58,
"timestamp": "2026-02-08T09:36:06.989428Z"
} | a5883f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 131,
"completion_tokens": 851
},
"timestamp": "2026-02-14T05:06:37.356Z",
"answer": 58
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
acff0c | comb_binomial_compute_v1_677425708_633 | Let $n$ be the number of integers $t$ such that $9 \leq t \leq 30$ and there exist integers $a$ and $b$ with $1 \leq a \leq 2$, $1 \leq b \leq 8$, and $t = 7a + 2b$. Compute the remainder when $\binom{n}{9}$ is multiplied by $44121$ and then divided by $96083$. | 20,241 | graphs = [
Graph(
let={
"_n": Const(96083),
"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=Va... | ALG | COMB | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_binomial_compute_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T03:38:05.803681Z | {
"verified": true,
"answer": 20241,
"timestamp": "2026-02-08T03:38:05.805612Z"
} | 76ee42 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 215,
"completion_tokens": 2969
},
"timestamp": "2026-02-08T20:51:54.850Z",
"answer": 20241
},
{
"... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} |
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