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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
aecd8e | nt_gcd_compute_v1_151522320_640 | Let $a = 374462$ and $b = 646798$. Compute $\gcd(a, b)$. Let $N$ be the number of ordered pairs $(i, j)$ of positive integers with $1 \leq i \leq 56$ and $1 \leq j \leq 85$ such that $\gcd(i, j) = 1$. Find the remainder when $N \cdot \gcd(a, b)$ is divided by $92043$. | 36,532 | graphs = [
Graph(
let={
"_n": Const(92043),
"a": Const(374462),
"b": Const(646798),
"result": GCD(a=Ref("a"), b=Ref("b")),
"Q": Mod(value=Mul(CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(GCD(a=Var("i"), b=Var... | NT | null | COMPUTE | sympy | COUNT_COPRIME_GRID | [
"COUNT_COPRIME_GRID"
] | 53d469 | nt_gcd_compute_v1 | affine_mod | 4 | 0 | [
"COUNT_COPRIME_GRID"
] | 1 | 0.004 | 2026-02-08T03:26:42.159225Z | {
"verified": true,
"answer": 36532,
"timestamp": "2026-02-08T03:26:42.163573Z"
} | 4decc3 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 215,
"completion_tokens": 3519
},
"timestamp": "2026-02-10T13:28:07.814Z",
"answer": 36532
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
a1511f | diophantine_fbi2_min_v1_48377204_1812 | Let $k$ be the number of integers $t$ such that $21 \leq t \leq 102$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 4$, $1 \leq b \leq 6$, and $t = 12a + 9b$. Let $\text{upper} = 32$. Define $d$ to be an integer satisfying $2 \leq d \leq \text{upper}$, $d$ divides $k$, and $\frac{k}{d} \geq 5$. Let $... | 27,592 | graphs = [
Graph(
let={
"_n": Const(5),
"k": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=4)), Geq(left=Var(na... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | diophantine_fbi2_min_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.005 | 2026-02-08T16:26:23.983823Z | {
"verified": true,
"answer": 27592,
"timestamp": "2026-02-08T16:26:23.988871Z"
} | 424f28 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 200,
"completion_tokens": 2522
},
"timestamp": "2026-02-17T02:58:21.222Z",
"answer": 27592
},
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": ... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
7d81b7 | nt_count_digit_sum_v1_655260480_2034 | Let $s$ be the number of nonnegative integers $j$ such that $j \leq 16908$ and $\binom{16908}{j}$ is odd. Define $T$ to be the number of positive integers $n \leq 58081$ such that the sum of the decimal digits of $n$ is equal to $s$. Compute $T$. | 2,996 | graphs = [
Graph(
let={
"_n": Const(16908),
"upper": Const(58081),
"target_sum": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Summation(var="k", start=Sub(Binom(n=Const(20), k=Const(20)), Const(1)), end=Const(5), expr=Mul(Pow(Const(-1), Var("k")... | COMB | null | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING",
"ZERO_BINOM_N",
"V8"
] | c1c391 | nt_count_digit_sum_v1 | null | 6 | 0 | [
"BINOMIAL_ALTERNATING",
"V8",
"ZERO_BINOM_N"
] | 3 | 3.053 | 2026-02-08T16:32:30.980473Z | {
"verified": true,
"answer": 2996,
"timestamp": "2026-02-08T16:32:34.033347Z"
} | 2e25f4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 124,
"completion_tokens": 3836
},
"timestamp": "2026-02-17T06:07:42.456Z",
"answer": 2996
},
{... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma... | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||
52eca5 | nt_count_intersection_v1_124444284_997 | Let $N$ be the number of prime numbers $n$ such that $2 \leq n \leq 48611$. Compute the number of positive integers $n$ not exceeding $N$ that are divisible by 7 and relatively prime to 12. | 238 | graphs = [
Graph(
let={
"_n": Const(2),
"N": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Const(48611)), IsPrime(Var("n"))))),
"a": Const(7),
"b": Const(12),
"result": CountOverSet(set=SolutionsS... | NT | null | COUNT | sympy | COUNT_PRIMES | [
"COUNT_PRIMES"
] | 07c874 | nt_count_intersection_v1 | null | 5 | 0 | [
"COUNT_PRIMES"
] | 1 | 5.165 | 2026-02-08T03:38:32.898916Z | {
"verified": true,
"answer": 238,
"timestamp": "2026-02-08T03:38:38.064151Z"
} | ec3c3c | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 169,
"completion_tokens": 3669
},
"timestamp": "2026-02-09T08:24:17.238Z",
"answer": 238
},
{
"i... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"stat... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
bcbf7b | diophantine_fbi2_min_v1_397696148_260 | Let $d$ be a positive divisor of $71339959$ such that $d \geq 2$. Let $N$ be the smallest such $d$. Find the smallest integer $k \geq 2$ such that $k$ is prime and $k \leq N$. Now, let $S$ be the set of all integers $d \geq 2$ such that $d$ divides $21$ and $\frac{21}{d} \geq 3$. Determine the value of the smallest ele... | 3 | graphs = [
Graph(
let={
"k": Const(21),
"upper": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(71339959)))))), Is... | NT | null | EXTREMUM | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/MAX_PRIME_BELOW"
] | e4e16c | diophantine_fbi2_min_v1 | null | 4 | 0 | [
"MAX_PRIME_BELOW",
"MIN_PRIME_FACTOR"
] | 2 | 0.005 | 2026-02-08T11:24:00.463450Z | {
"verified": true,
"answer": 3,
"timestamp": "2026-02-08T11:24:00.468943Z"
} | 2ffe71 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 158,
"completion_tokens": 2025
},
"timestamp": "2026-02-14T13:34:34.014Z",
"answer": 3
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_... | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
7f142b | antilemma_sum_equals_v1_124444284_8730 | Let $n = 72$. Let $x$ be the number of ordered pairs $(i, j)$ of positive integers such that $i + j = 72$, $1 \leq i \leq 70$, and $1 \leq j \leq 70$. Compute the remainder when $80820x$ is divided by $75581$. | 59,167 | graphs = [
Graph(
let={
"_n": Const(72),
"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(70)), right=IntegerRange(start=Const(1), end=Con... | COMB | GEOM | COMPUTE | sympy | LIN_FORM | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 3 | 0 | [
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 2 | 0.038 | 2026-02-08T11:52:58.645845Z | {
"verified": true,
"answer": 59167,
"timestamp": "2026-02-08T11:52:58.683406Z"
} | 784ba7 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 186,
"completion_tokens": 1571
},
"timestamp": "2026-02-24T14:57:26.931Z",
"answer": 59167
},
{
"... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SU... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
7641b3 | nt_max_prime_below_v1_1439011603_950 | Let $S$ be the set of all positive integers $n_1$ with $1 \le n_1 \le 2$ such that the sum of the digits of $n_1$ is odd. Let $c$ be the number of elements in $S$. Determine the value of the largest prime number $n$ such that $n \ge c$ and $n \le 82944$. | 82,939 | graphs = [
Graph(
let={
"upper": Const(82944),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(1)), Leq(Var("n1"), Const(2)), Eq(Mod(value=DigitSum(Var("n1")), modulus=Cons... | NT | null | EXTREMUM | sympy | L3B | [
"L3B"
] | cc148f | nt_max_prime_below_v1 | null | 3 | 0 | [
"L3B"
] | 1 | 3.068 | 2026-02-08T15:49:47.397621Z | {
"verified": true,
"answer": 82939,
"timestamp": "2026-02-08T15:49:50.465390Z"
} | 85260b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 133,
"completion_tokens": 2515
},
"timestamp": "2026-02-16T14:10:15.069Z",
"answer": 82939
},
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3B",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
251b14 | comb_catalan_compute_v1_151522320_159 | Let $n$ be the number of integers $t$ such that $10 \leq t \leq 34$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 3$, $1 \leq b \leq 4$, and $t = 6a + 4b$. Let $C_n$ denote the $n$-th Catalan number. Compute the remainder when $81710 \cdot C_n$ is divided by $95929$. | 47,172 | graphs = [
Graph(
let={
"_n": Const(95929),
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=3)), Geq(left=Va... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_catalan_compute_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.003 | 2026-02-08T03:00:32.408486Z | {
"verified": true,
"answer": 47172,
"timestamp": "2026-02-08T03:00:32.411752Z"
} | 89f67b | 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": 2230
},
"timestamp": "2026-02-10T12:29:24.010Z",
"answer": 47172
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
eb97a1 | modular_mod_compute_v1_1978505735_6890 | Let $a = -3081$ and $m = 4900$. Define $r$ to be the remainder when $a$ is divided by $m$, so $r = a \mod m$. Let $S$ be the set of all positive integers $n$ such that $1 \leq n \leq 81$ and $n \equiv 0 \pmod{81}$. Compute the sum of all elements in $S$, subtract $r$ from this sum, and then take the result modulo $6151... | 59,772 | graphs = [
Graph(
let={
"_n": Const(61510),
"a": Const(-3081),
"m": Const(4900),
"result": Mod(value=Ref("a"), modulus=Ref("m")),
"Q": Mod(value=Sub(SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Cons... | NT | null | COMPUTE | sympy | SUM_DIVISIBLE | [
"SUM_DIVISIBLE"
] | 75b1e7 | modular_mod_compute_v1 | negation_mod | 2 | 0 | [
"SUM_DIVISIBLE"
] | 1 | 0.002 | 2026-02-08T19:52:41.955799Z | {
"verified": true,
"answer": 59772,
"timestamp": "2026-02-08T19:52:41.958055Z"
} | 6aa596 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 165,
"completion_tokens": 922
},
"timestamp": "2026-02-18T23:38:12.377Z",
"answer": 59772
},
{... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "SUM_DIVISIBLE",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
977951 | nt_count_primes_v1_1918700295_4518 | Let $k$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p < q$, $pq = 24$, and $\gcd(p, q) = 1$. Let $S$ be the set of all prime numbers $n$ such that $k \leq n \leq 10267$. Let $N$ be the number of elements in $S$. Compute the remainder when $42979 \cdot N$ is divided by... | 12,335 | graphs = [
Graph(
let={
"upper": Const(10267),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'),... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_count_primes_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.507 | 2026-02-08T09:25:07.279297Z | {
"verified": true,
"answer": 12335,
"timestamp": "2026-02-08T09:25:07.785975Z"
} | 6cb205 | 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": 1352
},
"timestamp": "2026-02-14T04:05:59.087Z",
"answer": 12335
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
adec28 | comb_count_permutations_fixed_v1_153355830_1295 | Let $n = 7$. Let $k$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 18$, $\gcd(p, q) = 1$, and $p < q$. Compute $\binom{n}{k} \cdot !{(n - k)}$, where $!m$ denotes the number of derangements of $m$ elements. | 924 | graphs = [
Graph(
let={
"n": Const(7),
"k": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=18)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')... | NT | COMB | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_count_permutations_fixed_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.002 | 2026-02-08T06:17:04.910453Z | {
"verified": true,
"answer": 924,
"timestamp": "2026-02-08T06:17:04.912027Z"
} | 90b132 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 137,
"completion_tokens": 1177
},
"timestamp": "2026-02-12T22:59:01.649Z",
"answer": 924
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
... | {
"lo": -5.92,
"mid": -3.14,
"hi": 0.26
} | ||
536d37 | nt_count_primes_v1_1918700295_2540 | 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 $m$ be the number of elements in $S$. Determine the number of prime numbers $n$ such that $m \leq n \leq 12996$. | 1,547 | graphs = [
Graph(
let={
"upper": Const(12996),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'),... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_count_primes_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.301 | 2026-02-08T07:56:57.005440Z | {
"verified": true,
"answer": 1547,
"timestamp": "2026-02-08T07:56:57.306105Z"
} | 07824e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 130,
"completion_tokens": 2389
},
"timestamp": "2026-02-13T13:53:19.901Z",
"answer": 1547
},
{... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
5174de | nt_max_prime_below_v1_717093673_3275 | Let $n$ be the largest prime number such that $2 \le n \le 45369$. Let $d_{\text{min}}$ be the smallest integer $d \ge 2$ that divides 5000567. Define $Q$ to be the Bell number $B_k$, where $k = n \bmod d_{\text{min}}$. Compute the value of $Q$. | 4,140 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": Const(45369),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Ref("upper")), IsPrime(Var("n"))))),
"Q": Bell(Mod(value=Abs(arg=Ref(name='result')), modul... | NT | COMB | EXTREMUM | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | 58d7e9 | nt_max_prime_below_v1 | bell_mod | 5 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 1.391 | 2026-02-08T17:28:24.770883Z | {
"verified": true,
"answer": 4140,
"timestamp": "2026-02-08T17:28:26.162117Z"
} | 5ff7c5 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 130,
"completion_tokens": 1911
},
"timestamp": "2026-02-18T02:06:47.419Z",
"answer": 4140
},
{... | 1 | [
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status":... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
196682 | antilemma_sum_factor_cartesian_v1_865884756_91 | Let $T$ be the set of all ordered pairs $(i, j)$ of positive integers such that $1 \leq i \leq 10$ and $1 \leq j \leq 22$. Define $x$ to be the sum of $i \cdot j$ over all pairs $(i, j)$ in $T$. Let $S$ be the set of all positive integers $n$ such that $1 \leq n \leq 279$ and $n \equiv \left\lfloor \frac{n}{2} \right\r... | 37,653 | graphs = [
Graph(
let={
"_n": Const(2),
"x": SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Const(1), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(10)), right=IntegerRange(start=Const(1), end=Const(22)))), expr=Mu... | NT | null | COMPUTE | sympy | L3C | [
"L3C",
"SUM_FACTOR_CARTESIAN"
] | fb4140 | antilemma_sum_factor_cartesian_v1 | quadratic_mod | 4 | 0 | [
"L3C",
"SUM_FACTOR_CARTESIAN"
] | 2 | 0.003 | 2026-02-08T15:09:56.141381Z | {
"verified": true,
"answer": 37653,
"timestamp": "2026-02-08T15:09:56.144089Z"
} | 199c18 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 277,
"completion_tokens": 1861
},
"timestamp": "2026-02-10T03:52:06.011Z",
"answer": 37653
}
] | 2 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_FACTOR_CARTESIAN",
"s... | {
"lo": -10,
"mid": -2.04,
"hi": 5.92
} | ||
6a9f7a | diophantine_fbi2_min_v1_1520064083_6389 | Let $k = 15$. Consider the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = 10$. Let $u$ be the maximum value of $xy$ over all such pairs. Find the smallest divisor $d \geq 2$ of $k$ such that $d \leq u$ and $\frac{k}{d} \geq 5$. | 3 | graphs = [
Graph(
let={
"k": Const(15),
"upper": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Const(10)))), expr=Mul(Var("x"), Var("y")))),
... | NT | null | EXTREMUM | sympy | K2 | [
"B1"
] | 5b950e | diophantine_fbi2_min_v1 | null | 4 | 0 | [
"B1",
"K2"
] | 2 | 0.746 | 2026-02-08T08:02:49.759668Z | {
"verified": true,
"answer": 3,
"timestamp": "2026-02-08T08:02:50.505690Z"
} | e41999 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 143,
"completion_tokens": 499
},
"timestamp": "2026-02-15T19:09:25.257Z",
"answer": 3
},
{
"id": 11,
"... | 2 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.73,
"hi": -5.46
} | ||
52e6e4 | modular_sum_quadratic_residues_v1_151522320_2283 | Let $m = 2$ and $n = 4$. Let $N$ be the number of positive integers $k$ such that $1 \leq k \leq 12195$, $9$ divides $k$, and $\gcd(k, 14) = 1$.
Let $p$ be the largest prime number $q$ such that $m \leq q \leq N$.
Compute $\frac{p(p-1)}{n}$. | 83,088 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(4),
"p": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_m")), Leq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(12195)), Div... | NT | null | SUM | sympy | C5 | [
"C5/MAX_PRIME_BELOW"
] | e03314 | modular_sum_quadratic_residues_v1 | null | 5 | 0 | [
"C5",
"MAX_PRIME_BELOW"
] | 2 | 0.003 | 2026-02-08T04:43:18.967073Z | {
"verified": true,
"answer": 83088,
"timestamp": "2026-02-08T04:43:18.969895Z"
} | 4c0041 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 212,
"completion_tokens": 1600
},
"timestamp": "2026-02-11T21:48:35.081Z",
"answer": 83088
},
{
... | 1 | [
{
"lemma": "C5",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status":... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
676e57 | geo_visible_lattice_v1_717093673_2929 | Let $n = 105$. Define a visible lattice point $(x, y)$ to be a point with integer coordinates such that $1 \leq x, y \leq n$ and $\gcd(x, y) = 1$. Let $r$ be the number of visible lattice points. Let $c = 48746$. Find the remainder when $c \cdot r$ is divided by $88837$. | 14,688 | graphs = [
Graph(
let={
"n": Const(105),
"result": VisibleLatticePoints(n=Ref(name='n')),
"_c": Const(48746),
"Q": Mod(value=Mul(Ref("_c"), Ref("result")), modulus=Const(88837)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 4 | 0 | null | null | 0.258 | 2026-02-08T17:17:30.132729Z | {
"verified": true,
"answer": 14688,
"timestamp": "2026-02-08T17:17:30.390853Z"
} | 4c32d9 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 132,
"completion_tokens": 3240
},
"timestamp": "2026-02-17T23:08:44.261Z",
"answer": 14688
},
... | 1 | [] | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||||
de8efa | comb_factorial_compute_v1_124444284_5989 | Let $a_0 = 1$, $a_1 = 1$, and $a_2 = a_0 + a_1$. Define $s = \sum_{k=0}^{a_2} (-1)^k \binom{a_2}{k}$, and let $n_1 = s$. Then define $f = \sum_{k=0}^{n_1} (-1)^k \binom{n_1}{k}$. Let $n = 7f$ and let $F = n!$. Let $S$ be the sum of the squares of the positions (1-indexed from the right) of each digit in the decimal rep... | 7,321 | graphs = [
Graph(
let={
"_n": Const(7),
"a": Const(1),
"b": Const(1),
"n2": Sum(Ref("a"), Ref("b")),
"s": Summation(var="k", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n2"), k=Var("k")))),
"n1": Ref("... | COMB | null | COMPUTE | sympy | COMB1 | [
"COMB1",
"BINOMIAL_ALTERNATING"
] | 47b00a | comb_factorial_compute_v1 | digits_weighted_mod | 6 | 2 | [
"BINOMIAL_ALTERNATING",
"COMB1"
] | 2 | 0.004 | 2026-02-08T06:58:23.120689Z | {
"verified": true,
"answer": 7321,
"timestamp": "2026-02-08T06:58:23.124539Z"
} | ab009c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 370,
"completion_tokens": 932
},
"timestamp": "2026-02-24T07:21:00.628Z",
"answer": 7321
},
{
"id... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
7083a2 | nt_gcd_compute_v1_260342960_162 | Let $a_2 = 8$ and $b_2 = 6$. Define $n_1 = (a_2 b_2)^2$. Let $u$ be the remainder when the number of positive divisors of $n_1$ is divided by 2, and let $g = 2u$. Let $m = 4$, and let $n$ be the minimum value of $x + y$ over all ordered pairs of positive integers $(x, y)$ such that $xy = 49$. Define $a_1 = g \cdot m$ a... | 35,940 | graphs = [
Graph(
let={
"a2": Const(8),
"b2": Const(6),
"n1": Pow(Mul(Ref("a2"), Ref("b2")), Const(2)),
"u": Mod(value=NumDivisors(n=Ref("n1")), modulus=Const(2)),
"g": Mul(Const(2), Ref("u")),
"m": Const(4),
"n": MinOverSet... | NT | null | COMPUTE | sympy | B3 | [
"B3/MOBIUS_COPRIME",
"DIVISOR_PARITY"
] | 9c27c0 | nt_gcd_compute_v1 | null | 5 | 2 | [
"B3",
"DIVISOR_PARITY",
"MOBIUS_COPRIME"
] | 3 | 0.005 | 2026-02-08T11:16:55.232992Z | {
"verified": true,
"answer": 35940,
"timestamp": "2026-02-08T11:16:55.238352Z"
} | 7d7d29 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 315,
"completion_tokens": 3004
},
"timestamp": "2026-02-08T20:32:29.791Z",
"answer": 35940
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DIVISOR_PARITY",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok_... | {
"lo": -6.69,
"mid": -2.4,
"hi": 1.74
} | ||
1f41a6 | sequence_fibonacci_compute_v1_397696148_2816 | Let $t$ be an integer. Define $N$ to be the number of integers $t$ such that $12 \leq t \leq 43$ and there exist positive integers $a$, $b$ with $1 \leq a \leq 5$, $1 \leq b \leq 6$, satisfying $t = 4a + 3b + 5$. Let $n$ be the number of ordered pairs $(i, j)$ of positive integers such that $1 \leq i \leq 24$, $1 \leq ... | 46,368 | 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=5)), Geq(left=Var(name='b'), right=Const(value=... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/COUNT_SUM_EQUALS"
] | 8a3f7a | sequence_fibonacci_compute_v1 | null | 5 | 0 | [
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 2 | 0.01 | 2026-02-08T14:06:00.976328Z | {
"verified": true,
"answer": 46368,
"timestamp": "2026-02-08T14:06:00.986625Z"
} | ef869f | 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": 2075
},
"timestamp": "2026-02-16T00:07:09.802Z",
"answer": 46368
},
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok_later"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"statu... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
134e5d | alg_poly4_min_v1_601307018_1842 | Let $E$ be the number of integers $t$ such that $t = 7a + 2b$ for some integers $a, b$ with $1 \leq a \leq 403$, $1 \leq b \leq 1080$, and $9 \leq t \leq 4981$. Find the minimum value of
\[
119208a^2b^2 - 158944ab^3 + 158944b^4 - 39736a^3b + E \cdot a^4
\]
over all positive integers $a, b$ with $1 \leq a \leq 450$, $1 ... | 79,472 | graphs = [
Graph(
let={
"_n": Const(450),
"result": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(450)), Geq(Var("b"), Const(1)), Leq(Var("b"), Ref("_n")))), expr=Sum(Mul(Const(119208), ... | ALG | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | alg_poly4_min_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 1.415 | 2026-03-10T02:35:05.054028Z | {
"verified": true,
"answer": 79472,
"timestamp": "2026-03-10T02:35:06.468659Z"
} | cc6e59 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 266,
"completion_tokens": 12497
},
"timestamp": "2026-03-29T03:34:19.140Z",
"answer": 79472
},
{
... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 0.86,
"mid": 3.78,
"hi": 5.89
} | ||
2f6560_n | comb_count_permutations_fixed_v1_1419126231_731 | A teacher assigns 11 students to present on 11 different topics. Exactly 9 students must get their preferred topic, while the remaining 2 must be assigned topics different from their preferences. In how many ways can the assignments be made so that the two non-preferred students do not receive their own choices? | 55 | COMB | null | COUNT | sympy | K13 | [
"STARS_BARS/POLY_ORBIT_HENSEL"
] | bde411 | comb_count_permutations_fixed_v1 | null | 2 | null | [
"K13",
"POLY_ORBIT_HENSEL",
"STARS_BARS"
] | 3 | 0.372 | 2026-02-25T10:14:02.053636Z | null | c5b189 | 2f6560 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 172,
"completion_tokens": 1480
},
"timestamp": "2026-03-31T03:53:54.594Z",
"answer": 55
},
{
"id"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "POLY_ORBIT_HENSEL",
"status": "ok_later"
},
{
"lemma": "STARS_BARS",
"status": "ok"
},
{
"lemma": "V7",
... | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | |
713c9c | antilemma_sum_equals_v1_1918700295_2763 | Let $a$, $b$, and $t$ be positive integers. Define $\mathcal{T}_1$ as the set of all integers $t$ such that $9 \leq t \leq 119$ and there exist integers $a$, $b$ with $1 \leq a \leq 21$, $1 \leq b \leq 7$, and $t = 4a + 5b$. Let $n$ be the number of elements in $\mathcal{T}_1$. Define $\mathcal{S}$ as the set of all or... | 503 | 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=21)), Geq(left=Var(name='b'), right=Const(value... | COMB | GEOM | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/COUNT_SUM_EQUALS",
"LIN_FORM",
"COUNT_SUM_EQUALS"
] | e5c57c | antilemma_sum_equals_v1 | negation_mod | 6 | 0 | [
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 2 | 0.004 | 2026-02-08T08:11:55.415610Z | {
"verified": true,
"answer": 503,
"timestamp": "2026-02-08T08:11:55.419835Z"
} | 119695 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 398,
"completion_tokens": 20234
},
"timestamp": "2026-02-24T09:04:44.629Z",
"answer": 514
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "LIN_F... | {
"lo": 3.25,
"mid": 5.68,
"hi": 8.81
} | ||
8c7e1b | nt_count_divisible_v1_1918700295_3061 | Let $t$ be an integer satisfying $7 \leq t \leq 24$. Suppose there exist integers $a$ and $b$ such that $1 \leq a \leq 3$, $1 \leq b \leq 4$, and $t = 4a + 3b$. Let $d$ be the number of such values of $t$.
Let $N$ be the number of positive integers $n$ such that $1 \leq n \leq 32400$ and $n$ is divisible by $d$.
Comp... | 39,544 | graphs = [
Graph(
let={
"upper": Const(32400),
"divisor": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=3)), Ge... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_count_divisible_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 1.349 | 2026-02-08T08:22:17.753400Z | {
"verified": true,
"answer": 39544,
"timestamp": "2026-02-08T08:22:19.101952Z"
} | d74732 | 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": 1552
},
"timestamp": "2026-02-13T17:50:21.045Z",
"answer": 39544
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
7842e8 | modular_sum_quadratic_residues_v1_898971024_2752 | Let $p$ be the largest prime number not exceeding $562$. Compute $\frac{p(p-1)}{4}$. | 77,423 | graphs = [
Graph(
let={
"_n": Const(562),
"p": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), Const(4)),
},
goal=Ref("re... | NT | null | SUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | modular_sum_quadratic_residues_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.002 | 2026-02-08T16:57:01.600867Z | {
"verified": true,
"answer": 77423,
"timestamp": "2026-02-08T16:57:01.602851Z"
} | 3fa656 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 71,
"completion_tokens": 685
},
"timestamp": "2026-02-17T16:08:17.695Z",
"answer": 77423
},
{
... | 1 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V7",
"status": ... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
d73de3 | comb_count_surjections_v1_1918700295_2854 | Let $n = 8$. Let $k$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 8$. Define $r = k! \cdot S(n, k)$, where $S(n, k)$ denotes the number of ways to partition a set of $n$ elements into $k$ nonempty unlabeled subsets. Compute the remainder when $64571 \cdot r$ is divided by ... | 48,264 | graphs = [
Graph(
let={
"_n": Const(64571),
"n": Const(8),
"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 | 4 | 0 | [
"COMB1"
] | 1 | 0.001 | 2026-02-08T08:15:38.240407Z | {
"verified": true,
"answer": 48264,
"timestamp": "2026-02-08T08:15:38.241562Z"
} | fceff7 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 219,
"completion_tokens": 3907
},
"timestamp": "2026-02-24T09:11:50.226Z",
"answer": 48264
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
8acd4b | nt_min_phi_inverse_v1_238844314_510 | Let $k = 2$. Let $r$ be the smallest positive integer $n$ with $1 \leq n \leq 10$ such that $\phi(n) = k$, where $\phi$ denotes Euler's totient function. Let $S$ be the set of all integers $t$ such that $33 \leq t \leq 1275$ and $t = 21a + 12b$ for some positive integers $a \leq 51$ and $b \leq 17$. Compute the value o... | 21,006 | graphs = [
Graph(
let={
"upper": Const(10),
"k": Const(2),
"result": MinOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(EulerPhi(n=Var("n")), Ref("k"))))),
"_c": Const(7001),
"Q": Sum(Mo... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"LIN_FORM"
] | d6c893 | nt_min_phi_inverse_v1 | two_moduli | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.012 | 2026-02-08T13:23:00.852637Z | {
"verified": true,
"answer": 21006,
"timestamp": "2026-02-08T13:23:00.864273Z"
} | 644aeb | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 180,
"completion_tokens": 3511
},
"timestamp": "2026-02-15T13:48:12.713Z",
"answer": 21006
},
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
a2e381_n | alg_qf_psd_min_v1_601307018_3361 | An engineer is designing a rectangular frame where the cost depends on its dimensions $a$ and $b$ (in meters), each between 1 and 500 inclusive. The total cost is modeled as $17810a^2 + 27400b^2 + d \cdot ab$ dollars, where $d$ is the largest divisor of $30,046,840$ that does not exceed $\sqrt{30,046,840}$. What is the... | 50,690 | ALG | null | COMPUTE | sympy | SUM_GEOM | [
"B3_CLOSEST"
] | 25e610 | alg_qf_psd_min_v1 | null | 5 | null | [
"B3_CLOSEST",
"SUM_GEOM"
] | 2 | 1.326 | 2026-03-10T03:55:34.501813Z | null | 63a968 | a2e381 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 213,
"completion_tokens": 12479
},
"timestamp": "2026-03-29T17:28:30.734Z",
"answer": 45250
},
{
... | 1 | [
{
"lemma": "B3_CLOSEST",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 1.7,
"mid": 5.03,
"hi": 8.38
} | |
7f51cb | geo_count_lattice_rect_v1_1918700295_502 | Compute the number of lattice points $(x, y)$ such that $0 \leq x \leq 89$ and $0 \leq y \leq 151$. | 13,680 | graphs = [
Graph(
let={
"a": Const(89),
"b": Const(151),
"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 | 0.002 | 2026-02-08T03:17:26.859897Z | {
"verified": true,
"answer": 13680,
"timestamp": "2026-02-08T03:17:26.862009Z"
} | d81935 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 148,
"completion_tokens": 122
},
"timestamp": "2026-02-10T13:45:20.479Z",
"answer": 13680
},
{
"i... | 2 | [] | {
"lo": -9.23,
"mid": -6.18,
"hi": -4.06
} | ||||
1e1278 | sequence_lucas_compute_v1_1125832087_320 | Let $ P $ be the set of all ordered pairs $ (x, y) $ of positive integers such that $ x \cdot y = 100 $. For each pair $ (x, y) $, define $ s = x + y $. Let $ n $ be the minimum value of $ s $ over all such pairs. Compute the $ n $-th Lucas number. | 15,127 | graphs = [
Graph(
let={
"_n": Const(100),
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_n")))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | sequence_lucas_compute_v1 | null | 3 | 0 | [
"B3"
] | 1 | 0.002 | 2026-02-08T03:01:20.571269Z | {
"verified": true,
"answer": 15127,
"timestamp": "2026-02-08T03:01:20.573142Z"
} | a771e7 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 188,
"completion_tokens": 913
},
"timestamp": "2026-02-10T12:24:47.591Z",
"answer": 15127
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -3.47,
"mid": 0.81,
"hi": 4.81
} | ||
b12ec0 | nt_count_divisible_v1_784195855_4473 | Let $c = \phi(2)$ and let
$$
s = \sum_{d \mid 42} \mu(d),
$$
where $\mu$ denotes the M\"obius function. Compute the number of positive integers $n \leq 84100$ such that $n \equiv s \pmod{3}$, and then compute the value of $(c - \text{this count}) \bmod{52928}$. | 24,896 | graphs = [
Graph(
let={
"upper": Const(84100),
"divisor": Const(3),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(value=Var("n"), modulus=Ref("divisor")), SumOverDivisors(n=Const(value=42),... | NT | null | COUNT | sympy | MOBIUS_SUM | [
"MOBIUS_SUM",
"ONE_PHI_2"
] | 749f23 | nt_count_divisible_v1 | null | 4 | 0 | [
"MOBIUS_SUM",
"ONE_PHI_2"
] | 2 | 4.684 | 2026-02-08T07:08:04.693642Z | {
"verified": true,
"answer": 24896,
"timestamp": "2026-02-08T07:08:09.378110Z"
} | 01eacb | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 194,
"completion_tokens": 618
},
"timestamp": "2026-02-19T23:59:33.846Z",
"answer": 24896
}
] | 2 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOBIUS_SUM",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "ONE_PHI_2",
"status": "ok"
... | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
f32761 | geo_visible_lattice_v1_1439011603_1121 | Let $n = 64$. A lattice point $(x, y)$ in the plane 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 $1 \leq x, y \leq n$. Determine the value of the remainder when $74863 \cdot V$ is divided by $83826$. | 55,223 | graphs = [
Graph(
let={
"n": Const(64),
"result": VisibleLatticePoints(n=Ref(name='n')),
"_c": Const(74863),
"Q": Mod(value=Mul(Ref("_c"), Ref("result")), modulus=Const(83826)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 4 | 0 | null | null | 0.127 | 2026-02-08T15:55:42.794500Z | {
"verified": true,
"answer": 55223,
"timestamp": "2026-02-08T15:55:42.921672Z"
} | e82b34 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 200,
"completion_tokens": 3029
},
"timestamp": "2026-02-24T19:04:08.931Z",
"answer": 55223
},
{
... | 1 | [] | {
"lo": -2.4,
"mid": 1.57,
"hi": 5.75
} | ||||
7c91ae | nt_sum_divisors_mod_v1_168721529_2068 | Let $n$ be the smallest positive integer such that $7^{278}$ divides $n!$. Let $\sigma(n)$ denote the sum of all positive divisors of $n$. Compute the remainder when $\sigma(n)$ is divided by $10499$, and subtract this remainder from $24649$. Find the resulting value. | 18,697 | graphs = [
Graph(
let={
"_n": Const(7),
"n": MinOverSet(set=SolutionsSet(var=Var("n"), condition=Geq(MaxKDivides(target=Factorial(Var("n")), base=Ref("_n")), Const(278)), domain='Z_{>0}')),
"M": Const(10499),
"sigma": SumDivisors(n=Ref("n")),
"resu... | NT | null | COMPUTE | sympy | V5 | [
"V5"
] | 79df37 | nt_sum_divisors_mod_v1 | null | 6 | 0 | [
"V5"
] | 1 | 0.003 | 2026-02-08T14:04:32.455019Z | {
"verified": true,
"answer": 18697,
"timestamp": "2026-02-08T14:04:32.457694Z"
} | 81430e | 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": 1490
},
"timestamp": "2026-02-10T01:41:38.925Z",
"answer": 18697
}
] | 2 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V5",
"status": "ok"
}
] | {
"lo": -10,
"mid": -1.96,
"hi": 6.09
} | ||
f3b63b | sequence_fibonacci_compute_v1_124444284_1358 | Let $m = 20$. Consider the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = m$. Let $P$ be the maximum value of $xy$ over all such pairs. Now, consider the set of all ordered pairs $(x, y)$ of positive integers such that $xy = P$. Let $n$ be the minimum value of $x + y$ over all such pairs. Def... | 11,239 | graphs = [
Graph(
let={
"_m": Const(20),
"_n": Const(62467),
"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")), MaxOverSet(set=Ma... | NT | null | COMPUTE | sympy | B1 | [
"B1/B3"
] | 80b49d | sequence_fibonacci_compute_v1 | null | 5 | 0 | [
"B1",
"B3"
] | 2 | 0.002 | 2026-02-08T03:50:44.628822Z | {
"verified": true,
"answer": 11239,
"timestamp": "2026-02-08T03:50:44.631035Z"
} | 58eb99 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 280,
"completion_tokens": 1533
},
"timestamp": "2026-02-10T14:33:19.126Z",
"answer": 11239
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
2f66bf | comb_binomial_compute_v1_2051736721_4250 | Let $n_2 = 0$, and define $$e = \sum_{k_1 = \sum_{k_2 = \binom{3}{3} - 1}^{9} (-1)^{k_2} \binom{9}{k_2}}^{n_2} (-1)^{k_1} \binom{n_2}{k_1}.$$ Let $n_1 = 2$ and $$u = \sum_{k_3 = 0}^{n_1} (-1)^{k_3} \binom{n_1}{k_3}.$$ Let $n = 12$ and $k = 5e + u$. Compute $\binom{n}{k}$. | 792 | graphs = [
Graph(
let={
"n2": Const(0),
"e": Summation(var="k1", start=Summation(var="k2", start=Sub(Binom(n=Const(3), k=Const(3)), Const(1)), end=Const(9), expr=Mul(Pow(Const(-1), Var("k2")), Binom(n=Const(9), k=Var("k2")))), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k1")), Binom(... | COMB | null | COMPUTE | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING",
"ZERO_BINOM_N"
] | ba7829 | comb_binomial_compute_v1 | null | 4 | 2 | [
"BINOMIAL_ALTERNATING",
"ZERO_BINOM_N"
] | 2 | 0.004 | 2026-02-08T17:51:16.863896Z | {
"verified": true,
"answer": 792,
"timestamp": "2026-02-08T17:51:16.868029Z"
} | eef405 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 195,
"completion_tokens": 915
},
"timestamp": "2026-02-18T08:36:02.206Z",
"answer": 792
},
{
... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_S... | {
"lo": -5.64,
"mid": -3.17,
"hi": -0.81
} | ||
cbb1e6 | nt_count_coprime_v1_1520064083_8651 | Let $k$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 121$. Let $S$ be the set of all positive integers $n \le 35721$ such that $\gcd(n, k) = 1$. Compute the remainder when $44121$ times the number of elements in $S$ is divided by $83620$. | 20,137 | graphs = [
Graph(
let={
"_n": Const(83620),
"upper": Const(35721),
"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(121))... | NT | null | COUNT | sympy | LTE_SUM | [
"B3"
] | 0cd20d | nt_count_coprime_v1 | null | 4 | 0 | [
"B3",
"LTE_SUM"
] | 2 | 5.03 | 2026-02-08T10:17:19.492031Z | {
"verified": true,
"answer": 20137,
"timestamp": "2026-02-08T10:17:24.521732Z"
} | e96b48 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 135,
"completion_tokens": 1565
},
"timestamp": "2026-02-14T06:59:55.176Z",
"answer": 20137
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
e4f491 | comb_catalan_compute_v1_153355830_2421 | Let $n'$ be the number of integers $t$ such that $32 \le t \le 68$ and there exist positive integers $a \le 3$ and $b \le 4$ satisfying $t = 9a + 6b + 17$. Let $n$ be the number of ordered pairs $(i, j)$ of integers with $1 \le i \le 10$ and $1 \le j \le 10$ such that $i + j = n'$. Compute the $n$-th Catalan number. | 16,796 | graphs = [
Graph(
let={
"_n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=3)), Geq(left=Var(name='b'), right=Const(value=... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/COUNT_SUM_EQUALS"
] | 8a3f7a | comb_catalan_compute_v1 | null | 6 | 0 | [
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 2 | 0.011 | 2026-02-08T07:07:06.408774Z | {
"verified": true,
"answer": 16796,
"timestamp": "2026-02-08T07:07:06.419773Z"
} | 395eab | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 229,
"completion_tokens": 1175
},
"timestamp": "2026-02-24T07:34:46.224Z",
"answer": 16796
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok_later"
},
{
"lemma": ... | {
"lo": -4.92,
"mid": -2.91,
"hi": -0.68
} | ||
753415 | nt_count_gcd_equals_v1_2051736721_1375 | Let $k$ be the number of integers $t$ such that $7 \leq t \leq 424$ and there exist positive integers $a \leq 22$ and $b \leq 157$ satisfying $t = 5a + 2b$. Let $d = 138$. Determine the number of positive integers $n$ such that $1 \leq n \leq 25921$ and $\gcd(n, k) = d$. | 125 | graphs = [
Graph(
let={
"upper": Const(25921),
"k": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=22)), Geq(lef... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"LIN_FORM"
] | 7b2633 | nt_count_gcd_equals_v1 | null | 4 | 0 | [
"LIN_FORM",
"MIN_PRIME_FACTOR"
] | 2 | 3.079 | 2026-02-08T16:00:22.652689Z | {
"verified": true,
"answer": 125,
"timestamp": "2026-02-08T16:00:25.731573Z"
} | 628e1f | 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": 3629
},
"timestamp": "2026-02-16T19:39:21.567Z",
"answer": 125
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
2c1c2e | nt_min_phi_inverse_v1_2051736721_505 | Let $n$ be a positive integer. Define $\text{upper}$ to be the sum of all even positive integers from $1$ to $8$, inclusive. Let $k = 6$. Define $\text{result}$ to be the smallest positive integer $n_1$ such that $1 \leq n_1 \leq \text{upper}$ and $\phi(n_1) = k$, where $\phi$ denotes Euler's totient function. Let $d$ ... | 7,070 | graphs = [
Graph(
let={
"_n": Const(8),
"upper": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_n")), Eq(Mod(value=Var("n"), modulus=Const(2)), Const(0))))),
"k": Const(6),
"result": MinOverSet(set=Solution... | NT | null | EXTREMUM | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR",
"SUM_DIVISIBLE"
] | e4a64b | nt_min_phi_inverse_v1 | two_moduli | 6 | 0 | [
"MIN_PRIME_FACTOR",
"SUM_DIVISIBLE"
] | 2 | 0.01 | 2026-02-08T15:28:41.050846Z | {
"verified": true,
"answer": 7070,
"timestamp": "2026-02-08T15:28:41.061159Z"
} | 21304b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 197,
"completion_tokens": 3331
},
"timestamp": "2026-02-16T06:42:49.908Z",
"answer": 7070
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "SUM_DIVISIBLE",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
16a630 | sequence_lucas_compute_v1_1918700295_402 | Let $n = 19$ and let $L_n$ denote the $n$th Lucas number. Define $$c = \sum_{k=1}^{36} \phi(k) \left\lfloor \frac{36}{k} \right\rfloor.$$ Compute the remainder when $c - L_n$ is divided by $80106$. | 71,423 | graphs = [
Graph(
let={
"_n": Const(36),
"n": Const(19),
"result": Lucas(arg=Ref(name='n')),
"_c": Summation(var="k", start=Const(1), end=Const(36), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Ref("_n"), Var("k"))))),
"Q": Mod(value=Sub(Ref("_c"), Ref... | NT | null | COMPUTE | sympy | K2 | [
"K2"
] | 9468ae | sequence_lucas_compute_v1 | negation_mod | 6 | 0 | [
"K2"
] | 1 | 0.001 | 2026-02-08T03:12:41.075716Z | {
"verified": true,
"answer": 71423,
"timestamp": "2026-02-08T03:12:41.076649Z"
} | 7edc05 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 184,
"completion_tokens": 2988
},
"timestamp": "2026-02-10T13:25:02.845Z",
"answer": 71423
},
{
"... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
0ab86e | comb_count_derangements_v1_153355830_2490 | Let $p$ be a positive integer. Define $n$ to be the number of positive integers $p$ such that $p < q$, $\gcd(p, q) = 1$, and $pq = 246527820$. Let $s$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = n$. Compute the number of derangements of $s$ 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=246527820)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(valu... | NT | COMB | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/B3"
] | 3f0fb0 | comb_count_derangements_v1 | null | 6 | 0 | [
"B3",
"COPRIME_PAIRS"
] | 2 | 0.002 | 2026-02-08T07:09:24.295679Z | {
"verified": true,
"answer": 14833,
"timestamp": "2026-02-08T07:09:24.297446Z"
} | 3a3c0e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 140,
"completion_tokens": 2177
},
"timestamp": "2026-02-13T08:25:51.298Z",
"answer": 14833
},
... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"st... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
790784 | nt_count_divisible_and_v1_153355830_990 | Let $d_1 = 8$. Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 36$. Let $d_2$ be the minimum value of $x + y$ as $(x, y)$ ranges over $S$. Let $r$ be the number of positive integers $n$ with $1 \leq n \leq 59784$ such that $n$ is divisible by both $d_1$ and $d_2$. Find the value of... | 2,491 | graphs = [
Graph(
let={
"upper": Const(59784),
"d1": Const(8),
"d2": 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)))), ... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | nt_count_divisible_and_v1 | null | 4 | 0 | [
"B3"
] | 1 | 3.072 | 2026-02-08T04:20:33.605065Z | {
"verified": true,
"answer": 2491,
"timestamp": "2026-02-08T04:20:36.677418Z"
} | e2de19 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 227,
"completion_tokens": 583
},
"timestamp": "2026-02-10T16:11:29.658Z",
"answer": 2491
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.33
} | ||
dd76cd | comb_sum_binomial_row_v1_1125832087_1575 | Let $n$ be the number of positive integers $p$ for which there exists a positive integer $q > p$ such that $pq = 2250$ and $\gcd(p, q) = 1$. Define $s = \sum_{k=1}^{n} \phi(k) \cdot \left\lfloor \frac{4}{k} \right\rfloor$, where $\phi$ denotes Euler's totient function. Let $r = 2^s$. Let $T$ be the set of all ordered p... | 1,560 | graphs = [
Graph(
let={
"_n": Const(4),
"n": Summation(var="k", start=Const(1), end=CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=2250)), Eq... | NT | null | SUM | sympy | B3 | [
"B3",
"COPRIME_PAIRS/K2"
] | 046c4e | comb_sum_binomial_row_v1 | negation_mod | 6 | 0 | [
"B3",
"COPRIME_PAIRS",
"K2"
] | 3 | 0.005 | 2026-02-08T03:47:54.409145Z | {
"verified": true,
"answer": 1560,
"timestamp": "2026-02-08T03:47:54.414034Z"
} | ec3fa1 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 275,
"completion_tokens": 1537
},
"timestamp": "2026-02-10T15:57:17.145Z",
"answer": 1560
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K2",
"status": "ok_later"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
... | {
"lo": -3.53,
"mid": 1.02,
"hi": 5.49
} | ||
d15f2e | geo_count_lattice_triangle_v1_1218484723_4908 | Let $P$ be the number of primes $n$ with $2 \leq n \leq 22549$. Let $A = \left|\{ (a, b) \mid 1 \leq a, b \leq 40,\ 10a^2 - 18ab + 25b^2 \leq P \}\right|$. Define $S = |233 \cdot 157 + 180 \cdot (0 - A)|$. Let $B = \left|\{ t \mid 25 \leq t \leq 228,\ \exists\, 1 \leq a \leq 29,\ 1 \leq b \leq 10\ \text{such that}\ t =... | 290 | graphs = [
Graph(
let={
"_c": Const(2),
"_m": Const(25),
"_n": Const(157),
"area_2x": Abs(arg=Sum(Mul(Const(value=233), Const(value=157)), Mul(Const(value=180), Sub(left=Const(value=0), right=CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var(name='a'), Var... | GEOM | NT | COUNT | sympy | COUNT_PRIMES | [
"COUNT_PRIMES/QF_PSD_COUNT_LEQ",
"LIN_FORM"
] | 6bb068 | geo_count_lattice_triangle_v1 | null | 6 | 0 | [
"COUNT_PRIMES",
"LIN_FORM",
"QF_PSD_COUNT_LEQ"
] | 3 | 0.022 | 2026-02-25T06:32:27.783014Z | {
"verified": true,
"answer": 290,
"timestamp": "2026-02-25T06:32:27.805075Z"
} | 9bf787 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 355,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T18:28:53.742Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
... | {
"lo": 3.81,
"mid": 6.33,
"hi": 9.49
} | ||
f42e7f | sequence_count_fib_divisible_v1_809748730_552 | Let $d = 5$ and let the upper bound be $410$. Define $S$ as the set of all positive integers $n$ such that $1 \leq n \leq 410$ and $d$ divides the $n$th Fibonacci number. Let $k$ be the number of elements in $S$. Let $p$ be the largest prime number less than or equal to $11$. Compute the Bell number $B_r$, where $r$ is... | 52 | graphs = [
Graph(
let={
"upper": Const(410),
"d": Const(5),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Divides(divisor=Ref("d"), dividend=Fibonacci(arg=Var(name='n')))))),
"Q": Bell... | NT | COMB | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | 88ea9c | sequence_count_fib_divisible_v1 | bell_mod | 5 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.027 | 2026-02-08T11:35:25.480500Z | {
"verified": true,
"answer": 52,
"timestamp": "2026-02-08T11:35:25.507741Z"
} | 6526e1 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 167,
"completion_tokens": 936
},
"timestamp": "2026-02-14T16:55:47.399Z",
"answer": 52
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
}... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
ce11d1 | comb_binomial_compute_v1_1520064083_2170 | Let $k$ be the number of positive integers $n$ such that $1 \leq n \leq 48$, $8$ divides $n$, and $\gcd(n, 35) = 1$. Compute $\binom{13}{k}$. | 1,287 | graphs = [
Graph(
let={
"_n": Const(48),
"n": Const(13),
"k": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_n")), Divides(divisor=Const(8), dividend=Var("n")), Eq(GCD(a=Var("n"), b=Const(35)), Const(1))))),
... | NT | null | COMPUTE | sympy | C5 | [
"C5"
] | 1d9668 | comb_binomial_compute_v1 | null | 4 | 0 | [
"C5"
] | 1 | 0.002 | 2026-02-08T04:32:41.760339Z | {
"verified": true,
"answer": 1287,
"timestamp": "2026-02-08T04:32:41.762059Z"
} | 25701f | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 167,
"completion_tokens": 556
},
"timestamp": "2026-02-10T17:07:44.674Z",
"answer": 1287
},
{
"i... | 1 | [
{
"lemma": "C5",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.33
} | ||
f17b4b | nt_count_divisible_and_v1_971394319_1510 | Let $d_1 = 6$ and $d_2 = \sum_{k=1}^{4} \phi(k) \left\lfloor \frac{4}{k} \right\rfloor$, where $\phi$ denotes Euler's totient function. Determine the value of $n$, the number of positive integers at most $114840$ that are divisible by both $d_1$ and $d_2$. | 3,828 | graphs = [
Graph(
let={
"_n": Const(4),
"upper": Const(114840),
"d1": Const(6),
"d2": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(4), Var("k"))))),
"result": CountOverSet(set=SolutionsSet(var=Var... | NT | null | COUNT | sympy | K2 | [
"K2"
] | 6897ab | nt_count_divisible_and_v1 | null | 5 | 0 | [
"K2"
] | 1 | 5.507 | 2026-02-08T13:42:56.873514Z | {
"verified": true,
"answer": 3828,
"timestamp": "2026-02-08T13:43:02.380514Z"
} | bc0833 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 135,
"completion_tokens": 722
},
"timestamp": "2026-02-15T20:16:50.314Z",
"answer": 3828
},
{
... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
ad4290 | alg_poly4_min_v1_1218484723_5446 | Let
\[C = \min\{x + y : x > 0,\ y > 0,\ xy = 15872256\}.\]
Let
\[S = \sum_{(a_1,b_1,c)} \bigl(a_1^{5} + b_1^{5} + c^{5}\bigr),\]
where the sum runs over all ordered triples $(a_1,b_1,c)$ of positive integers satisfying
\[a_1^{2} + b_1^{2} + c^{2} = a_1b_1 + b_1c + ca_1, \qquad 5a_1 + 8b_1 + 7c = 40, \qquad a_1 \ge 1,\ ... | 21,248 | graphs = [
Graph(
let={
"_m": Const(5),
"_n": Const(4),
"result": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(96)), Geq(Var("b"), Const(1)), Leq(Var("b"), SumOverSet(set=Ma... | ALG | null | COMPUTE | sympy | QF_PSD_COUNT | [
"SUM_SQUARES_IDENTITY",
"B3"
] | 8e1621 | alg_poly4_min_v1 | null | 8 | 0 | [
"B3",
"QF_PSD_COUNT",
"SUM_SQUARES_IDENTITY"
] | 3 | 0.138 | 2026-02-25T07:00:32.609213Z | {
"verified": true,
"answer": 21248,
"timestamp": "2026-02-25T07:00:32.747196Z"
} | 4c5b56 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 393,
"completion_tokens": 4319
},
"timestamp": "2026-03-29T21:09:22.576Z",
"answer": 21331
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_SQUARES_IDENTITY",
"status": "ok"
}
] | {
"lo": 1.53,
"mid": 4.7,
"hi": 7.23
} | ||
e7a58c | comb_count_surjections_v1_124444284_3436 | Let $n = 8$. Let $k$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 8$. Compute $k! \cdot S(n, k)$, where $S(n, k)$ denotes the number of partitions of an $n$-element set into $k$ nonempty subsets. | 40,824 | graphs = [
Graph(
let={
"n": Const(8),
"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(Sum(Var("x1"), Var("x2")), Cons... | COMB | null | COUNT | sympy | COMB1 | [
"COMB1"
] | 567f58 | comb_count_surjections_v1 | null | 5 | 0 | [
"COMB1"
] | 1 | 0.002 | 2026-02-08T05:24:21.023951Z | {
"verified": true,
"answer": 40824,
"timestamp": "2026-02-08T05:24:21.026270Z"
} | dd424d | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 195,
"completion_tokens": 1509
},
"timestamp": "2026-02-24T03:33:25.699Z",
"answer": 40824
},
{
"... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -4.93,
"mid": -2.91,
"hi": -0.71
} | ||
0dcd57 | nt_count_divisible_v1_168721529_1616 | Let $p = 23$ and $q = 73$, and define $n_1 = pq$. Let $u = \lambda(n_1)$, where $\lambda$ denotes the Liouville function. Let $T$ be the set of all integers $t$ such that there exist integers $a$ and $b$ satisfying $1 \leq a \leq 46$, $1 \leq b \leq 13$, $16 \leq t \leq 142$, and $t = 2a + 3b + 11$. Let $n = |T|$, and ... | 2,980 | graphs = [
Graph(
let={
"p": Const(23),
"q": Const(73),
"n1": Mul(Ref("p"), Ref("q")),
"u": LiouvilleLambda(n=Ref(name='n1')),
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), ... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/OMEGA_ONE",
"LIOUVILLE_ONE"
] | 0bde15 | nt_count_divisible_v1 | null | 6 | 2 | [
"LIN_FORM",
"LIOUVILLE_ONE",
"OMEGA_ONE"
] | 3 | 11.432 | 2026-02-08T13:48:27.113293Z | {
"verified": true,
"answer": 2980,
"timestamp": "2026-02-08T13:48:38.545432Z"
} | cb5816 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 304,
"completion_tokens": 6942
},
"timestamp": "2026-02-09T19:26:15.525Z",
"answer": 2980
},
{
"i... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LIOUVILLE_ONE",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"le... | {
"lo": -6.5,
"mid": -0.2,
"hi": 6.11
} | ||
018d76 | comb_bell_compute_v1_655260480_5408 | Let $m = 113$ and $n = 31$. Define $n'$ to be the number of positive integers $n_1$ such that $1 \leq n_1 \leq n$ and $\gcd\left(n_1, \text{the number of primes } n_2 \text{ satisfying } 2 \leq n_2 \leq m\right) = 1$. Let $\text{result} = B_{n'}$, the $n'$-th Bell number. Determine the value of $\text{result}$. | 21,147 | graphs = [
Graph(
let={
"_m": Const(113),
"_n": Const(31),
"n": CountOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(1)), Leq(Var("n1"), Ref("_n")), Eq(GCD(a=Var("n1"), b=CountOverSet(set=SolutionsSet(var=Var("n2"), condition=And(Geq(Var("n2"), ... | NT | COMB | COMPUTE | sympy | COUNT_PRIMES | [
"COUNT_PRIMES/C4"
] | b1cab2 | comb_bell_compute_v1 | null | 5 | 0 | [
"C4",
"COUNT_PRIMES"
] | 2 | 0.002 | 2026-02-08T18:27:37.501231Z | {
"verified": true,
"answer": 21147,
"timestamp": "2026-02-08T18:27:37.502992Z"
} | 243d03 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 161,
"completion_tokens": 1531
},
"timestamp": "2026-02-18T17:08:21.036Z",
"answer": 21147
},
... | 1 | [
{
"lemma": "C4",
"status": "ok_later"
},
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma":... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
17f028 | antilemma_v1_legendre_1918700295_44 | Let $A$ be the set of all ordered pairs $(a, b)$ of integers such that $1 \leq a \leq 3$, $1 \leq b \leq 5$, and $t = 9a + 6b$ satisfies $15 \leq t \leq 57$. Let $s$ be the number of distinct values of $t$ that can be expressed in this form.
Let $x$ be the largest integer $k$ such that $s^k$ divides $96655!$.
Compute... | 8,052 | graphs = [
Graph(
let={
"_n": Const(96655),
"x": MaxKDivides(target=Factorial(Ref("_n")), base=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... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/V1",
"V1"
] | d38e85 | antilemma_v1_legendre | null | 7 | 0 | [
"LIN_FORM",
"V1"
] | 2 | 0.001 | 2026-02-08T02:57:32.577130Z | {
"verified": true,
"answer": 8052,
"timestamp": "2026-02-08T02:57:32.578008Z"
} | c5ee77 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 234,
"completion_tokens": 1605
},
"timestamp": "2026-02-08T22:04:47.536Z",
"answer": 8052
},
{
"... | 1 | [
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "same_pattern_wrong"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V1",
"status": "ok"
... | {
"lo": -6.49,
"mid": 0.51,
"hi": 7.52
} | ||
3e5af9 | comb_catalan_compute_v1_2080023795_164 | Let $m = 13$. Define $k$ to be the number of ordered pairs $(i, j)$ of integers with $1 \leq i \leq 13$ and $1 \leq j \leq 13$ such that $i + j = m$. Define $n$ to be the number of ordered pairs $(i, j)$ of integers with $1 \leq i \leq 11$ and $1 \leq j \leq 11$ such that $i + j = k$. Compute the $n$-th Catalan number. | 58,786 | graphs = [
Graph(
let={
"_m": Const(13),
"_n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref("_m")), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(13)), right=IntegerRange(start=Const(1), end=Co... | COMB | null | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS/COUNT_SUM_EQUALS"
] | 756129 | comb_catalan_compute_v1 | null | 4 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.02 | 2026-02-08T11:35:14.388207Z | {
"verified": true,
"answer": 58786,
"timestamp": "2026-02-08T11:35:14.408458Z"
} | a29e4c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 238,
"completion_tokens": 1060
},
"timestamp": "2026-02-08T20:47:55.942Z",
"answer": 58786
},
{
"... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
... | {
"lo": -3.87,
"mid": -1.84,
"hi": 0.27
} | ||
72ab77 | modular_count_residue_v1_153355830_2393 | Let $m$ be the number of positive integers $n \leq 365$ that are divisible by $5$ and relatively prime to $6$. Let $\text{upper} = 62500$ and $r = 11$. Compute the number of positive integers $n \leq \text{upper}$ such that $n \equiv r \pmod{m}$. | 2,500 | graphs = [
Graph(
let={
"upper": Const(62500),
"m": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(365)), Divides(divisor=Const(5), dividend=Var("n")), Eq(GCD(a=Var("n"), b=Const(6)), Const(1))))),
"r": Const(11),
... | NT | null | COUNT | sympy | C5 | [
"C5"
] | 1d9668 | modular_count_residue_v1 | null | 4 | 0 | [
"C5"
] | 1 | 2.069 | 2026-02-08T07:06:47.202992Z | {
"verified": true,
"answer": 2500,
"timestamp": "2026-02-08T07:06:49.272203Z"
} | 9b7333 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 123,
"completion_tokens": 1007
},
"timestamp": "2026-02-13T07:47:11.050Z",
"answer": 2500
},
{... | 1 | [
{
"lemma": "C5",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
4d2f62 | comb_binomial_compute_v1_601307018_7740 | Let $N = \sum_{k=0}^{15} (2k + 106)$ and $R = \binom{15}{8}$. Find the remainder when $N - R$ is divided by $79111$. | 74,612 | graphs = [
Graph(
let={
"_n": Const(79111),
"n": Const(15),
"k": Const(8),
"result": Binom(n=Ref("n"), k=Ref("k")),
"_c": Summation(var="k1", start=Const(0), end=Const(15), expr=Sum(Mul(Const(2), Var("k1")), Const(106))),
"Q": Mod(value... | COMB | null | COMPUTE | sympy | SUM_AP | [
"SUM_AP"
] | 28df0a | comb_binomial_compute_v1 | negation_mod | 2 | 0 | [
"SUM_AP"
] | 1 | 0.004 | 2026-03-10T08:19:44.596086Z | {
"verified": true,
"answer": 74612,
"timestamp": "2026-03-10T08:19:44.599978Z"
} | 29648f | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 159,
"completion_tokens": 579
},
"timestamp": "2026-04-19T07:23:53.335Z",
"answer": 74612
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "SUM_AP",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
... | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
51dd85 | modular_count_residue_v1_717093673_3494 | Let $\text{result}$ be the number of positive integers $n$ such that $1 \leq n \leq 61504$ and $n \equiv 14 \pmod{29}$. Let $T$ be the set of all integers $d \geq 2$ that divide $1517$, and let $c$ be the smallest element of $T$. Compute the remainder when $c - \text{result}$ is divided by $66813$. | 64,729 | graphs = [
Graph(
let={
"upper": Const(61504),
"m": Const(29),
"r": Const(14),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(value=Var("n"), modulus=Ref("m")), Ref("r"))))),
... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | fd27b3 | modular_count_residue_v1 | negation_mod | 3 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 2.449 | 2026-02-08T17:38:31.548480Z | {
"verified": true,
"answer": 64729,
"timestamp": "2026-02-08T17:38:33.997054Z"
} | 8410c8 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 143,
"completion_tokens": 794
},
"timestamp": "2026-02-18T05:20:31.419Z",
"answer": 64729
},
{... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"s... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
6489a2 | modular_mod_compute_v1_1742523217_2320 | Let $a = -65025$ and $n = 54346$. Let $m$ be the number of integers $t$ with $7 \leq t \leq 9811$ such that there exist positive integers $a'$ and $b'$ with $1 \leq a' \leq 1297$, $1 \leq b' \leq 1663$, and $t = 5a' + 2b'$. Define $r$ to be the remainder when $a$ is divided by $m$, satisfying $0 \leq r < m$. Compute th... | 53,337 | graphs = [
Graph(
let={
"_n": Const(54346),
"a": Const(-65025),
"m": 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'), ri... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | modular_mod_compute_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.004 | 2026-02-08T04:42:36.113756Z | {
"verified": true,
"answer": 53337,
"timestamp": "2026-02-08T04:42:36.118019Z"
} | b2d5bc | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 254,
"completion_tokens": 4872
},
"timestamp": "2026-02-11T21:45:57.035Z",
"answer": 19838
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"st... | {
"lo": 3.24,
"mid": 5.68,
"hi": 8.81
} | ||
8b44ab | modular_sum_quadratic_residues_v1_1918700295_210 | Let $p$ be the largest prime number such that $2 \leq p \leq 161$. Compute $\frac{p(p-1)}{4}$. | 6,123 | graphs = [
Graph(
let={
"_n": Const(2),
"p": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Const(161)), IsPrime(Var("n"))))),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), Const(4)),
},
goal=Ref("re... | NT | null | SUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | modular_sum_quadratic_residues_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.002 | 2026-02-08T03:05:15.210112Z | {
"verified": true,
"answer": 6123,
"timestamp": "2026-02-08T03:05:15.212265Z"
} | b4335f | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 146,
"completion_tokens": 214
},
"timestamp": "2026-02-10T12:37:47.579Z",
"answer": 6123
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8",
"status... | {
"lo": -5.55,
"mid": -3.02,
"hi": 0.3
} | ||
a311dd | geo_count_lattice_triangle_v1_1742523217_1144 | Let $A$ be twice the area of the triangle with vertices at $(0,0)$, $(128,1)$, and $(6,121)$. Let $B$ be the sum of the greatest common divisors of the absolute values of the differences in coordinates along each side of the triangle. Specifically, compute $\gcd(128,1) + \gcd(|6 - 128|, |121 - 1|) + \gcd(|0 - 6|, |0 - ... | 7,740 | graphs = [
Graph(
let={
"_n": Const(128),
"area_2x": Abs(arg=Sum(Mul(Const(value=128), Const(value=121)), Mul(Const(value=6), Sub(left=Const(value=0), right=Const(value=1))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=128)), b=Abs(arg=Const(value=1))), GCD(a=Abs(arg=Sub(... | ALG | NT | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | geo_count_lattice_triangle_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.005 | 2026-02-08T03:28:30.422052Z | {
"verified": true,
"answer": 7740,
"timestamp": "2026-02-08T03:28:30.426990Z"
} | 62e9ee | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 301,
"completion_tokens": 6184
},
"timestamp": "2026-02-10T04:10:11.811Z",
"answer": 7740
},
{
"i... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -3.53,
"mid": 1.02,
"hi": 5.49
} | ||
cfe994_l | nt_max_prime_below_v1_1520064083_1382 | Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 54$, $\gcd(p, q) = 1$, and $p < q$. Let $k$ be the number of elements in $S$. Determine the value of the largest prime number $n$ such that $k \leq n \leq 19321$. | 19,321 | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_max_prime_below_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.456 | 2026-02-08T03:57:09.944900Z | {
"verified": false,
"answer": 19319,
"timestamp": "2026-02-08T03:57:10.401292Z"
} | 1f569d | cfe994 | 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": 198,
"completion_tokens": 2140
},
"timestamp": "2026-02-10T16:13:56.359Z",
"answer": 19319
},
{
"... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.02,
"hi": 0.31
} | |
37d065 | algebra_poly_eval_v1_1978505735_488 | Let $z = 9$. Define $S$ to be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 6$, $\gcd(p, q) = 1$, and $p < q$. Compute the value of $4 \cdot z^{|S|} + 4 \cdot z + 7$. | 367 | graphs = [
Graph(
let={
"_n": Const(7),
"z": Const(9),
"result": Sum(Mul(Const(4), Pow(Ref("z"), 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')), rig... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | algebra_poly_eval_v1 | null | 3 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.003 | 2026-02-08T15:24:20.816347Z | {
"verified": true,
"answer": 367,
"timestamp": "2026-02-08T15:24:20.818925Z"
} | 170a6d | 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": 655
},
"timestamp": "2026-02-16T05:42:49.271Z",
"answer": 367
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
4a4d50 | antilemma_k3_v1_151522320_173 | Let $n = 95130$. Define $x = \sum_{d \mid n} \phi(d)$. Compute the remainder when $27154 \cdot x$ is divided by $99405$. | 21,690 | graphs = [
Graph(
let={
"_n": Const(95130),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"_c": Const(27154),
"Q": Mod(value=Mul(Ref("_c"), Ref("x")), modulus=Const(99405)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 4 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T03:01:57.863328Z | {
"verified": true,
"answer": 21690,
"timestamp": "2026-02-08T03:01:57.863948Z"
} | e34656 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 154,
"completion_tokens": 3379
},
"timestamp": "2026-02-10T12:29:42.935Z",
"answer": 21690
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.55,
"mid": 0.8,
"hi": 4.81
} | ||
af909e | modular_mod_compute_v1_784195855_1574 | Let $m$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 1119364$. Find the remainder when $-22222$ is divided by $m$. | 1,054 | graphs = [
Graph(
let={
"a": Const(-22222),
"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(1119364)))), expr=Sum(Var("x"), Var("y")... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | modular_mod_compute_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.002 | 2026-02-08T05:09:01.432795Z | {
"verified": true,
"answer": 1054,
"timestamp": "2026-02-08T05:09:01.435134Z"
} | ee9adf | 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": 1135
},
"timestamp": "2026-02-11T22:57:43.238Z",
"answer": 1054
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"statu... | {
"lo": -3.45,
"mid": 1.15,
"hi": 6.18
} | ||
41bab6 | diophantine_fbi2_count_v1_168721529_1505 | Let $c=5$ and $m=173$. Let $n$ be the number of integers $t$ with $1\le t\le 6$ such that
$$t \equiv \left\lfloor \frac{t}{2} \right\rfloor \pmod{3}.$$
Let $k$ be the number of ordered pairs $(i,j)$ of integers with $1\le i\le 3$ and $1\le j\le 166$ such that $\gcd(i,j)=1$.
Let $L$ be the number of integers $u$ with ... | 877 | graphs = [
Graph(
let={
"_c": Const(5),
"_m": Const(173),
"_n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(6)), Congruent(a=Var(name='n'), b=Floor(arg=Div(left=Var(name='n'), right=Const(value=2))), modulus=Const... | NT | COMB | COUNT | sympy | COUNT_COPRIME_GRID | [
"COUNT_COPRIME_GRID",
"L3C/LIN_FORM"
] | 952b7d | diophantine_fbi2_count_v1 | null | 8 | 0 | [
"COUNT_COPRIME_GRID",
"L3C",
"LIN_FORM"
] | 3 | 0.018 | 2026-02-08T13:44:34.807234Z | {
"verified": true,
"answer": 877,
"timestamp": "2026-02-08T13:44:34.825481Z"
} | 530611 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 437,
"completion_tokens": 2507
},
"timestamp": "2026-02-09T18:16:32.922Z",
"answer": 877
},
{
"id... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "LIN_FORM",
"status": "ok_later"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
... | {
"lo": -1.86,
"mid": 0.78,
"hi": 3.11
} | ||
6c5402 | comb_binomial_compute_v1_1520064083_4177 | Let $n$ be the number of nonnegative integers $j$ with $0 \le j \le 145$ such that $\binom{145}{j}$ is odd. Let $N = n + 6$. Compute $\binom{N}{7}$. | 3,432 | graphs = [
Graph(
let={
"_n": Const(145),
"n": Sum(CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(145)), Eq(Mod(value=Binom(n=Ref("_n"), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')), Const(6)),
... | ALG | COMB | COMPUTE | sympy | K2 | [
"V8"
] | 86348e | comb_binomial_compute_v1 | null | 6 | 0 | [
"K2",
"V8"
] | 2 | 0.008 | 2026-02-08T06:08:19.111682Z | {
"verified": true,
"answer": 3432,
"timestamp": "2026-02-08T06:08:19.120156Z"
} | ec60d1 | 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": 714
},
"timestamp": "2026-02-24T05:28:08.307Z",
"answer": 3432
},
{
"id... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
}
] | {
"lo": -3.84,
"mid": -1.69,
"hi": 1.09
} | ||
02e93c | sequence_count_fib_divisible_v1_238844314_1052 | Let $A$ be the set of all positive integers $t$ such that $15 \leq t \leq 1143$ and there exist positive integers $a$, $b$ with $1 \leq a \leq 51$, $1 \leq b \leq 93$, and $t = 6a + 9b$. Let $u = |A|$. Let $d = 14$. Define $B$ as the set of all positive integers $n$ such that $1 \leq n \leq u$ and $F_n$, the $n$th Fibo... | 66,151 | graphs = [
Graph(
let={
"_n": Const(44121),
"upper": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=51)), Geq(le... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | sequence_count_fib_divisible_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.018 | 2026-02-08T13:52:25.414895Z | {
"verified": true,
"answer": 66151,
"timestamp": "2026-02-08T13:52:25.432862Z"
} | d31eb0 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 211,
"completion_tokens": 4574
},
"timestamp": "2026-02-15T21:26:41.602Z",
"answer": 66151
},
... | 1 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
9890c1 | nt_sum_gcd_range_mod_v1_971394319_1450 | Let $N$ be the number of positive integers $k$ such that $1 \leq k \leq 559433$ and $233$ divides $k$. Let $k_0$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 14400$. Define $S = \sum_{n=1}^{N} \gcd(n, k_0)$. Compute the remainder when $S$ is divided by $11827$. | 9,774 | graphs = [
Graph(
let={
"_m": Const(14400),
"_n": Const(233),
"N": CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(1)), Leq(Var("k"), Const(559433)), Divides(divisor=Ref("_n"), dividend=Var("k"))), domain='positive_integers')),
"k... | NT | null | COMPUTE | sympy | C2 | [
"C2",
"B3"
] | 83578c | nt_sum_gcd_range_mod_v1 | null | 6 | 0 | [
"B3",
"C2"
] | 2 | 0.518 | 2026-02-08T13:41:57.636985Z | {
"verified": true,
"answer": 9774,
"timestamp": "2026-02-08T13:41:58.155369Z"
} | e43018 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 153,
"completion_tokens": 3021
},
"timestamp": "2026-02-15T19:39:13.635Z",
"answer": 9774
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
edf53b | comb_factorial_compute_v1_1918700295_50 | Let $d$ be the smallest divisor of $847$ that is at least $2$. Compute the remainder when $44121 \cdot d!$ is divided by $85691$. | 1,695 | graphs = [
Graph(
let={
"_n": Const(847),
"n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Ref("_n"))))),
"result": Factorial(Ref("n")),
"Q": Mod(value=Mul(Const(44121), Ref("result")), mo... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | comb_factorial_compute_v1 | null | 4 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.002 | 2026-02-08T02:57:54.705315Z | {
"verified": true,
"answer": 1695,
"timestamp": "2026-02-08T02:57:54.706856Z"
} | 25204c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 149,
"completion_tokens": 3008
},
"timestamp": "2026-02-10T12:03:44.745Z",
"answer": 1695
},
{
"i... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"... | {
"lo": -3.47,
"mid": 0.81,
"hi": 4.81
} | ||
343e1b | antilemma_sum_equals_v1_2051736721_1678 | Let $n$ be the number of integers $t$ such that $21 \le t \le 231$ and there exist positive integers $a$ and $b$ with $1 \le a \le 5$, $1 \le b \le 26$, and $t = 15a + 6b$. Let $x$ be the number of ordered pairs $(i,j)$ of positive integers such that $1 \le i \le 66$, $1 \le j \le 67$, and $i + j = n$. Compute $x$. | 66 | 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=5)), Geq(left=Var(name='b'), right=Const(value=... | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"LIN_FORM/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | ada383 | antilemma_sum_equals_v1 | null | 4 | 0 | [
"COUNT_CARTESIAN",
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 3 | 0.095 | 2026-02-08T16:09:04.912635Z | {
"verified": true,
"answer": 66,
"timestamp": "2026-02-08T16:09:05.007685Z"
} | 6400ff | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 230,
"completion_tokens": 2332
},
"timestamp": "2026-02-24T19:53:54.852Z",
"answer": 66
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status... | {
"lo": -4.1,
"mid": -1.76,
"hi": 1.3
} | ||
5feac6 | geo_count_lattice_triangle_v1_655260480_3956 | Let $A$ be the value of $|169 \cdot 120 + 27 \cdot (-55)|$. Let $B$ be the sum
$$
\gcd(|169|, |55|) + \gcd(|27 - 169|, |120 - 55|) + \gcd(|0 - 27|, |0 - 120|).
$$
Define $R = \frac{A + 2 - B}{2}$. Compute the remainder when $44121 \cdot R$ is divided by $85672$. | 79,780 | graphs = [
Graph(
let={
"area_2x": Abs(arg=Sum(Mul(Const(value=169), Const(value=120)), Mul(Const(value=27), Sub(left=Const(value=0), right=Const(value=55))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=169)), b=Abs(arg=Const(value=55))), GCD(a=Abs(arg=Sub(left=Const(value=27), right... | ALG | NT | COUNT | sympy | [] | geo_count_lattice_triangle_v1 | null | 4 | 0 | null | null | 0.005 | 2026-02-08T17:38:28.640613Z | {
"verified": true,
"answer": 79780,
"timestamp": "2026-02-08T17:38:28.645584Z"
} | 351975 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 158,
"completion_tokens": 2048
},
"timestamp": "2026-02-18T05:11:45.180Z",
"answer": 79780
},
... | 1 | [] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||||
d3fa1d | modular_mod_compute_v1_677425708_2178 | Let $n = 237$. Define $a$ to be the largest prime number $n$ such that $2 \leq n \leq \sum_{d \mid n} \phi(d)$, where $\phi$ denotes Euler's totient function. Find the remainder when $a$ is divided by $17161$. | 233 | graphs = [
Graph(
let={
"_n": Const(237),
"a": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d')))), IsPrime(Var("n"))))),
"m": Const(17161),
... | NT | null | COMPUTE | sympy | K3 | [
"K3/MAX_PRIME_BELOW"
] | d8e8cc | modular_mod_compute_v1 | null | 4 | 0 | [
"K3",
"MAX_PRIME_BELOW"
] | 2 | 0.002 | 2026-02-08T04:50:30.423185Z | {
"verified": true,
"answer": 233,
"timestamp": "2026-02-08T04:50:30.425508Z"
} | c8c4a8 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 128,
"completion_tokens": 548
},
"timestamp": "2026-02-11T21:55:28.583Z",
"answer": 401
},
{
"id": 11,
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VA... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
59153a | comb_count_surjections_v1_1125832087_2179 | Let $n = 5$ and $k = 4$. Define $R = k! \cdot S(n, k)$, where $S(n, k)$ is the number of ways to partition a set of $n$ elements into $k$ nonempty subsets. Let $S$ be the set of all ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 2450$. Compute $|S| - R$. | 985 | graphs = [
Graph(
let={
"n": Const(5),
"k": Const(4),
"result": Mul(Factorial(Ref("k")), Stirling2(n=Ref(name='n'), k=Ref(name='k'))),
"Q": Sub(CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1'... | COMB | null | COUNT | sympy | COMB1 | [
"COMB1"
] | 9f12f1 | comb_count_surjections_v1 | negation_mod | 5 | 0 | [
"COMB1"
] | 1 | 0.001 | 2026-02-08T04:23:47.312522Z | {
"verified": true,
"answer": 985,
"timestamp": "2026-02-08T04:23:47.313921Z"
} | 8f8222 | 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": 833
},
"timestamp": "2026-02-24T00:26:17.456Z",
"answer": 985
},
{
"id"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
... | {
"lo": -4.92,
"mid": -2.9,
"hi": -0.7
} | ||
1e1204 | nt_sum_gcd_range_mod_v1_168721529_1067 | Let $N = 1024$ and $k = 480$. Define $s = \sum_{n=1}^{N} \gcd(n, k)$. Let $M = 11617$ and let $r$ be the remainder when $s$ is divided by $M$. Let $d$ be the smallest integer greater than or equal to $2$ that divides $3397301$. Compute the remainder when $d - r$ is divided by $85828$. | 75,275 | graphs = [
Graph(
let={
"_n": Const(2),
"N": Const(1024),
"k": Const(480),
"M": Const(11617),
"sum": Summation(var="n", start=Const(1), end=Ref("N"), expr=GCD(a=Var("n"), b=Ref("k"))),
"result": Mod(value=Ref("sum"), modulus=Ref("M")),
... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | fd27b3 | nt_sum_gcd_range_mod_v1 | negation_mod | 5 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.048 | 2026-02-08T13:26:37.482266Z | {
"verified": true,
"answer": 75275,
"timestamp": "2026-02-08T13:26:37.530267Z"
} | 642503 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 211,
"completion_tokens": 6301
},
"timestamp": "2026-02-11T07:48:04.251Z",
"answer": 75275
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -5.48,
"mid": 0.74,
"hi": 7.52
} | ||
a691ad | alg_qf_psd_orbit_v1_1218484723_5026 | Find the number of ordered triples $(a, b, c)$ of positive integers with $1 \leq a \leq b \leq c \leq 42$ satisfying $$38b^2 + 38c^2 - 22ab - 22bc - 22ac + K \cdot a^2 = 39798,$$ where $$K = \left|\left\{ (a_1, b_1) : 1 \leq a_1, b_1 \leq 40,\ 91a_1^3 + 273a_1^2b_1 + 273a_1b_1^2 + 91b_1^3 = 5398029 \right\}\right|.$$ | 6 | graphs = [
Graph(
let={
"_n": Const(273),
"result": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b"), Var("c")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(42)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(42)), Geq(Var("c"), Const(1)), Leq(Var("... | ALG | null | COUNT | sympy | POLY3_COUNT | [
"POLY3_COUNT"
] | 355dbe | alg_qf_psd_orbit_v1 | null | 5 | 0 | [
"POLY3_COUNT"
] | 1 | 0.156 | 2026-02-25T06:39:09.131710Z | {
"verified": true,
"answer": 6,
"timestamp": "2026-02-25T06:39:09.287399Z"
} | c196c8 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 272,
"completion_tokens": 8112
},
"timestamp": "2026-03-29T19:07:51.386Z",
"answer": 6
},
{
"id":... | 1 | [
{
"lemma": "POLY3_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 1.53,
"mid": 4.7,
"hi": 7.23
} | ||
b0375b | nt_num_divisors_compute_v1_1520064083_814 | Let $S$ be the set of all nonnegative integers $j$ such that $0 \le j \le 9592$ and $\binom{9592}{j}$ is odd. Let $n$ be the number of elements in $S$. Let $d(n)$ denote the number of positive divisors of $n$. Compute $19881 - d(n)$. | 19,873 | graphs = [
Graph(
let={
"_n": Const(2),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(9592)), Eq(Mod(value=Binom(n=Const(9592), k=Var("j")), modulus=Ref("_n")), Const(1))), domain='nonnegative_integers')),
"res... | NT | null | COMPUTE | sympy | V8 | [
"V8"
] | 86348e | nt_num_divisors_compute_v1 | null | 5 | 0 | [
"V8"
] | 1 | 0.001 | 2026-02-08T03:37:11.064583Z | {
"verified": true,
"answer": 19873,
"timestamp": "2026-02-08T03:37:11.065765Z"
} | 62f494 | 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": 671
},
"timestamp": "2026-02-10T15:06:53.168Z",
"answer": 19873
},
{
"i... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8",... | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
3d9cde | modular_mod_compute_v1_124444284_9753 | Let $k$ be a positive integer. Define $m$ as the number of positive integers $k$ such that $k \leq 682112$ and $128$ divides $k$. Find the remainder when $-84100$ is divided by $m$. | 1,164 | graphs = [
Graph(
let={
"_n": Const(128),
"a": Const(-84100),
"m": CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(1)), Leq(Var("k"), Const(682112)), Divides(divisor=Ref("_n"), dividend=Var("k"))), domain='positive_integers')),
"r... | NT | null | COMPUTE | sympy | C2 | [
"C2"
] | 9685eb | modular_mod_compute_v1 | null | 2 | 0 | [
"C2"
] | 1 | 0.001 | 2026-02-08T12:39:49.408753Z | {
"verified": true,
"answer": 1164,
"timestamp": "2026-02-08T12:39:49.410056Z"
} | 854c73 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 101,
"completion_tokens": 799
},
"timestamp": "2026-02-15T03:22:00.783Z",
"answer": 1164
},
{
... | 1 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
f47615 | antilemma_cartesian_v1_548369836_83 | Let $x$ be the number of ordered pairs $(a,b)$ such that $a$ is an integer satisfying $1 \le a \le 26$ and $b$ is an integer satisfying $1 \le b \le 27$. Compute $x$. | 702 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(26)), right=IntegerRange(start=Const(1), end=Const(27)))),
},
goal=Ref("x"),
)
] | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | antilemma_cartesian_v1 | null | 2 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0 | 2026-02-08T02:45:00.879969Z | {
"verified": true,
"answer": 702,
"timestamp": "2026-02-08T02:45:00.880297Z"
} | d59970 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 169,
"completion_tokens": 401
},
"timestamp": "2026-02-08T19:48:04.762Z",
"answer": 702
},
{
"id"... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"statu... | {
"lo": -10,
"mid": -8.03,
"hi": -6.06
} | ||
014824 | antilemma_k3_v1_971394319_725 | Compute the sum $\sum_{d \mid 22641} \phi(d)$, where $\phi$ denotes Euler's totient function. Find the value of this sum. | 22,641 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=22641), var='d', expr=EulerPhi(n=Var(name='d'))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T13:17:08.834013Z | {
"verified": true,
"answer": 22641,
"timestamp": "2026-02-08T13:17:08.834562Z"
} | f6ea3d | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 96,
"completion_tokens": 925
},
"timestamp": "2026-02-16T04:29:11.159Z",
"answer": 22577
},
{
"id": 11,
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
feca23_l | antilemma_sum_equals_v1_677425708_3090 | Let $m$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 166$. Let $x$ be the number of ordered pairs $(i, j)$ with $1 \leq i \leq 83$ and $1 \leq j \leq 83$ such that $i + j = m$. Find the remainder when $|x|$ is divided by $70741$. | 83 | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COMB1/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | 3e1adf | antilemma_sum_equals_v1 | null | 3 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS"
] | 2 | 0.046 | 2026-02-08T05:29:10.686969Z | {
"verified": false,
"answer": 82,
"timestamp": "2026-02-08T05:29:10.733038Z"
} | f5e35f | feca23 | 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": 213,
"completion_tokens": 1062
},
"timestamp": "2026-02-24T03:49:06.135Z",
"answer": 82
},
{
"id"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V8",
"status":... | {
"lo": -4.93,
"mid": -2.91,
"hi": -0.71
} | |
4193b6 | modular_mod_compute_v1_48377204_2529 | Let $n = 2209$. Let $m$ be the largest positive divisor $d$ of $4888517$ such that $1 \leq d \leq n$. Let $a = -529$, and let $r$ be the remainder when $a$ is divided by $m$. Let $k$ be the smallest positive integer such that the $k$-th Fibonacci number is divisible by $|r| + 2$. Compute $k$. | 1,218 | graphs = [
Graph(
let={
"_n": Const(2209),
"a": Const(-529),
"m": MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Leq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(4888517))))),
"result": Mod(value=Ref("a"), mo... | NT | null | COMPUTE | sympy | MAX_DIVISOR | [
"MAX_DIVISOR"
] | 51757e | modular_mod_compute_v1 | null | 5 | 0 | [
"MAX_DIVISOR"
] | 1 | 0.001 | 2026-02-08T16:48:28.293684Z | {
"verified": true,
"answer": 1218,
"timestamp": "2026-02-08T16:48:28.294948Z"
} | 5dde8f | 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": 7431
},
"timestamp": "2026-02-17T12:12:38.966Z",
"answer": 1218
},
{... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
05b301 | comb_count_permutations_fixed_v1_1080341949_323 | Let $n$ be the smallest divisor of $5929$ that is at least $2$. Compute the remainder when $\binom{n}{0} \cdot !(n - 0)$ is multiplied by $17616$ and then divided by $78185$, where $!k$ denotes the number of derangements of $k$ elements. | 56,919 | graphs = [
Graph(
let={
"_n": Const(78185),
"n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(5929))))),
"k": Const(0),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=S... | NT | COMB | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | comb_count_permutations_fixed_v1 | null | 3 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.003 | 2026-02-08T13:25:40.826259Z | {
"verified": true,
"answer": 56919,
"timestamp": "2026-02-08T13:25:40.829118Z"
} | d3c302 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 118,
"completion_tokens": 2416
},
"timestamp": "2026-02-15T16:06:04.553Z",
"answer": 56919
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V3",
"status... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
cfeacd | comb_count_permutations_fixed_v1_677425708_1585 | Let $n = 6$ and $k = 1$. Define $r = \binom{n}{k} \cdot !(n - k)$, where $!m$ denotes the number of derangements of $m$ elements. Let $t$ be the number of decimal digits of $|r|$. For each integer $i$ from $0$ to $t-1$, let $d_i$ be the $i$-th decimal digit of $|r|$ (with $d_0$ the units digit). Let $s$ be the number o... | 15,175 | graphs = [
Graph(
let={
"n": Const(6),
"k": Const(1),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub(left=Ref(name='n'), right=Ref(name='k')))),
"Q": Sum(Summation(var="i", start=Const(0), end=Sub(NumDigits(x=Abs(arg=Ref(name='result')), bas... | NT | COMB | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | a9a663 | comb_count_permutations_fixed_v1 | digits_weighted_mod | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.005 | 2026-02-08T04:18:26.669015Z | {
"verified": true,
"answer": 15175,
"timestamp": "2026-02-08T04:18:26.674202Z"
} | a28bf1 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 301,
"completion_tokens": 837
},
"timestamp": "2026-02-09T21:54:05.337Z",
"answer": 15175
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
... | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
cf9fdc | diophantine_fbi2_min_v1_784195855_8149 | Let $d$ be the smallest integer such that $4 \leq d \leq 106$, $d$ divides $96$, and $\frac{96}{d} \geq 7$. Compute $d$. | 4 | graphs = [
Graph(
let={
"k": Const(96),
"a": Const(3),
"b": Const(6),
"upper": Const(106),
"result": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(4)), Leq(Var("d"), Ref("upper")), Divides(divisor=Var("d"), dividend=Re... | NT | null | EXTREMUM | sympy | LTE_DIFF_P2 | [
"B3"
] | 0cd20d | diophantine_fbi2_min_v1 | null | 3 | 0 | [
"B3",
"LTE_DIFF_P2"
] | 2 | 0.286 | 2026-02-08T15:54:53.054280Z | {
"verified": true,
"answer": 4,
"timestamp": "2026-02-08T15:54:53.340450Z"
} | 6fb2a7 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 104,
"completion_tokens": 707
},
"timestamp": "2026-02-16T06:37:08.953Z",
"answer": 4
},
{
"id": 11,
"... | 2 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
726f97 | alg_poly4_sum_v1_1419126231_1140 | Compute the remainder when
$$
\sum_{\substack{a=1 \\ b=1}}^{375} \left( 97a^4 + 150a^2b^2 - 52ab^3 + 17b^4 + 44a^p b \right)
$$
is divided by $70983$, where $p = \max\{ n : n \ge 2,\ n \le 4,\ n \text{ is prime}\}$. | 47,391 | graphs = [
Graph(
let={
"_n": Const(4),
"result": Mod(value=SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(375)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(375)))), expr=Sum(Mul(Const(... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | alg_poly4_sum_v1 | null | 5 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.795 | 2026-02-25T10:38:49.522328Z | {
"verified": true,
"answer": 47391,
"timestamp": "2026-02-25T10:38:50.317631Z"
} | 1ca618 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 213,
"completion_tokens": 6480
},
"timestamp": "2026-03-30T11:32:32.853Z",
"answer": 36765
},
{
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": 1.5,
"mid": 4.69,
"hi": 7.23
} | ||
f42135 | antilemma_cartesian_v1_1439011603_774 | Let $x$ be the number of ordered pairs $(a, b)$ such that $1 \leq a \leq 38$ and $1 \leq b \leq 45$. Compute $x + \phi(|x| + \binom{16}{16}) + \tau(|x| + 1)$, where $\phi$ denotes Euler's totient function and $\tau(n)$ denotes the number of positive divisors of $n$. | 3,338 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(38)), right=IntegerRange(start=Const(1), end=Const(45)))),
"Q": Sum(Ref("x"), EulerPhi(n=Sum(Abs(arg=Ref(name='x')), Binom(n=Const(16), k=Const(16)))), NumDivisors(n=Sum(Abs(arg... | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN",
"ONE_BINOM_N"
] | f14704 | antilemma_cartesian_v1 | null | 3 | 0 | [
"COUNT_CARTESIAN",
"ONE_BINOM_N"
] | 2 | 0.002 | 2026-02-08T15:42:34.306915Z | {
"verified": true,
"answer": 3338,
"timestamp": "2026-02-08T15:42:34.309332Z"
} | 5e7992 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 207,
"completion_tokens": 750
},
"timestamp": "2026-02-24T18:27:58.610Z",
"answer": 3338
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "ONE_BINOM_N",
"status": "ok"
},
{
"lemma": "V7",
"... | {
"lo": -5.65,
"mid": -3.17,
"hi": -0.81
} | ||
616a47 | comb_catalan_compute_v1_151522320_849 | Let $m$ be the number of elements in the Cartesian product of the sets $\{1, 2, 3\}$ and $\{1, 2, 3, 4\}$. Let $n'$ be the number of ordered pairs $(i, j)$ of integers with $1 \leq i, j \leq 11$ such that $i + j = m$. Let $n$ be the number of ordered pairs $(i, j)$ of integers with $1 \leq i \leq 10$ and $1 \leq j \leq... | 16,796 | graphs = [
Graph(
let={
"_m": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(3)), right=IntegerRange(start=Const(1), end=Const(4)))),
"_n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref... | COMB | null | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS/COUNT_SUM_EQUALS",
"COUNT_CARTESIAN/COUNT_SUM_EQUALS"
] | 459ae8 | comb_catalan_compute_v1 | null | 4 | 0 | [
"COUNT_CARTESIAN",
"COUNT_SUM_EQUALS"
] | 2 | 0.027 | 2026-02-08T03:34:54.293225Z | {
"verified": true,
"answer": 16796,
"timestamp": "2026-02-08T03:34:54.319786Z"
} | 444911 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 257,
"completion_tokens": 935
},
"timestamp": "2026-02-10T15:04:04.731Z",
"answer": 16796
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no... | {
"lo": -5.97,
"mid": -3.96,
"hi": -1.93
} | ||
b9ba33 | antilemma_k2_v1_2051736721_2769 | Let $m = 2$. Let $n$ be the sum of all positive integers $x_1$ such that $x_1^2 - 412x_1 + 30772 = 0$. Let $x = \sum_{k=1}^{412} \phi(k) \left\lfloor \frac{n}{k} \right\rfloor$, where $\phi$ denotes Euler's totient function. Compute the remainder when $87467 \cdot x$ is divided by $56130$. | 26,546 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": SumOverSet(set=SolutionsSet(var=Var("x1"), condition=Eq(Sum(Pow(Var("x1"), Ref("_m")), Mul(Const(-412), Var("x1")), Const(30772)), Const(0)))),
"x": Summation(var="k", start=Const(1), end=Const(412), 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 | 0.002 | 2026-02-08T16:54:29.212490Z | {
"verified": true,
"answer": 26546,
"timestamp": "2026-02-08T16:54:29.214199Z"
} | b549d6 | 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": 3280
},
"timestamp": "2026-02-17T14:49:04.640Z",
"answer": 26546
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
8ede78 | nt_count_divisible_v1_153355830_1193 | Let $A$ be the set of all positive integers $p$ such that there exists an integer $q$ with $pq = 18$, $\gcd(p,q) = 1$, and $p < q$. Let $n = |A|$. Let $S$ be the set of all prime numbers $n$ such that $n \geq n$ and $n \leq 18$. Let $d$ be the maximum element of $S$. Compute the number of positive integers $n$ at most ... | 1,842 | graphs = [
Graph(
let={
"_n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=18)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(value=1)), ... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/MAX_PRIME_BELOW"
] | 2248fc | nt_count_divisible_v1 | null | 4 | 0 | [
"COPRIME_PAIRS",
"MAX_PRIME_BELOW"
] | 2 | 2.604 | 2026-02-08T06:11:00.431819Z | {
"verified": true,
"answer": 1842,
"timestamp": "2026-02-08T06:11:03.035476Z"
} | 2518b2 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 221,
"completion_tokens": 419
},
"timestamp": "2026-02-19T02:44:25.741Z",
"answer": 1843
},
{
"id": 11,... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "M... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.34
} | ||
c80c48 | geo_visible_lattice_v1_124444284_766 | A lattice point $(x, y)$ in the plane is said to be visible from the origin if $\gcd(x, y) = 1$. Let $V(n)$ denote the number of visible lattice points $(x, y)$ with $1 \leq x, y \leq n$. Compute the remainder when $44121 \cdot V(70)$ is divided by $53261$. | 21,713 | graphs = [
Graph(
let={
"n": Const(70),
"result": VisibleLatticePoints(n=Ref(name='n')),
"Q": Mod(value=Mul(Const(44121), Ref("result")), modulus=Const(53261)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 5 | 0 | null | null | 0.108 | 2026-02-08T03:30:11.078855Z | {
"verified": true,
"answer": 21713,
"timestamp": "2026-02-08T03:30:11.187116Z"
} | db92c6 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 193,
"completion_tokens": 3895
},
"timestamp": "2026-02-09T21:44:09.402Z",
"answer": 21713
},
{
"... | 1 | [] | {
"lo": 1.97,
"mid": 4.36,
"hi": 6.69
} | ||||
a035dd | algebra_quadratic_discriminant_v1_153355830_734 | Let $a = \sum_{k=1}^{3} \phi(k) \left\lfloor \frac{3}{k} \right\rfloor$, $b = 8$, $c = 7$, and $n = 4$. Define $D = b^2 - 4ac$. Let $r = 2$ if $D > 0$, $r = 1$ if $D = 0$, and $r = 0$ otherwise. Compute the value of $r$. | 0 | graphs = [
Graph(
let={
"_n": Const(4),
"a": Summation(var="k", start=Const(1), end=Const(3), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(3), Var("k"))))),
"b": Const(8),
"c": Const(7),
"D": Sub(Pow(Ref("b"), Const(2)), Mul(Ref("_n"), Ref("a"), ... | NT | null | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | algebra_quadratic_discriminant_v1 | null | 4 | 0 | [
"K2"
] | 1 | 0.003 | 2026-02-08T04:09:02.212726Z | {
"verified": true,
"answer": 0,
"timestamp": "2026-02-08T04:09:02.215232Z"
} | 9d52d2 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 219,
"completion_tokens": 507
},
"timestamp": "2026-02-10T15:31:29.182Z",
"answer": 0
},
{
"id":... | 2 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.73,
"hi": -5.46
} | ||
e77ec6 | nt_count_coprime_v1_677425708_3573 | Let $k=45$ and let $N$ be the number of integers $n$ with $1\le n\le 46656$ and $\gcd(n,k)=1$.
Let $A$ be the number of integers $n$ with $1\le n\le 10261$ such that
\[n\equiv \left\lfloor\frac{n}{2}\right\rfloor \pmod{7}.
\]
Let $B$ be the number of integers $n$ with $1\le n\le A$ such that $5$ divides $F_n$, where $... | 53,917 | graphs = [
Graph(
let={
"_m": Const(337),
"_n": Const(84825),
"upper": Const(46656),
"k": Const(45),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(GCD(a=Var("n"), b=Ref(... | NT | null | COUNT | sympy | L3C | [
"L3C/COUNT_FIB_DIVISIBLE",
"MIN_PRIME_FACTOR"
] | 072f91 | nt_count_coprime_v1 | two_moduli | 5 | 0 | [
"COUNT_FIB_DIVISIBLE",
"L3C",
"MIN_PRIME_FACTOR"
] | 3 | 4.37 | 2026-02-08T05:50:02.624988Z | {
"verified": true,
"answer": 53917,
"timestamp": "2026-02-08T05:50:06.995090Z"
} | a498c0 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 285,
"completion_tokens": 7211
},
"timestamp": "2026-02-12T15:14:46.610Z",
"answer": 53917
},
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok_later"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
fe71ce | antilemma_v1_legendre_677425708_3857 | Let $n = 34593$. Compute the largest integer $k$ such that $13^k$ divides $34593!$. | 2,881 | graphs = [
Graph(
let={
"_n": Const(34593),
"x": MaxKDivides(target=Factorial(Ref("_n")), base=Const(13)),
},
goal=Ref("x"),
)
] | NT | null | COMPUTE | sympy | V1 | [
"V1"
] | dae96f | antilemma_v1_legendre | null | 6 | 0 | [
"V1"
] | 1 | 0.001 | 2026-02-08T05:58:41.887069Z | {
"verified": true,
"answer": 2881,
"timestamp": "2026-02-08T05:58:41.888104Z"
} | 027669 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 128,
"completion_tokens": 627
},
"timestamp": "2026-02-18T22:13:28.480Z",
"answer": 2881
}
] | 2 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K5",
"status": "same_pattern_wrong"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V1",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
},
{
... | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
cbe29f | comb_count_partitions_v1_1978505735_684 | Let $n = 40$. Let $p(n)$ denote the number of integer partitions of $n$. Find the remainder when $7569 - p(n)$ is divided by $81570$. | 51,801 | graphs = [
Graph(
let={
"n": Const(40),
"result": Partition(arg=Ref(name='n')),
"Q": Mod(value=Sub(Const(7569), Ref("result")), modulus=Const(81570)),
},
goal=Ref("Q"),
)
] | COMB | null | COUNT | sympy | L3C | [
"L3C"
] | fba717 | comb_count_partitions_v1 | negation_mod | 4 | 0 | [
"L3C"
] | 1 | 0.012 | 2026-02-08T15:32:37.740411Z | {
"verified": true,
"answer": 51801,
"timestamp": "2026-02-08T15:32:37.752462Z"
} | 89057c | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 150,
"completion_tokens": 646
},
"timestamp": "2026-02-24T17:57:34.845Z",
"answer": 51801
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -2.4,
"mid": 1.57,
"hi": 5.75
} | ||
6e20dd | sequence_lucas_compute_v1_601307018_900 | Let $n$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 20$ such that
$$
17a^4 + 102a^2b^2 + 68ab^3 + 17b^4 + \left|\{ (a_1, b_1) : 1 \le a_1, b_1 \le 35,\ 16a_1^2 - 32a_1b_1 + 16b_1^2 = 16 \}\right| \cdot a^3b = 3982352.
$$
Let $S = L_n$, the $n$-th Lucas number. Find the remainder wh... | 32,201 | graphs = [
Graph(
let={
"_m": Const(35),
"_n": Const(3),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(20)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(20)), Eq(Sum(Mul(Const(17), ... | ALG | null | COMPUTE | sympy | QF_PSD_COUNT | [
"QF_PSD_COUNT/POLY4_COUNT"
] | 84aa99 | sequence_lucas_compute_v1 | null | 7 | 0 | [
"POLY4_COUNT",
"QF_PSD_COUNT"
] | 2 | 0.006 | 2026-03-10T01:30:50.565794Z | {
"verified": true,
"answer": 32201,
"timestamp": "2026-03-10T01:30:50.572175Z"
} | a7e125 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 283,
"completion_tokens": 3440
},
"timestamp": "2026-03-29T00:30:36.484Z",
"answer": 32201
},
{
"... | 1 | [
{
"lemma": "POLY4_COUNT",
"status": "ok_later"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT",
"status": "ok"
}
] | {
"lo": -0.92,
"mid": 2.07,
"hi": 4.68
} | ||
67e3f5 | nt_num_divisors_compute_v1_898971024_624 | Let $n$ be the smallest possible value of $x + y$ where $x$ and $y$ are positive integers such that $xy = 396900$. Compute the number of positive divisors of $n$. Find the remainder when $44121$ times this number is divided by $71219$. | 21,538 | graphs = [
Graph(
let={
"_n": Const(71219),
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(396900)))), expr=Sum(Var("x"), Var("y"))... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_num_divisors_compute_v1 | null | 3 | 0 | [
"B3"
] | 1 | 0.004 | 2026-02-08T15:34:09.435539Z | {
"verified": true,
"answer": 21538,
"timestamp": "2026-02-08T15:34:09.439399Z"
} | 902445 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 110,
"completion_tokens": 1324
},
"timestamp": "2026-02-16T08:07:27.378Z",
"answer": 21538
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
1caae3 | antilemma_product_of_sums_v1_1520064083_4687 | Let $S_1$ be the sum of the first coordinates $k$ over all ordered pairs $(k, j)$ of integers with $1 \leq k \leq 6$ and $1 \leq j \leq 6$.
Let $S_2 = \sum_{k=1}^{6} k$.
Compute $S_1 \cdot S_2$. | 2,646 | graphs = [
Graph(
let={
"_n": Const(6),
"S1": SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("k"), Var("_j")]), condition=Const(1), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(6)), right=IntegerRange(start=Const(1), end=Const(6)))), expr=Va... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"PRODUCT_OF_SUMS",
"ONE_PHI_1"
] | 10ba65 | antilemma_product_of_sums_v1 | null | 3 | 0 | [
"MIN_PRIME_FACTOR",
"ONE_PHI_1",
"PRODUCT_OF_SUMS"
] | 3 | 0.014 | 2026-02-08T06:23:06.770029Z | {
"verified": true,
"answer": 2646,
"timestamp": "2026-02-08T06:23:06.783715Z"
} | 7fb507 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 173,
"completion_tokens": 423
},
"timestamp": "2026-02-19T05:24:54.540Z",
"answer": 2646
}
] | 2 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "ONE_PHI_1",
"status": "ok"
},
{
"lemma": "PRODUCT_OF_SUMS",
"status": "ok"
},
... | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
33f5e7 | sequence_lucas_compute_v1_1248542787_887 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 100$. Let $n$ be the minimum value of $x + y$ over all pairs in $S$. Let $r = L_n$, the $n$-th Lucas number. Compute the remainder when $36 - r$ is divided by $64602$. | 49,511 | graphs = [
Graph(
let={
"_n": Const(100),
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_n")))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | sequence_lucas_compute_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.002 | 2026-02-08T03:28:23.471461Z | {
"verified": true,
"answer": 49511,
"timestamp": "2026-02-08T03:28:23.473151Z"
} | da7c8f | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 194,
"completion_tokens": 1067
},
"timestamp": "2026-02-09T09:34:14.725Z",
"answer": 49511
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
}
] | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
eb4802 | sequence_fibonacci_compute_v1_717093673_3194 | Let $n$ be the number of integers $t$ such that $27 \leq t \leq 102$ and there exist integers $a$ and $b$ with $1 \leq a \leq 2$, $1 \leq b \leq 10$, and $t = 21a + 6b$. Compute the value of the $n$-th Fibonacci number. | 6,765 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=2)), Geq(left=Var(name='b'), right=Const(value=1... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | sequence_fibonacci_compute_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T17:25:15.012156Z | {
"verified": true,
"answer": 6765,
"timestamp": "2026-02-08T17:25:15.014050Z"
} | ed3bdb | 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": 1157
},
"timestamp": "2026-02-18T01:54:44.585Z",
"answer": 6765
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
7939f9 | antilemma_coprime_grid_v1_677425708_1606 | Let $S$ be the set of all ordered pairs $(i,j)$ of positive integers such that $1 \leq i \leq 23$ and $1 \leq j \leq 24$, and $\gcd(i,j) = \phi(1)$. Compute the number of elements in $S$. | 351 | graphs = [
Graph(
let={
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(GCD(a=Var("i"), b=Var("j")), EulerPhi(n=Const(1))), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(23)), right=IntegerRange(start=Const(1), end=Const(24))))),
... | NT | COMB | COMPUTE | sympy | COUNT_COPRIME_GRID | [
"COUNT_COPRIME_GRID",
"ONE_PHI_1"
] | 3d404c | antilemma_coprime_grid_v1 | null | 3 | 0 | [
"COUNT_COPRIME_GRID",
"ONE_PHI_1"
] | 2 | 0.001 | 2026-02-08T04:18:45.129142Z | {
"verified": true,
"answer": 351,
"timestamp": "2026-02-08T04:18:45.129693Z"
} | e53b74 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 178,
"completion_tokens": 3529
},
"timestamp": "2026-02-09T22:18:01.669Z",
"answer": 351
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "ONE_PHI_1",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
... | {
"lo": -6.5,
"mid": -0.2,
"hi": 6.11
} | ||
176dfe | comb_binomial_compute_v1_809748730_1362 | Let $n = \sum_{k=1}^{5} k$ and let $k = 7$. Define $C$ to be the binomial coefficient $\binom{n}{k}$. Compute $19321 - C$. | 12,886 | graphs = [
Graph(
let={
"n": Summation(var="k", start=Const(1), end=Const(5), expr=Var("k")),
"k": Const(7),
"result": Binom(n=Ref("n"), k=Ref("k")),
"Q": Sub(Const(19321), Ref("result")),
},
goal=Ref("Q"),
)
] | ALG | COMB | COMPUTE | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | comb_binomial_compute_v1 | null | 2 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.001 | 2026-02-08T12:22:47.268717Z | {
"verified": true,
"answer": 12886,
"timestamp": "2026-02-08T12:22:47.269815Z"
} | 81ff39 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 159,
"completion_tokens": 409
},
"timestamp": "2026-02-24T15:35:40.715Z",
"answer": 12886
},
{
"i... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
}
] | {
"lo": -9.23,
"mid": -6.18,
"hi": -4.06
} |
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