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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
305627 | lin_form_endings_v1_48377204_283 | Let $a = 24$, $b = 40$, and $k = 43$. Let $s = \gcd(a, b)$. Compute $\left\lfloor \frac{k}{\gcd(k, s)} \right\rfloor$, multiply the result by $13524$, and then take the remainder when divided by $56955$. | 11,982 | graphs = [
Graph(
let={
"a_coeff": Const(24),
"b_coeff": Const(40),
"k_val": Const(43),
"step": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"_inner_result": Floor(Div(Ref("k_val"), GCD(a=Ref("k_val"), b=Ref("step")))),
"_scale_k": Const(13... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 3 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T15:20:03.403783Z | {
"verified": true,
"answer": 11982,
"timestamp": "2026-02-08T15:20:03.404684Z"
} | b721f2 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 116,
"completion_tokens": 458
},
"timestamp": "2026-02-16T03:07:22.907Z",
"answer": 11982
},
{... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
4dc1a6 | sequence_count_fib_divisible_v1_1439011603_1515 | Let $d_1$ be a positive integer divisor of 769113 such that $1 \leq d_1 \leq 873$. Define $u$ to be the largest such $d_1$. Let $d = 20$. Consider the set of all positive integers $n$ such that $1 \leq n \leq u$ and $d$ divides the $n$-th Fibonacci number. Compute the number of elements in this set. | 29 | graphs = [
Graph(
let={
"upper": MaxOverSet(set=SolutionsSet(var=Var("d1"), condition=And(Geq(Var("d1"), Const(1)), Leq(Var("d1"), Const(873)), Divides(divisor=Var("d1"), dividend=Const(769113))))),
"d": Const(20),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), con... | NT | null | COUNT | sympy | B3 | [
"MAX_DIVISOR"
] | 51757e | sequence_count_fib_divisible_v1 | null | 5 | 0 | [
"B3",
"MAX_DIVISOR"
] | 2 | 0.09 | 2026-02-08T16:09:19.290612Z | {
"verified": true,
"answer": 29,
"timestamp": "2026-02-08T16:09:19.380794Z"
} | a89f64 | 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": 2080
},
"timestamp": "2026-02-16T21:29:54.412Z",
"answer": 29
},
{
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
656b2f | antilemma_cartesian_v1_655260480_5732 | Let $x$ be the number of ordered pairs $(a, b)$ such that $1 \leq a \leq 12$ and $1 \leq b \leq 15$. Compute the smallest positive integer $k$ such that the $k$th Fibonacci number is divisible by $x + 2$. | 168 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(12)), right=IntegerRange(start=Const(1), end=Const(15)))),
"Q": FibonacciEntryPoint(modulus=Sum(Abs(arg=Ref(name='x')), Const(value=2))),
},
goal=Ref("Q"),
)... | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | antilemma_cartesian_v1 | null | 2 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.001 | 2026-02-08T18:38:37.282870Z | {
"verified": true,
"answer": 168,
"timestamp": "2026-02-08T18:38:37.283425Z"
} | 8b59d5 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 111,
"completion_tokens": 1577
},
"timestamp": "2026-02-18T18:14:45.641Z",
"answer": 168
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"statu... | {
"lo": -3.12,
"mid": 1.47,
"hi": 6.57
} | ||
94a11e_n | comb_count_derangements_v1_1218484723_56 | A theater group has $n$ actors, each assigned a unique role. On opening night, due to a mix-up, every actor takes a role that isn't their own—an arrangement called a derangement. The value $n$ is computed as $2^0 + 2^1 + 2^2 = 7$. Let $R$ be the number of such possible mix-ups. Compute the remainder when $96031 \cdot R... | 7,354 | COMB | null | COUNT | sympy | SUM_GEOM | [
"SUM_GEOM",
"ZERO_BINOM_N"
] | 4e18d8 | comb_count_derangements_v1 | null | 4 | null | [
"SUM_GEOM",
"ZERO_BINOM_N"
] | 2 | 0.002 | 2026-02-25T01:45:38.643646Z | null | c50dc1 | 94a11e | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 210,
"completion_tokens": 2314
},
"timestamp": "2026-03-30T14:41:25.648Z",
"answer": 7354
},
{
"i... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "SUM_GEOM",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"st... | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | |
c4f953 | comb_factorial_compute_v1_1218484723_2537 | Find the number of ordered pairs $(a, b)$ of positive integers with $1 \leq a \leq b \leq 15$ such that $2a^2 - 4ab + 2b^2 = 128$. Let $Q$ be the factorial of this number. Compute $Q$. | 5,040 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(2),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a1"), Var("b1")]), condition=An... | COMB | null | COMPUTE | sympy | QF_PSD_ORBIT | [
"QF_PSD_ORBIT/QF_PSD_ORBIT",
"B3/QF_PSD_ORBIT"
] | 0242d3 | comb_factorial_compute_v1 | null | 5 | 0 | [
"B3",
"QF_PSD_ORBIT"
] | 2 | 0.009 | 2026-02-25T04:16:56.198405Z | {
"verified": true,
"answer": 5040,
"timestamp": "2026-02-25T04:16:56.207385Z"
} | 2b0e4f | 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": 652
},
"timestamp": "2026-03-29T05:16:17.193Z",
"answer": 5040
},
{
"id... | 2 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "QF_PS... | {
"lo": -10,
"mid": -6.41,
"hi": -2.82
} | ||
b48b53 | diophantine_fbi2_min_v1_124444284_2712 | Let $n$ range over the positive integers from 1 to 154 such that $$ n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{7}. $$ Let $k$ be the number of such integers. Find the smallest divisor $d \ge 2$ of $k$ for which $\frac{k}{d} \ge 7$ and $d \le 32$. Compute the remainder when $72774$ times this divisor is divid... | 31,342 | graphs = [
Graph(
let={
"_n": Const(57103),
"k": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(154)), Congruent(a=Var(name='n'), b=Floor(arg=Div(left=Var(name='n'), right=Const(value=2))), modulus=Const(value=7))))),
... | NT | null | EXTREMUM | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC",
"L3C"
] | 22c5b7 | diophantine_fbi2_min_v1 | null | 6 | 0 | [
"L3C",
"SUM_ARITHMETIC"
] | 2 | 0.005 | 2026-02-08T04:53:57.660661Z | {
"verified": true,
"answer": 31342,
"timestamp": "2026-02-08T04:53:57.665452Z"
} | 30716a | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 221,
"completion_tokens": 1342
},
"timestamp": "2026-02-11T22:42:06.301Z",
"answer": 31342
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
},
{
"lem... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
fbc7a3 | diophantine_fbi2_count_v1_1915831931_3405 | Let $B$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $p < q$, $pq = 6$, and $\gcd(p, q) = 1$. Let $t$ be the number of elements in $B$. Define $S$ as the set of all positive integers $d$ such that $t \le d \le 89$, $d$ divides 720, $\frac{720}{d} \ge 2$, and $\frac{720... | 16 | graphs = [
Graph(
let={
"k": Const(720),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(n... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | diophantine_fbi2_count_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.008 | 2026-02-08T17:38:30.927916Z | {
"verified": true,
"answer": 16,
"timestamp": "2026-02-08T17:38:30.935941Z"
} | c0d9b4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 175,
"completion_tokens": 1101
},
"timestamp": "2026-02-18T05:36:56.724Z",
"answer": 16
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
c55962 | nt_sum_divisors_compute_v1_2080023795_57 | Let $c = \mu(47)^k$, where $\mu$ denotes the M\"obius function and $k$ is the number of unordered pairs of coprime positive integers $(p,q)$ such that $p < q$ and $pq = 12$. Let $u = \lambda(3) + 1$, where $\lambda$ denotes the Liouville function. Define $n = 44521 + u$. Let $\sigma(n)$ denote the sum of the positive d... | 35,923 | graphs = [
Graph(
let={
"n2": Const(47),
"c": Pow(MoebiusMu(n=Ref(name='n2')), 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=12)), Eq(left=G... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/MOBIUS_SQUAREFREE",
"LIOUVILLE_MINUS_ONE"
] | 6b62be | nt_sum_divisors_compute_v1 | null | 5 | 2 | [
"COPRIME_PAIRS",
"LIOUVILLE_MINUS_ONE",
"MOBIUS_SQUAREFREE"
] | 3 | 0.003 | 2026-02-08T11:30:51.924549Z | {
"verified": true,
"answer": 35923,
"timestamp": "2026-02-08T11:30:51.927964Z"
} | ed8b76 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 235,
"completion_tokens": 2382
},
"timestamp": "2026-02-08T20:38:56.704Z",
"answer": 35923
},
{
"... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIOUVILLE_MINUS_ONE",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
... | {
"lo": -6.69,
"mid": -2.4,
"hi": 1.76
} | ||
7786a1 | comb_catalan_compute_v1_1915831931_3466 | Let $w = \sum_{k=0}^{10} (-1)^k \binom{10}{k}$ and $t = \sum_{k_1=0}^{0} (-1)^{k_1} \binom{0}{k_1}$. Let $C_{10}$ denote the 10th Catalan number. Let $Q$ be the remainder when $ (41383 + w) \cdot t \cdot C_{10} $ is divided by $80559$. Compute the value of $Q$. | 5,816 | graphs = [
Graph(
let={
"n2": Const(10),
"w": Summation(var="k", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n2"), k=Var("k")))),
"n1": Const(0),
"t": Summation(var="k1", start=Const(0), end=Ref("n1"), expr=Mul(Pow(Const(-1),... | COMB | null | COMPUTE | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING"
] | c21569 | comb_catalan_compute_v1 | null | 3 | 2 | [
"BINOMIAL_ALTERNATING"
] | 1 | 0.003 | 2026-02-08T17:41:32.445124Z | {
"verified": true,
"answer": 5816,
"timestamp": "2026-02-08T17:41:32.447641Z"
} | aae825 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 155,
"completion_tokens": 1430
},
"timestamp": "2026-02-18T05:43:51.040Z",
"answer": 5816
},
{... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
... | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||
b97aca | comb_count_surjections_v1_1520064083_3198 | Let $n$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2$ equals the number of integers $t$ in the range $22 \leq t \leq 61$ for which there exist integers $a$ and $b$ satisfying $1 \leq a \leq 5$, $1 \leq b \leq 2$, and $t = 6a + 15b + 1$. Let $k = 4$. Compute $k! \cdot S(n, k)... | 240 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2")), CountOverSet(set=SolutionsSet(v... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/COMB1"
] | 268a62 | comb_count_surjections_v1 | null | 6 | 0 | [
"COMB1",
"LIN_FORM"
] | 2 | 0.004 | 2026-02-08T05:30:43.662437Z | {
"verified": true,
"answer": 240,
"timestamp": "2026-02-08T05:30:43.666745Z"
} | cd0542 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 256,
"completion_tokens": 1259
},
"timestamp": "2026-02-24T03:51:43.407Z",
"answer": 240
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok_later"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM"... | {
"lo": -3.84,
"mid": -1.69,
"hi": 1.09
} | ||
656087 | comb_sum_binomial_row_v1_1520064083_534 | Let $n$ be the number of positive integers less than or equal to 47 that are relatively prime to 12. Find the value of $2^n$. | 65,536 | graphs = [
Graph(
let={
"_n": Const(12),
"n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(47)), Eq(GCD(a=Var("n"), b=Ref("_n")), Const(1))))),
"result": Pow(Const(2), Ref("n")),
},
goal=Ref("result... | NT | null | SUM | sympy | C4 | [
"C4"
] | 08d162 | comb_sum_binomial_row_v1 | null | 4 | 0 | [
"C4"
] | 1 | 0.001 | 2026-02-08T03:28:00.125641Z | {
"verified": true,
"answer": 65536,
"timestamp": "2026-02-08T03:28:00.126777Z"
} | c93a12 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 144,
"completion_tokens": 581
},
"timestamp": "2026-02-10T14:27:28.619Z",
"answer": 65536
},
{
"i... | 1 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.02,
"hi": 0.31
} | ||
720c62 | nt_num_divisors_compute_v1_124444284_6122 | Let $m$ be the sum of all integers $x$ satisfying
$$x^2-2936x-201201=0.$$
Let $n$ be the number of nonnegative integers $j$ such that
$$0\le j\le M\quad\text{and}\quad\binom{m}{j}\equiv1\pmod{2},$$
where $M$ is the minimum value of $x+y$ over all ordered pairs $(x,y)$ of positive integers satisfying $xy=2155024$.
Let $... | 8 | graphs = [
Graph(
let={
"_c": Const(2),
"_m": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Ref("_c")), Mul(Const(-2936), Var("x")), Const(-201201)), Const(0)))),
"_n": Const(2),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condi... | NT | null | COMPUTE | sympy | VIETA_SUM | [
"VIETA_SUM/B3/V8"
] | 4734d2 | nt_num_divisors_compute_v1 | null | 8 | 0 | [
"B3",
"V8",
"VIETA_SUM"
] | 3 | 0.003 | 2026-02-08T08:08:37.763486Z | {
"verified": true,
"answer": 8,
"timestamp": "2026-02-08T08:08:37.766942Z"
} | 8adece | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 173,
"completion_tokens": 1438
},
"timestamp": "2026-02-13T15:24:51.202Z",
"answer": 8
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lem... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
54dc97 | nt_count_with_divisor_count_v1_124444284_7971 | Let $m = 15$ and $n = 2$. Define $T$ to be the set of all integers $t$ such that $21 \leq t \leq 28383$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 3343$, $1 \leq b \leq 555$, and $t = 6a + 15b$. Let $U$ be the number of positive integers $n$ such that $1 \leq n \leq U'$ and $\gcd(n, m) = 1$, wher... | 1,034 | graphs = [
Graph(
let={
"_m": Const(15),
"_n": Const(2),
"upper": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name... | NT | null | COUNT | sympy | COUNT_PRIMES | [
"LIN_FORM/C4"
] | 067e5d | nt_count_with_divisor_count_v1 | null | 6 | 0 | [
"C4",
"COUNT_PRIMES",
"LIN_FORM"
] | 3 | 14.822 | 2026-02-08T09:29:18.038018Z | {
"verified": true,
"answer": 1034,
"timestamp": "2026-02-08T09:29:32.860045Z"
} | fdcb01 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 262,
"completion_tokens": 4851
},
"timestamp": "2026-02-14T04:19:54.108Z",
"answer": 1034
},
{... | 1 | [
{
"lemma": "C4",
"status": "ok_later"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
f2f68f | sequence_fibonacci_compute_v1_168721529_257 | Let $n$ be the largest prime number such that $2 \leq n \leq 25$.
Compute the $n$-th Fibonacci number, where the Fibonacci sequence is defined by $F_1 = 1$, $F_2 = 1$, and $F_k = F_{k-1} + F_{k-2}$ for all $k \geq 3$.
Find the value of this result. | 28,657 | graphs = [
Graph(
let={
"_n": Const(25),
"n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))),
"result": Fibonacci(arg=Ref(name='n')),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | sequence_fibonacci_compute_v1 | null | 4 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.001 | 2026-02-08T12:56:11.575733Z | {
"verified": true,
"answer": 28657,
"timestamp": "2026-02-08T12:56:11.576493Z"
} | c02872 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 207,
"completion_tokens": 439
},
"timestamp": "2026-02-09T02:57:41.133Z",
"answer": 28657
},
{
"i... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": ... | {
"lo": -5.3,
"mid": -2.05,
"hi": 1.82
} | ||
004236 | antilemma_sum_equals_v1_865884756_4577 | Let $n = 24$. Let $x$ be the number of ordered pairs $(i, j)$ of positive integers such that $1 \leq i \leq 23$, $1 \leq j \leq 23$, and $i + j = n$. Compute the remainder when $44121 \cdot x$ is divided by $64574$. | 46,173 | graphs = [
Graph(
let={
"_n": Const(24),
"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(23)), 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 | 0.047 | 2026-02-08T17:59:42.167600Z | {
"verified": true,
"answer": 46173,
"timestamp": "2026-02-08T17:59:42.214365Z"
} | db5628 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 120,
"completion_tokens": 781
},
"timestamp": "2026-02-18T11:49:36.136Z",
"answer": 46173
},
{... | 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": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||
41d17b | sequence_count_fib_divisible_v1_1742523217_3349 | Let $t$ be an integer. Determine the number of values of $t$ such that $24 \leq t \leq 541$ and there exist positive integers $a \leq 132$ and $b \leq 52$ satisfying $t = 2a + 5b + 17$. Let this number be $u$. Now, let $F_n$ denote the $n$th Fibonacci number, with $F_1 = F_2 = 1$ and $F_n = F_{n-1} + F_{n-2}$ for $n \g... | 77,169 | graphs = [
Graph(
let={
"_n": Const(77230),
"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=132)), Geq(l... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | sequence_count_fib_divisible_v1 | null | 7 | 0 | [
"LIN_FORM"
] | 1 | 0.024 | 2026-02-08T05:48:35.673858Z | {
"verified": true,
"answer": 77169,
"timestamp": "2026-02-08T05:48:35.698017Z"
} | 205899 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 227,
"completion_tokens": 3306
},
"timestamp": "2026-02-12T14:53:27.810Z",
"answer": 77169
},
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
740a4c | nt_lcm_compute_v1_1978505735_3538 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 186624$. For each such pair, compute $x + y$. Let $b$ be the minimum value among all such sums. Let $a = 1103$. Define $c = \operatorname{lcm}(a, b)$. Find the remainder when $17950 \cdot c$ is divided by $68789$. | 33,036 | graphs = [
Graph(
let={
"a": Const(1103),
"b": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(186624)))), expr=Sum(Var("x"), Var("y"))))... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_lcm_compute_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.001 | 2026-02-08T17:42:39.391127Z | {
"verified": true,
"answer": 33036,
"timestamp": "2026-02-08T17:42:39.392450Z"
} | 0198fa | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 138,
"completion_tokens": 5301
},
"timestamp": "2026-02-18T06:21:57.047Z",
"answer": 33036
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
60ec0f | modular_min_modexp_v1_1915831931_2183 | Let $N$ be the number of positive integers $n_1$ such that $1 \leq n_1 \leq 4075$ and $5$ divides the $n_1$-th Fibonacci number. Let $m$ be the largest prime number $n$ such that $2 \leq n \leq N$. Let $x$ be the smallest positive integer such that $1 \leq x \leq 405$ and $11^x \equiv 30 \pmod{m}$. Compute the remainde... | 44,204 | graphs = [
Graph(
let={
"_n": Const(4075),
"a": Const(11),
"b": Const(30),
"m": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(1)), ... | NT | null | EXTREMUM | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE/MAX_PRIME_BELOW"
] | c3fe6d | modular_min_modexp_v1 | null | 7 | 0 | [
"COUNT_FIB_DIVISIBLE",
"MAX_PRIME_BELOW"
] | 2 | 0.033 | 2026-02-08T16:39:32.209718Z | {
"verified": true,
"answer": 44204,
"timestamp": "2026-02-08T16:39:32.242641Z"
} | be7ac2 | 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": 2243
},
"timestamp": "2026-02-17T09:01:22.591Z",
"answer": 44204
},
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
8c05ec | antilemma_sum_factor_cartesian_v1_677425708_1617 | Let $T$ be the set of all integers $t$ such that $21 \leq t \leq 43$ and there exist positive integers $a$, $b$ with $1 \leq a \leq 5$, $1 \leq b \leq 3$, satisfying $t = 3a + 5b + 13$. Let $g = \gcd(8, |T|)$. Let $D$ be the set of positive divisors of $g$. Define $\mu(d)$ as the M\"obius function. Let $S$ be the set o... | 29,484 | graphs = [
Graph(
let={
"_n": Const(8),
"x": SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=SumOverDivisors(n=GCD(a=Ref(name='_n'), b=CountOverSet(set=SolutionsSet(var=Var(name='t'), condition=Exists(var=Var(name='a'), condition=Exists(... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/MOBIUS_COPRIME/SUM_FACTOR_CARTESIAN",
"SUM_FACTOR_CARTESIAN"
] | a038a8 | antilemma_sum_factor_cartesian_v1 | null | 6 | 0 | [
"LIN_FORM",
"MOBIUS_COPRIME",
"SUM_FACTOR_CARTESIAN"
] | 3 | 0.001 | 2026-02-08T04:18:51.039791Z | {
"verified": true,
"answer": 29484,
"timestamp": "2026-02-08T04:18:51.041207Z"
} | 614359 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 312,
"completion_tokens": 1236
},
"timestamp": "2026-02-09T22:23:15.070Z",
"answer": 0
},
{
"i... | 0 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok_late... | {
"lo": 2.2,
"mid": 6.06,
"hi": 9.93
} | ||
80f728 | diophantine_fbi2_count_v1_1470522791_977 | Let $k$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $x \cdot y = 176400$. Determine the number of positive integers $d$ such that $6 \leq d \leq 172$, $d$ divides $k$, and $\frac{k}{d}$ is at least $4$ and at most the sum of the solutions to the equation $x^2 - 170x + ... | 23 | graphs = [
Graph(
let={
"_n": Const(5704),
"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(176400)))), expr=Sum(Var("x"), Var("y")))... | NT | null | COUNT | sympy | V1 | [
"VIETA_SUM",
"B3"
] | 018050 | diophantine_fbi2_count_v1 | null | 6 | 0 | [
"B3",
"V1",
"VIETA_SUM"
] | 3 | 0.124 | 2026-02-08T13:21:31.189710Z | {
"verified": true,
"answer": 23,
"timestamp": "2026-02-08T13:21:31.313214Z"
} | d1bb1f | 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": 2029
},
"timestamp": "2026-02-15T14:04:28.305Z",
"answer": 23
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"l... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
261ebe | nt_min_coprime_above_v1_1439011603_1943 | Let $P$ be the set of all ordered pairs of positive integers $(x, y)$ such that $xy = 17842176$. For each such pair, compute $x + y$, and let $s$ be the minimum value of $x + y$ over all such pairs. Let $n$ be the smallest integer greater than $8192$ and at most $s$ that is relatively prime to $246$. Determine the valu... | 8,195 | graphs = [
Graph(
let={
"start": Const(8192),
"upper": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(17842176)))), expr=Sum(Var("x"), V... | NT | null | EXTREMUM | sympy | B3 | [
"B3"
] | 0cd20d | nt_min_coprime_above_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.043 | 2026-02-08T16:23:29.115139Z | {
"verified": true,
"answer": 8195,
"timestamp": "2026-02-08T16:23:29.158083Z"
} | 55eb52 | 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": 1497
},
"timestamp": "2026-02-17T03:53:50.496Z",
"answer": 8195
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
d49ad2 | nt_num_divisors_compute_v1_153355830_2927 | Let $n = 169$. Define $r$ to be the number of positive divisors of $n$. Let $s = \sum_{k=1}^{87} k$. Compute $r^2 + 7r + s$. | 3,858 | graphs = [
Graph(
let={
"_n": Const(7),
"n": Const(169),
"result": NumDivisors(n=Ref("n")),
"_c": Summation(var="k", start=Const(1), end=Const(87), expr=Var("k")),
"Q": Sum(Pow(Ref("result"), Const(2)), Mul(Ref("_n"), Ref("result")), Ref("_c")),
... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"SUM_ARITHMETIC"
] | 609463 | nt_num_divisors_compute_v1 | quadratic_mod | 3 | 0 | [
"MAX_PRIME_BELOW",
"SUM_ARITHMETIC"
] | 2 | 0.03 | 2026-02-08T07:28:50.045632Z | {
"verified": true,
"answer": 3858,
"timestamp": "2026-02-08T07:28:50.075740Z"
} | 86d9b3 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 108,
"completion_tokens": 243
},
"timestamp": "2026-02-15T18:59:39.110Z",
"answer": 3954
},
{
"id": 11,... | 1 | [
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -9.14,
"mid": -6.05,
"hi": -3.73
} | ||
11815a | sequence_count_fib_divisible_v1_168721529_1527 | Let $n$ be a positive integer. Define $\text{upper}$ to be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 97344$. Define $d$ to be the maximum value of $xy$ over all ordered pairs $(x, y)$ of positive integers such that $x + y = 6$. Determine the value of the number of... | 52 | graphs = [
Graph(
let={
"_m": Const(6),
"_n": Const(97344),
"upper": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_n")))), ... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"B3",
"B1"
] | 655d51 | sequence_count_fib_divisible_v1 | null | 6 | 0 | [
"B1",
"B3",
"MIN_PRIME_FACTOR"
] | 3 | 0.132 | 2026-02-08T13:44:47.407270Z | {
"verified": true,
"answer": 52,
"timestamp": "2026-02-08T13:44:47.539503Z"
} | 042222 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 234,
"completion_tokens": 3242
},
"timestamp": "2026-02-09T18:36:52.115Z",
"answer": 52
},
{
"id"... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ... | {
"lo": -5.49,
"mid": 0.03,
"hi": 6.12
} | ||
f5ba92 | antilemma_sum_equals_v1_124444284_5679 | Compute the number of ordered pairs $(i, j)$ of integers such that $1 \le i \le 41$, $1 \le j \le 41$, and $i + j = 42$. | 41 | graphs = [
Graph(
let={
"_n": Const(42),
"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(41)), right=IntegerRange(start=Const(1), end=Con... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | antilemma_sum_equals_v1 | null | 3 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.013 | 2026-02-08T06:46:18.088342Z | {
"verified": true,
"answer": 41,
"timestamp": "2026-02-08T06:46:18.101601Z"
} | 3fbc4b | 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": 231
},
"timestamp": "2026-02-24T07:00:01.636Z",
"answer": 41
},
{
"id":... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V8",
... | {
"lo": -10,
"mid": -7.79,
"hi": -5.57
} | ||
9649c1 | nt_max_prime_below_v1_865884756_6709 | Let $p$ be the largest prime number less than or equal to $63001$. Compute the Bell number $B_r$, where $r$ is the remainder when $p$ is divided by $11$. | 5 | graphs = [
Graph(
let={
"upper": Const(63001),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("upper")), IsPrime(Var("n"))))),
"Q": Bell(Mod(value=Abs(arg=Ref(name='result')), modulus=Const(11))),
},
... | NT | COMB | EXTREMUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | 88ea9c | nt_max_prime_below_v1 | bell_mod | 2 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 2.743 | 2026-02-08T19:21:38.629698Z | {
"verified": true,
"answer": 5,
"timestamp": "2026-02-08T19:21:41.373078Z"
} | 2319f3 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 90,
"completion_tokens": 4302
},
"timestamp": "2026-02-18T22:04:16.181Z",
"answer": 5
},
{
... | 1 | [
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
535019 | comb_catalan_compute_v1_153355830_935 | Let $ n = 10 $ and let $ C_n $ denote the $ n $-th Catalan number. Define
$$
S = \sum_{i=a}^{b} d_i (i+1)^2,
$$
where $ d_i $ is the $ i $-th decimal digit of $ |C_n| $ (starting from the units digit at $ i = 0 $),
$$
a = \sum_{k=0}^{8} (-1)^k \binom{8}{k},
$$
and $ b = \text{number of digits of } |C_n| - 0! $.
Let $ Q... | 50,226 | graphs = [
Graph(
let={
"n": Const(10),
"result": Catalan(Ref("n")),
"_c": Const(50000),
"Q": Sum(Summation(var="i", start=Summation(var="k", start=Const(0), end=Const(8), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Const(8), k=Var("k")))), end=Sub(NumDigits(x=... | COMB | null | COMPUTE | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING",
"ONE_FACTORIAL_0"
] | 8794cb | comb_catalan_compute_v1 | null | 4 | 0 | [
"BINOMIAL_ALTERNATING",
"ONE_FACTORIAL_0"
] | 2 | 0.002 | 2026-02-08T04:16:39.842941Z | {
"verified": true,
"answer": 50226,
"timestamp": "2026-02-08T04:16:39.845047Z"
} | 088d22 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 258,
"completion_tokens": 805
},
"timestamp": "2026-02-24T00:08:57.233Z",
"answer": 50226
},
{
"i... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "ONE_FACTORIAL_0",
"status": "ok"
},
{
"... | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
d3fc82 | sequence_fibonacci_compute_v1_1742523217_902 | Let $n$ be the number of ordered pairs $(i,j)$ of positive integers such that $1 \leq i \leq 3$, $1 \leq j \leq 10$, and $\gcd(i,j) = 1$. Let $a = F_n$, where $F_n$ denotes the $n$th Fibonacci number. Compute $$a + \varphi(|a| + 1) + \tau(|a| + 1),$$ where $\varphi(k)$ denotes Euler's totient function and $\tau(k)$ den... | 23,511 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(GCD(a=Var("i"), b=Var("j")), Const(1)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(3)), right=IntegerRange(start=Const(1), end=Const(10))))),
"re... | NT | null | COMPUTE | sympy | COUNT_COPRIME_GRID | [
"COUNT_COPRIME_GRID"
] | 20ec03 | sequence_fibonacci_compute_v1 | null | 4 | 0 | [
"COUNT_COPRIME_GRID"
] | 1 | 0.002 | 2026-02-08T03:21:12.467862Z | {
"verified": true,
"answer": 23511,
"timestamp": "2026-02-08T03:21:12.469552Z"
} | 5e6bb6 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 245,
"completion_tokens": 1146
},
"timestamp": "2026-02-10T00:20:09.393Z",
"answer": 23511
},
{
"... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V5",
"status": ... | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
89ab46 | alg_sum_powers_v1_1218484723_74 | Find the remainder when $\sum_{k=1}^{1084} k^2$ is divided by $\left|\left\{ x : 1 \le x \le 7885,\ |4x - 15600| \le 15596 \right\}\right|$. | 4,326 | graphs = [
Graph(
let={
"_n": Const(7885),
"result": Mod(value=Summation(var="k", start=Const(1), end=Const(1084), expr=Pow(Var("k"), Const(2))), modulus=CountOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), Const(1)), Leq(Var("x"), Ref("_n")), Leq(Abs(arg=Sub(left=... | ALG | null | COMPUTE | sympy | ABS_INEQ | [
"ABS_INEQ"
] | 1c5bb8 | alg_sum_powers_v1 | null | 4 | 0 | [
"ABS_INEQ"
] | 1 | 0.052 | 2026-02-25T01:46:50.932452Z | {
"verified": true,
"answer": 4326,
"timestamp": "2026-02-25T01:46:50.984187Z"
} | e26dd3 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 171,
"completion_tokens": 2260
},
"timestamp": "2026-03-10T08:01:15.798Z",
"answer": 4326
},
{
"i... | 1 | [
{
"lemma": "ABS_INEQ",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -0.93,
"mid": 2.04,
"hi": 4.6
} | ||
0371e3 | algebra_poly_eval_v1_458359167_5108 | Let $x = 12$. Define $e$ to be the number of positive integers $p$ for which there exists a positive integer $q$ such that:
- $p \cdot q = 54$,
- $\gcd(p, q) = 1$,
- $p < q$.
Let $r = 6x^e - 4x + 3$. Let $Q = (34843 \cdot r) \mod 58087$.
Find the value of $Q$. | 15,700 | graphs = [
Graph(
let={
"x": Const(12),
"result": Sum(Mul(Const(6), Pow(Ref("x"), 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=54)), Eq(lef... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | algebra_poly_eval_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.002 | 2026-02-08T12:16:59.665777Z | {
"verified": true,
"answer": 15700,
"timestamp": "2026-02-08T12:16:59.667705Z"
} | 1b7439 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 151,
"completion_tokens": 1355
},
"timestamp": "2026-02-14T23:56:17.255Z",
"answer": 15700
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
6f86f2 | comb_binomial_compute_v1_1520064083_9107 | Let $m = 72250$ and $n = 88187$. Define $k$ to be the largest prime number $p$ such that $$2 \le p \le \sum_{k=1}^{3} \varphi(k) \left\lfloor \frac{3}{k} \right\rfloor,$$ where $\varphi$ denotes Euler's totient function. Let $r = \binom{12}{k}$. Compute the remainder when $n \cdot r$ is divided by $m$. | 50,604 | graphs = [
Graph(
let={
"_m": Const(72250),
"_n": Const(88187),
"n": Const(12),
"k": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Summation(var="k", start=Const(1), end=Const(3), expr=Mul(EulerPhi(n=Var("k")), ... | NT | null | COMPUTE | sympy | K2 | [
"K2/MAX_PRIME_BELOW"
] | f058da | comb_binomial_compute_v1 | null | 5 | 0 | [
"K2",
"MAX_PRIME_BELOW"
] | 2 | 0.005 | 2026-02-08T10:32:53.577235Z | {
"verified": true,
"answer": 50604,
"timestamp": "2026-02-08T10:32:53.581765Z"
} | 4dc9c1 | 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": 1567
},
"timestamp": "2026-02-14T07:40:31.537Z",
"answer": 50604
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "V1",
"status": "no"
},
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
f9e80a | nt_gcd_compute_v1_677425708_1505 | Let $a_1 = 1591$ and let $b_1$ be the smallest divisor of $212341$ that is at least $2$. Let $w = \sum_{d \mid \gcd(a_1, b_1)} \mu(d)$, where $\mu$ is the M\"obius function. Let $m = \mu(23)^2$. Define $a = 318535$ and $b = 591565 \cdot w \cdot m$. Compute $\gcd(a, b)$. | 45,505 | graphs = [
Graph(
let={
"_n": Const(2),
"a1": Const(1591),
"b1": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(212341))))),
"w": SumOverDivisors(n=GCD(a=Ref(name='a1'), b=Ref(name='b1... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/MOBIUS_COPRIME",
"MOBIUS_SQUAREFREE"
] | 931c50 | nt_gcd_compute_v1 | null | 6 | 2 | [
"MIN_PRIME_FACTOR",
"MOBIUS_COPRIME",
"MOBIUS_SQUAREFREE"
] | 3 | 0.002 | 2026-02-08T04:14:01.536681Z | {
"verified": true,
"answer": 45505,
"timestamp": "2026-02-08T04:14:01.538446Z"
} | bdabae | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 225,
"completion_tokens": 7015
},
"timestamp": "2026-02-09T20:48:47.117Z",
"answer": 45505
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok_later"
},
{
"lemma": "MOBIUS_SQUAREFR... | {
"lo": -6.5,
"mid": -0.2,
"hi": 6.11
} | ||
96e4a9 | comb_catalan_compute_v1_1520064083_5852 | Let $k$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 44$. Let $n$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = k$. Let $C_n$ denote the $n$-th Catalan number. Compute $94249 - C_n$. | 35,463 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2")), CountOverSet(set=SolutionsSet(v... | COMB | null | COMPUTE | sympy | COMB1 | [
"COMB1/COMB1"
] | b2c526 | comb_catalan_compute_v1 | null | 5 | 0 | [
"COMB1"
] | 1 | 0.002 | 2026-02-08T07:40:55.064687Z | {
"verified": true,
"answer": 35463,
"timestamp": "2026-02-08T07:40:55.066940Z"
} | 918e9e | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 207,
"completion_tokens": 2842
},
"timestamp": "2026-02-24T08:19:34.725Z",
"answer": 35463
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -4.92,
"mid": -2.91,
"hi": -0.68
} | ||
09f2c8 | nt_count_divisible_and_v1_1978505735_5990 | Let $A$ be the number of positive integers $n$ such that $n \leq 110304$, $n$ is divisible by 9, and $n$ is divisible by 12. Let $S$ be the set of all ordered pairs $(a,b)$ of positive integers such that $1 \leq a \leq 11$, $1 \leq b \leq 4$, and $t = 8a + 10b + 7$ satisfies $25 \leq t \leq 135$. Let $m = |S|$. Let $P$... | 50,165 | graphs = [
Graph(
let={
"_n": Const(52745),
"upper": Const(110304),
"d1": Const(9),
"d2": Const(12),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(value=Var("n"), mo... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/B1"
] | 36d1f4 | nt_count_divisible_and_v1 | negation_mod | 6 | 0 | [
"B1",
"LIN_FORM"
] | 2 | 3.465 | 2026-02-08T19:21:51.317287Z | {
"verified": true,
"answer": 50165,
"timestamp": "2026-02-08T19:21:54.782493Z"
} | 92a18d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 223,
"completion_tokens": 1556
},
"timestamp": "2026-02-18T22:04:16.746Z",
"answer": 50165
},
... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
ebba60_n | alg_qf_psd_count_v1_1218484723_6873 | A shipping company numbers its containers from $1$ to $112112$. A container is marked "bulk" if its number is divisible by $44$. Let $M$ be the total number of bulk containers. An engineer studies the set of values $v$ between $13$ and $M$ for which there exist dimensions $a$ and $b$ (in meters) with $1 \le a \le 14$ a... | 10 | ALG | null | COUNT | sympy | POLY3_COUNT | [
"C2/QF_PSD_DISTINCT"
] | 389a25 | alg_qf_psd_count_v1 | null | 7 | null | [
"C2",
"POLY3_COUNT",
"QF_PSD_DISTINCT"
] | 3 | 3.825 | 2026-02-25T08:19:51.596019Z | null | 729fd4 | ebba60 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 322,
"completion_tokens": 32768
},
"timestamp": "2026-03-31T01:56:04.291Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "QF_PSD_DISTINCT",
"status": "ok_later"
},
{
"lemma": "V5",
"status": "no"
},
... | {
"lo": 1.5,
"mid": 4.69,
"hi": 7.23
} | |
02a01d | nt_count_gcd_equals_v1_1520064083_4237 | Let $k$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 10201$. Let $d$ be the number of positive integers $n$ such that $1 \leq n \leq 40320$ and $\gcd(n, k) = 2$. Compute the remainder when $31447 \cdot d$ is divided by $59200$. | 15,967 | graphs = [
Graph(
let={
"_n": Const(59200),
"upper": Const(40320),
"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(10201... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | nt_count_gcd_equals_v1 | null | 5 | 0 | [
"B3"
] | 1 | 3.219 | 2026-02-08T06:10:11.348601Z | {
"verified": true,
"answer": 15967,
"timestamp": "2026-02-08T06:10:14.567478Z"
} | e92493 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 136,
"completion_tokens": 2356
},
"timestamp": "2026-02-12T20:18:32.058Z",
"answer": 15967
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
c6608f | sequence_count_fib_divisible_v1_784195855_6411 | Let $u$ be the number of positive integers $n$ such that $1 \leq n \leq 6454$ and $13$ divides the $n$-th Fibonacci number. Let $d = 5$. Compute the number of positive integers $n$ such that $1 \leq n \leq u$ and $d$ divides the $n$-th Fibonacci number. | 184 | graphs = [
Graph(
let={
"_n": Const(13),
"upper": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(6454)), Divides(divisor=Ref("_n"), dividend=Fibonacci(arg=Var(name='n')))))),
"d": Const(5),
"result": Coun... | NT | null | COUNT | sympy | L3B | [
"COUNT_FIB_DIVISIBLE"
] | 66de3c | sequence_count_fib_divisible_v1 | null | 6 | 0 | [
"COUNT_FIB_DIVISIBLE",
"L3B"
] | 2 | 0.098 | 2026-02-08T08:39:02.252260Z | {
"verified": true,
"answer": 184,
"timestamp": "2026-02-08T08:39:02.350607Z"
} | f157a7 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 126,
"completion_tokens": 1751
},
"timestamp": "2026-02-13T20:07:16.775Z",
"answer": 184
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
}... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
3c2000 | algebra_poly_eval_v1_784195855_1699 | Let $n$ be an integer. Define $b$ to be the largest prime number $n$ such that $2 \leq n \leq 17$. Compute the value of
$$
\frac{b^5 + 11b^4 - 30b^3 - 61b^2 - 123b - 78}{30}.
$$Then let $Q$ be the remainder when $32881$ times this value is divided by $95006$. Find the value of $Q$. | 26,480 | graphs = [
Graph(
let={
"_n": Const(17),
"b": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))),
"result": Div(Sum(Pow(Ref("b"), Const(5)), Mul(Const(11), Pow(Ref("b"), Const(4))), Mul(Const(-30... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | algebra_poly_eval_v1 | null | 6 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.003 | 2026-02-08T05:13:53.757071Z | {
"verified": true,
"answer": 26480,
"timestamp": "2026-02-08T05:13:53.760556Z"
} | b118b3 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 149,
"completion_tokens": 1360
},
"timestamp": "2026-02-12T06:09:11.524Z",
"answer": 26480
},
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8",
"status"... | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
ffe56e | geo_visible_lattice_v1_1520064083_1618 | Let $n = 55$. Define $\text{result}$ to be the number of ordered pairs $(x, y)$ of positive integers such that $1 \leq x, y \leq n$ and $\gcd(x, y) = 1$. Let $Q$ be the remainder when $44121 \cdot \text{result}$ is divided by $52825$. Compute $Q$. | 20,934 | graphs = [
Graph(
let={
"n": Const(55),
"result": VisibleLatticePoints(n=Ref(name='n')),
"Q": Mod(value=Mul(Const(44121), Ref("result")), modulus=Const(52825)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 4 | 0 | null | null | 1.687 | 2026-02-08T04:08:23.856248Z | {
"verified": true,
"answer": 20934,
"timestamp": "2026-02-08T04:08:25.542765Z"
} | edeec9 | 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": 30246
},
"timestamp": "2026-02-23T23:46:25.976Z",
"answer": 20934
},
{
... | 1 | [] | {
"lo": 1.97,
"mid": 4.36,
"hi": 6.69
} | ||||
ff56ed | sequence_fibonacci_compute_v1_1520064083_7110 | Let $n$ be the number of integers $t$ such that $24 \le t \le 108$ and there exist integers $a$ and $b$ with $1 \le a \le 7$, $1 \le b \le 3$, and $t = 9a + 15b$. Let $F_n$ denote the $n$th Fibonacci number, where $F_1 = F_2 = 1$ and $F_k = F_{k-1} + F_{k-2}$ for $k \ge 3$. Compute the remainder when $75433 \cdot F_n$ ... | 10,544 | graphs = [
Graph(
let={
"_n": Const(75433),
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=7)), Geq(left=Va... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | sequence_fibonacci_compute_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T08:45:59.489076Z | {
"verified": true,
"answer": 10544,
"timestamp": "2026-02-08T08:45:59.490163Z"
} | 81e5e2 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 187,
"completion_tokens": 2625
},
"timestamp": "2026-02-13T21:31:01.156Z",
"answer": 10544
},
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
55c3cd | algebra_poly_eval_v1_677425708_1238 | Let $m = 16908$ and $n = 67375$. Define $t$ to be the number of nonnegative integers $j$ such that $0 \le j \le m$ and $\binom{m}{j}$ is odd. Let $d_0$ be the smallest divisor of $n$ that is at least $2$. Compute the value of $t^4 + d_0 \cdot t^3 + 3t^2 - 10t + 8$. | 86,632 | graphs = [
Graph(
let={
"_m": Const(16908),
"_n": Const(67375),
"t": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(16908)), Eq(Mod(value=Binom(n=Ref("_m"), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnega... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR",
"V8"
] | aeb95e | algebra_poly_eval_v1 | null | 6 | 0 | [
"MIN_PRIME_FACTOR",
"V8"
] | 2 | 0.003 | 2026-02-08T04:02:52.877966Z | {
"verified": true,
"answer": 86632,
"timestamp": "2026-02-08T04:02:52.881000Z"
} | 0c2476 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 217,
"completion_tokens": 2329
},
"timestamp": "2026-02-09T17:23:36.489Z",
"answer": 86632
},
{
"... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
... | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
eaf96b | antilemma_k3_v1_1520064083_5631 | Compute the sum of $\phi(d)$ over all positive divisors $d$ of $46583$, where $\phi$ is Euler's totient function. | 46,583 | graphs = [
Graph(
let={
"_n": Const(46583),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T07:30:16.846917Z | {
"verified": true,
"answer": 46583,
"timestamp": "2026-02-08T07:30:16.847470Z"
} | 6c83d0 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 77,
"completion_tokens": 4072
},
"timestamp": "2026-02-13T10:48:11.400Z",
"answer": 46583
},
{... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"... | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
de2998 | antilemma_k2_v1_1125832087_2027 | Let $x = \sum_{k=1}^{61} \phi(k) \left\lfloor \frac{61}{k} \right\rfloor$, where $\phi(k)$ denotes Euler's totient function. Let $Q$ be the remainder when $2676x$ is divided by $99991$. Compute $Q$. | 60,766 | graphs = [
Graph(
let={
"x": Summation(var="k", start=Const(1), end=Const(61), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(61), Var("k"))))),
"Q": Mod(value=Mul(Const(2676), Ref("x")), modulus=Const(99991)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | antilemma_k2_v1 | null | 5 | 0 | [
"K2"
] | 1 | 0.001 | 2026-02-08T04:17:30.130980Z | {
"verified": true,
"answer": 60766,
"timestamp": "2026-02-08T04:17:30.132071Z"
} | 0d6557 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 181,
"completion_tokens": 912
},
"timestamp": "2026-02-10T16:05:23.664Z",
"answer": 60766
},
{
"... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
9ad3e8 | nt_count_divisors_in_range_v1_1742523217_4707 | Determine the number of positive divisors $d$ of 5040 such that $34 \leq d \leq 5042$. Let this number be $r$. Compute $r^2 + 19r + 76^2$. | 8,136 | graphs = [
Graph(
let={
"_n": Const(2),
"n": Const(5040),
"a": Const(34),
"b": Const(5042),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Divides(divisor=Var("d"), dividend=Ref("n")), Geq(Var("d"), Ref("a")), Leq(Var("d"), Ref... | NT | null | COUNT | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | a1d5cf | nt_count_divisors_in_range_v1 | quadratic_mod | 3 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.046 | 2026-02-08T09:05:52.079922Z | {
"verified": true,
"answer": 8136,
"timestamp": "2026-02-08T09:05:52.125699Z"
} | 7fdb8e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 95,
"completion_tokens": 2091
},
"timestamp": "2026-02-14T00:19:44.063Z",
"answer": 8136
},
{
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V5",
"s... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
abba56_n | alg_qf_psd_orbit_v1_1419126231_319 | A game board consists of tiles arranged in rectangular grids, each with dimensions $a \times b$ where $1 \le a \le b \le 191$. A tile configuration is valid if $16a^2 + 16b^2 = 442000$. How many valid configurations exist? | 8 | ALG | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | alg_qf_psd_orbit_v1 | null | 4 | null | [
"MAX_PRIME_BELOW"
] | 1 | 0.057 | 2026-02-25T09:50:08.682072Z | null | db2825 | abba56 | 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": 21413
},
"timestamp": "2026-03-31T03:33:39.394Z",
"answer": 8
},
{
"id"... | 1 | [
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | |
857ea3 | modular_modexp_compute_v1_1915831931_2056 | Let $e$ be the minimum value of $x + y$ over all ordered pairs $(x,y)$ of positive integers such that $xy = 197136$. Compute the remainder when $13^e$ is divided by $81225$. | 59,671 | graphs = [
Graph(
let={
"a": Const(13),
"e": 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(197136)))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | modular_modexp_compute_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.001 | 2026-02-08T16:36:14.841326Z | {
"verified": true,
"answer": 59671,
"timestamp": "2026-02-08T16:36:14.842325Z"
} | b5f170 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 97,
"completion_tokens": 3612
},
"timestamp": "2026-02-17T07:37:50.065Z",
"answer": 59671
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
bbd883 | antilemma_v7_kummer_458359167_278 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 2500$. Let $n$ be the minimum value of $x + y$ over all such pairs.
Let $m = 2$, and let $k$ be the largest integer such that $m^k$ divides $\binom{n}{40}$.
Compute the remainder when $44121 \cdot k$ is divided by $95855$. | 36,508 | graphs = [
Graph(
let={
"_m": Const(2),
"_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(2500)))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | COMPUTE | sympy | B3 | [
"B3/V7",
"V7"
] | 664b43 | antilemma_v7_kummer | null | 6 | 0 | [
"B3",
"V7"
] | 2 | 0.001 | 2026-02-08T03:09:46.131797Z | {
"verified": true,
"answer": 36508,
"timestamp": "2026-02-08T03:09:46.132864Z"
} | 503c7f | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 205,
"completion_tokens": 1047
},
"timestamp": "2026-02-17T20:18:03.268Z",
"answer": 36508
}
] | 2 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "V7",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_... | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
776f1c | antilemma_count_primes_v1_677425708_1686 | Compute the number of prime numbers $ n $ such that $ 2 \leq n \leq 1117 $. | 187 | graphs = [
Graph(
let={
"x": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(1117)), IsPrime(Var("n"))))),
},
goal=Ref("x"),
)
] | NT | null | COMPUTE | sympy | COUNT_PRIMES | [
"COUNT_PRIMES"
] | 07c874 | antilemma_count_primes_v1 | null | 4 | 0 | [
"COUNT_PRIMES"
] | 1 | 0.001 | 2026-02-08T04:22:25.791153Z | {
"verified": true,
"answer": 187,
"timestamp": "2026-02-08T04:22:25.791829Z"
} | 7c70b7 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 136,
"completion_tokens": 7378
},
"timestamp": "2026-02-09T23:30:29.081Z",
"answer": 187
},
{
"id... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
... | {
"lo": -6.5,
"mid": -0.2,
"hi": 6.11
} | ||
f4f382 | algebra_poly_eval_v1_865884756_2404 | Let $m = 6$. Define $p$ to be the number of positive integers $a$ for which there exists a positive integer $b$ such that $a \cdot b = 4410$, $\gcd(a, b) = 1$, and $a < b$. Compute the value of
$$
p \cdot m^3 - 10m^2 - 3m + 1.
$$ | 1,351 | graphs = [
Graph(
let={
"m": Const(6),
"result": Sum(Mul(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=4410)), Eq(left=GCD(a=Var(name='p'), ... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | algebra_poly_eval_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.003 | 2026-02-08T16:45:57.339322Z | {
"verified": true,
"answer": 1351,
"timestamp": "2026-02-08T16:45:57.342541Z"
} | b133a3 | 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": 1314
},
"timestamp": "2026-02-17T11:04:48.895Z",
"answer": 1351
},
{... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
be52fd | alg_telescope_v1_1419126231_59 | Find the remainder when $$\sum_{k=0}^{m} (3k^2 + 3k + 1)$$ is divided by $5148$, where $m = \min\{x + y \mid x, y > 0,\ xy = 727609\}$. | 4,419 | graphs = [
Graph(
let={
"_n": Const(5148),
"result": Mod(value=Summation(var="k", start=Const(0), end=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(... | ALG | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | alg_telescope_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.108 | 2026-02-25T09:36:54.622245Z | {
"verified": true,
"answer": 4419,
"timestamp": "2026-02-25T09:36:54.730025Z"
} | 67a283 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 173,
"completion_tokens": 10388
},
"timestamp": "2026-03-30T06:46:31.363Z",
"answer": 4419
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -3.33,
"mid": 1.03,
"hi": 5.26
} | ||
033d28 | comb_catalan_compute_v1_153355830_1968 | Let $n$ be the number of integers $t$ in the range $21 \leq t \leq 60$ for which there exist integers $a$ and $b$ with $1 \leq a \leq 2$, $1 \leq b \leq 5$, and $t = 15a + 6b$. Compute the remainder when $44121$ times the $n$-th Catalan number is divided by $85555$. | 64,461 | graphs = [
Graph(
let={
"_n": Const(85555),
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=2)), Geq(left=Va... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_catalan_compute_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.003 | 2026-02-08T06:49:53.088098Z | {
"verified": true,
"answer": 64461,
"timestamp": "2026-02-08T06:49:53.091281Z"
} | a881b0 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 211,
"completion_tokens": 2434
},
"timestamp": "2026-02-24T07:07:33.640Z",
"answer": 64461
},
{
"... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"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
} | ||
6a2a21 | sequence_count_fib_divisible_v1_1915831931_3199 | Let $S$ be the set of all positive integers $n$ such that $n \leq \sum_{k=1}^{30} k$ and $6$ divides the $n$-th Fibonacci number $F_n$. Compute the number of elements in $S$. | 38 | graphs = [
Graph(
let={
"upper": Summation(var="k", start=Const(1), end=Const(30), expr=Var("k")),
"d": Const(6),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Divides(divisor=Ref("d"), dividend=F... | NT | null | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | sequence_count_fib_divisible_v1 | null | 4 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.021 | 2026-02-08T17:24:57.064414Z | {
"verified": true,
"answer": 38,
"timestamp": "2026-02-08T17:24:57.085816Z"
} | a3822c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 103,
"completion_tokens": 1172
},
"timestamp": "2026-02-18T02:53:56.783Z",
"answer": 38
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": ... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
8d5069 | nt_count_coprime_and_v1_124444284_6017 | Let $n = 5$. Let $U$ be the number of ordered pairs $(a,b)$ such that $1 \leq a \leq 16$ and $1 \leq b \leq 577$. Let $k_1 = 8$ and $k_2 = \sum_{i=1}^{n} i$.
Compute the number of positive integers $m$ such that $1 \leq m \leq U$, $\gcd(m, k_1) = 1$, and $\gcd(m, k_2) = 1$. | 2,462 | graphs = [
Graph(
let={
"_n": Const(5),
"upper": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(16)), right=IntegerRange(start=Const(1), end=Const(577)))),
"k1": Const(8),
"k2": Summation(var="k", start=Const(1), end=Ref("_n"), e... | NT | null | COUNT | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN",
"SUM_ARITHMETIC"
] | b1d095 | nt_count_coprime_and_v1 | null | 5 | 0 | [
"COUNT_CARTESIAN",
"SUM_ARITHMETIC"
] | 2 | 1.666 | 2026-02-08T06:59:05.062832Z | {
"verified": true,
"answer": 2462,
"timestamp": "2026-02-08T06:59:06.728788Z"
} | 1ae422 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 162,
"completion_tokens": 1307
},
"timestamp": "2026-02-13T14:35:33.419Z",
"answer": 2462
},
{... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
fcdbe8 | alg_poly3_min_v1_601307018_5928 | Find the remainder when the minimum value of $-375a^2b - 375ab^2 - 133a^3 - 125b^3$, taken over all integers $a, b$ such that $1 \leq a \leq 70$ and $1 \leq b \leq \min\{ |x - y| : x > 0, y > 0, xy = 10011 \}$, is divided by $77456$. | 19,584 | graphs = [
Graph(
let={
"_n": Const(3),
"result": Mod(value=MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(70)), Geq(Var("b"), Const(1)), Leq(Var("b"), MinOverSet(set=MapOverSet(set=Solut... | ALG | null | COMPUTE | sympy | B3_DIFF | [
"B3_DIFF"
] | b47ea7 | alg_poly3_min_v1 | null | 4 | 0 | [
"B3_DIFF"
] | 1 | 0.02 | 2026-03-10T06:30:02.304639Z | {
"verified": true,
"answer": 19584,
"timestamp": "2026-03-10T06:30:02.324193Z"
} | 87f500 | 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": 2782
},
"timestamp": "2026-04-19T03:11:59.011Z",
"answer": 19584
},
{
... | 1 | [
{
"lemma": "B3_DIFF",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.35,
"mid": 0.52,
"hi": 5.84
} | ||
ca0705 | geo_count_lattice_triangle_v1_153355830_610 | Let $m = 233$ and $n = 233$. Define $A$ to be twice the area of the polygon with vertices at $(0,0)$, $(m,0)$, and $(276,-240)$, adjusted by the number of interior lattice points along certain diagonals generated by linear combinations $t = 7a + 4b$ where $a$ and $b$ are integers satisfying $1 \le a \le 40$, $1 \le b \... | 8,814 | graphs = [
Graph(
let={
"_m": Const(233),
"_n": Const(233),
"area_2x": Abs(arg=Sum(Mul(Ref(name='_m'), CountOverSet(set=SolutionsSet(var=Var(name='t'), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Cons... | NT | null | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC",
"LIN_FORM"
] | 7209d0 | geo_count_lattice_triangle_v1 | null | 6 | 0 | [
"LIN_FORM",
"SUM_ARITHMETIC"
] | 2 | 0.013 | 2026-02-08T04:05:09.138178Z | {
"verified": true,
"answer": 8814,
"timestamp": "2026-02-08T04:05:09.151017Z"
} | 97ba0c | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 449,
"completion_tokens": 7029
},
"timestamp": "2026-02-10T15:15:36.904Z",
"answer": 8814
},
{
"... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
8012b4 | comb_count_surjections_v1_124444284_6697 | Let $m = 15$. Define $\ell$ to be the number of ordered pairs $(i, j)$ of positive integers such that $i + j = m$ and $1 \leq i, j \leq 15$. Let $n$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = \ell$. Let $k = 5$. Define $r = k! \cdot S(n, k)$, where $S(n, k)$ denotes the ... | 270 | graphs = [
Graph(
let={
"_m": Const(15),
"_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(15)), right=IntegerRange(start=Const(1), end=Co... | COMB | NT | COUNT | sympy | LIN_FORM | [
"COUNT_SUM_EQUALS/COMB1"
] | 5b2e59 | comb_count_surjections_v1 | null | 7 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 3 | 0.068 | 2026-02-08T08:35:26.668779Z | {
"verified": true,
"answer": 270,
"timestamp": "2026-02-08T08:35:26.736524Z"
} | 4b02ea | 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": 9063
},
"timestamp": "2026-02-24T09:41:25.969Z",
"answer": 270
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok_later"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"st... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
2caa26 | nt_num_divisors_compute_v1_153355830_921 | Let $p_1 = 67$, $q_1 = 29$, and $r = 47$. Let $n_2 = p_1 q_1 r$. Let $h = \mu(n_2)^2$, where $\mu$ denotes the M\"obius function. Let $p = 37$ and $q = 13$, and let $n_1 = p q$. Let $w = \mu(n_1)^{2h}$. Let $n = 31 \cdot w$. Determine the number of positive divisors of $n$. | 2 | graphs = [
Graph(
let={
"p1": Const(67),
"q1": Const(29),
"r": Const(47),
"n2": Mul(Ref("p1"), Ref("q1"), Ref("r")),
"h": Pow(MoebiusMu(n=Ref(name='n2')), Const(2)),
"p": Const(37),
"q": Const(13),
"n1": Mul(Ref(... | NT | null | COMPUTE | sympy | MOBIUS_SQUAREFREE | [
"MOBIUS_SQUAREFREE"
] | 6fcd31 | nt_num_divisors_compute_v1 | null | 3 | 2 | [
"MOBIUS_SQUAREFREE"
] | 1 | 0.001 | 2026-02-08T04:15:23.853200Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-02-08T04:15:23.854648Z"
} | 14b474 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 220,
"completion_tokens": 430
},
"timestamp": "2026-02-18T10:19:10.357Z",
"answer": 2
}
] | 2 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOBIUS_SQUAREFREE",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
... | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
87a018 | diophantine_fbi2_count_v1_784195855_2972 | Let $n = 66$. Let $k = 180$. Compute the number of integers $d$ such that $d \ge 3$, $d$ divides $k$, $\frac{k}{d} \ge 3$, $\frac{k}{d} \le n$, and $d \le 1 + 2 + \cdots + 11$. | 14 | graphs = [
Graph(
let={
"_n": Const(66),
"k": Const(180),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(3)), Leq(Var("d"), Summation(var="k", start=Const(1), end=Const(11), expr=Var("k"))), Divides(divisor=Var("d"), dividend=Ref("... | NT | null | COUNT | sympy | COUNT_COPRIME_GRID | [
"SUM_ARITHMETIC"
] | eb34f0 | diophantine_fbi2_count_v1 | null | 4 | 0 | [
"COUNT_COPRIME_GRID",
"SUM_ARITHMETIC"
] | 2 | 0.052 | 2026-02-08T06:09:33.885967Z | {
"verified": true,
"answer": 14,
"timestamp": "2026-02-08T06:09:33.937999Z"
} | ba35ae | 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": 1136
},
"timestamp": "2026-02-12T20:52:12.474Z",
"answer": 14
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
f62d77 | nt_sum_divisors_range_v1_865884756_4417 | Let $m = 27447$. Define $N$ as the number of integers $t$ such that $20 \leq t \leq 12042$ and there exist integers $a$, $b$ with $1 \leq a \leq 426$, $1 \leq b \leq 1013$, and $t = 14a + 6b$. Let $D$ be the largest positive divisor of $36066000$ that is at most $N$. Define $S$ as the sum of the number of positive divi... | 10,625 | graphs = [
Graph(
let={
"_m": Const(27447),
"_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=426)), Geq(left... | NT | null | SUM | sympy | LIN_FORM | [
"LIN_FORM/MAX_DIVISOR"
] | 8c55ae | nt_sum_divisors_range_v1 | null | 6 | 0 | [
"LIN_FORM",
"MAX_DIVISOR"
] | 2 | 0.214 | 2026-02-08T17:55:33.115302Z | {
"verified": true,
"answer": 10625,
"timestamp": "2026-02-08T17:55:33.329570Z"
} | 7a36b1 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 188,
"completion_tokens": 6976
},
"timestamp": "2026-02-18T09:51:39.607Z",
"answer": 10625
},
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok_later"
},
{
"lemma": "MOD_MUL",
"sta... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
ae2a89 | nt_count_gcd_equals_v1_48377204_1937 | Let $d$ be the number of positive integers $n$ such that $1 \leq n \leq 641$ and $\gcd(n, 10) = 1$. Compute the number of positive integers $n_1$ such that $1 \leq n_1 \leq 41616$ and $\gcd(n_1, 257) = d$. | 161 | graphs = [
Graph(
let={
"upper": Const(41616),
"k": Const(257),
"d": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(641)), Eq(GCD(a=Var("n"), b=Const(10)), Const(1))))),
"result": CountOverSet(set=Solutio... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"C4"
] | 08d162 | nt_count_gcd_equals_v1 | null | 6 | 0 | [
"C4",
"MIN_PRIME_FACTOR"
] | 2 | 8.405 | 2026-02-08T16:30:57.779275Z | {
"verified": true,
"answer": 161,
"timestamp": "2026-02-08T16:31:06.184620Z"
} | e82dcc | 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": 1684
},
"timestamp": "2026-02-17T06:19:05.776Z",
"answer": 161
},
{
... | 1 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
357d75 | comb_factorial_compute_v1_1874849503_1673 | Let $S$ be the set of all integers $t$ such that there exist positive integers $a$ and $b$ with $1 \le a \le 3611$, $1 \le b \le 204$, $15 \le t \le 8250$, and $t = 2a + 5b + 8$. For each nonnegative integer $j$, let $\alpha_j = 1$ if $\binom{|S|}{j}$ is odd, and $\alpha_j = 0$ otherwise. Let $n$ be the number of nonne... | 33,284 | graphs = [
Graph(
let={
"_m": Const(8232),
"_n": Const(60325),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Ref("_m")), Eq(Mod(value=Binom(n=CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name=... | ALG | COMB | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/V8"
] | 654a7e | comb_factorial_compute_v1 | null | 7 | 0 | [
"LIN_FORM",
"V8"
] | 2 | 0.004 | 2026-02-08T14:01:54.047585Z | {
"verified": true,
"answer": 33284,
"timestamp": "2026-02-08T14:01:54.051478Z"
} | ef04b4 | 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": 13444
},
"timestamp": "2026-02-24T19:35:18.017Z",
"answer": 33284
},
{
... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8",
"status": "ok_later"
}
] | {
"lo": 1.15,
"mid": 4.18,
"hi": 6.61
} | ||
cc740b | geo_count_lattice_rect_v1_458359167_2366 | Compute the number of lattice points $(x, y)$ such that $0 \leq x \leq 169$ and $0 \leq y \leq 497$. | 84,660 | graphs = [
Graph(
let={
"a": Const(169),
"b": Const(497),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 2 | 0 | null | null | 0 | 2026-02-08T05:20:01.829127Z | {
"verified": true,
"answer": 84660,
"timestamp": "2026-02-08T05:20:01.829465Z"
} | 8221dd | 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": 232
},
"timestamp": "2026-02-24T03:24:45.668Z",
"answer": 84660
},
{
"i... | 1 | [] | {
"lo": -5.98,
"mid": -3.97,
"hi": -1.94
} | ||||
c2482b | antilemma_cartesian_v1_2051736721_3301 | Let $x$ be the number of ordered pairs $(a, b)$ where $a$ is an integer satisfying $1 \leq a \leq 25$ and $b$ is an integer satisfying $1 \leq b \leq 40$. Let $S$ be the set of all integers $t$ such that $15 \leq t \leq 51$ and there exist integers $a$ and $b$ with $1 \leq a \leq 4$, $1 \leq b \leq 3$, and $t = 6a + 9b... | 14,139 | graphs = [
Graph(
let={
"_n": Const(50918),
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(25)), right=IntegerRange(start=Const(1), end=Const(40)))),
"Q": Mod(value=Bell(Mod(value=Abs(arg=Ref(name='x')), modulus=CountOverSet(set=Solutio... | COMB | GEOM | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM",
"COUNT_CARTESIAN"
] | 6e491f | antilemma_cartesian_v1 | bell_mod | 5 | 0 | [
"COUNT_CARTESIAN",
"LIN_FORM"
] | 2 | 0.015 | 2026-02-08T17:14:29.630007Z | {
"verified": true,
"answer": 14139,
"timestamp": "2026-02-08T17:14:29.645410Z"
} | 4cf909 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 204,
"completion_tokens": 1252
},
"timestamp": "2026-02-17T22:26:04.162Z",
"answer": 14139
},
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": ... | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||
249ac6 | geo_count_lattice_triangle_v1_124444284_8085 | Let $c=180$, and consider the quadratic polynomial
$$f(x) = x^2 - 121x + K,$$
where
$$K = \min (x+y),$$
with the minimum taken over all ordered pairs $(x,y)$ of positive integers such that $xy = 1610361$.
Let $S$ be the set of all integers $x$ such that $f(x)=0$. Let $n=180$ and define
$$A = \left|\, n\sum_{x\in S} x +... | 9,444 | graphs = [
Graph(
let={
"_c": Const(180),
"_m": Const(10),
"_n": Const(180),
"area_2x": Abs(arg=Sum(Mul(SumOverSet(set=SolutionsSet(var=Var(name='x'), condition=Eq(left=Sum(Pow(base=Var(name='x'), exp=Const(value=2)), Mul(Const(value=-121), Var(name='x')), Min... | NT | null | COUNT | sympy | B3 | [
"B3/VIETA_SUM",
"LIN_FORM"
] | 46452c | geo_count_lattice_triangle_v1 | null | 8 | 0 | [
"B3",
"LIN_FORM",
"VIETA_SUM"
] | 3 | 0.012 | 2026-02-08T09:33:34.468852Z | {
"verified": true,
"answer": 9444,
"timestamp": "2026-02-08T09:33:34.480732Z"
} | 8a2bf0 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 322,
"completion_tokens": 6481
},
"timestamp": "2026-02-14T04:46:51.602Z",
"answer": 9444
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
296457 | sequence_count_fib_divisible_v1_971394319_229 | Let $n = 56390$ and $\text{upper} = 175$. Define
$$
d = \sum_{k=1}^{3} \varphi(k) \left\lfloor \frac{3}{k} \right\rfloor.
$$
Let $\text{result}$ be the number of positive integers $n$ with $1 \leq n \leq \text{upper}$ such that $d$ divides the $n$-th Fibonacci number. Let $Q$ be the remainder when $44121 \cdot \text{re... | 53,794 | graphs = [
Graph(
let={
"_n": Const(56390),
"upper": Const(175),
"d": Summation(var="k", start=Const(1), end=Const(3), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(3), Var("k"))))),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var(... | NT | null | COUNT | sympy | K2 | [
"K2"
] | 6897ab | sequence_count_fib_divisible_v1 | null | 5 | 0 | [
"K2"
] | 1 | 0.012 | 2026-02-08T12:54:24.167923Z | {
"verified": true,
"answer": 53794,
"timestamp": "2026-02-08T12:54:24.179575Z"
} | 0bd412 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 170,
"completion_tokens": 1400
},
"timestamp": "2026-02-15T08:01:26.591Z",
"answer": 53794
},
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
e563b3 | antilemma_cartesian_v1_1742523217_1493 | Let $x$ be the number of ordered pairs $(a,b)$ where $a$ is an integer between 1 and 25, inclusive, and $b$ is an integer between 1 and 32, inclusive. Compute the remainder when $10877 \cdot x$ is divided by 53151. | 37,987 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(25)), right=IntegerRange(start=Const(1), end=Const(32)))),
"_c": Const(10877),
"Q": Mod(value=Mul(Ref("_c"), Ref("x")), modulus=Const(53151)),
},
goa... | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | antilemma_cartesian_v1 | null | 2 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.001 | 2026-02-08T04:01:58.555184Z | {
"verified": true,
"answer": 37987,
"timestamp": "2026-02-08T04:01:58.555843Z"
} | bb6ccb | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 175,
"completion_tokens": 2962
},
"timestamp": "2026-02-10T16:33:49.916Z",
"answer": 37987
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
... | {
"lo": -0.05,
"mid": 2.89,
"hi": 5.27
} | ||
eee24b | nt_max_prime_below_v1_677425708_4187 | Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 6$, $\gcd(p, q) = 1$, and $p < q$. Let $m$ be the number of elements in $S$. Determine the largest prime number $n$ such that $m \leq n \leq 30276$. | 30,271 | graphs = [
Graph(
let={
"upper": Const(30276),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), V... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_max_prime_below_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.708 | 2026-02-08T06:29:15.456784Z | {
"verified": true,
"answer": 30271,
"timestamp": "2026-02-08T06:29:16.164617Z"
} | e97611 | 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": 1565
},
"timestamp": "2026-02-13T00:32:55.463Z",
"answer": 30271
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V1",
"status": ... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
feaf2d_n | alg_linear_system_2x2_v1_1218484723_1221 | A cryptographer uses a system of linear combinations: values $t = 6a + 4b$ (with $1 \leq a \leq 3$, $1 \leq b \leq 4$) form a codebook of size $d$. From a matrix equation, they compute $R = \frac{N}{\det} + \frac{M}{\det}$ using given constants, then set $k = |R| \bmod d$. The security level is the $k$-th Bell number. ... | 5 | ALG | COMB | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 1ae498 | alg_linear_system_2x2_v1 | bell_mod | 3 | null | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-25T02:59:39.312006Z | null | c7ecd3 | feaf2d | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 230,
"completion_tokens": 2700
},
"timestamp": "2026-03-30T16:31:58.985Z",
"answer": 52
},
{
"i... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 3.8,
"mid": 6.33,
"hi": 9.49
} | |
d6d70d | algebra_quadratic_discriminant_v1_865884756_1740 | Let $a = -2$, $b = 16$, and $c = 0$. Define $\Delta = b^2 - 4ac$. Compute the remainder when $44121 \cdot \Delta$ is divided by $58390$. | 25,706 | graphs = [
Graph(
let={
"a": Const(-2),
"b": Const(16),
"c": Const(0),
"result": Sub(Pow(Ref("b"), Const(2)), Mul(Const(4), Ref("a"), Ref("c"))),
"Q": Mod(value=Mul(Const(44121), Ref("result")), modulus=Const(58390)),
},
goal=Ref("Q... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | algebra_quadratic_discriminant_v1 | null | 2 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.019 | 2026-02-08T16:15:02.139586Z | {
"verified": true,
"answer": 25706,
"timestamp": "2026-02-08T16:15:02.158370Z"
} | cf5727 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 98,
"completion_tokens": 678
},
"timestamp": "2026-02-17T00:17:51.905Z",
"answer": 25706
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V7",
"status": "... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
673b2c | comb_count_surjections_v1_124444284_7723 | Let $k$ be the number of integers $t$ with $5 \leq t \leq 12$ for which there exist integers $a$ and $b$ such that $1 \leq a \leq 2$, $1 \leq b \leq 3$, and $t = 3a + 2b$. Define $r = k! \cdot S(6, k)$, where $S(6, k)$ denotes the Stirling number of the second kind. Compute the remainder when $18847 \cdot r$ is divided... | 4,302 | graphs = [
Graph(
let={
"n": Const(6),
"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=2)), Geq(left=Var(nam... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_count_surjections_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.003 | 2026-02-08T09:20:07.278235Z | {
"verified": true,
"answer": 4302,
"timestamp": "2026-02-08T09:20:07.280884Z"
} | 070754 | 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": 1670
},
"timestamp": "2026-02-24T11:02:44.266Z",
"answer": 4302
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"statu... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
0e934e | comb_factorial_compute_v1_1520064083_7042 | Let $n$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 9450$, $\gcd(p, q) = 1$, and $p < q$. Compute $n!$. | 40,320 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=9450)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(value=1)),... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_factorial_compute_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.003 | 2026-02-08T08:43:25.941090Z | {
"verified": true,
"answer": 40320,
"timestamp": "2026-02-08T08:43:25.944169Z"
} | 8fd120 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 103,
"completion_tokens": 1198
},
"timestamp": "2026-02-13T20:56:00.009Z",
"answer": 40320
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
a5f9aa | comb_bell_compute_v1_784195855_5792 | Let $n$ be the number of integers $t$ with $15 \leq t \leq 45$ such that $t = 6a + 9b$ for some integers $a$ and $b$ satisfying $1 \leq a \leq 3$ and $1 \leq b \leq 3$. Let $B_n$ denote the $n$-th Bell number, which counts the number of partitions of a set of $n$ elements. Compute $46656 - B_n$. | 25,509 | graphs = [
Graph(
let={
"_n": Const(46656),
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=3)), Geq(left=Va... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_bell_compute_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T08:06:53.904897Z | {
"verified": true,
"answer": 25509,
"timestamp": "2026-02-08T08:06:53.906455Z"
} | d164fa | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 222,
"completion_tokens": 1573
},
"timestamp": "2026-02-24T08:50:58.683Z",
"answer": 25509
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.84,
"mid": -1.67,
"hi": 1.32
} | ||
3f4016 | comb_count_partitions_v1_784195855_8373 | Let $m = 2$. Define $s$ to be the sum of all positive integers $n$ such that $1 \leq n \leq 2$ and $n$ is even. Let $n$ be the largest positive integer $k$ such that $s^k \leq 1086369939509$. Compute the number of integer partitions of $n$. | 31,185 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(2)), Eq(Mod(value=Var("n"), modulus=Ref("_m")), Const(0))))),
"n": MaxOverSet(set=SolutionsSet(var=Var("k"), condition=Leq(Po... | COMB | null | COUNT | sympy | SUM_DIVISIBLE | [
"SUM_DIVISIBLE/MAX_VAL"
] | 622ecb | comb_count_partitions_v1 | null | 5 | 0 | [
"MAX_VAL",
"SUM_DIVISIBLE"
] | 2 | 0.002 | 2026-02-08T16:02:19.547249Z | {
"verified": true,
"answer": 31185,
"timestamp": "2026-02-08T16:02:19.549448Z"
} | a15efa | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 191,
"completion_tokens": 1003
},
"timestamp": "2026-02-24T19:31:29.996Z",
"answer": 31185
},
{
... | 1 | [
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "ok_later"
},
{
"lemma": "SUM_DIVISIBLE",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"st... | {
"lo": -2.4,
"mid": 1.57,
"hi": 5.75
} | ||
5daab2 | geo_count_lattice_triangle_v1_601307018_9316 | Let $N = \left|111 \cdot 100 + 8 \cdot (0 - 77)\right|$ and let $$M = \gcd(111, 77) + \gcd(|8 - 111|, |100 - 77|) + \gcd(|0 - 8|, |0 - 100|).$$ Compute $\frac{N + 2 - M}{2}$. | 5,240 | graphs = [
Graph(
let={
"area_2x": Abs(arg=Sum(Mul(Const(value=111), Const(value=100)), Mul(Const(value=8), Sub(left=Const(value=0), right=Const(value=77))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=111)), b=Abs(arg=Const(value=77))), GCD(a=Abs(arg=Sub(left=Const(value=8), right=C... | GEOM | NT | COUNT | sympy | [] | geo_count_lattice_triangle_v1 | null | 4 | 0 | null | null | 0.003 | 2026-03-10T09:43:55.733542Z | {
"verified": true,
"answer": 5240,
"timestamp": "2026-03-10T09:43:55.736728Z"
} | b5fe69 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 203,
"completion_tokens": 563
},
"timestamp": "2026-04-19T11:05:43.746Z",
"answer": 5240
},
{
"i... | 1 | [] | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||||
2aba2f | comb_count_derangements_v1_1915831931_3688 | Let $n$ be the sum of all positive integers from 1 to 7 that are divisible by 7. Let $!n$ denote the subfactorial of $n$, the number of derangements of $n$ elements. Compute the remainder when $85151 \cdot (!n)$ is divided by $52040$. | 32,634 | graphs = [
Graph(
let={
"_n": Const(85151),
"n": SumOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(1)), Leq(Var("n1"), Const(7)), Eq(Mod(value=Var("n1"), modulus=Const(7)), Const(0))))),
"result": Subfactorial(arg=Ref(name='n')),
"Q... | COMB | null | COUNT | sympy | SUM_DIVISIBLE | [
"SUM_DIVISIBLE"
] | 02dbe3 | comb_count_derangements_v1 | null | 3 | 0 | [
"SUM_DIVISIBLE"
] | 1 | 0.002 | 2026-02-08T17:49:23.425787Z | {
"verified": true,
"answer": 32634,
"timestamp": "2026-02-08T17:49:23.427580Z"
} | 2a1f34 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 115,
"completion_tokens": 2183
},
"timestamp": "2026-02-18T08:11:00.262Z",
"answer": 32634
},
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "SUM_DIVISIBLE",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
... | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||
8a60ca | nt_sum_divisors_mod_v1_1978505735_3066 | Let $n = \sum_{k=1}^{15} k$. Let $M = 10687$. Define $\sigma(n)$ to be the sum of the positive divisors of $n$. Let $r$ be the remainder when $\sigma(n)$ is divided by $M$. Compute the value of $7^{|r|} + 13924$ modulo $99991$. | 63,047 | graphs = [
Graph(
let={
"n": Summation(var="k", start=Const(1), end=Const(15), expr=Var("k")),
"M": Const(10687),
"sigma": SumDivisors(n=Ref("n")),
"result": Mod(value=Ref("sigma"), modulus=Ref("M")),
"Q": Sum(ModExp(base=Const(7), exp=Abs(arg=Ref(... | NT | null | COMPUTE | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | nt_sum_divisors_mod_v1 | null | 3 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.003 | 2026-02-08T17:19:02.637257Z | {
"verified": true,
"answer": 63047,
"timestamp": "2026-02-08T17:19:02.640450Z"
} | fc4e9f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 125,
"completion_tokens": 5361
},
"timestamp": "2026-02-18T00:40:29.819Z",
"answer": 63047
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
af5cce | nt_count_intersection_v1_784195855_9943 | Let $N$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 6250000$. Determine the value of the number of positive integers $n$ such that $1 \leq n \leq N$, $7$ divides $n$, and $\gcd(n, 6) = 1$. | 238 | graphs = [
Graph(
let={
"N": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(6250000)))), expr=Sum(Var("x"), Var("y")))),
"a": Const(7),
... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | nt_count_intersection_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.177 | 2026-02-08T17:20:21.664869Z | {
"verified": true,
"answer": 238,
"timestamp": "2026-02-08T17:20:21.841530Z"
} | 95f00d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 125,
"completion_tokens": 1440
},
"timestamp": "2026-02-18T00:17:45.949Z",
"answer": 238
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
20fa0f | nt_count_coprime_and_v1_677425708_1666 | Let $u = 13950$. Compute the number of positive integers $n$ such that $1 \leq n \leq u$, $\gcd(n, 8) = \phi(2)$, and $\gcd(n, 9) = 1$. Multiply this number by 69316 and find the remainder when the result is divided by 89707. | 2,149 | graphs = [
Graph(
let={
"upper": Const(13950),
"k1": Const(8),
"k2": Const(9),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(GCD(a=Var("n"), b=Ref("k1")), EulerPhi(n=Const(2))), Eq(... | NT | null | COUNT | sympy | ONE_PHI_2 | [
"ONE_PHI_2"
] | e19278 | nt_count_coprime_and_v1 | null | 5 | 0 | [
"ONE_PHI_2"
] | 1 | 6.676 | 2026-02-08T04:21:57.003478Z | {
"verified": true,
"answer": 2149,
"timestamp": "2026-02-08T04:22:03.679761Z"
} | d6a86e | 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": 3355
},
"timestamp": "2026-02-09T23:05:58.013Z",
"answer": 2149
},
{
"i... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "ONE_PHI_2",
"sta... | {
"lo": -6.5,
"mid": -0.2,
"hi": 6.11
} | ||
5f3471 | lin_form_endings_v1_124444284_9854 | Let $a = 30$ and $b = 70$. Compute the remainder when $6790 \left\lfloor \frac{70}{\gcd(a,b)} \right\rfloor$ is divided by $90287$. | 47,530 | graphs = [
Graph(
let={
"a_coeff": Const(30),
"b_coeff": Const(70),
"_inner_result": Floor(Div(Const(70), GCD(a=Ref("a_coeff"), b=Ref("b_coeff")))),
"_scale_k": Const(6790),
"_scaled": Mul(Ref("_scale_k"), Ref("_inner_result")),
"_mod_M... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 2 | null | [
"LIN_FORM"
] | 1 | 0 | 2026-02-08T12:42:15.404533Z | {
"verified": true,
"answer": 47530,
"timestamp": "2026-02-08T12:42:15.405013Z"
} | 193f4a | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 114,
"completion_tokens": 297
},
"timestamp": "2026-02-16T04:02:27.158Z",
"answer": 47530
},
{
"id": 11,
... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -9.12,
"mid": -6.02,
"hi": -3.62
} | ||
ee94e8 | nt_max_prime_below_v1_1918700295_4120 | Let $p$ and $q$ be positive integers such that $pq = 18$, $\gcd(p, q) = 1$, and $p < q$. Let $A$ be the set of all such integers $p$. Let $m$ be the number of elements in $A$. Let $S$ be the set of all prime numbers $n$ such that $m \leq n \leq 37401$. Let $r$ be the largest element of $S$. Compute the remainder when $... | 5,449 | graphs = [
Graph(
let={
"_n": Const(68340),
"upper": Const(37401),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_max_prime_below_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 2.804 | 2026-02-08T09:09:06.929111Z | {
"verified": true,
"answer": 5449,
"timestamp": "2026-02-08T09:09:09.733248Z"
} | 49ac5f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 166,
"completion_tokens": 5544
},
"timestamp": "2026-02-14T00:52:43.604Z",
"answer": 5449
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
4ee3cd | nt_count_divisors_in_range_v1_809748730_331 | Let $n = 5040$, $a = 10$, and $b = 321$. Determine the number of positive divisors $d$ of $n$ such that $a \leq d \leq b$. | 38 | graphs = [
Graph(
let={
"n": Const(5040),
"a": Const(10),
"b": Const(321),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Divides(divisor=Var("d"), dividend=Ref("n")), Geq(Var("d"), Ref("a")), Leq(Var("d"), Ref("b"))))),
},
... | NT | null | COUNT | sympy | C3 | [
"C3/SUM_INDEPENDENT/SUM_ARITHMETIC"
] | 03a60c | nt_count_divisors_in_range_v1 | null | 3 | 0 | [
"C3",
"SUM_ARITHMETIC",
"SUM_INDEPENDENT"
] | 3 | 0.214 | 2026-02-08T11:28:29.526671Z | {
"verified": true,
"answer": 38,
"timestamp": "2026-02-08T11:28:29.740747Z"
} | 8eafc2 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 92,
"completion_tokens": 1973
},
"timestamp": "2026-02-14T14:56:33.033Z",
"answer": 38
},
{
... | 1 | [
{
"lemma": "C3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok_l... | {
"lo": -5.14,
"mid": 0.3,
"hi": 6.27
} | ||
61ac4f | comb_catalan_compute_v1_1520064083_9193 | Let $T$ be the set of all integers $t$ such that $21 \leq t \leq 60$ and there exist positive integers $a \leq 5$ and $b \leq 2$ satisfying $t = 6a + 15b$. Let $n$ be the number of elements in $T$. Let $C_n$ denote the $n$-th Catalan number. Compute the remainder when $44121 \cdot C_n$ is divided by $76540$. | 72,576 | graphs = [
Graph(
let={
"_n": Const(44121),
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=5)), Geq(left=Va... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_catalan_compute_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.003 | 2026-02-08T10:35:39.472641Z | {
"verified": true,
"answer": 72576,
"timestamp": "2026-02-08T10:35:39.475648Z"
} | 36d959 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 220,
"completion_tokens": 6978
},
"timestamp": "2026-02-24T12:09:55.386Z",
"answer": 72576
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
c3fbe8 | algebra_poly_eval_v1_124444284_5231 | Let $m = 6$. Compute $-m^2 + 8m + \max\{n \mid n \text{ is a prime and } 2 \le n \le 9\}$. | 19 | graphs = [
Graph(
let={
"_n": Const(2),
"m": Const(6),
"result": Sum(Mul(Const(-1), Pow(Ref("m"), Ref("_n"))), Mul(Const(8), Ref("m")), MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(9)), IsPrime(Var("n")))))),
... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | algebra_poly_eval_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.001 | 2026-02-08T06:27:15.176037Z | {
"verified": true,
"answer": 19,
"timestamp": "2026-02-08T06:27:15.177369Z"
} | 64df72 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 98,
"completion_tokens": 225
},
"timestamp": "2026-02-15T17:33:06.320Z",
"answer": 19
},
{
"id": 11,
"... | 2 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
... | {
"lo": -10,
"mid": -7.73,
"hi": -5.46
} | ||
b64e4e | nt_count_divisible_and_v1_717093673_1136 | Let $d_1$ be the number of integers $t$ such that $7 \leq t \leq 24$ and there exist integers $a$ and $b$ with $1 \leq a \leq 3$, $1 \leq b \leq 4$, and $t = 4a + 3b$. Let $d_2 = 15$. Define $S$ as the set of all positive integers $n$ such that $n \leq 233340$, $n$ is divisible by $d_1$, and $n$ is divisible by $d_2$. ... | 59,408 | graphs = [
Graph(
let={
"upper": Const(233340),
"d1": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=3)), Geq(le... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_count_divisible_and_v1 | null | 3 | 0 | [
"LIN_FORM"
] | 1 | 27.81 | 2026-02-08T15:52:17.925678Z | {
"verified": true,
"answer": 59408,
"timestamp": "2026-02-08T15:52:45.735265Z"
} | 673fdf | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 212,
"completion_tokens": 2452
},
"timestamp": "2026-02-16T15:23:50.371Z",
"answer": 59408
},
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V7",
"st... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
aa6329 | lte_diff_endings_v1_151522320_63 | Let $a = 121$, $b = 9$, $n = 24$, $m = 30$, and $p = 2$. Define $d_n = a^n - b^n$ and $d_m = a^m - b^m$. Let $G = \gcd(d_n, d_m)$. Determine the largest integer $k$ such that $p^k$ divides $G$. Multiply this $k$ by $13033$, and find the remainder when the result is divided by $96913$. | 65,165 | graphs = [
Graph(
let={
"a_val": Const(121),
"b_val": Const(9),
"n_val": Const(24),
"m_val": Const(30),
"p_val": Const(2),
"a_pow_n": Pow(Ref("a_val"), Ref("n_val")),
"b_pow_n": Pow(Ref("b_val"), Ref("n_val")),
"... | NT | null | COMPUTE | sympy | LTE_DIFF | [
"LTE_DIFF"
] | cf8260 | lte_diff_endings_v1 | null | 6 | null | [
"LTE_DIFF"
] | 1 | 0.001 | 2026-02-08T02:56:29.470386Z | {
"verified": true,
"answer": 65165,
"timestamp": "2026-02-08T02:56:29.471680Z"
} | e79ed2 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 228,
"completion_tokens": 787
},
"timestamp": "2026-02-08T22:25:00.216Z",
"answer": 65165
},
{
"... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}... | {
"lo": -6.49,
"mid": 0.51,
"hi": 7.52
} | ||
6eff3b | antilemma_sum_primes_v1_1520064083_1121 | Let $m = 4$. Let $n_0$ be the smallest positive integer $n$ such that the largest power of 2 dividing $n!$ is at least $1$. Let $x$ be the sum of all prime numbers $n$ satisfying $n_0 \leq n \leq m$. Compute $x$. | 5 | graphs = [
Graph(
let={
"_m": Const(4),
"_n": MinOverSet(set=SolutionsSet(var=Var("n"), condition=Geq(MaxKDivides(target=Factorial(Var("n")), base=Const(2)), Const(1)), domain='Z_{>0}')),
"x": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"V5/SUM_PRIMES",
"SUM_PRIMES"
] | 3729fd | antilemma_sum_primes_v1 | null | 4 | 0 | [
"COPRIME_PAIRS",
"SUM_PRIMES",
"V5"
] | 3 | 0.008 | 2026-02-08T03:48:08.483369Z | {
"verified": true,
"answer": 5,
"timestamp": "2026-02-08T03:48:08.491135Z"
} | ecd3bd | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 163,
"completion_tokens": 376
},
"timestamp": "2026-02-18T06:18:00.236Z",
"answer": 5
}
] | 2 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "SUM_PRIMES",
... | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
501b60 | comb_binomial_compute_v1_2051736721_2378 | Let $n$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq = 1956570$, $\gcd(p, q) = 1$, and $p < q$. Let $k$ be the largest prime number satisfying $2 \leq k \leq 9$. Compute $\binom{n}{k}$. | 11,440 | graphs = [
Graph(
let={
"_n": Const(2),
"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=1956570)), Eq(left=GCD(a=Var(name='p'), b=Var(nam... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW",
"COPRIME_PAIRS"
] | 05d703 | comb_binomial_compute_v1 | null | 4 | 0 | [
"COPRIME_PAIRS",
"MAX_PRIME_BELOW"
] | 2 | 0.005 | 2026-02-08T16:37:55.447361Z | {
"verified": true,
"answer": 11440,
"timestamp": "2026-02-08T16:37:55.452233Z"
} | 924532 | 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": 1854
},
"timestamp": "2026-02-17T08:43:20.084Z",
"answer": 11440
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
feb6de | modular_mod_compute_v1_1978505735_4773 | Let $n = 96631$. Let $a$ be the largest positive divisor of $538731$ that is at most $729$. Let $m = 12996$. Define $r$ to be the remainder when $a$ is divided by $m$, and let $Q$ be the remainder when $n \cdot r$ is divided by $57635$. Find the value of $Q$. | 14,029 | graphs = [
Graph(
let={
"_n": Const(96631),
"a": MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Leq(Var("d"), Const(729)), Divides(divisor=Var("d"), dividend=Const(538731))))),
"m": Const(12996),
"result": Mod(value=Ref("a"), ... | NT | null | COMPUTE | sympy | MAX_DIVISOR | [
"MAX_DIVISOR"
] | 51757e | modular_mod_compute_v1 | null | 3 | 0 | [
"MAX_DIVISOR"
] | 1 | 0.002 | 2026-02-08T18:30:28.113161Z | {
"verified": true,
"answer": 14029,
"timestamp": "2026-02-08T18:30:28.115219Z"
} | 5ffe34 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 131,
"completion_tokens": 1644
},
"timestamp": "2026-02-18T17:43:12.908Z",
"answer": 14029
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
}... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
5274e7 | nt_min_coprime_above_v1_2051736721_1289 | Let $\text{start}$ be the largest prime number $n$ such that $2 \leq n \leq 1018$. Let $T$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x \cdot y = 549081$. Let $\text{upper}$ be the minimum value of $x + y$ as $(x, y)$ ranges over $T$. Define $\text{result}$ to be the smallest integer $n_1$... | 1,015 | graphs = [
Graph(
let={
"_n": Const(1018),
"start": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))),
"upper": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]... | NT | null | EXTREMUM | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW",
"B3"
] | 78ed98 | nt_min_coprime_above_v1 | null | 5 | 0 | [
"B3",
"MAX_PRIME_BELOW"
] | 2 | 0.181 | 2026-02-08T15:55:58.530874Z | {
"verified": true,
"answer": 1015,
"timestamp": "2026-02-08T15:55:58.712124Z"
} | 2ffba3 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 186,
"completion_tokens": 1847
},
"timestamp": "2026-02-16T18:13:40.095Z",
"answer": 1015
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"sta... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
62c2e1 | comb_count_surjections_v1_153355830_1285 | Let $n$ be the number of ordered pairs $(i,j)$ of integers with $1 \le i \le 6$ and $1 \le j \le 6$ such that $i + j = 7$. Let $k = 4$. Compute $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. | 1,560 | graphs = [
Graph(
let={
"_n": Const(7),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref("_n")), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(6)), right=IntegerRange(start=Const(1), end=Const... | COMB | null | COUNT | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | comb_count_surjections_v1 | null | 5 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.011 | 2026-02-08T06:16:54.712477Z | {
"verified": true,
"answer": 1560,
"timestamp": "2026-02-08T06:16:54.723375Z"
} | 801e6e | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 209,
"completion_tokens": 919
},
"timestamp": "2026-02-24T05:43:09.754Z",
"answer": 1560
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"stat... | {
"lo": -4.93,
"mid": -2.91,
"hi": -0.71
} | ||
576eb0 | geo_count_lattice_rect_v1_784195855_7122 | Let $R$ be the number of lattice points $(x, y)$ such that $0 \leq x \leq 105$ and $0 \leq y \leq 43$. Compute the remainder when $44121 \cdot R$ is divided by $65071$. | 25,842 | graphs = [
Graph(
let={
"a": Const(105),
"b": Const(43),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"Q": Mod(value=Mul(Const(44121), Ref("result")), modulus=Const(65071)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 2 | 0 | null | null | 0.001 | 2026-02-08T09:06:11.432911Z | {
"verified": true,
"answer": 25842,
"timestamp": "2026-02-08T09:06:11.434062Z"
} | daaba8 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 171,
"completion_tokens": 1433
},
"timestamp": "2026-02-24T10:27:21.746Z",
"answer": 25842
},
{
"... | 1 | [] | {
"lo": 1.15,
"mid": 4.18,
"hi": 6.61
} | ||||
ad91a2 | antilemma_v7_kummer_784195855_3291 | Let $x$ be the largest integer $k$ such that $7^k$ divides $\binom{160}{64}$. Compute $73663x$. | 73,663 | graphs = [
Graph(
let={
"_n": Const(7),
"x": MaxKDivides(target=Binom(n=Const(160), k=Const(64)), base=Ref("_n")),
"Q": Mul(Const(73663), Ref("x")),
},
goal=Ref("Q"),
)
] | NT | null | COMPUTE | sympy | C2 | [
"V7"
] | 0672d4 | antilemma_v7_kummer | null | 5 | 0 | [
"C2",
"V7"
] | 2 | 0.007 | 2026-02-08T06:19:33.403153Z | {
"verified": true,
"answer": 73663,
"timestamp": "2026-02-08T06:19:33.410545Z"
} | fa7f76 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 132,
"completion_tokens": 669
},
"timestamp": "2026-02-19T05:02:21.915Z",
"answer": 73663
}
] | 2 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V7",
"status": "... | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
53a82d | nt_count_digit_sum_v1_1431428450_1040 | Let $T$ be the set of all integers $t$ such that $21 \le t \le 108$ and there exist integers $a$ and $b$ with $1 \le a \le 2$, $1 \le b \le 13$, and $t = 15a + 6b$. Let $s = |T|$. Let $N$ be the number of integers $n$ with $1 \le n \le 68644$ such that the sum of the decimal digits of $n$ is equal to $s$. Compute the r... | 3,204 | graphs = [
Graph(
let={
"_n": Const(67249),
"upper": Const(68644),
"target_sum": 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(n... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_count_digit_sum_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 3.055 | 2026-02-08T13:51:59.547371Z | {
"verified": true,
"answer": 3204,
"timestamp": "2026-02-08T13:52:02.602135Z"
} | 44d0e4 | 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": 4920
},
"timestamp": "2026-02-15T21:35:05.527Z",
"answer": 3204
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
260ad4 | comb_catalan_compute_v1_601307018_7311 | Let $B_n$ denote the $n$-th Bell number and $C_n$ the $n$-th Catalan number. Let $N = C_{10}$. Find the remainder when $B_{N \bmod 11}$ is divided by $95215$. | 20,760 | graphs = [
Graph(
let={
"n": Const(10),
"result": Catalan(Ref("n")),
"Q": Mod(value=Bell(Mod(value=Abs(arg=Ref(name='result')), modulus=Const(11))), modulus=Const(95215)),
},
goal=Ref("Q"),
)
] | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM",
"K3"
] | 2db00f | comb_catalan_compute_v1 | bell_mod | 3 | 0 | [
"K3",
"LIN_FORM"
] | 2 | 0.035 | 2026-03-10T07:54:33.937798Z | {
"verified": true,
"answer": 20760,
"timestamp": "2026-03-10T07:54:33.972969Z"
} | ebb0b1 | 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": 475
},
"timestamp": "2026-04-19T06:23:49.876Z",
"answer": 20760
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
... | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
c96f75 | alg_qf_psd_min_v1_601307018_8935 | Let $Q$ be the minimum value of
$$
37220a^2 - 89328ab - 119104ac - 89328ad + 119104b^2 + 89328bc + 119104bd + 126548c^2 + 141436cd + 93050d^2
$$
over all ordered quadruples $(a, b, c, d)$ of positive integers satisfying $1 \le a, b, d \le 4$ and $1 \le c \le \min\{x + y : x, y > 0,\, xy = 4,\, x \le y\}$. Find $Q$. | 93,050 | graphs = [
Graph(
let={
"_n": Const(2),
"result": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b"), Var("c"), Var("d")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(4)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(4)), Geq(Var("c"), C... | ALG | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | alg_qf_psd_min_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.023 | 2026-03-10T09:21:34.008524Z | {
"verified": true,
"answer": 93050,
"timestamp": "2026-03-10T09:21:34.031583Z"
} | 91a2d8 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 254,
"completion_tokens": 20595
},
"timestamp": "2026-04-19T10:13:16.714Z",
"answer": 93050
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
2340ab | geo_count_lattice_rect_v1_397696148_2820 | Let $a = 128$ and $b = 471$. The number of lattice points in the rectangle $[0, a] \times [0, b]$, including the boundary, is denoted by $R$. Compute the remainder when $673 \cdot R$ is divided by $61208$. | 29,472 | graphs = [
Graph(
let={
"a": Const(128),
"b": Const(471),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"Q": Mod(value=Mul(Const(673), Ref("result")), modulus=Const(61208)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.001 | 2026-02-08T14:06:07.483318Z | {
"verified": true,
"answer": 29472,
"timestamp": "2026-02-08T14:06:07.484116Z"
} | de68fc | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 175,
"completion_tokens": 1318
},
"timestamp": "2026-02-24T19:50:37.648Z",
"answer": 29472
},
{
"... | 1 | [] | {
"lo": -2.43,
"mid": 1.2,
"hi": 4.84
} | ||||
767bf7 | sequence_fibonacci_compute_v1_1470522791_415 | Let $n$ be the number of prime numbers $p$ such that $2 \leq p \leq 73$. Compute the $n$th Fibonacci number. | 10,946 | graphs = [
Graph(
let={
"_n": Const(2),
"n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Const(73)), IsPrime(Var("n"))))),
"result": Fibonacci(arg=Ref(name='n')),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | COUNT_PRIMES | [
"COUNT_PRIMES"
] | 07c874 | sequence_fibonacci_compute_v1 | null | 3 | 0 | [
"COUNT_PRIMES"
] | 1 | 0.001 | 2026-02-08T13:00:42.057436Z | {
"verified": true,
"answer": 10946,
"timestamp": "2026-02-08T13:00:42.058805Z"
} | 4e44f7 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 81,
"completion_tokens": 561
},
"timestamp": "2026-02-15T08:26:25.271Z",
"answer": 10946
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
f64cca | nt_min_crt_v1_2051736721_4631 | Let $m = 7$ and $k = 11$. Find the smallest positive integer $n$ such that $1 \leq n \leq 77$, $n \equiv 4 \pmod{7}$, and $n \equiv 1 \pmod{11}$. | 67 | graphs = [
Graph(
let={
"m": Const(7),
"k": Const(11),
"a": Const(4),
"b": Const(1),
"upper": Const(77),
"result": MinOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(valu... | NT | null | EXTREMUM | sympy | MOBIUS_COPRIME | [
"V8"
] | 86348e | nt_min_crt_v1 | null | 4 | 0 | [
"MOBIUS_COPRIME",
"V8"
] | 2 | 0.118 | 2026-02-08T18:03:29.460807Z | {
"verified": true,
"answer": 67,
"timestamp": "2026-02-08T18:03:29.578352Z"
} | 921cee | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 106,
"completion_tokens": 850
},
"timestamp": "2026-02-18T13:20:20.354Z",
"answer": 67
},
{
... | 1 | [
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
1a3e80 | antilemma_cartesian_v1_655260480_1741 | Let $m = 43$. Define $n$ to be the number of ordered pairs $(i, j)$ of integers with $1 \leq i \leq 42$, $1 \leq j \leq 43$, and $i + j = m$. Let $x$ be the number of ordered pairs $(a, b)$ such that $1 \leq a \leq 14$ and $1 \leq b \leq 17$. Define $c$ to be the number of ordered pairs $(i_1, j_1)$ with $1 \leq i_1 \l... | 57,161 | graphs = [
Graph(
let={
"_m": Const(43),
"_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(42)), right=IntegerRange(start=Const(1), end=Co... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS/COUNT_SUM_EQUALS",
"COUNT_CARTESIAN"
] | 961465 | antilemma_cartesian_v1 | quadratic_mod | 3 | 0 | [
"COUNT_CARTESIAN",
"COUNT_SUM_EQUALS"
] | 2 | 0.018 | 2026-02-08T16:19:09.336647Z | {
"verified": true,
"answer": 57161,
"timestamp": "2026-02-08T16:19:09.354612Z"
} | 271658 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 283,
"completion_tokens": 1033
},
"timestamp": "2026-02-24T20:37:25.339Z",
"answer": 57161
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "n... | {
"lo": -5.65,
"mid": -3.17,
"hi": -0.81
} | ||
2ccf43 | nt_min_coprime_above_v1_2051736721_4313 | Let $m = 180$ and $n = 2$. Define $t_{\text{mod}}$ to be the number of integers $t$ such that $13 \leq t \leq 259$ and $t = 3a + 4b + 6$ for some positive integers $a \leq 59$ and $b \leq 19$. Let $r$ be the smallest integer $k$ such that $66667 \leq k \leq 66917$ and $\gcd(k, t_{\text{mod}}) = 1$. Let $f$ be the numbe... | 66,795 | graphs = [
Graph(
let={
"_m": Const(180),
"_n": Const(2),
"start": Const(66666),
"upper": Const(66917),
"modulus": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq... | NT | null | EXTREMUM | sympy | COUNT_FIB_DIVISIBLE | [
"COUNT_FIB_DIVISIBLE",
"LIN_FORM"
] | d91a57 | nt_min_coprime_above_v1 | mod_exp | 6 | 0 | [
"COUNT_FIB_DIVISIBLE",
"LIN_FORM"
] | 2 | 0.027 | 2026-02-08T17:54:40.926327Z | {
"verified": true,
"answer": 66795,
"timestamp": "2026-02-08T17:54:40.952837Z"
} | 169c1a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 236,
"completion_tokens": 5039
},
"timestamp": "2026-02-18T10:05:01.820Z",
"answer": 66795
},
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_ADD",
"stat... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
fb1dbc | comb_count_derangements_v1_124444284_6977 | Let $n$ be the smallest divisor of $77$ that is at least $2$. Define $Q$ to be the remainder when $44121$ multiplied by the subfactorial of $n$ is divided by $50521$. Compute $Q$. | 6,835 | graphs = [
Graph(
let={
"_n": Const(50521),
"n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(77))))),
"result": Subfactorial(arg=Ref(name='n')),
"Q": Mod(value=Mul(Const(44121), Ref(... | NT | COMB | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | comb_count_derangements_v1 | null | 3 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.001 | 2026-02-08T08:44:45.072421Z | {
"verified": true,
"answer": 6835,
"timestamp": "2026-02-08T08:44:45.073623Z"
} | ee3412 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 100,
"completion_tokens": 1214
},
"timestamp": "2026-02-13T21:22:59.720Z",
"answer": 6835
},
{... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8",
"status": "... | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} |
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