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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
8c81a1 | nt_num_divisors_compute_v1_1742523217_2105 | Let $n = 8192$. Determine the number of positive divisors of $n$. | 14 | graphs = [
Graph(
let={
"n": Const(8192),
"result": NumDivisors(n=Ref("n")),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_num_divisors_compute_v1 | null | 2 | 0 | [
"B3"
] | 1 | 0.022 | 2026-02-08T04:28:02.743451Z | {
"verified": true,
"answer": 14,
"timestamp": "2026-02-08T04:28:02.765242Z"
} | a8e144 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 129,
"completion_tokens": 285
},
"timestamp": "2026-02-10T16:42:59.990Z",
"answer": 14
},
{
"id"... | 2 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.73,
"hi": -5.46
} | ||
8e6012 | algebra_poly_eval_v1_655260480_5539 | Let $t = 8$. Let $A$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 259081$, and let $s_1 = \min\{x + y : (x, y) \in A\}$. Let $B$ be the set of all ordered pairs $(x_1, y_1)$ of positive integers such that $x_1 y_1 = 59049$, and let $s_2 = \min\{x_1 + y_1 : (x_1, y_1) \in B\}$. Compute $... | 3,753 | graphs = [
Graph(
let={
"_m": Const(36),
"_n": Const(336),
"t": Const(8),
"result": Div(Sum(Mul(Ref("_m"), Pow(Ref("t"), Const(5))), Mul(Ref("_n"), Pow(Ref("t"), Const(4))), Mul(MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | algebra_poly_eval_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.007 | 2026-02-08T18:33:13.923522Z | {
"verified": true,
"answer": 3753,
"timestamp": "2026-02-08T18:33:13.930800Z"
} | f8ec86 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 225,
"completion_tokens": 2306
},
"timestamp": "2026-02-18T17:30:42.821Z",
"answer": 3753
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
0111e8 | comb_count_permutations_fixed_v1_48377204_1783 | Let $n$ be the smallest divisor of $1225$ that is at least $2$. Compute the value of $\binom{n}{0} \cdot !(n - 0)$, where $!k$ denotes the number of derangements of $k$ elements, and then find the remainder when this value is multiplied by $44121$ and divided by $98513$. | 69,577 | graphs = [
Graph(
let={
"_n": Const(98513),
"n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(1225))))),
"k": Const(0),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=S... | NT | COMB | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | comb_count_permutations_fixed_v1 | null | 3 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.003 | 2026-02-08T16:23:36.352951Z | {
"verified": true,
"answer": 69577,
"timestamp": "2026-02-08T16:23:36.356105Z"
} | 62dcc1 | 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": 1051
},
"timestamp": "2026-02-17T02:54:54.219Z",
"answer": 69577
},
... | 1 | [
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V7",
"status... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
b16b84 | geo_count_lattice_rect_v1_1742523217_4592 | Let $a = 81$ and $b = 269$. Consider the rectangle with vertices at $(0,0)$, $(a,0)$, $(0,b)$, and $(a,b)$. Let $R$ be the number of lattice points (points with integer coordinates) that lie inside or on the boundary of this rectangle.
Compute the remainder when $65648 \cdot R$ is divided by $65223$. | 17,388 | graphs = [
Graph(
let={
"a": Const(81),
"b": Const(269),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"Q": Mod(value=Mul(Const(65648), Ref("result")), modulus=Const(65223)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.002 | 2026-02-08T08:58:35.843645Z | {
"verified": true,
"answer": 17388,
"timestamp": "2026-02-08T08:58:35.845713Z"
} | 2ab902 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 199,
"completion_tokens": 986
},
"timestamp": "2026-02-24T10:16:39.941Z",
"answer": 17388
},
{
"i... | 1 | [] | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||||
f23959 | comb_sum_binomial_row_v1_1419126231_1856 | Let $n$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \le a \le b \le 20$ such that $32b^2 + 32a^2 - 64ab = 1568$. Compute $2^n$. | 8,192 | graphs = [
Graph(
let={
"_n": Const(20),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Ref("_n")), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(20)), Leq(Var("a"), Var("b")), Eq(Sum(Mul(Const(32), Pow... | COMB | null | SUM | sympy | QF_PSD_ORBIT | [
"QF_PSD_ORBIT"
] | 1d37f3 | comb_sum_binomial_row_v1 | null | 4 | 0 | [
"QF_PSD_ORBIT"
] | 1 | 0.001 | 2026-02-25T11:24:23.100245Z | {
"verified": true,
"answer": 8192,
"timestamp": "2026-02-25T11:24:23.101702Z"
} | dad008 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 170,
"completion_tokens": 595
},
"timestamp": "2026-03-30T14:19:37.436Z",
"answer": 8192
},
{
"id... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "QF_PSD_ORBIT",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "n... | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | ||
58cb24 | geo_visible_lattice_v1_1470522791_1463 | Let $n = 99$. Define $L$ to be the number of visible lattice points $(x, y)$ such that $1 \leq x, y \leq n$ and $\gcd(x, y) = 1$. Compute the remainder when $44121 \cdot L$ is divided by $80491$. | 58,475 | graphs = [
Graph(
let={
"n": Const(99),
"result": VisibleLatticePoints(n=Ref(name='n')),
"Q": Mod(value=Mul(Const(44121), Ref("result")), modulus=Const(80491)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 4 | 0 | null | null | 0.46 | 2026-02-08T13:40:42.381160Z | {
"verified": true,
"answer": 58475,
"timestamp": "2026-02-08T13:40:42.841040Z"
} | 05d758 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 180,
"completion_tokens": 9344
},
"timestamp": "2026-02-24T18:50:51.316Z",
"answer": 58475
},
{
"... | 1 | [] | {
"lo": 1.15,
"mid": 4.18,
"hi": 6.61
} | ||||
18beae | nt_count_with_divisor_count_v1_1918700295_1127 | Let $A$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 24$, $\gcd(p, q) = 1$, and $p < q$. Let $B$ be the number of positive integers $n \leq 70756$ that have exactly two positive divisors. Let $C$ be the number of ordered pairs $(x_1, x_2)$ of positive odd i... | 7,705 | graphs = [
Graph(
let={
"_m": Const(15842),
"_n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=24)), Eq(left=GCD(a=Var(name='p'), b=Var(nam... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/COMB1"
] | a141ad | nt_count_with_divisor_count_v1 | quadratic_mod | 5 | 0 | [
"COMB1",
"COPRIME_PAIRS"
] | 2 | 4.703 | 2026-02-08T05:36:09.410865Z | {
"verified": true,
"answer": 7705,
"timestamp": "2026-02-08T05:36:14.113699Z"
} | bb1445 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 182,
"completion_tokens": 2602
},
"timestamp": "2026-02-12T11:02:35.458Z",
"answer": 7705
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok_later"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma... | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
988efd | comb_count_surjections_v1_153355830_239 | Let $n$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 14$. Let $k = 5$. Define $\text{result} = k! \cdot S(n, k)$, where $S(n, k)$ denotes the Stirling number of the second kind. Compute $38416 - \text{result}$. | 21,616 | graphs = [
Graph(
let={
"_n": Const(14),
"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")), Re... | COMB | null | COUNT | sympy | COMB1 | [
"COMB1"
] | 567f58 | comb_count_surjections_v1 | null | 6 | 0 | [
"COMB1"
] | 1 | 0.002 | 2026-02-08T02:58:43.360174Z | {
"verified": true,
"answer": 21616,
"timestamp": "2026-02-08T02:58:43.362216Z"
} | 9daad6 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 200,
"completion_tokens": 860
},
"timestamp": "2026-02-10T12:25:26.678Z",
"answer": 21616
},
{
"i... | 1 | [
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"statu... | {
"lo": -0.05,
"mid": 2.89,
"hi": 5.27
} | ||
4ee015 | diophantine_product_count_v1_717093673_1153 | Let $x$ and $y$ be positive integers such that $x + y = 76$. Consider the set of all such pairs $(x, y)$ that maximize the product $xy$. Let $N$ be the maximum value of $xy$ over all such pairs. Now, let $S$ be the set of all pairs of positive integers $(x_1, y_1)$ such that $x_1 y_1 = N$. Define $M$ to be the minimum ... | 14 | graphs = [
Graph(
let={
"_n": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Const(76)))), expr=Mul(Var("x"), Var("y")))),
"k": Const(120),
... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"B1/B3"
] | 80b49d | diophantine_product_count_v1 | null | 6 | 0 | [
"B1",
"B3",
"MIN_PRIME_FACTOR"
] | 3 | 0.045 | 2026-02-08T15:53:26.851895Z | {
"verified": true,
"answer": 14,
"timestamp": "2026-02-08T15:53:26.896949Z"
} | 752b60 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 214,
"completion_tokens": 1766
},
"timestamp": "2026-02-16T15:28:23.330Z",
"answer": 14
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lem... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
8a2689 | nt_count_divisible_and_v1_677425708_560 | Let $N$ be the number of positive integers $n$ such that $n \leq 46224$, $n$ is divisible by 6, and $n$ is divisible by 8. Compute
$$
\sum_{k=1}^{|N|} \tau(k),
$$
where $\tau(k)$ denotes the number of positive divisors of $k$. | 14,877 | graphs = [
Graph(
let={
"upper": Const(46224),
"d1": Const(6),
"d2": Const(8),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(value=Var("n"), modulus=Ref("d1")), Const(0)), Eq(Mo... | NT | null | COUNT | sympy | ONE_PHI_1 | [
"ONE_PHI_1"
] | f6b5a5 | nt_count_divisible_and_v1 | null | 3 | 0 | [
"ONE_PHI_1"
] | 1 | 1.556 | 2026-02-08T03:35:53.770860Z | {
"verified": true,
"answer": 14877,
"timestamp": "2026-02-08T03:35:55.326617Z"
} | ad5d61 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 194,
"completion_tokens": 5366
},
"timestamp": "2026-02-08T20:45:58.915Z",
"answer": 14879
},
{
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "ONE_PHI_1",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V3",
"st... | {
"lo": 1.69,
"mid": 5.03,
"hi": 8.38
} | ||
d463bf | alg_qf_psd_sum_v1_1419126231_430 | Compute the remainder when $$\sum_{\substack{1 \le a \le 351 \\ 1 \le b \le 351}} (5a^2 + b^2 + 2ab)$$ is divided by $74212$. | 10,148 | graphs = [
Graph(
let={
"result": Mod(value=SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(351)), Geq(Var("b"), Const(1)), Leq(Var("b"), Const(351)))), expr=Sum(Mul(Const(5), Pow(Var("a"), Const(2)))... | ALG | null | COMPUTE | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC/QF_PSD_COUNT_LEQ"
] | 6e1a47 | alg_qf_psd_sum_v1 | null | 3 | null | [
"QF_PSD_COUNT_LEQ",
"SUM_ARITHMETIC"
] | 2 | 0.265 | 2026-02-25T09:58:01.547916Z | {
"verified": true,
"answer": 10148,
"timestamp": "2026-02-25T09:58:01.812444Z"
} | 6137a1 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 162,
"completion_tokens": 4857
},
"timestamp": "2026-03-30T08:26:39.875Z",
"answer": 10148
},
{
"... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok_later"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
}
] | {
"lo": -5.37,
"mid": 0.23,
"hi": 5.22
} | ||
68f3ee | geo_visible_lattice_v1_1742523217_2141 | Let $n = 55$. Define $\text{result}$ to be the number of visible lattice points $(x, y)$ with $1 \leq x, y \leq n$, where a point $(x, y)$ is visible if $\gcd(x, y) = 1$. Let $Q$ be the remainder when $54658 \cdot \text{result}$ is divided by $98505$. Compute $Q$. | 60,172 | graphs = [
Graph(
let={
"n": Const(55),
"result": VisibleLatticePoints(n=Ref(name='n')),
"Q": Mod(value=Mul(Const(54658), Ref("result")), modulus=Const(98505)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_visible_lattice_v1 | null | 5 | 0 | null | null | 0.302 | 2026-02-08T04:30:10.832234Z | {
"verified": true,
"answer": 60172,
"timestamp": "2026-02-08T04:30:11.133784Z"
} | cc83a9 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 202,
"completion_tokens": 5977
},
"timestamp": "2026-02-24T01:05:51.125Z",
"answer": 60172
},
{
"... | 1 | [] | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||||
3902e7 | nt_count_divisible_and_v1_1918700295_3728 | Let $n$ be the number of ordered pairs $(a,b)$ where $a$ is an integer from 1 to 48 and $b$ is an integer from 1 to 107. Let $d_1$ be the number of nonnegative integers $j \leq n$ such that $\binom{5136}{j}$ is odd. Determine the number of positive integers $m$ such that $1 \leq m \leq 82920$, $m$ is divisible by $d_1$... | 3,455 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(48)), right=IntegerRange(start=Const(1), end=Const(107)))),
"upper": Const(82920),
"d1": CountOverSet(set=SolutionsSet(var=Var("j"), con... | ALG | COMB | COUNT | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN/V8"
] | 565c9e | nt_count_divisible_and_v1 | null | 5 | 0 | [
"COUNT_CARTESIAN",
"V8"
] | 2 | 6.879 | 2026-02-08T08:50:20.311804Z | {
"verified": true,
"answer": 3455,
"timestamp": "2026-02-08T08:50:27.191196Z"
} | df1b29 | 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": 1550
},
"timestamp": "2026-02-24T10:10:33.977Z",
"answer": 3455
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8"... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
06c4d4 | geo_count_lattice_rect_v1_124444284_5054 | Let $a = 181$ and $b = 71$. Compute the number of lattice points $(x, y)$ such that $0 \leq x \leq a$ and $0 \leq y \leq b$.\n\nFind the value of this number. | 13,104 | graphs = [
Graph(
let={
"a": Const(181),
"b": Const(71),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.001 | 2026-02-08T06:22:23.832931Z | {
"verified": true,
"answer": 13104,
"timestamp": "2026-02-08T06:22:23.833746Z"
} | a749b1 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 170,
"completion_tokens": 226
},
"timestamp": "2026-02-24T06:04:38.850Z",
"answer": 13104
},
{
"i... | 1 | [] | {
"lo": -5.98,
"mid": -3.97,
"hi": -1.94
} | ||||
38811c | v1_endings_v1_1742523217_1061 | Let $n = 23681$. Let $v_5(k)$ denote the largest integer $k$ such that $5^k$ divides $k!$. Compute the value of $v_5((2n)!) - v_5(n!) - n \cdot v_5(2)$. | 5,920 | graphs = [
Graph(
let={
"n_val": Const(23681),
"two_n_val": Const(47362),
"p_val": Const(5),
"two": Const(2),
"fact_2n": Factorial(Ref("two_n_val")),
"fact_n": Factorial(Ref("n_val")),
"vp_2n": MaxKDivides(target=Ref("fact_2... | NT | null | COMPUTE | sympy | V1 | [
"V1"
] | dae96f | v1_endings_v1 | null | 6 | null | [
"V1"
] | 1 | 0.001 | 2026-02-08T03:24:03.549359Z | {
"verified": true,
"answer": 5920,
"timestamp": "2026-02-08T03:24:03.550260Z"
} | 78e8fb | 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": 1637
},
"timestamp": "2026-02-10T02:42:12.681Z",
"answer": 5920
},
{
"i... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K5",
"status": "same_pattern_wrong"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V1",
"status":... | {
"lo": -6.51,
"mid": -0.31,
"hi": 5.43
} | ||
71e288 | nt_max_prime_below_v1_865884756_4215 | Let $A$ be the set of all ordered pairs $(p, q)$ of positive integers such that $pq = 54$, $\gcd(p, q) = 1$, and $p < q$. Let $s = |A|$. Let $B$ be the set of all prime numbers $n$ such that $s \leq n \leq 33333$. Compute the largest element of $B$. | 33,331 | graphs = [
Graph(
let={
"upper": Const(33333),
"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 | 0.799 | 2026-02-08T17:47:12.619321Z | {
"verified": true,
"answer": 33331,
"timestamp": "2026-02-08T17:47:13.417952Z"
} | a3a676 | 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": 3212
},
"timestamp": "2026-02-18T08:20:33.349Z",
"answer": 33331
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
75692d | comb_count_permutations_fixed_v1_151522320_1672 | Let $n$ be the largest prime number satisfying $2 \leq n \leq 7$. Let $k = 2$. Define $r = \binom{n}{k} \cdot !(n - k)$, where $!m$ denotes the number of derangements of $m$ elements. Let $Q$ be the remainder when $54947 \cdot r$ is divided by $80666$. Compute $Q$. | 32,114 | graphs = [
Graph(
let={
"_n": Const(2),
"n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Const(7)), IsPrime(Var("n"))))),
"k": Const(2),
"result": Mul(Binom(n=Ref("n"), k=Ref("k")), Subfactorial(arg=Sub(left=... | NT | COMB | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | comb_count_permutations_fixed_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.001 | 2026-02-08T04:10:51.993620Z | {
"verified": true,
"answer": 32114,
"timestamp": "2026-02-08T04:10:51.994845Z"
} | 0cb56c | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 204,
"completion_tokens": 945
},
"timestamp": "2026-02-10T15:38:24.628Z",
"answer": 32114
},
{
"... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
2428d2 | nt_count_phi_equals_v1_784195855_4410 | Let $k = 1440$ and let $N$ be the number of positive integers $n$ with $1 \leq n \leq 2028$ such that $\phi(n) = k$. Compute $N$. | 4 | graphs = [
Graph(
let={
"upper": Const(2028),
"k": Const(1440),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(EulerPhi(n=Var("n")), Ref("k"))))),
},
goal=Ref("result"),
)
] | NT | null | COUNT | sympy | COUNT_COPRIME_GRID | [
"LIN_FORM",
"B3"
] | 688dbe | nt_count_phi_equals_v1 | null | 6 | 0 | [
"B3",
"COUNT_COPRIME_GRID",
"LIN_FORM"
] | 3 | 4.628 | 2026-02-08T07:05:12.974919Z | {
"verified": true,
"answer": 4,
"timestamp": "2026-02-08T07:05:17.602660Z"
} | 49aba4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 94,
"completion_tokens": 6546
},
"timestamp": "2026-02-13T07:38:33.433Z",
"answer": 4
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
104a9e | antilemma_sum_equals_v1_865884756_2631 | Let $n$ be the number of ordered pairs $(i, j)$ such that $1 \leq i \leq 2$ and $1 \leq j \leq 17$. Let $x$ be the number of ordered pairs $(i, j)$ with $1 \leq i \leq 32$, $1 \leq j \leq 33$, and $i + j = n$. Let $m = |x| + 2$. The Fibonacci sequence is defined by $F_1 = 1$, $F_2 = 1$, and $F_k = F_{k-1} + F_{k-2}$ fo... | 9 | graphs = [
Graph(
let={
"_n": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(2)), right=IntegerRange(start=Const(1), end=Const(17)))),
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref... | COMB | GEOM | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_CARTESIAN/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | 8bee9e | antilemma_sum_equals_v1 | null | 4 | 0 | [
"COUNT_CARTESIAN",
"COUNT_SUM_EQUALS"
] | 2 | 0.047 | 2026-02-08T16:51:36.903764Z | {
"verified": true,
"answer": 9,
"timestamp": "2026-02-08T16:51:36.950707Z"
} | 5a8954 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 210,
"completion_tokens": 1237
},
"timestamp": "2026-02-17T12:48:56.186Z",
"answer": 9
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no... | {
"lo": -5.64,
"mid": -3.17,
"hi": -0.81
} | ||
a6e11f | geo_count_lattice_rect_v1_784195855_6608 | Compute the number of lattice points $(x, y)$ such that $0 \leq x \leq 128$ and $0 \leq y \leq 275$. | 35,604 | graphs = [
Graph(
let={
"a": Const(128),
"b": Const(275),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"Q": Abs(arg=Ref(name='result')),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 5 | 0 | null | null | 0.001 | 2026-02-08T08:45:11.466304Z | {
"verified": true,
"answer": 35604,
"timestamp": "2026-02-08T08:45:11.467256Z"
} | 358ce5 | 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": 246
},
"timestamp": "2026-02-24T09:55:16.484Z",
"answer": 35604
},
{
"i... | 1 | [] | {
"lo": -3.84,
"mid": -1.67,
"hi": 1.32
} | ||||
0a21d2 | nt_count_divisible_and_v1_1520064083_8538 | Let $d_1 = \sum_{k=1}^{3} \phi(k) \left\lfloor \frac{3}{k} \right\rfloor$ and $d_2 = 9$.
Let $S$ be the set of all positive integers $n$ such that $1 \leq n \leq 83466$, $n$ is divisible by $d_1$, and $n$ is divisible by $d_2$. Let $r$ be the number of elements in $S$.
Compute the value of $B_{|r| \bmod 11}$, where $... | 203 | graphs = [
Graph(
let={
"_n": Const(11),
"upper": Const(83466),
"d1": Summation(var="k", start=Const(1), end=Const(3), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(3), Var("k"))))),
"d2": Const(9),
"result": CountOverSet(set=SolutionsSet(var=Var(... | NT | COMB | COUNT | sympy | K2 | [
"K2"
] | 6897ab | nt_count_divisible_and_v1 | null | 5 | 0 | [
"K2"
] | 1 | 12.204 | 2026-02-08T10:14:40.842526Z | {
"verified": true,
"answer": 203,
"timestamp": "2026-02-08T10:14:53.046881Z"
} | c19d2a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 184,
"completion_tokens": 747
},
"timestamp": "2026-02-14T06:52:19.248Z",
"answer": 203
},
{
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
7ba5aa | comb_count_surjections_v1_168721529_779 | Let $n_2 = 5$. Define $m = \sum_{k=0}^{n_2} (-1)^k \binom{n_2}{k}$. Let $n_1 = 0$ and define $t = \sum_{k=0}^{n_1} (-1)^k \binom{n_1}{k}$. Let $n = 4$ and let $k = (3 + m) \cdot t$. Compute $k! \cdot S(n, k)$, where $S(n, k)$ denotes the Stirling number of the second kind. | 36 | graphs = [
Graph(
let={
"n2": Const(5),
"m": Summation(var="k", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n2"), k=Var("k")))),
"n1": Const(0),
"t": Summation(var="k", start=Const(0), end=Ref("n1"), expr=Mul(Pow(Const(-1), V... | COMB | null | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING"
] | c21569 | comb_count_surjections_v1 | null | 4 | 2 | [
"BINOMIAL_ALTERNATING"
] | 1 | 0.002 | 2026-02-08T13:17:26.273675Z | {
"verified": true,
"answer": 36,
"timestamp": "2026-02-08T13:17:26.275355Z"
} | 8737cc | 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": 608
},
"timestamp": "2026-02-09T09:04:06.044Z",
"answer": 36
},
{
"id":... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"sta... | {
"lo": -5.98,
"mid": -3.99,
"hi": -2
} | ||
d36084 | comb_count_permutations_fixed_v1_784195855_8013 | Let $n = \sum_{k=1}^{3} \phi(k) \left\lfloor \frac{3}{k} \right\rfloor$, where $\phi$ is Euler's totient function. Compute $\binom{n}{2} \cdot !(n-2)$, where $!m$ denotes the number of derangements of $m$ elements. | 135 | graphs = [
Graph(
let={
"_n": Summation(var="k", start=Const(1), end=Const(2), expr=Var("k")),
"n": Summation(var="k", start=Const(1), end=Const(3), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Ref("_n"), Var("k"))))),
"k": Const(2),
"result": Mul(Binom(n=Ref("n")... | NT | COMB | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC/K2"
] | 06cc86 | comb_count_permutations_fixed_v1 | null | 4 | 0 | [
"K2",
"SUM_ARITHMETIC"
] | 2 | 0.002 | 2026-02-08T09:39:38.065599Z | {
"verified": true,
"answer": 135,
"timestamp": "2026-02-08T09:39:38.067326Z"
} | be2fa6 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 138,
"completion_tokens": 651
},
"timestamp": "2026-02-15T21:02:28.625Z",
"answer": 135
},
{
"id": 11,
... | 2 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K2",
"status": "ok_later"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": ... | {
"lo": -9.12,
"mid": -6.02,
"hi": -3.62
} | ||
71c329 | alg_qf_psd_min_v1_1218484723_3791 | Let $N$ be the number of ordered pairs $(a_1,b_1)$ of integers with $1 \le a_1 \le 25$ and $1 \le b_1 \le 25$ such that
$$20b_1^{2} - 12a_1b_1 + 41a_1^{2} \le 19792.$$
Let $S$ be the number of integers $v$ with $17 \le v \le N$ for which there exist integers $a,b$ with $1 \le a \le 5$ and $1 \le b \le 5$ such that
$$16... | 83,611 | graphs = [
Graph(
let={
"_m": Const(27640),
"_n": Const(17),
"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(22)), Geq(Var("b"), Const(1)), Leq(Va... | ALG | null | COMPUTE | sympy | QF_PSD_COUNT_LEQ | [
"QF_PSD_COUNT_LEQ/QF_PSD_DISTINCT"
] | 0cf842 | alg_qf_psd_min_v1 | null | 7 | 0 | [
"QF_PSD_COUNT_LEQ",
"QF_PSD_DISTINCT"
] | 2 | 1.07 | 2026-02-25T05:26:18.192021Z | {
"verified": true,
"answer": 83611,
"timestamp": "2026-02-25T05:26:19.262241Z"
} | 56621d | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 419,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T12:19:05.936Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
},
{
"lemma": "QF_PSD_DISTINCT",
"status": "ok_later"
}
] | {
"lo": 1.55,
"mid": 4.7,
"hi": 7.23
} | ||
4c674c | nt_min_phi_inverse_v1_1978505735_6947 | Let $S$ be the set of all ordered pairs of positive integers $(x, y)$ such that $x + y = 20$. Let $M$ be the maximum value of $xy$ over all such pairs. Let $k = 24$. Determine the smallest positive integer $n \leq M$ such that $\phi(n) = k$. | 35 | graphs = [
Graph(
let={
"_n": Const(20),
"upper": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Ref("_n")))), expr=Mul(Var("x"), Var("y")))),... | NT | null | EXTREMUM | sympy | COUNT_CARTESIAN | [
"B1"
] | 5b950e | nt_min_phi_inverse_v1 | null | 6 | 0 | [
"B1",
"COUNT_CARTESIAN"
] | 2 | 0.068 | 2026-02-08T19:54:34.166245Z | {
"verified": true,
"answer": 35,
"timestamp": "2026-02-08T19:54:34.234058Z"
} | 7a1c19 | 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": 2497
},
"timestamp": "2026-02-18T23:42:38.629Z",
"answer": 35
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
28bf94 | comb_count_partitions_v1_655260480_4940 | Let $n$ be the number of integers $t$ in the range $26 \le t \le 91$ for which there exist positive integers $a \le 7$ and $b \le 6$ such that $t = 5a + 7b + 14$. Let $\text{result}$ be the number of integer partitions of $n$. Compute the sum of the digits of $|\text{result}|$, each multiplied by the square of its posi... | 36,314 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=7)), Geq(left=Var(name='b'), right=Const(value=1... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_count_partitions_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T18:13:33.987173Z | {
"verified": true,
"answer": 36314,
"timestamp": "2026-02-08T18:13:33.989208Z"
} | 7a1fec | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 163,
"completion_tokens": 3766
},
"timestamp": "2026-02-18T15:25:46.923Z",
"answer": 36314
},
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -3.12,
"mid": 1.47,
"hi": 6.57
} | ||
dda26e | nt_lcm_compute_v1_1978505735_460 | Let $a$ be the number of ordered pairs $(i, j)$ of positive integers with $1 \leq i \leq 36$, $1 \leq j \leq 107$, and $\gcd(i, j) = 1$. Let $b$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 910116$. Let $r = \mathrm{lcm}(a, b)$. Compute the remainder when $r + 2^{... | 29,514 | graphs = [
Graph(
let={
"_n": Const(81526),
"a": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(GCD(a=Var("i"), b=Var("j")), Const(1)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(36)), right=IntegerRange(start=Const(1), e... | NT | null | COMPUTE | sympy | COUNT_COPRIME_GRID | [
"COUNT_COPRIME_GRID",
"B3"
] | a8b7cb | nt_lcm_compute_v1 | null | 6 | 0 | [
"B3",
"COUNT_COPRIME_GRID"
] | 2 | 0.004 | 2026-02-08T15:23:33.157654Z | {
"verified": true,
"answer": 29514,
"timestamp": "2026-02-08T15:23:33.161811Z"
} | 1cfa9c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 176,
"completion_tokens": 3437
},
"timestamp": "2026-02-16T05:40:35.330Z",
"answer": 29514
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status":... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
454389 | algebra_quadratic_discriminant_v1_1218484723_2750 | Let
\[
D = -10^{2} - 4(-7)(-4).
\]
Define
\[
M = 2\Biggl[ D > \sum_{k = \binom{4}{4} - 1}^{\left|\{ a_1 : a_1 \ge 0,\ a_1 \le 66,\ 2\bigl(2a_1^{4} - 3a_1^{3} + 2a_1^{2} - 1a_1 - 5 \bmod 67\bigr)^{4} - 3\bigl(2a_1^{4} - 3a_1^{3} + 2a_1^{2} - 1a_1 - 5 \bmod 67\bigr)^{3}
\\[4pt]
\qquad + 2\bigl(2a_1^{4} - 3a_1^{3} + 2a_1... | 0 | graphs = [
Graph(
let={
"_n": Const(2),
"a": Const(-7),
"b": Const(-10),
"c": Const(-4),
"D": Sub(Pow(Ref("b"), Ref("_n")), Mul(Const(4), Ref("a"), Ref("c"))),
"result": Sum(Mul(Const(2), Iverson(condition=Gt(Ref("D"), Summation(var="k"... | ALG | COMB | COMPUTE | sympy | POLY_ORBIT_LEGENDRE | [
"POLY_ORBIT_LEGENDRE/BINOMIAL_ALTERNATING",
"ZERO_BINOM_N"
] | bd9040 | algebra_quadratic_discriminant_v1 | null | 7 | 0 | [
"BINOMIAL_ALTERNATING",
"POLY_ORBIT_LEGENDRE",
"ZERO_BINOM_N"
] | 3 | 0.123 | 2026-02-25T04:27:35.543175Z | {
"verified": true,
"answer": 0,
"timestamp": "2026-02-25T04:27:35.666326Z"
} | cd8025 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 585,
"completion_tokens": 23770
},
"timestamp": "2026-03-29T06:23:33.285Z",
"answer": 0
},
{
"id"... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok_later"
},
{
"lemma": "POLY_ORBIT_LEGENDRE",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "ZERO_BINOM_N",
"status": "ok"
}
] | {
"lo": -4.26,
"mid": -1.8,
"hi": 1.26
} | ||
e6e92d | antilemma_product_of_sums_v1_677425708_2843 | Let $ S_1 $ be the sum of all integers $ j $ with $ 0 \le j \le 7 $ such that $ \binom{7}{j} $ is odd. Let $ d_0 = \sum_{d \mid \gcd(4,9)} \mu(d) $, where $ \mu $ is the M\"obius function. Let $ S_2 = \sum_{k = d_0}^{17} k $. Let $ x = S_1 \times S_2 $. Compute the value of $ 3^{|x|} + 24025 $ modulo $ 99991 $. | 54,684 | graphs = [
Graph(
let={
"S1": SumOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(7)), Eq(Mod(value=Binom(n=Const(7), k=Var("j")), modulus=Const(2)), Const(1))))),
"S2": Summation(var="k", start=SumOverDivisors(n=GCD(a=Const(value=4), ... | NT | null | COMPUTE | sympy | MOBIUS_COPRIME | [
"MOBIUS_COPRIME",
"PRODUCT_OF_SUMS"
] | 17cc0f | antilemma_product_of_sums_v1 | null | 5 | 0 | [
"MOBIUS_COPRIME",
"PRODUCT_OF_SUMS"
] | 2 | 0.002 | 2026-02-08T05:20:00.901489Z | {
"verified": true,
"answer": 54684,
"timestamp": "2026-02-08T05:20:00.903526Z"
} | 37a2cf | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 237,
"completion_tokens": 689
},
"timestamp": "2026-02-18T15:50:43.859Z",
"answer": 24026
}
] | 0 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"sta... | {
"lo": -6.48,
"mid": 1.54,
"hi": 9.56
} | ||
aa74a9 | geo_count_lattice_triangle_v1_1470522791_130 | Let $A$ be the area of the triangle with vertices at $(0, 0)$, $(210, 200)$, and $(60, 111)$, multiplied by 2. Let $B$ be the number of integers $t$ in the interval $18 \le t \le 440$ for which there exist integers $a$ and $b$ such that $1 \le a \le 24$, $1 \le b \le 25$, and $t = 10a + 8b$. Then $A = |210 \cdot 111 - ... | 53,270 | graphs = [
Graph(
let={
"_n": Const(2000),
"area_2x": Abs(arg=Sum(Mul(Const(value=210), Const(value=111)), Mul(Const(value=60), Sub(left=Const(value=0), right=CountOverSet(set=SolutionsSet(var=Var(name='t'), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), cond... | ALG | NT | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | geo_count_lattice_triangle_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.006 | 2026-02-08T12:50:07.329410Z | {
"verified": true,
"answer": 53270,
"timestamp": "2026-02-08T12:50:07.335796Z"
} | 8a6623 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 267,
"completion_tokens": 3230
},
"timestamp": "2026-02-15T07:02:47.017Z",
"answer": 53270
},
... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
2f1999 | nt_min_with_divisor_count_v1_124444284_39 | Let $m = 7569$. Let $s$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = m$. Let $p$ be the maximum value of $xy$ over all pairs of positive integers $(x, y)$ such that $x + y = s$. Find the smallest positive integer $n \leq p$ that has exactly 10 positive divisors. | 48 | graphs = [
Graph(
let={
"_m": Const(7569),
"_n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_m")))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | EXTREMUM | sympy | LIN_FORM | [
"B3/B1"
] | 7f76f7 | nt_min_with_divisor_count_v1 | null | 6 | 0 | [
"B1",
"B3",
"LIN_FORM"
] | 3 | 29.585 | 2026-02-08T02:54:42.717639Z | {
"verified": true,
"answer": 48,
"timestamp": "2026-02-08T02:55:12.302383Z"
} | 78819a | 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": 1974
},
"timestamp": "2026-02-09T12:47:12.685Z",
"answer": 48
},
{
"id"... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma":... | {
"lo": -3.97,
"mid": -1.31,
"hi": 0.91
} | ||
dcf9ad | diophantine_fbi2_min_v1_168721529_22 | Let $c = 22$. Define $n$ to be the maximum value of $xy$ over all ordered pairs $(x, y)$ of positive integers such that $x + y = c$. Let $k$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = n$. Let $u$ be the number of nonnegative integers $j$ with $0 \le j \le 51224$... | 2 | graphs = [
Graph(
let={
"_c": Const(22),
"_m": Const(2),
"_n": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Ref("_c")))), expr=M... | NT | null | EXTREMUM | sympy | B1 | [
"B1/B3",
"V8"
] | c1bd68 | diophantine_fbi2_min_v1 | null | 7 | 0 | [
"B1",
"B3",
"V8"
] | 3 | 0.015 | 2026-02-08T12:46:15.611069Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-02-08T12:46:15.625575Z"
} | 65cfda | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 272,
"completion_tokens": 2228
},
"timestamp": "2026-02-08T20:54:07.568Z",
"answer": 2
},
{
"id":... | 2 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_... | {
"lo": -9.12,
"mid": -6.02,
"hi": -3.64
} | ||
6d680c | algebra_vieta_sum_v1_1978505735_5744 | Let $ r $ be the sum of all real solutions $ x $ to the equation
$$
x^3 - 14x^2 + 45x = 0.
$$
Let $ m $ be the maximum value of $ x_1 y $ over all pairs of positive integers $ (x_1, y) $ such that $ x_1 + y = 142 $.
Compute $ r^2 + 37r + m $. | 5,755 | graphs = [
Graph(
let={
"_n": Const(142),
"result": SumOverSet(set=SolutionsSet(var=Var("x"), condition=Eq(Sum(Pow(Var("x"), Const(3)), Mul(Const(-14), Pow(Var("x"), Const(2))), Mul(Const(45), Var("x"))), Const(0)))),
"Q": Sum(Pow(Ref("result"), Const(2)), Mul(Const(37), ... | NT | null | COMPUTE | sympy | B1 | [
"B1"
] | bf138c | algebra_vieta_sum_v1 | quadratic_mod | 5 | 0 | [
"B1"
] | 1 | 0.006 | 2026-02-08T19:12:09.960766Z | {
"verified": true,
"answer": 5755,
"timestamp": "2026-02-08T19:12:09.967110Z"
} | dc73fd | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 163,
"completion_tokens": 755
},
"timestamp": "2026-02-16T18:35:46.657Z",
"answer": 855
},
{
"id": 11,
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
2d3b64 | sequence_lucas_compute_v1_153355830_650 | Let $n$ be the number of positive integers $k$ with $1 \leq k \leq 295$ such that $5$ divides $k$ and $\gcd(k, 6) = 1$. Let $L_n$ denote the $n$-th Lucas number, defined by $L_1 = 1$, $L_2 = 3$, and $L_m = L_{m-1} + L_{m-2}$ for $m \geq 3$. Compute the remainder when $44121 \cdot L_n$ is divided by $86630$. | 20,847 | graphs = [
Graph(
let={
"_n": Const(6),
"n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(295)), Divides(divisor=Const(5), dividend=Var("n")), Eq(GCD(a=Var("n"), b=Ref("_n")), Const(1))))),
"result": Lucas(arg=Ref(... | NT | null | COMPUTE | sympy | C5 | [
"C5"
] | 1d9668 | sequence_lucas_compute_v1 | null | 5 | 0 | [
"C5"
] | 1 | 0.001 | 2026-02-08T04:06:08.303184Z | {
"verified": true,
"answer": 20847,
"timestamp": "2026-02-08T04:06:08.304668Z"
} | 49070e | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 238,
"completion_tokens": 1738
},
"timestamp": "2026-02-10T15:29:33.460Z",
"answer": 20847
},
{
... | 1 | [
{
"lemma": "C5",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -3.49,
"mid": 1.84,
"hi": 7.55
} | ||
067184 | nt_count_divisible_v1_784195855_9338 | Let $n = 144$ and define $\text{upper} = 37249$. Let $\text{divisor}$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 144$. Determine the number of positive integers $k$ with $1 \leq k \leq 37249$ such that $\text{divisor}$ divides $k$. | 1,552 | graphs = [
Graph(
let={
"_n": Const(144),
"upper": Const(37249),
"divisor": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_n... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | nt_count_divisible_v1 | null | 3 | 0 | [
"B3"
] | 1 | 1.209 | 2026-02-08T16:42:41.559447Z | {
"verified": true,
"answer": 1552,
"timestamp": "2026-02-08T16:42:42.768497Z"
} | 75cbf9 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 159,
"completion_tokens": 262
},
"timestamp": "2026-02-16T07:50:45.359Z",
"answer": 503
},
{
"id": 11,
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
e92dfd | algebra_quadratic_discriminant_v1_458359167_474 | Let $a = 2$, $b = -3$, and $c = 5$. Let $r = b^2 - 4ac$. Compute $$r^2 + 37r + \sum x,$$ where the sum is taken over all solutions $x$ to the equation $x^2 - 9999x + 980100 = 0$. | 9,813 | graphs = [
Graph(
let={
"a": Const(2),
"b": Const(-3),
"c": Const(5),
"result": Sub(Pow(Ref("b"), Const(2)), Mul(Const(4), Ref("a"), Ref("c"))),
"Q": Sum(Pow(Ref("result"), Const(2)), Mul(Const(37), Ref("result")), SumOverSet(set=SolutionsSet(var=V... | NT | null | COMPUTE | sympy | VIETA_SUM | [
"VIETA_SUM"
] | 833c91 | algebra_quadratic_discriminant_v1 | quadratic_mod | 4 | 0 | [
"VIETA_SUM"
] | 1 | 0.003 | 2026-02-08T03:21:27.211510Z | {
"verified": true,
"answer": 9813,
"timestamp": "2026-02-08T03:21:27.214600Z"
} | f32d9c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 188,
"completion_tokens": 446
},
"timestamp": "2026-02-10T14:07:06.540Z",
"answer": 9813
},
{
"id... | 1 | [
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "VIETA_SUM",
"status":... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
f22cde | algebra_quadratic_discriminant_v1_1978505735_5370 | Let $m = 4$. Let $n$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 108$, $\gcd(p, q) = 1$, and $p < q$. Define $a = 2$, $b = -6$, $c = 0$, and let $D = b^k - 4ac$, where $k$ is the number of positive integers $p_1$ for which there exists a positive integer $... | 2 | graphs = [
Graph(
let={
"_m": Const(4),
"_n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=108)), Eq(left=GCD(a=Var(name='p'), b=Var(name='... | NT | null | COMPUTE | sympy | B1 | [
"COPRIME_PAIRS/COPRIME_PAIRS"
] | 3bbd71 | algebra_quadratic_discriminant_v1 | null | 6 | 0 | [
"B1",
"COPRIME_PAIRS"
] | 2 | 0.034 | 2026-02-08T18:57:41.956397Z | {
"verified": true,
"answer": 2,
"timestamp": "2026-02-08T18:57:41.990512Z"
} | 8de80b | 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": 2313
},
"timestamp": "2026-02-18T20:51:20.812Z",
"answer": 2
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
f56439 | comb_count_surjections_v1_798873815_484 | Let $n$ be the number of ordered pairs $(i,j)$ of positive integers such that $1 \le i \le 5$, $1 \le j \le 6$, and $i + j = 6$. Let $k = 3$. Compute $k! \cdot S(n, k)$, where $S(n, k)$ denotes the Stirling number of the second kind. Determine the value of this expression. | 150 | graphs = [
Graph(
let={
"_n": Const(6),
"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(5)), right=IntegerRange(start=Const(1), end=Const... | COMB | null | COUNT | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | comb_count_surjections_v1 | null | 3 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.012 | 2026-02-08T02:40:06.319722Z | {
"verified": true,
"answer": 150,
"timestamp": "2026-02-08T02:40:06.331272Z"
} | 247b2b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 206,
"completion_tokens": 566
},
"timestamp": "2026-02-08T19:36:47.491Z",
"answer": 150
},
{
"id"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status":... | {
"lo": -4.8,
"mid": -2.89,
"hi": -0.93
} | ||
53c197 | nt_count_gcd_equals_v1_1440796553_1119 | Let $n = 2$ and $d = 67$. Let $k$ be the smallest divisor of $21354173$ that is at least $n$. Compute the number of positive integers $m$ such that $1 \leq m \leq 9216$ and $\gcd(m, k) = d$. | 137 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": Const(9216),
"k": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(21354173))))),
"d": Const(67),
"result": CountOverSet(set=... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | nt_count_gcd_equals_v1 | null | 6 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 1.1 | 2026-02-08T12:11:41.881024Z | {
"verified": true,
"answer": 137,
"timestamp": "2026-02-08T12:11:42.981440Z"
} | a0443c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 114,
"completion_tokens": 1683
},
"timestamp": "2026-02-14T23:01:08.496Z",
"answer": 137
},
{
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
05c4f2 | alg_poly3_min_v1_1218484723_1342 | Find the remainder when the minimum value of $120a \cdot b^{2} + 16a^{3} - 56b^{3} - 24a^{2}b$ over positive integers $a$ and $b$ with $1 \leq a \leq \pi(3541)$ and $1 \leq b \leq 496$ is divided by $97078$, where $\pi(3541)$ denotes the number of primes between $2$ and $3541$ inclusive. | 75,402 | graphs = [
Graph(
let={
"_n": Const(2),
"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"), CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq... | NT | null | COMPUTE | sympy | COUNT_PRIMES | [
"COUNT_PRIMES"
] | 07c874 | alg_poly3_min_v1 | null | 5 | 0 | [
"COUNT_PRIMES"
] | 1 | 0.316 | 2026-02-25T03:03:55.786595Z | {
"verified": true,
"answer": 75402,
"timestamp": "2026-02-25T03:03:56.102245Z"
} | 0adc04 | 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": 2989
},
"timestamp": "2026-03-10T06:35:36.392Z",
"answer": 75402
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": 0.8,
"mid": 3.7,
"hi": 5.71
} | ||
842f44 | algebra_poly_eval_v1_1125832087_724 | Let $a = 7$. Let $S$ be the set of all integers $t$ such that there exist integers $a'$ and $b$ satisfying $1 \leq a' \leq 2$, $1 \leq b \leq 4$, $7 \leq t \leq 16$, and $t = 3a' + 2b + 2$. Let $m$ be the number of elements in $S$. Let $P$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x + y =... | 21,993 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(3),
"a": Const(7),
"result": Sum(Mul(CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM",
"B1"
] | 2f9b70 | algebra_poly_eval_v1 | null | 4 | 0 | [
"B1",
"LIN_FORM"
] | 2 | 0.008 | 2026-02-08T03:13:53.270714Z | {
"verified": true,
"answer": 21993,
"timestamp": "2026-02-08T03:13:53.279031Z"
} | 0447c5 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 287,
"completion_tokens": 1241
},
"timestamp": "2026-02-10T13:33:14.329Z",
"answer": 21993
},
{
"... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemm... | {
"lo": -5.55,
"mid": -3.02,
"hi": 0.31
} | ||
11bd13 | nt_min_phi_inverse_v1_397696148_2426 | Let $n$ range over the positive integers. Define $k = 2$. Let $\alpha$ be the number of prime numbers $n$ such that $n \le 6$ and $n \ge m$, where $m$ is the number of positive integers $p$ for which there exists a positive integer $q$ satisfying $p \cdot q = 12$, $\gcd(p, q) = 1$, and $p < q$. Let $\beta$ be the small... | 6,801 | graphs = [
Graph(
let={
"_n": Const(6),
"upper": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name=... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/SUM_PRIMES"
] | 79509a | nt_min_phi_inverse_v1 | null | 5 | 0 | [
"COPRIME_PAIRS",
"SUM_PRIMES"
] | 2 | 0.011 | 2026-02-08T13:19:45.663763Z | {
"verified": true,
"answer": 6801,
"timestamp": "2026-02-08T13:19:45.674311Z"
} | 3069b4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 189,
"completion_tokens": 915
},
"timestamp": "2026-02-15T12:47:38.438Z",
"answer": 6801
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "SUM_PRIMES",
"status": "ok_lat... | {
"lo": -6.96,
"mid": -4.56,
"hi": -1.46
} | ||
208ddc | modular_mod_compute_v1_1116507919_283 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x y = 4225$. Let $T$ be the set of all values of $x + y$ as $(x, y)$ ranges over $S$. Let $m$ be the maximum value of $x y$ over all ordered pairs $(x, y)$ of positive integers such that $x + y$ is equal to the minimum element of $T$. Find... | 72,004 | graphs = [
Graph(
let={
"_m": Const(4225),
"_n": Const(74206),
"a": Const(-29),
"m": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"... | NT | null | COMPUTE | sympy | B3 | [
"B3/B1"
] | 7f76f7 | modular_mod_compute_v1 | null | 5 | 0 | [
"B1",
"B3"
] | 2 | 0.004 | 2026-02-08T02:30:31.468798Z | {
"verified": true,
"answer": 72004,
"timestamp": "2026-02-08T02:30:31.472437Z"
} | 101917 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 236,
"completion_tokens": 3736
},
"timestamp": "2026-02-08T19:21:01.397Z",
"answer": 72004
},
{
"... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"... | {
"lo": 0.08,
"mid": 1.78,
"hi": 3.31
} | ||
299395 | nt_count_coprime_v1_677425708_1725 | Let $k$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq = 150$, $\gcd(p, q) = 1$, and $p < q$. Let $N$ be the number of positive integers $n \leq 26569$ such that $\gcd(n, k) = \varphi(2)$, where $\varphi$ denotes Euler's totient function. Compute $N$. | 13,285 | graphs = [
Graph(
let={
"upper": Const(26569),
"k": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=150)), Eq(left=GCD(a=Var(name='p'), b=Var(... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS",
"ONE_PHI_2"
] | e45f97 | nt_count_coprime_v1 | null | 5 | 0 | [
"COPRIME_PAIRS",
"ONE_PHI_2"
] | 2 | 2.345 | 2026-02-08T04:23:51.983726Z | {
"verified": true,
"answer": 13285,
"timestamp": "2026-02-08T04:23:54.328686Z"
} | f447fb | 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": 1951
},
"timestamp": "2026-02-09T23:56:27.674Z",
"answer": 13285
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K17",
"status":... | {
"lo": -6.5,
"mid": -0.2,
"hi": 6.11
} | ||
3f64dd | antilemma_product_of_sums_v1_1125832087_1349 | Let $A$ be the set of all positive integers $n \leq 90$ such that $n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{5}$. Let $S_1 = \sum_{k=1}^{|A|} k$. Let $B$ be the set of all ordered pairs $(k, j)$ where $k$ ranges from 1 to 15 and $j$ ranges from 1 to 4. Let $S_2$ be the sum of all $k$ over $(k, j) \in B$. Co... | 82,080 | graphs = [
Graph(
let={
"_n": Const(90),
"S1": Summation(var="k", start=Const(1), end=CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_n")), Congruent(a=Var(name='n'), b=Floor(arg=Div(left=Var(name='n'), right=Const(value=2))), mo... | NT | null | COMPUTE | sympy | L3C | [
"L3C/SUM_ARITHMETIC",
"PRODUCT_OF_SUMS"
] | 873a62 | antilemma_product_of_sums_v1 | null | 6 | 0 | [
"L3C",
"PRODUCT_OF_SUMS",
"SUM_ARITHMETIC"
] | 3 | 0.001 | 2026-02-08T03:41:33.049800Z | {
"verified": true,
"answer": 82080,
"timestamp": "2026-02-08T03:41:33.051106Z"
} | 301e6c | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 235,
"completion_tokens": 745
},
"timestamp": "2026-02-18T04:52:20.210Z",
"answer": 138600
}
] | 0 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "PRODUCT_OF_SUMS",
"status": "ok"
},
... | {
"lo": -6.48,
"mid": 1.54,
"hi": 9.56
} | ||
a93c08 | modular_count_residue_v1_1915831931_4109 | Let $m$ be the number of integers $j$ with $0 \leq j \leq 40961$ such that $\binom{40961}{j}$ is odd. Let $n$ be the number of positive integers $k$ such that $1 \leq k \leq 56169$ and $k$ is divisible by $m$. Let $r = |n| + 2$. Determine the value of the smallest positive integer $t$ such that the $t$-th Fibonacci num... | 2,340 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": Const(56169),
"m": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(40961)), Eq(Mod(value=Binom(n=Const(40961), k=Var("j")), modulus=Ref("_n")), Const(1))), domain='nonn... | NT | null | COUNT | sympy | V8 | [
"V8"
] | 86348e | modular_count_residue_v1 | null | 6 | 0 | [
"V8"
] | 1 | 1.94 | 2026-02-08T18:06:57.138200Z | {
"verified": true,
"answer": 2340,
"timestamp": "2026-02-08T18:06:59.077768Z"
} | 0a7c6e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 157,
"completion_tokens": 6057
},
"timestamp": "2026-02-18T14:27:03.945Z",
"answer": 2340
},
{... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
8dbba1 | antilemma_sum_factor_cartesian_v1_1742523217_1350 | Let $S$ be the set of all ordered pairs $(i, j)$ of integers with $1 \leq i \leq 7$ and $1 \leq j \leq 17$. For each pair $(i, j)$, compute the product $i \cdot j$. Let $x$ be the sum of all such products. Compute $8192 - x$. | 3,908 | graphs = [
Graph(
let={
"x": SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Const(1), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(7)), right=IntegerRange(start=Const(1), end=Const(17)))), expr=Mul(Var("i"), Var("j")))),
... | NT | null | COMPUTE | sympy | SUM_FACTOR_CARTESIAN | [
"SUM_FACTOR_CARTESIAN"
] | d9e436 | antilemma_sum_factor_cartesian_v1 | null | 3 | 0 | [
"SUM_FACTOR_CARTESIAN"
] | 1 | 0 | 2026-02-08T03:41:21.431260Z | {
"verified": true,
"answer": 3908,
"timestamp": "2026-02-08T03:41:21.431613Z"
} | 8edf79 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 172,
"completion_tokens": 491
},
"timestamp": "2026-02-18T04:37:52.537Z",
"answer": 3908
}
] | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "SUM_FACTOR_CARTESIAN",
"status": "ok"
}
] | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
44f9be | comb_sum_binomial_row_v1_1440796553_1437 | Let $n = 15$ and let $\_n = 2$. Define $\text{result} = \_n^n$. Let $S$ be the set of all positive integers $p$ such that there exists a positive integer $q$ with $p < q$, $pq = 108$, and $\gcd(p, q) = 1$. Let $m$ be the number of elements in $S$. Let $T$ be the set of all positive divisors $d$ of 20449 such that $d \g... | 30,696 | graphs = [
Graph(
let={
"_n": Const(2),
"n": Const(15),
"result": Pow(Ref("_n"), Ref("n")),
"Q": Mod(value=Bell(Mod(value=Abs(arg=Ref(name='result')), modulus=MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), CountOverSet(set=SolutionsSet(v... | NT | COMB | SUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/MIN_PRIME_FACTOR"
] | c17aaa | comb_sum_binomial_row_v1 | bell_mod | 6 | 0 | [
"COPRIME_PAIRS",
"MIN_PRIME_FACTOR"
] | 2 | 0.003 | 2026-02-08T14:00:20.781344Z | {
"verified": true,
"answer": 30696,
"timestamp": "2026-02-08T14:00:20.784745Z"
} | 74cab8 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 200,
"completion_tokens": 2072
},
"timestamp": "2026-02-15T22:57:37.763Z",
"answer": 30696
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok_later"
}... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
79f6c8 | nt_count_gcd_equals_v1_655260480_611 | Let $n = 72074$ and $U = 15129$. Let $k$ be the number of positive integers $n$ such that $1 \le n \le 1541$ and $\gcd(n, 30) = 1$. Let $d = 3$. Define $S$ to be the set of all positive integers $n_1$ such that $1 \le n_1 \le U$ and $\gcd(n_1, k) = d$. Let $r$ be the number of elements in $S$. Compute the remainder whe... | 7,037 | graphs = [
Graph(
let={
"_n": Const(72074),
"upper": Const(15129),
"k": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(1541)), Eq(GCD(a=Var("n"), b=Const(30)), Const(1))))),
"d": Const(3),
"re... | NT | null | COUNT | sympy | C4 | [
"C4"
] | 08d162 | nt_count_gcd_equals_v1 | null | 4 | 0 | [
"C4"
] | 1 | 10.489 | 2026-02-08T15:29:10.225815Z | {
"verified": true,
"answer": 7037,
"timestamp": "2026-02-08T15:29:20.714427Z"
} | 167e0c | 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": 1674
},
"timestamp": "2026-02-16T07:09:51.740Z",
"answer": 7037
},
{... | 1 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
1d3d53 | antilemma_k2_v1_1520064083_4830 | Let $n = 324$. Define
$$
x = \sum_{k=1}^{n} \phi(k) \left\lfloor \frac{324}{k} \right\rfloor,
$$
where $\phi(k)$ denotes Euler's totient function. Let $Q$ be the remainder when $75727x$ is divided by $60766$. Compute $Q$. | 47,758 | graphs = [
Graph(
let={
"_n": Const(324),
"x": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(324), Var("k"))))),
"Q": Mod(value=Mul(Const(75727), Ref("x")), modulus=Const(60766)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K13 | [
"K2"
] | 6897ab | antilemma_k2_v1 | null | 5 | 0 | [
"K13",
"K2"
] | 2 | 0.002 | 2026-02-08T06:27:02.840925Z | {
"verified": true,
"answer": 47758,
"timestamp": "2026-02-08T06:27:02.843212Z"
} | bec372 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 124,
"completion_tokens": 1939
},
"timestamp": "2026-02-13T00:21:13.219Z",
"answer": 47758
},
... | 1 | [
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
db7a0c | algebra_quadratic_discriminant_v1_1218484723_808 | Let $c$ be the number of ordered pairs $(a_1, b_1)$ of positive integers with $1 \leq a_1 \leq b_1 \leq 25$ such that $2b_1^2 - 4a_1b_1 + 2a_1^2 = 578$. Let $d = \left|\{ (a_2, b_2) : 1 \leq a_2, b_2 \leq 20,\ 34a_2^2 - 2a_2b_2 + 5b_2^2 = 845 \}\right|$, and let $R = 1^d - 8c$. Find the remainder when $44121R$ is divid... | 24,947 | graphs = [
Graph(
let={
"_m": Const(20),
"_n": Const(4),
"a": Const(2),
"b": Const(1),
"c": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a1"), Var("b1")]), condition=And(Geq(Var("a1"), Const(1)), Leq(Var("a1"), Const(25)), Geq(Var("b1"), ... | ALG | null | COMPUTE | sympy | QF_PSD_COUNT_LEQ | [
"QF_PSD_COUNT",
"QF_PSD_ORBIT"
] | 96120d | algebra_quadratic_discriminant_v1 | null | 5 | 0 | [
"QF_PSD_COUNT",
"QF_PSD_COUNT_LEQ",
"QF_PSD_ORBIT"
] | 3 | 0.035 | 2026-02-25T02:32:17.196561Z | {
"verified": true,
"answer": 24947,
"timestamp": "2026-02-25T02:32:17.231758Z"
} | 52cbcd | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 281,
"completion_tokens": 2113
},
"timestamp": "2026-03-10T01:52:17.128Z",
"answer": 23947
},
{
... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT",
"status": "ok"
},
{
"lemma": "QF_PSD_ORBIT",
"status": "ok"
}
] | {
"lo": 2.74,
"mid": 4.78,
"hi": 6.68
} | ||
5b5ff1 | geo_count_lattice_rect_v1_1125832087_2444 | Let $a = 33$ and $b = 127$. Define $L$ to be the number of lattice points in the rectangle $[0, a] \times [0, b]$. Compute $20000 - L$. | 15,648 | graphs = [
Graph(
let={
"a": Const(33),
"b": Const(127),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"Q": Sub(Const(20000), Ref("result")),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 4 | 0 | null | null | 0.001 | 2026-02-08T04:37:23.233236Z | {
"verified": true,
"answer": 15648,
"timestamp": "2026-02-08T04:37:23.233872Z"
} | 822ce8 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 159,
"completion_tokens": 466
},
"timestamp": "2026-02-24T01:14:16.415Z",
"answer": 15648
},
{
"i... | 2 | [] | {
"lo": -10,
"mid": -7.79,
"hi": -5.57
} | ||||
a30d76 | geo_count_lattice_rect_v1_1520064083_3710 | Compute the number of lattice points $(x, y)$ such that $0 \leq x \leq 256$ and $0 \leq y \leq 295$. Multiply this number by $44121$, and find the remainder when the result is divided by $60716$. | 52,948 | graphs = [
Graph(
let={
"a": Const(256),
"b": Const(295),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
"Q": Mod(value=Mul(Const(44121), Ref("result")), modulus=Const(60716)),
},
goal=Ref("Q"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.003 | 2026-02-08T05:49:37.927420Z | {
"verified": true,
"answer": 52948,
"timestamp": "2026-02-08T05:49:37.930562Z"
} | 03ef16 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 170,
"completion_tokens": 1687
},
"timestamp": "2026-02-24T04:34:58.798Z",
"answer": 52948
},
{
"... | 1 | [] | {
"lo": -0.06,
"mid": 2.89,
"hi": 5.27
} | ||||
538428 | nt_sum_gcd_range_mod_v1_1520064083_7339 | Let $N$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 1327104$. Let $k$ be the minimum value of $x + y$ over all pairs of positive integers $(x, y)$ such that $xy = 8100$. Let $S = \sum_{n=1}^{N} \gcd(n, k)$. Compute the remainder when $S$ is divided by $11821$. | 7,451 | graphs = [
Graph(
let={
"_n": Const(8100),
"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(1327104)))), expr=Sum(Var("x"), Var("y"))... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_gcd_range_mod_v1 | null | 7 | 0 | [
"B3"
] | 1 | 0.202 | 2026-02-08T08:58:27.717412Z | {
"verified": true,
"answer": 7451,
"timestamp": "2026-02-08T08:58:27.919164Z"
} | 82cf58 | 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": 2321
},
"timestamp": "2026-02-13T22:57:58.118Z",
"answer": 7451
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
}
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
52023b | algebra_poly_eval_v1_677425708_1955 | Let $n$ be the maximum value of $xy$ over all ordered pairs $(x,y)$ of positive integers such that $x + y = 6$. Compute $2n^3 + 5n^2 + p n - 10$, where $p$ is the largest prime number satisfying $2 \leq p \leq 4$. | 1,880 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(6),
"n": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Ref("_n")))), expr=Mul... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW",
"B1"
] | 7086d0 | algebra_poly_eval_v1 | null | 4 | 0 | [
"B1",
"MAX_PRIME_BELOW"
] | 2 | 0.004 | 2026-02-08T04:40:17.684764Z | {
"verified": true,
"answer": 1880,
"timestamp": "2026-02-08T04:40:17.688551Z"
} | 7315f7 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 184,
"completion_tokens": 600
},
"timestamp": "2026-02-10T03:36:49.782Z",
"answer": 1880
},
{
"id... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V5... | {
"lo": -9.14,
"mid": -6.05,
"hi": -3.74
} | ||
801bca | comb_count_surjections_v1_655260480_1995 | Let $u = \sum_{k=0}^{0} (-1)^k \binom{0}{k}$, and let $n_1 = 11u$. Let $w = \sum_{k=0}^{n_1} (-1)^k \binom{n_1}{k}$, and define $n = 7 + w$. Compute $3! \cdot S(n, 3)$, where $S(n, 3)$ denotes the Stirling number of the second kind. | 1,806 | graphs = [
Graph(
let={
"n2": Const(0),
"u": Summation(var="k1", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k1")), Binom(n=Ref("n2"), k=Var("k1")))),
"n1": Mul(Const(11), Ref("u")),
"w": Summation(var="k2", start=Const(0), end=Ref("n1"), expr=... | COMB | null | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING"
] | c21569 | comb_count_surjections_v1 | null | 4 | 2 | [
"BINOMIAL_ALTERNATING"
] | 1 | 0.002 | 2026-02-08T16:30:26.567016Z | {
"verified": true,
"answer": 1806,
"timestamp": "2026-02-08T16:30:26.568518Z"
} | 688386 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 219,
"completion_tokens": 1284
},
"timestamp": "2026-02-24T21:10:48.298Z",
"answer": 1806
},
{
"... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"st... | {
"lo": -5.65,
"mid": -3.17,
"hi": -0.81
} | ||
14a8ab | modular_sum_quadratic_residues_v1_601307018_2119 | Let $N$ be the largest positive integer divisor of $13348032$ such that $N^2 \le 13348032$. Let $p = 257$ and $R = \frac{p(p-1)}{4}$. Find the remainder when $N \cdot R$ is divided by $77033$. | 70,630 | graphs = [
Graph(
let={
"_n": Const(4),
"p": Const(257),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), Ref("_n")),
"_c": MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Divides(divisor=Var("d"), dividend=Const(13348032)... | NT | null | SUM | sympy | B3_CLOSEST | [
"B3_CLOSEST"
] | 498f8c | modular_sum_quadratic_residues_v1 | affine_mod | 3 | 0 | [
"B3_CLOSEST"
] | 1 | 0.004 | 2026-03-10T02:48:58.725235Z | {
"verified": true,
"answer": 70630,
"timestamp": "2026-03-10T02:48:58.728776Z"
} | d1f942 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 180,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T04:26:00.486Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "B3_CLOSEST",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": 1.23,
"mid": 4.27,
"hi": 6.7
} | ||
8900b3 | nt_lcm_compute_v1_124444284_1041 | Let $a$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 168921$. Let $b = 2877$. Compute the least common multiple of $a$ and $b$. | 5,754 | graphs = [
Graph(
let={
"a": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(168921)))), expr=Sum(Var("x"), Var("y")))),
"b": Const(2877)... | NT | null | COMPUTE | sympy | C3 | [
"B3"
] | 0cd20d | nt_lcm_compute_v1 | null | 5 | 0 | [
"B3",
"C3"
] | 2 | 0.002 | 2026-02-08T03:40:02.211742Z | {
"verified": true,
"answer": 5754,
"timestamp": "2026-02-08T03:40:02.213399Z"
} | de9bfd | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 166,
"completion_tokens": 1492
},
"timestamp": "2026-02-10T01:46:33.307Z",
"answer": 5754
},
{
"i... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no... | {
"lo": -3.46,
"mid": 1.03,
"hi": 5.49
} | ||
a0d697 | comb_binomial_compute_v1_1520064083_412 | Let $a = 3$ and $b = 1$. Define $n_2 = a + b$. Let
$$
e = \sum_{k=0}^{n_2} (-1)^k \binom{n_2}{k}.
$$
Set $n_1 = e$, and define
$$
c = \sum_{k=0}^{n_1} (-1)^k \binom{n_1}{k}.
$$
Let $n = 12c$. Let $k$ be the number of ordered triples $(x_1, x_2, x_3)$ of positive odd integers such that $x_1 + x_2 + x_3 = 7$. Compute $\b... | 924 | graphs = [
Graph(
let={
"a": Const(3),
"b": Const(1),
"n2": Sum(Ref("a"), Ref("b")),
"e": Summation(var="k", start=Const(0), end=Ref("n2"), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Ref("n2"), k=Var("k")))),
"n1": Ref("e"),
"c": Summat... | COMB | null | COMPUTE | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING",
"COMB1"
] | e741ba | comb_binomial_compute_v1 | null | 4 | 2 | [
"BINOMIAL_ALTERNATING",
"COMB1"
] | 2 | 0.003 | 2026-02-08T03:21:03.095996Z | {
"verified": true,
"answer": 924,
"timestamp": "2026-02-08T03:21:03.098900Z"
} | f0b708 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 272,
"completion_tokens": 559
},
"timestamp": "2026-02-10T13:53:25.583Z",
"answer": 924
},
{
"id"... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUAL... | {
"lo": -9.23,
"mid": -6.18,
"hi": -4.06
} | ||
f85d05 | comb_count_derangements_v1_168721529_1925 | Let $n$ be the number of integers $j$ with $0 \leq j \leq 16464$ such that $\binom{16464}{j}$ is odd. Compute the subfactorial of $n$. | 14,833 | graphs = [
Graph(
let={
"_n": Const(16464),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Ref("_n")), Eq(Mod(value=Binom(n=Const(16464), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')),
"r... | COMB | null | COUNT | sympy | V8 | [
"V8"
] | 86348e | comb_count_derangements_v1 | null | 6 | 0 | [
"V8"
] | 1 | 0.001 | 2026-02-08T14:00:19.731033Z | {
"verified": true,
"answer": 14833,
"timestamp": "2026-02-08T14:00:19.732132Z"
} | 569764 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 159,
"completion_tokens": 2232
},
"timestamp": "2026-02-09T23:33:31.177Z",
"answer": 14833
},
{
"... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
}
] | {
"lo": -2.37,
"mid": 1.22,
"hi": 4.84
} | ||
168b59 | algebra_quadratic_discriminant_v1_1470522791_1416 | Let $c$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 1323000$, $\gcd(p, q) = 1$, and $p < q$. Compute the value of $(-6)^2 - 4 \cdot 1 \cdot c$. | 4 | graphs = [
Graph(
let={
"_n": Const(2),
"a": Const(1),
"b": Const(-6),
"c": 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(... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | algebra_quadratic_discriminant_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.002 | 2026-02-08T13:36:54.359084Z | {
"verified": true,
"answer": 4,
"timestamp": "2026-02-08T13:36:54.361344Z"
} | 6c0460 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 119,
"completion_tokens": 1213
},
"timestamp": "2026-02-15T19:20:17.538Z",
"answer": 4
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": ... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
836abd | nt_count_divisible_and_v1_1520064083_9685 | Let $n$ be a positive integer such that $1 \leq n \leq 22896$, $n$ is divisible by 4, and $n$ is divisible by 6. Let $A$ be the number of such integers $n$.
Let $d$ be a positive divisor of 401875 such that $1 \leq d \leq 625$. Let $B$ be the largest such divisor $d$.
Compute the remainder when $B - A$ is divided by ... | 98,229 | graphs = [
Graph(
let={
"upper": Const(22896),
"d1": Const(4),
"d2": Const(6),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(value=Var("n"), modulus=Ref("d1")), Const(0)), Eq(Mo... | NT | null | COUNT | sympy | MAX_DIVISOR | [
"MAX_DIVISOR"
] | ad1a9b | nt_count_divisible_and_v1 | negation_mod | 3 | 0 | [
"MAX_DIVISOR"
] | 1 | 2.753 | 2026-02-08T10:58:08.355584Z | {
"verified": true,
"answer": 98229,
"timestamp": "2026-02-08T10:58:11.108359Z"
} | e3e553 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 180,
"completion_tokens": 474
},
"timestamp": "2026-02-15T21:06:01.222Z",
"answer": 98229
},
{
"id": 11,
... | 2 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
}
] | {
"lo": -9.12,
"mid": -6.02,
"hi": -3.62
} | ||
e6bca0 | nt_min_with_divisor_count_v1_655260480_1130 | Let $k$ be the number of positive integers less than or equal to $6622$ that are divisible by $43$. Let $P$ be the set of all ordered pairs of positive integers $(x, y)$ such that $x + y = k$. Let $M$ be the maximum value of $xy$ over all such pairs. Determine the smallest positive integer $n \leq M$ that has exactly $... | 36 | graphs = [
Graph(
let={
"_n": CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(1)), Leq(Var("k"), Const(6622)), Divides(divisor=Const(43), dividend=Var("k"))), domain='positive_integers')),
"upper": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(ele... | NT | null | EXTREMUM | sympy | V1 | [
"C2/B1"
] | a0cd95 | nt_min_with_divisor_count_v1 | null | 5 | 0 | [
"B1",
"C2",
"V1"
] | 3 | 21.145 | 2026-02-08T15:55:18.533632Z | {
"verified": true,
"answer": 36,
"timestamp": "2026-02-08T15:55:39.678479Z"
} | da5a60 | 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": 985
},
"timestamp": "2026-02-16T16:58:18.551Z",
"answer": 36
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"le... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
7a4b58 | nt_min_phi_inverse_v1_124444284_1654 | Let $S$ be the set of all positive integers $n$ such that $1 \leq n \leq 330$ and $n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{11}$. Let $\ell$ be the number of elements in $S$. Let $n_0$ be the smallest positive integer such that $1 \leq n_0 \leq \ell$ and $\phi(n_0) = 10$. Compute
$$
\sum_{n=1}^{|n_0|} \tau... | 29 | graphs = [
Graph(
let={
"upper": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(330)), Congruent(a=Var(name='n'), b=Floor(arg=Div(left=Var(name='n'), right=Const(value=2))), modulus=Const(value=11))))),
"k": Const(10),
... | NT | null | EXTREMUM | sympy | MAX_PRIME_BELOW | [
"L3C"
] | 73f8b0 | nt_min_phi_inverse_v1 | null | 6 | 0 | [
"L3C",
"MAX_PRIME_BELOW"
] | 2 | 0.025 | 2026-02-08T04:04:26.784371Z | {
"verified": true,
"answer": 29,
"timestamp": "2026-02-08T04:04:26.809763Z"
} | 5a8bba | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 258,
"completion_tokens": 2396
},
"timestamp": "2026-02-10T15:21:34.082Z",
"answer": 29
},
{
"id... | 1 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.33
} | ||
028abe | comb_bell_compute_v1_601307018_3413 | Let $B_n$ denote the $n$-th Bell number. For a non-negative integer $a$ with $0 \le a \le 7920$, define \[
M = (3a^5 - 3a^4 - 3a^3 - 2a^2 + 5a + 3) \bmod 7921,
\] \[
R = (3M^5 - 3M^4 - 3M^3 - 2M^2 + 5M + 3) \bmod 7921,
\] \[
S = (3R^5 - 3R^4 - 3R^3 - 2R^2 + 5R + 3) \bmod 7921.
\] Let $n$ be the number of such $a$ for w... | 52 | graphs = [
Graph(
let={
"_n": Const(5),
"n": CountOverSet(set=SolutionsSet(var=Var("a"), condition=And(Geq(Var("a"), Const(0)), Leq(Var("a"), Const(7920)), Eq(Ref("_po_p3"), Var("a")), Neq(Ref("_po_p1"), Var("a")), Neq(Ref("_po_p2"), Var("a"))))),
"result": Bell(Ref("n"))... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM",
"POLY_ORBIT_HENSEL"
] | 669d9e | comb_bell_compute_v1 | bell_mod | 8 | 0 | [
"LIN_FORM",
"POLY_ORBIT_HENSEL"
] | 2 | 0.006 | 2026-03-10T03:59:39.148155Z | {
"verified": true,
"answer": 52,
"timestamp": "2026-03-10T03:59:39.154312Z"
} | d87e79 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 408,
"completion_tokens": 5821
},
"timestamp": "2026-04-18T23:27:58.073Z",
"answer": 1
},
{
"... | 0 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": ... | {
"lo": 2.12,
"mid": 5.37,
"hi": 8.63
} | ||
de316d | comb_count_derangements_v1_2051736721_996 | Let $n = 8$. The subfactorial of $n$, denoted $!n$, is the number of derangements of $n$ distinct elements. Let $R = !8$.
Let $C$ be the number of ordered pairs $(i, j)$ such that $1 \leq i \leq 66$, $1 \leq j \leq 126$, and $\gcd(i, j) = 1$.
Compute the remainder when $C \cdot R$ is divided by $72381$. | 70,048 | graphs = [
Graph(
let={
"_n": Const(72381),
"n": Const(8),
"result": Subfactorial(arg=Ref(name='n')),
"_c": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(GCD(a=Var("i"), b=Var("j")), Const(1)), domain=CartesianProduct(lef... | NT | COMB | COUNT | sympy | COUNT_COPRIME_GRID | [
"COUNT_COPRIME_GRID"
] | 53d469 | comb_count_derangements_v1 | affine_mod | 4 | 0 | [
"COUNT_COPRIME_GRID"
] | 1 | 0.001 | 2026-02-08T15:47:12.207077Z | {
"verified": true,
"answer": 70048,
"timestamp": "2026-02-08T15:47:12.207958Z"
} | 8de93b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 152,
"completion_tokens": 4224
},
"timestamp": "2026-02-16T13:47:49.251Z",
"answer": 70048
},
... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "ok"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemm... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
c2ea8d | modular_count_residue_v1_1915831931_786 | Let $r$ be the smallest divisor of $141151$ that is at least $2$. Determine the number of positive integers $n$ such that $n \leq 42849$ and $n \equiv r \pmod{28}$. | 1,530 | graphs = [
Graph(
let={
"upper": Const(42849),
"m": Const(28),
"r": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(141151))))),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), con... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | modular_count_residue_v1 | null | 4 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 1.693 | 2026-02-08T15:40:45.281155Z | {
"verified": true,
"answer": 1530,
"timestamp": "2026-02-08T15:40:46.974353Z"
} | 1b177f | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 116,
"completion_tokens": 683
},
"timestamp": "2026-02-16T06:15:21.288Z",
"answer": 1530
},
{
"id": 11,
... | 2 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
}
... | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
094c8f | comb_factorial_compute_v1_865884756_1167 | Let $j$ be a nonnegative integer. Compute the number of values of $j$ such that $0 \leq j \leq 24704$ and $\binom{24704}{j}$ is odd. Let $n$ be this count. Compute $n!$. Let $P$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 2250000$. Let $s$ be the minimum value of $x + y$ over all such ... | 37,549 | graphs = [
Graph(
let={
"_n": Const(24704),
"n": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(24704)), Eq(Mod(value=Binom(n=Ref("_n"), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonnegative_integers')),
"r... | ALG | COMB | COMPUTE | sympy | B3 | [
"B3",
"V8"
] | 7c01c3 | comb_factorial_compute_v1 | negation_mod | 7 | 0 | [
"B3",
"V8"
] | 2 | 0.004 | 2026-02-08T15:49:29.443261Z | {
"verified": true,
"answer": 37549,
"timestamp": "2026-02-08T15:49:29.447449Z"
} | 5e2b02 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 235,
"completion_tokens": 1509
},
"timestamp": "2026-02-24T18:43:55.372Z",
"answer": 37549
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"statu... | {
"lo": -2.4,
"mid": 1.57,
"hi": 5.75
} | ||
1abcdc | nt_count_primes_v1_458359167_2040 | Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 18$, $\gcd(p, q) = 1$, and $p < q$. Let $k$ be the number of elements in $S$. Determine the value of $k$. Now consider the set of all prime numbers $n$ such that $k \leq n \leq 10201$. Compute the number... | 1,252 | graphs = [
Graph(
let={
"upper": Const(10201),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'),... | NT | null | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_count_primes_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.233 | 2026-02-08T04:59:45.615905Z | {
"verified": true,
"answer": 1252,
"timestamp": "2026-02-08T04:59:45.849349Z"
} | f87eeb | 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": 1249
},
"timestamp": "2026-02-12T05:13:25.230Z",
"answer": 1252
},
{... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
ab6f73 | nt_count_gcd_equals_v1_1520064083_5413 | Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 986049$. Let $s$ be the minimum value of $x + y$ as $(x,y)$ ranges over $S$. Let $k$ be the number of positive integers $n$ with $1 \leq n \leq s$ such that $8$ divides the $n$th Fibonacci number. Let $d = 331$ and let $T$ be the set o... | 45,706 | graphs = [
Graph(
let={
"_m": Const(8),
"_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(986049)))), expr=Sum(Var("x"), Var("y")))),... | NT | null | COUNT | sympy | B3 | [
"B3/COUNT_FIB_DIVISIBLE"
] | 9b7a57 | nt_count_gcd_equals_v1 | null | 6 | 0 | [
"B3",
"COUNT_FIB_DIVISIBLE"
] | 2 | 5.321 | 2026-02-08T06:46:45.476554Z | {
"verified": true,
"answer": 45706,
"timestamp": "2026-02-08T06:46:50.797499Z"
} | 0bb157 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 199,
"completion_tokens": 2691
},
"timestamp": "2026-02-13T09:41:09.691Z",
"answer": 45706
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok_later"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V5",
"status": "n... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
1effe6 | nt_sum_gcd_range_mod_v1_1742523217_5420 | Let $N$ be the maximum value of $xy$ where $x$ and $y$ are positive integers such that $x + y = 76$. Let $k = 144$ and $M = 11471$. Define
$$
\text{sum} = \sum_{n=1}^{N} \gcd(n, k).
$$
Let $\text{result}$ be the remainder when $\text{sum}$ is divided by $M$, and let $Q$ be the remainder when $44121 \cdot \text{result}$... | 47,370 | graphs = [
Graph(
let={
"N": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Const(76)))), expr=Mul(Var("x"), Var("y")))),
"k": Const(144),
... | NT | null | COMPUTE | sympy | B1 | [
"B1"
] | 5b950e | nt_sum_gcd_range_mod_v1 | null | 5 | 0 | [
"B1"
] | 1 | 0.068 | 2026-02-08T10:59:07.443214Z | {
"verified": true,
"answer": 47370,
"timestamp": "2026-02-08T10:59:07.511428Z"
} | 269977 | 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": 2614
},
"timestamp": "2026-02-14T09:44:49.870Z",
"answer": 47370
},
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
92f83e | modular_mod_compute_v1_124444284_3753 | Let $m$ be the largest prime number $n$ such that $2 \leq n \leq 1753$. Compute the remainder when $-23716$ is divided by $m$. | 826 | graphs = [
Graph(
let={
"_n": Const(2),
"a": Const(-23716),
"m": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), Const(1753)), IsPrime(Var("n"))))),
"result": Mod(value=Ref("a"), modulus=Ref("m")),
},
... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | modular_mod_compute_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.003 | 2026-02-08T05:35:12.479413Z | {
"verified": true,
"answer": 826,
"timestamp": "2026-02-08T05:35:12.482448Z"
} | fbe1cf | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 86,
"completion_tokens": 914
},
"timestamp": "2026-02-12T11:09:28.477Z",
"answer": 826
},
{
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
f235e5 | comb_factorial_compute_v1_153355830_2214 | Let $S$ be the set of integers $t$ such that $11 \leq t \leq 5490$ and $t = 5a + 2b + 4$ for some positive integers $a \leq 834$ and $b \leq 658$. Let $N$ be the number of elements in $S$. Compute the remainder when $N - 8!$ is divided by $91597$. | 56,753 | graphs = [
Graph(
let={
"_n": Const(91597),
"n": Const(8),
"result": Factorial(Ref("n")),
"Q": Mod(value=Sub(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'... | ALG | COMB | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 324ba4 | comb_factorial_compute_v1 | negation_mod | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T06:59:18.374983Z | {
"verified": true,
"answer": 56753,
"timestamp": "2026-02-08T06:59:18.376358Z"
} | 94f228 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 204,
"completion_tokens": 19869
},
"timestamp": "2026-02-24T07:26:57.544Z",
"answer": 56756
},
{
... | 1 | [
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": 3.25,
"mid": 5.68,
"hi": 8.81
} | ||
35d5fd | nt_sum_over_divisible_v1_1978505735_3061 | Let $ \mathcal{D} $ be the set of all positive integers $ n $ such that $ 1 \leq n \leq 5231 $ and $ n $ is divisible by $ 181 $. Compute the sum of all elements in $ \mathcal{D} $. | 73,486 | graphs = [
Graph(
let={
"upper": Const(5231),
"divisor": Const(181),
"result": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(Mod(value=Var("n"), modulus=Ref("divisor")), Const(0))))),
},
go... | NT | null | SUM | sympy | LIN_FORM | [
"COUNT_FIB_DIVISIBLE/COUNT_FIB_DIVISIBLE/C4"
] | f9a154 | nt_sum_over_divisible_v1 | null | 3 | 0 | [
"C4",
"COUNT_FIB_DIVISIBLE",
"LIN_FORM"
] | 3 | 1.21 | 2026-02-08T17:19:01.352960Z | {
"verified": true,
"answer": 73486,
"timestamp": "2026-02-08T17:19:02.563302Z"
} | 1970db | 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": 577
},
"timestamp": "2026-02-18T00:35:12.068Z",
"answer": 73486
},
{... | 1 | [
{
"lemma": "C4",
"status": "ok_later"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": ... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
9fcbac | antilemma_k3_v1_1742523217_3182 | Let $n = 94216$. Compute the sum of $\phi(d)$ over all positive divisors $d$ of $n$, where $\phi$ denotes Euler's totient function. Find the value of this sum. | 94,216 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=94216), 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 | 2026-02-08T05:42:38.920869Z | {
"verified": true,
"answer": 94216,
"timestamp": "2026-02-08T05:42:38.921139Z"
} | 046bd3 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 91,
"completion_tokens": 6057
},
"timestamp": "2026-02-12T12:39:23.508Z",
"answer": 94216
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
b82027 | comb_bell_compute_v1_1915831931_2762 | Let $a = 3$. Let $B$ be the set of all ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 10$. Let $b$ be the number of elements in $B$. Define $n_2 = a + b$. Compute $$f = \sum_{k=0}^{n_2} (-1)^k \binom{n_2}{k}.$$ Let $u = 5 + f$ and $n_1 = u + 1$. Compute $$h = \sum_{k_1=0}^{n_1} (-1)^{k_1} \b... | 15,948 | graphs = [
Graph(
let={
"a": Const(3),
"b": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2")), Cons... | COMB | null | COMPUTE | sympy | COMB1 | [
"COMB1/BINOMIAL_ALTERNATING"
] | e72f96 | comb_bell_compute_v1 | null | 6 | 2 | [
"BINOMIAL_ALTERNATING",
"COMB1"
] | 2 | 0.003 | 2026-02-08T17:05:37.045777Z | {
"verified": true,
"answer": 15948,
"timestamp": "2026-02-08T17:05:37.048690Z"
} | b6a995 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 253,
"completion_tokens": 4640
},
"timestamp": "2026-02-17T20:19:49.434Z",
"answer": 15948
},
... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok_later"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"l... | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||
c54d29 | diophantine_fbi2_count_v1_124444284_5776 | Let $k = 840$. Consider the set of all positive integers $d$ satisfying $4 \leq d \leq 131$, $d$ divides $k$, and $3 \leq \frac{k}{d} \leq 130$. Let $r$ be the number of such integers $d$. Compute $12885 \times r$ modulo $57064$. Find the value of $Q$, the remainder when this product is divided by $57064$. | 29,444 | graphs = [
Graph(
let={
"k": Const(840),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(4)), Leq(Var("d"), Const(131)), Divides(divisor=Var("d"), dividend=Ref("k")), Geq(Div(Ref("k"), Var("d")), Const(3)), Leq(Div(Ref("k"), Var("d")), Const(13... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | diophantine_fbi2_count_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.016 | 2026-02-08T06:49:53.465078Z | {
"verified": true,
"answer": 29444,
"timestamp": "2026-02-08T06:49:53.481101Z"
} | fb7e0c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 143,
"completion_tokens": 1526
},
"timestamp": "2026-02-13T05:11:05.122Z",
"answer": 29444
},
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
}
] | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
efb3ce | comb_count_derangements_v1_898971024_2661 | Let $f = \sum_{k=0}^{0} (-1)^k \binom{0}{k}$ and $m = \sum_{k_1=0}^{10} (-1)^{k_1} \binom{10}{k_1}$. Let $n = 8$ and define $\text{result} = !n$, the subfactorial of $n$. Compute the remainder when $44121 \cdot f \cdot \text{result}$ is divided by $52336 + m$. | 37,449 | graphs = [
Graph(
let={
"n2": Const(0),
"f": 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(10),
"m": Summation(var="k1", start=Const(0), end=Ref("n1"), expr=Mul(Pow(Const(-1),... | COMB | null | COUNT | sympy | BINOMIAL_ALTERNATING | [
"BINOMIAL_ALTERNATING"
] | c21569 | comb_count_derangements_v1 | null | 4 | 2 | [
"BINOMIAL_ALTERNATING"
] | 1 | 0.001 | 2026-02-08T16:54:00.455733Z | {
"verified": true,
"answer": 37449,
"timestamp": "2026-02-08T16:54:00.457104Z"
} | c74f81 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 154,
"completion_tokens": 2526
},
"timestamp": "2026-02-17T14:15:37.773Z",
"answer": 37449
},
... | 1 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"stat... | {
"lo": -2.38,
"mid": 1.74,
"hi": 6.59
} | ||
ccf211 | modular_mod_compute_v1_124444284_4871 | Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $xy = 4937284$. Define $a$ to be the minimum value of $x + y$ over all pairs $(x,y) \in S$. Compute the remainder when $a$ is divided by $29929$. | 4,444 | graphs = [
Graph(
let={
"a": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(4937284)))), expr=Sum(Var("x"), Var("y")))),
"m": Const(2992... | NT | null | COMPUTE | sympy | LIN_FORM | [
"B3"
] | 0cd20d | modular_mod_compute_v1 | null | 5 | 0 | [
"B3",
"LIN_FORM"
] | 2 | 0.036 | 2026-02-08T06:16:34.307890Z | {
"verified": true,
"answer": 4444,
"timestamp": "2026-02-08T06:16:34.344239Z"
} | cfe5c0 | 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": 1034
},
"timestamp": "2026-02-12T22:31:59.759Z",
"answer": 4444
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
37b005 | antilemma_sum_equals_v1_677425708_2347 | Let $n$ be the number of ordered pairs $(i, j)$ where $i \in \{1, 2\}$ and $j \in \{1, 2, \dots, 13\}$. Determine the number of ordered pairs $(i, j)$ of integers with $1 \leq i \leq 26$ and $1 \leq j \leq 26$ such that $i + j = n$. | 25 | graphs = [
Graph(
let={
"_n": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(2)), right=IntegerRange(start=Const(1), end=Const(13)))),
"x": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref... | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | 8bee9e | antilemma_sum_equals_v1 | null | 2 | 0 | [
"COUNT_CARTESIAN",
"COUNT_SUM_EQUALS"
] | 2 | 0.009 | 2026-02-08T05:00:48.250403Z | {
"verified": true,
"answer": 25,
"timestamp": "2026-02-08T05:00:48.259196Z"
} | 7bf527 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 206,
"completion_tokens": 678
},
"timestamp": "2026-02-24T02:35:12.578Z",
"answer": 25
},
{
"id":... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
... | {
"lo": -5.97,
"mid": -3.96,
"hi": -1.93
} | ||
c787b6 | comb_count_permutations_fixed_v1_601307018_7038 | Let $D_n$ denote the number of derangements of $n$ elements. For an integer $a$ with $0 \le a \le 1848$, define $S = (2a^3 - a^2 - 5a - 2) \bmod 1849$, $T = (2S^3 - S^2 - 5S - 2) \bmod 1849$, $K = (2T^3 - T^2 - 5T - 2) \bmod 1849$, and $L = (2K^3 - K^2 - 5K - 2) \bmod 1849$. Let $n$ be the number of values of $a$ such ... | 44,216 | graphs = [
Graph(
let={
"_m": Const(1849),
"_n": Const(2),
"n": CountOverSet(set=SolutionsSet(var=Var("a"), condition=And(Geq(Var("a"), Const(0)), Leq(Var("a"), Const(1848)), Eq(Ref("_po_p4"), Var("a")), Neq(Ref("_po_p1"), Var("a")), Neq(Ref("_po_p2"), Var("a")), Neq(Ref(... | COMB | null | COUNT | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN/POLY_ORBIT_HENSEL"
] | 210e2a | comb_count_permutations_fixed_v1 | null | 7 | 0 | [
"COUNT_CARTESIAN",
"POLY_ORBIT_HENSEL"
] | 2 | 0.011 | 2026-03-10T07:41:05.983426Z | {
"verified": true,
"answer": 44216,
"timestamp": "2026-03-10T07:41:05.994466Z"
} | 74e5e2 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 313,
"completion_tokens": 11774
},
"timestamp": "2026-04-19T05:51:01.197Z",
"answer": 44216
},
{
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "POLY_ORBIT_HENSEL",
"status": "ok_later"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma":... | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
71c2b4 | comb_binomial_compute_v1_677425708_1311 | Let $n = 13$. Let $k$ be the smallest divisor of $148225$ that is at least $2$. Compute $\binom{n}{k}$. | 1,287 | graphs = [
Graph(
let={
"n": Const(13),
"k": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(148225))))),
"result": Binom(n=Ref("n"), k=Ref("k")),
},
goal=Ref("result"),
)
] | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | comb_binomial_compute_v1 | null | 3 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.002 | 2026-02-08T04:05:08.873691Z | {
"verified": true,
"answer": 1287,
"timestamp": "2026-02-08T04:05:08.875616Z"
} | 9b7140 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 147,
"completion_tokens": 952
},
"timestamp": "2026-02-09T18:23:13.820Z",
"answer": 1287
},
{
"id... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
}... | {
"lo": -9.14,
"mid": -6.05,
"hi": -3.74
} | ||
b79b11 | geo_count_lattice_triangle_v1_1820931509_406 | Let $A$ be the area of a triangle with vertices at $(0,0)$, $(169,8)$, and $(41,120)$, multiplied by 2. Let $B$ be the number of lattice points on the boundary of this triangle. Compute the value of $2584 - \frac{A - B + 2}{2}$, and find the remainder when this value is divided by $71566$. | 64,182 | graphs = [
Graph(
let={
"area_2x": Abs(arg=Sum(Mul(Const(value=169), Const(value=120)), Mul(Const(value=41), Sub(left=Const(value=0), right=Const(value=8))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=169)), b=Abs(arg=Const(value=8))), GCD(a=Abs(arg=Sub(left=Const(value=41), right=C... | ALG | NT | COUNT | sympy | [] | geo_count_lattice_triangle_v1 | null | 4 | 0 | null | null | 0.002 | 2026-02-08T11:34:54.180494Z | {
"verified": true,
"answer": 64182,
"timestamp": "2026-02-08T11:34:54.182794Z"
} | c0549d | 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": 1742
},
"timestamp": "2026-02-14T16:05:52.645Z",
"answer": 64182
},
... | 1 | [] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||||
56ee80 | sequence_lucas_compute_v1_655260480_73 | Let $n$ be the largest prime number not exceeding 21. Define $L_n$ to be the $n$-th Lucas number, where the Lucas sequence is defined by $L_1 = 1$, $L_2 = 3$, and $L_k = L_{k-1} + L_{k-2}$ for $k \geq 3$. Compute the remainder when $12887 \cdot L_n$ is divided by 73947. | 20,900 | graphs = [
Graph(
let={
"_n": Const(21),
"n": MaxOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(2)), Leq(Var("n1"), Ref("_n")), IsPrime(Var("n1"))))),
"result": Lucas(arg=Ref(name='n')),
"Q": Mod(value=Mul(Const(12887), Ref("result"... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | sequence_lucas_compute_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.003 | 2026-02-08T15:09:51.661266Z | {
"verified": true,
"answer": 20900,
"timestamp": "2026-02-08T15:09:51.663933Z"
} | 2d7511 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 144,
"completion_tokens": 1306
},
"timestamp": "2026-02-16T00:29:08.064Z",
"answer": 20900
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
e4ae65 | antilemma_k3_v1_865884756_3624 | Let $n = 35663$. Define $x$ to be the sum of $\phi(d)$ over all positive divisors $d$ of $n$, where $\phi$ denotes Euler's totient function. Let $Q$ be the remainder when $76223 \cdot x$ is divided by $98104$. Compute $Q$. | 75,217 | graphs = [
Graph(
let={
"_n": Const(35663),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Mod(value=Mul(Const(76223), Ref("x")), modulus=Const(98104)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T17:31:30.067958Z | {
"verified": true,
"answer": 75217,
"timestamp": "2026-02-08T17:31:30.068678Z"
} | 954ce7 | 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": 2293
},
"timestamp": "2026-02-18T03:33:25.048Z",
"answer": 75217
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
d12222 | antilemma_sum_equals_v1_1918700295_3511 | Let $d = 57600$. Let $c$ be the number of integers $t$ such that $27 \leq t \leq 408$ and there exist integers $a$ and $b$ with $1 \leq a \leq 8$, $1 \leq b \leq 40$, and $t = 21a + 6b$. Let $m$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = c$. Let $n$ be the number of orde... | 57,542 | graphs = [
Graph(
let={
"_d": Const(57600),
"_c": 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=8)), Geq(left=V... | COMB | GEOM | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/COMB1/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | bb8f40 | antilemma_sum_equals_v1 | null | 5 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 3 | 0.013 | 2026-02-08T08:40:34.265818Z | {
"verified": true,
"answer": 57542,
"timestamp": "2026-02-08T08:40:34.278457Z"
} | 35b428 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 334,
"completion_tokens": 16835
},
"timestamp": "2026-02-24T09:49:36.138Z",
"answer": 57542
},
{
... | 1 | [
{
"lemma": "COMB1",
"status": "ok_later"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
59e685 | antilemma_k2_v1_1742523217_3527 | Let $ S $ be the set of all ordered pairs $ (k, j) $ of positive integers such that $ 1 \leq k \leq 362 $ and $ 1 \leq j \leq 8 $. For each such pair, compute $ \phi(k) \left\lfloor \frac{362}{k} \right\rfloor $. Let $ T $ be the sum of these values over all pairs in $ S $. Compute $ \frac{3T}{24} $. | 65,703 | graphs = [
Graph(
let={
"_m": Const(24),
"_n": Const(362),
"x": Div(Mul(Const(3), SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("k"), Var("_j")]), condition=Const(1), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(362)), right=Int... | NT | COMB | COMPUTE | sympy | SUM_INDEPENDENT | [
"SUM_INDEPENDENT",
"K2"
] | d64c9f | antilemma_k2_v1 | null | 6 | 0 | [
"K2",
"SUM_INDEPENDENT"
] | 2 | 0.002 | 2026-02-08T05:55:37.553088Z | {
"verified": true,
"answer": 65703,
"timestamp": "2026-02-08T05:55:37.554741Z"
} | 6914a2 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 148,
"completion_tokens": 1237
},
"timestamp": "2026-02-12T17:34:06.648Z",
"answer": 65703
},
... | 1 | [
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "SUM_I... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
380428 | modular_mod_compute_v1_784195855_3803 | Let $m$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 3694084$. Compute the remainder when $-231$ is divided by $m$. | 3,613 | graphs = [
Graph(
let={
"a": Const(-231),
"m": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(3694084)))), expr=Sum(Var("x"), Var("y")))... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | modular_mod_compute_v1 | null | 4 | 0 | [
"B3"
] | 1 | 0.001 | 2026-02-08T06:39:01.449864Z | {
"verified": true,
"answer": 3613,
"timestamp": "2026-02-08T06:39:01.451152Z"
} | 565d65 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 96,
"completion_tokens": 707
},
"timestamp": "2026-02-13T02:46:27.783Z",
"answer": 3613
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
9ec3a5 | alg_qf_psd_min_v1_1218484723_7015 | Find the minimum value of $38800b^2 + 12125a^2 + 19400ab$ over all ordered pairs $(a, b)$ of positive integers with $1 \leq a \leq 159$ and $1 \leq b \leq B$, where $B$ is the number of pairs $(a_1, b_1)$ of positive integers with $1 \leq a_1, b_1 \leq 25$ such that $-2a_1b_1 + C \cdot a_1^2 + 2b_1^2 \leq 1000$, and $C... | 70,325 | graphs = [
Graph(
let={
"_m": Const(4),
"_n": Const(25),
"result": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(159)), Geq(Var("b"), Const(1)), Leq(Var("b"), CountOverSet(se... | ALG | null | COMPUTE | sympy | POLY4_COUNT | [
"POLY4_COUNT/QF_PSD_COUNT_LEQ"
] | 94cd2a | alg_qf_psd_min_v1 | null | 7 | 0 | [
"POLY4_COUNT",
"QF_PSD_COUNT_LEQ"
] | 2 | 0.052 | 2026-02-25T08:26:39.661594Z | {
"verified": true,
"answer": 70325,
"timestamp": "2026-02-25T08:26:39.714011Z"
} | 9cea64 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 343,
"completion_tokens": 4430
},
"timestamp": "2026-05-03T11:45:13.760Z",
"answer": 70325
},
{
... | 1 | [
{
"lemma": "POLY4_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok_later"
}
] | {
"lo": -6.2,
"mid": -2.86,
"hi": 0.47
} | ||
52988d | comb_count_surjections_v1_1520064083_4540 | Let $n$ be the number of elements in the Cartesian product $\{1,2\} \times \{1,2,3\}$. Let $k$ be the number of ordered pairs $(i,j)$ of integers with $1 \leq i,j \leq 6$ such that $i+j = 8$. Define $x = k! \cdot S(n,k)$, where $S(n,k)$ denotes the Stirling number of the second kind. Find the remainder when $44121x$ is... | 48,512 | graphs = [
Graph(
let={
"_m": Const(8),
"_n": Const(72616),
"n": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(2)), right=IntegerRange(start=Const(1), end=Const(3)))),
"k": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("... | COMB | null | COUNT | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS",
"COUNT_CARTESIAN"
] | e4fc6a | comb_count_surjections_v1 | null | 4 | 0 | [
"COUNT_CARTESIAN",
"COUNT_SUM_EQUALS"
] | 2 | 0.011 | 2026-02-08T06:19:05.015702Z | {
"verified": true,
"answer": 48512,
"timestamp": "2026-02-08T06:19:05.026536Z"
} | 154e51 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 227,
"completion_tokens": 1149
},
"timestamp": "2026-02-24T05:50:19.688Z",
"answer": 48512
},
{
"... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
... | {
"lo": -2.46,
"mid": 0.47,
"hi": 3.59
} | ||
4ceb69 | nt_sum_over_divisible_v1_1439011603_1107 | Let $P$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 255025$. Let $s_{\text{min}}$ be the minimum value of $x + y$ over all $(x, y) \in P$. Let $U$ be the set of all positive integers $n$ such that $n \leq s_{\text{min}}$ and $n$ is divisible by 101. Define $N$ to be the sum of all elem... | 84,165 | graphs = [
Graph(
let={
"_m": Const(101),
"_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(255025)))), expr=Sum(Var("x"), Var("y")))... | NT | null | SUM | sympy | LIN_FORM | [
"B3/SUM_DIVISIBLE"
] | 138b1a | nt_sum_over_divisible_v1 | null | 5 | 0 | [
"B3",
"LIN_FORM",
"SUM_DIVISIBLE"
] | 3 | 4.782 | 2026-02-08T15:54:47.362785Z | {
"verified": true,
"answer": 84165,
"timestamp": "2026-02-08T15:54:52.145041Z"
} | 2ab03e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 203,
"completion_tokens": 1224
},
"timestamp": "2026-02-16T16:38:20.359Z",
"answer": 84165
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "SUM_DIVISIBLE",
"status":... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
c18ca5_n | comb_count_permutations_fixed_v1_1419126231_1631 | A puzzle designer creates combinations using two types of tokens: red tokens worth 3 points and blue tokens worth 2 points. Each combination uses between 1 and 3 red tokens and 1 to 4 blue tokens. Let $n$ be the number of distinct total scores between 5 and 17 achievable this way. Separately, a cryptographic counter co... | 2,970 | COMB | null | COUNT | sympy | POLY_ORBIT_LEGENDRE | [
"POLY_ORBIT_HENSEL/SUM_GEOM",
"LIN_FORM",
"ZERO_BINOM_N"
] | 60b437 | comb_count_permutations_fixed_v1 | null | 6 | null | [
"LIN_FORM",
"POLY_ORBIT_HENSEL",
"POLY_ORBIT_LEGENDRE",
"SUM_GEOM",
"ZERO_BINOM_N"
] | 5 | 0.025 | 2026-02-25T11:10:13.043709Z | null | 2fccb7 | c18ca5 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 280,
"completion_tokens": 3773
},
"timestamp": "2026-03-31T04:58:50.838Z",
"answer": 14684570
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_ORBIT_HENSEL",
"status": "ok"
},
{
"lemma": "SUM_GEOM",
... | {
"lo": 3.8,
"mid": 6.33,
"hi": 9.49
} | |
87c399 | nt_count_with_divisor_count_v1_677425708_3717 | Let $S$ be the set of all ordered pairs $(x,y)$ of positive integers such that $x + y = 6$. Let $M$ be the maximum value of $xy$ over all pairs $(x,y) \in S$. Determine the number of positive integers $n \leq 32768$ such that the number of positive divisors of $n$ is equal to $M$. | 54 | graphs = [
Graph(
let={
"upper": Const(32768),
"div_count": MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Sum(Var("x"), Var("y")), Const(6)))), expr=Mul(Var("x"), Var... | NT | null | COUNT | sympy | B1 | [
"B1"
] | 5b950e | nt_count_with_divisor_count_v1 | null | 4 | 0 | [
"B1"
] | 1 | 1.605 | 2026-02-08T05:54:52.939353Z | {
"verified": true,
"answer": 54,
"timestamp": "2026-02-08T05:54:54.544365Z"
} | fc0d31 | 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": 1665
},
"timestamp": "2026-02-12T16:43:06.379Z",
"answer": 54
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
1cc2cf | antilemma_k3_v1_1915831931_1312 | Let $x = \sum_{d \mid 88820} \phi(d)$, where $\phi$ denotes Euler's totient function. Compute the remainder when $37747 \cdot x$ is divided by $93430$. | 46,420 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=88820), var='d', expr=EulerPhi(n=Var(name='d'))),
"_c": Const(37747),
"Q": Mod(value=Mul(Ref("_c"), Ref("x")), modulus=Const(93430)),
},
goal=Ref("Q"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 2 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T15:59:48.658814Z | {
"verified": true,
"answer": 46420,
"timestamp": "2026-02-08T15:59:48.659749Z"
} | 40ad2b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 93,
"completion_tokens": 6407
},
"timestamp": "2026-02-16T19:32:29.610Z",
"answer": 46420
},
{... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
eb83d0 | nt_sum_gcd_range_mod_v1_1978505735_4547 | Let $k$ be the number of integers $t$ such that $20 \leq t \leq 330$ and there exist integers $a$ and $b$ satisfying $1 \leq a \leq 48$, $1 \leq b \leq 3$, and $t = 6a + 14b$. Define
$$
S = \sum_{n=1}^{2023} \gcd(n, k).
$$
Let $M = 10067$ and let $r$ be the remainder when $S$ is divided by $M$. Compute the remainder wh... | 1,483 | graphs = [
Graph(
let={
"_n": Const(55889),
"N": Const(2023),
"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'), righ... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_sum_gcd_range_mod_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.088 | 2026-02-08T18:19:06.591502Z | {
"verified": true,
"answer": 1483,
"timestamp": "2026-02-08T18:19:06.679598Z"
} | 5cb133 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 181,
"completion_tokens": 5125
},
"timestamp": "2026-02-18T16:07:20.817Z",
"answer": 1483
},
{... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status":... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
5c7908 | comb_bell_compute_v1_458359167_1821 | Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers such that $xy = 16$. Define $n$ to be the minimum value of $x + y$ as $(x, y)$ ranges over $S$. Let $B_n$ denote the $n$th Bell number, which counts the number of partitions of an $n$-element set. Compute the sum of the number of positive divisors of... | 35,136 | graphs = [
Graph(
let={
"_n": Const(16),
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_n")))), expr=Sum(Var("x"), Var("y")))),
... | NT | COMB | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | comb_bell_compute_v1 | null | 7 | 0 | [
"B3"
] | 1 | 0.002 | 2026-02-08T04:51:59.618961Z | {
"verified": true,
"answer": 35136,
"timestamp": "2026-02-08T04:51:59.620490Z"
} | 3f6b0b | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 214,
"completion_tokens": 2946
},
"timestamp": "2026-02-11T22:25:49.162Z",
"answer": 35136
},
{
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
07ad10 | algebra_quadratic_discriminant_v1_655260480_2894 | Let $a = 1$, $b$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 36$, and $c = 36$. Compute the value of $b^2 - 4ac$. | 0 | graphs = [
Graph(
let={
"_n": Const(36),
"a": Const(1),
"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")), Ref("_n")))), expr=Sum... | NT | null | COMPUTE | sympy | MOBIUS_COPRIME | [
"B3"
] | 0cd20d | algebra_quadratic_discriminant_v1 | null | 4 | 0 | [
"B3",
"MOBIUS_COPRIME"
] | 2 | 0.05 | 2026-02-08T17:03:19.312349Z | {
"verified": true,
"answer": 0,
"timestamp": "2026-02-08T17:03:19.362430Z"
} | ce9fd9 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 118,
"completion_tokens": 233
},
"timestamp": "2026-02-16T08:58:33.163Z",
"answer": 0
},
{
"id": 11,
"... | 2 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
672366 | alg_poly_orbit_count_v1_601307018_8229 | Let $N = a^2 \bmod 43$, $M = N^2 \bmod 43$, and $R = M^2 \bmod 43$. Find the number of non-negative integers $a$ with $0 \leq a \leq 39000$ such that $R = a$, $N \neq a$, and $M \neq a$. | 5,442 | graphs = [
Graph(
let={
"p1": Mod(value=Pow(Var("a"), Const(2)), modulus=Const(43)),
"p2": Mod(value=Pow(Ref("p1"), Const(2)), modulus=Const(43)),
"p3": Mod(value=Pow(Ref("p2"), Const(2)), modulus=Const(43)),
"result": CountOverSet(set=SolutionsSet(var=Var("a"... | ALG | null | COUNT | sympy | POLY_ORBIT_COUNT | [
"POLY_ORBIT_COUNT"
] | 4ad965 | alg_poly_orbit_count_v1 | null | 7 | null | [
"POLY_ORBIT_COUNT"
] | 1 | 0.011 | 2026-03-10T08:44:51.857329Z | {
"verified": true,
"answer": 5442,
"timestamp": "2026-03-10T08:44:51.868586Z"
} | 2aaada | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 192,
"completion_tokens": 3001
},
"timestamp": "2026-04-19T08:32:09.157Z",
"answer": 5442
},
{
"... | 1 | [
{
"lemma": "POLY_ORBIT_COUNT",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}
] | {
"lo": -5.34,
"mid": 1.1,
"hi": 7.53
} | ||
521904 | algebra_quadratic_discriminant_v1_677425708_4117 | Let $a = 2$, $b = 0$, and $c = \sum_{k=0}^{10} (-1)^k \binom{10}{k}$. Compute $b^2 - 4ac$. | 0 | graphs = [
Graph(
let={
"a": Const(2),
"b": Const(0),
"c": Summation(var="k", start=Const(0), end=Const(10), expr=Mul(Pow(Const(-1), Var("k")), Binom(n=Const(10), k=Var("k")))),
"result": Sub(Pow(Ref("b"), Const(2)), Mul(Const(4), Ref("a"), Ref("c"))),
... | COMB | null | COMPUTE | sympy | COPRIME_PAIRS | [
"BINOMIAL_ALTERNATING"
] | c21569 | algebra_quadratic_discriminant_v1 | null | 2 | 0 | [
"BINOMIAL_ALTERNATING",
"COPRIME_PAIRS"
] | 2 | 0.002 | 2026-02-08T06:26:01.779744Z | {
"verified": true,
"answer": 0,
"timestamp": "2026-02-08T06:26:01.782095Z"
} | 8b07d8 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 159,
"completion_tokens": 249
},
"timestamp": "2026-02-24T06:08:36.205Z",
"answer": 0
},
{
"id": ... | 2 | [
{
"lemma": "BINOMIAL_ALTERNATING",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"stat... | {
"lo": -10,
"mid": -7.79,
"hi": -5.57
} | ||
7f557a | algebra_quadratic_discriminant_v1_124444284_1807 | Let $a = 1$, $b = 5$, and $c = 15$. Compute the discriminant $D = b^2 - 4ac$. Define $$\alpha = \begin{cases} 2 & \text{if } D > 0, \\ 1 & \text{if } D = 0, \\ 0 & \text{otherwise}. \end{cases}$$ Let $S$ be the set of all real solutions to the equation $x^2 - 4x - 357 = 0$. Compute the value of $$\left( \sum_{x \in S} ... | 4 | graphs = [
Graph(
let={
"a": Const(1),
"b": Const(5),
"c": Const(15),
"D": Sub(Pow(Ref("b"), Const(2)), Mul(Const(4), Ref("a"), Ref("c"))),
"result": Sum(Mul(Const(2), Iverson(condition=Gt(Ref("D"), Const(0)))), Iverson(condition=Eq(Ref("D"), Const... | NT | null | COMPUTE | sympy | VIETA_SUM | [
"VIETA_SUM"
] | 4b7103 | algebra_quadratic_discriminant_v1 | negation_mod | 3 | 0 | [
"VIETA_SUM"
] | 1 | 0.002 | 2026-02-08T04:09:30.158185Z | {
"verified": true,
"answer": 4,
"timestamp": "2026-02-08T04:09:30.160211Z"
} | 1e1b42 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 250,
"completion_tokens": 456
},
"timestamp": "2026-02-10T15:33:48.443Z",
"answer": 4
},
{
"id":... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "VIETA_SUM",
"status": "ok"
}
] | {
"lo": -9.14,
"mid": -6.05,
"hi": -3.73
} |
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