Math and counting

Number theory, combinatorics, and geometry

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Still being built. Things may change

Total results13,152 problems

Grid Game
Hard9
Game theory, Bit manipulation+2
No attempts yet
Time limit
2s
Memory limit
1024 MB
Judgeable
Short Function
Hard9
Math, Number theory+2
No attempts yet
Time limit
2s
Memory limit
1024 MB
Judgeable
\prod_{i=1}^N(R_i-L_i+1) Trees
Hard9
Tree, Dynamic programming+2
No attempts yet
Time limit
2s
Memory limit
1024 MB
Judgeable
Escaping the Curse of Eungeung-i
Hard9
Probability, Game theory+2
No attempts yet
Time limit
2s
Memory limit
1024 MB
Judgeable
Manipulating the Torus Game
Hard9
Game theory, Math
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
\mathbb{E}\left(\operatorname{LCS}\right)
Hard9
Probability, Combinatorics+1
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
Infiltration
Hard9
Tree, Game theory+1
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
Sums over a Power Sequence
Hard9
Number theory, Math+1
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
Expected Beauty
Hard9
Dynamic programming, Probability+1
No attempts yet
Time limit
1s
Memory limit
2048 MB
Judgeable
Grid Game 3-angle
Hard9
Game theory, Math+1
No attempts yet
Time limit
1s
Memory limit
2048 MB
Judgeable
Collision
Hard9
Math, Number theory+1
No attempts yet
Time limit
9s
Memory limit
2048 MB
Judgeable
Electromagnetic Attacks
Hard9
Geometry, Graph+1
No attempts yet
Time limit
1s
Memory limit
2048 MB
Judgeable
Grand Prix of Array Count
Hard9
Math, Number theory+1
No attempts yet
Time limit
1s
Memory limit
2048 MB
Judgeable
Don't Try This at Home
Hard9
Array, Combinatorics+1
No attempts yet
Time limit
1s
Memory limit
2048 MB
Judgeable
Mod Graph
Hard9
Graph, Number theory+2
No attempts yet
Time limit
1s
Memory limit
2048 MB
Judgeable
Divisible Trees
Hard9
Tree, Number theory+1
No attempts yet
Time limit
5s
Memory limit
2048 MB
Judgeable
Sum of Characteristics
Hard9
Divide and conquer, Math+1
No attempts yet
Time limit
4s
Memory limit
2048 MB
Judgeable
Hardcore String Counting
Hard9
String matching, Dynamic programming+1
No attempts yet
Time limit
8s
Memory limit
2048 MB
Judgeable
Lines
Hard9
Geometry, Sorting+1
No attempts yet
Time limit
1s
Memory limit
2048 MB
Judgeable
01tree
Hard9
Tree, Dynamic programming+1
No attempts yet
Time limit
1s
Memory limit
2048 MB
Judgeable
Geometry Enjoyer
Hard9
Geometry, Math+1
No attempts yet
Time limit
7s
Memory limit
2048 MB
Judgeable
Trial of the Tile Master
Hard9
Math, Number theory+1
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Sugar Sweet II
Hard9
Probability, Dynamic programming+1
No attempts yet
Time limit
2s
Memory limit
2048 MB
Judgeable
Deep Abyss
Hard9
Bit manipulation, Implementation+1
No attempts yet
Time limit
1s
Memory limit
2048 MB
Judgeable
Apple Family Reunion
Hard9
Array, Math+1
No attempts yet
Time limit
1s
Memory limit
2048 MB
Judgeable
Wide Expression
Hard9
Math, Combinatorics+1
No attempts yet
Time limit
1s
Memory limit
2048 MB
Judgeable
Sum of a Sequence
Hard9
Math, Number theory+1
No attempts yet
Time limit
1.5s
Memory limit
1024 MB
Judgeable
f and g
Hard10
Math, Combinatorics+2
No attempts yet
Time limit
3s
Memory limit
512 MB
Judgeable
Find Marble Positions and Velocities
Hard10
Math, Combinatorics+2
No attempts yet
Time limit
2s
Memory limit
128 MB
Judgeable
Coalescing Continents
Hard10
Brute force, Math+2
No attempts yet
Time limit
1s
Memory limit
128 MB
Judgeable
Cubes
Hard10
Combinatorics, Math+2
No attempts yet
Time limit
1s
Memory limit
128 MB
Judgeable
Suneung Fractions
Hard10
Math, Number theory+2
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
Hyperrectangle
Hard10
Math, Divide and conquer+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Screamers in the Storm
Hard10
Geometry, Shortest path+1
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
The Creation
Hard10
Geometry, String matching+2
No attempts yet
Time limit
8s
Memory limit
1024 MB
Judgeable
Shadow Companion
Hard10
Simulation, Bit manipulation+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Joke
Hard10
Game theory, Simulation+1
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Sail Shreds - 3
Hard10
Geometry, Greedy+1
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Xorshift64
Hard10
Math, Bit manipulation+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Jiae Constant
Hard10
Probability, Geometry+1
No attempts yet
Time limit
22.222s
Memory limit
222 MB
Judgeable
Mysterious … Host
Hard10
Combinatorics, Math+2
No attempts yet
Time limit
2s
Memory limit
256 MB
Judgeable
Fast Bridges
Hard10
Shortest path, Sorting+2
No attempts yet
Time limit
2s
Memory limit
1024 MB
Judgeable
Huge Tree
Hard10
Game theory, Combinatorics+1
No attempts yet
Time limit
9s
Memory limit
1024 MB
Judgeable
Matrix nightmare
Hard10
Matrix, Combinatorics+2
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
Good and Lucky Matrices
Hard10
Combinatorics, Math+1
No attempts yet
Time limit
2s
Memory limit
1024 MB
Judgeable
Joint Training
Hard10
Graph, Dynamic programming+1
No attempts yet
Time limit
3s
Memory limit
1024 MB
Judgeable
ChatGPT's Masterpiece
Hard10
Implementation, Math+1
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
Monthly Advisory Match
Hard10
Graph, Game theory+1
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
Two Rings
Hard10
Geometry, Binary search+1
No attempts yet
Time limit
2s
Memory limit
2048 MB
Judgeable
Edges and Divisors
Hard10
Graph, Dynamic programming+1
No attempts yet
Time limit
1s
Memory limit
2048 MB
Judgeable
Huge Sequences
Hard10
Divide and conquer, Bit manipulation+2
No attempts yet
Time limit
1s
Memory limit
2048 MB
Judgeable
Master of Both V
Hard10
Geometry, Segment tree+1
No attempts yet
Time limit
5s
Memory limit
2048 MB
Judgeable

Title	Level	Topics	Solved	Time limit	Memory limit	Judge
Grid GameTwo players alternate moving along right and down paths on a grid of XOR-modified values, and the task is to decide which player wins with optimal play.	Hard9	Game theoryBit manipulation+2	No attempts yet	2s	1024 MB	Judgeable
Short FunctionGiven array A of length N and K, find the final B after K rounds where round i sets B[j] to A[j] times A[(j+2i) mod N], modulo 998244353.	Hard9	MathNumber theory+2	No attempts yet	2s	1024 MB	Judgeable
\prod_{i=1}^N(R_i-L_i+1) TreesGiven a rooted tree with per-vertex caps and subtree sum lower bounds, sum the minimum weighted cost over all cost vectors in given ranges, modulo 998244353.	Hard9	TreeDynamic programming+2	No attempts yet	2s	1024 MB	Judgeable
Escaping the Curse of Eungeung-iGiven N turns and M, find Hyeoncheol's optimal winning probability, where he wins if the overlaid polygons split the circle into an even number of pieces.	Hard9	ProbabilityGame theory+2	No attempts yet	2s	1024 MB	Judgeable
Manipulating the Torus GamePlayers alternately add edges to N tori without crossings; choose which tori to fill into spheres so the first player loses, or report impossible.	Hard9	Game theoryMath	No attempts yet	1s	1024 MB	Judgeable
\mathbb{E}\left(\operatorname{LCS}\right)Given N and M, find for each K from 1 to N the expected LCS length of M sequences built by random record draws from 1 to K, modulo 1e9+7.	Hard9	ProbabilityCombinatorics+1	No attempts yet	1s	1024 MB	Judgeable
InfiltrationOutput a move schedule for two spies on a 100-room tree that minimizes the worst ratio of meeting time to starting distance.	Hard9	TreeGame theory+1	No attempts yet	1s	1024 MB	Judgeable
Sums over a Power SequenceGiven c and M, find for each m up to M the sum S(m) of all starting values a_1 where a_m + a_{m+1} = c+1, modulo 1000000007.	Hard9	Number theoryMath+1	No attempts yet	1s	1024 MB	Judgeable
Expected BeautyEach A_i is uniform in [L_i, R_i]. Find the expected maximum score squared when deleting one of two adjacent equal elements adds its value to the score, mod 998244353.	Hard9	Dynamic programmingProbability+1	No attempts yet	1s	2048 MB	Judgeable
Grid Game 3-angleGiven stones on a triangular grid of up to 1e9 rows, decide whether the first player wins the game where each move removes up to K stones and adds up to K stones to cells below.	Hard9	Game theoryMath+1	No attempts yet	1s	2048 MB	Judgeable
CollisionGiven a roster of runners on a circular lake of length L, count how many pairs meet during T seconds after each add or remove query.	Hard9	MathNumber theory+1	No attempts yet	9s	2048 MB	Judgeable
Electromagnetic AttacksGiven a planar triangulation of base stations, decide for each axis-aligned rectangle whether the stations and links outside it stay connected.	Hard9	GeometryGraph+1	No attempts yet	1s	2048 MB	Judgeable
Grand Prix of Array CountCount arrays of length n with values from 1 to k where a[(i+j)/2] equals gcd(a[i], a[j]) for every pair with i+j even, modulo 1e9+7.	Hard9	MathNumber theory+1	No attempts yet	1s	2048 MB	Judgeable
Don't Try This at HomeFind the smallest k where applying f k times to array a flips some value between appearing once and at least twice, modulo 1e9+7, or -1.	Hard9	ArrayCombinatorics+1	No attempts yet	1s	2048 MB	Judgeable
Mod GraphGiven a connected graph where each vertex counter wraps modulo b_v on every visit, decide whether a walk from s can zero all counters, with point updates to counter values.	Hard9	GraphNumber theory+2	No attempts yet	1s	2048 MB	Judgeable
Divisible TreesGiven a tree T, count the distinct trees A such that T can be built from k copies of A joined by k-1 new edges.	Hard9	TreeNumber theory+1	No attempts yet	5s	2048 MB	Judgeable
Sum of CharacteristicsGiven a pseudorandom array of n integers, compute the sum over all subsegments of length at least 2 of the minimum over pairs i<j in the segment of max(a_i + j, a_j + i).	Hard9	Divide and conquerMath+1	No attempts yet	4s	2048 MB	Judgeable
Hardcore String CountingCount strings of length m over 26 letters where s first appears as a substring at the very end, modulo 998244353, with n up to 1e5 and m up to 1e9.	Hard9	String matchingDynamic programming+1	No attempts yet	8s	2048 MB	Judgeable
LinesGiven three arrays a, b, c, find every index i where line F_i is strictly above all other 3n lines at some real t, and print those indices.	Hard9	GeometrySorting+1	No attempts yet	1s	2048 MB	Judgeable
01treeGiven a tree of 0/1 node values with partial start and end states, sum the minimum flip counts over all consistent state pairs, modulo 1e9+7.	Hard9	TreeDynamic programming+1	No attempts yet	1s	2048 MB	Judgeable
Geometry EnjoyerGiven the pairwise intersection points of the extended sides of a convex polygon with no parallel sides, recover the polygon's vertices as exact rational coordinates.	Hard9	GeometryMath+1	No attempts yet	7s	2048 MB	Judgeable
Trial of the Tile MasterFor each timeline step, decide whether the accumulated flipped rectangles can be cleared back to all light-side-up using the row and column interval scrolls.	Hard9	MathNumber theory+1	No attempts yet	1s	512 MB	Judgeable
Sugar Sweet IIEach child gains w_i when event i fires with fewer sugar than child b_i, events in random order; output each child's expected final sugar mod 1e9+7.	Hard9	ProbabilityDynamic programming+1	No attempts yet	2s	2048 MB	Judgeable
Deep AbyssGiven a 128-bit hash function written as a short Frog program, find the smallest fixed point x with h(x) equal to x, or report that none exists.	Hard9	Bit manipulationImplementation+1	No attempts yet	1s	2048 MB	Judgeable
Apple Family ReunionGiven a permutation, find its family under the 123-transformation, then output the family size if its index is at most 65,472, or the index modulo 998244353 otherwise.	Hard9	ArrayMath+1	No attempts yet	1s	2048 MB	Judgeable
Wide ExpressionGiven n, m, k, l, compute the sum of (ab + cd + 1) raised to the power e XOR f over all a, b, c, d, e, f in the stated ranges, modulo 998244353.	Hard9	MathCombinatorics+1	No attempts yet	1s	2048 MB	Judgeable
Sum of a SequenceGiven N, S, and L, find the smallest X where 3^(X^3) matches the hash of all length-N sequences with entries 0 to L and sum S modulo 998244353, or print -1.	Hard9	MathNumber theory+1	No attempts yet	1.5s	1024 MB	Judgeable
f and gCompute g(T,k)=sum_{x=0}^{T} sum_i (x+a_i)^k mod 1e9+7 for every k from 0 to K, given N up to 1e5, K up to 5e4, T up to 1e18.	Hard10	MathCombinatorics+2	No attempts yet	3s	512 MB	Judgeable
Find Marble Positions and VelocitiesReconstruct each marble's starting x-coordinate and constant velocity from N+1 unordered snapshots of N linearly moving marbles.	Hard10	MathCombinatorics+2	No attempts yet	2s	128 MB	Judgeable
Coalescing ContinentsGiven K rectangles with total area 25 on a 20x20 grid, decide if they can be translated to tile a square, and find the minimum total moves.	Hard10	Brute forceMath+2	No attempts yet	1s	128 MB	Judgeable
CubesCount the orbits of general-purpose chip placements on cube faces under face rotations and cube rearrangement, given a fixed pattern of encoding chips.	Hard10	CombinatoricsMath+2	No attempts yet	1s	128 MB	Judgeable
Suneung FractionsGiven x in [A,B] and y in [C,D] up to 1e12, count pairs where the reduced numerator and denominator sum to at most 999.	Hard10	MathNumber theory+2	No attempts yet	1s	1024 MB	Judgeable
HyperrectangleCompute d!V for the volume of a box with side lengths li where sum xi <= s via characteristic polynomials and Lenstra inclusion of capped orthants.	Hard10	MathDivide and conquer+2	No attempts yet	2s	512 MB	Judgeable
Screamers in the StormGiven a rectilinear roof polygon with two pigeon positions, compute the shortest walking-and-flying path length across the sloped roof surface.	Hard10	GeometryShortest path+1	No attempts yet	2s	512 MB	Judgeable
The CreationGiven N named points, weight Voronoi neighbor links by shared substring length, then answer minimum-path queries while parent links change.	Hard10	GeometryString matching+2	No attempts yet	8s	1024 MB	Judgeable
Shadow CompanionConstruct a fixed program over a bit tape with a shadow that transforms every input n < 2^10 into n squared.	Hard10	SimulationBit manipulation+2	No attempts yet	2s	512 MB	Judgeable
JokeGiven both starting hands, the deck order, and the trump suit, decide which player wins the Fool's Game variant under optimal play, or whether it is a draw.	Hard10	Game theorySimulation+1	No attempts yet	2s	512 MB	Judgeable
Sail Shreds - 3Given N triangles and a rectangle X by Y, place each triangle (translation only) so they tile the rectangle exactly with no overlaps.	Hard10	GeometryGreedy+1	No attempts yet	2s	512 MB	Judgeable
Xorshift64Given a start value x, find the 1-based index at which the target value t first appears in the xorshift64 sequence.	Hard10	MathBit manipulation+2	No attempts yet	2s	512 MB	Judgeable
Jiae ConstantPrint the expected Euclidean distance between two random points on the Sierpinski triangle, rounded to 222 digits after the decimal point.	Hard10	ProbabilityGeometry+1	No attempts yet	22.222s	222 MB	Judgeable
Mysterious … HostFor each n up to N, find the minimum number of permutations needed so that every permutation of order n shares its answers to all consecutive-segment queries with one of them, modulo a prime P.	Hard10	CombinatoricsMath+2	No attempts yet	2s	256 MB	Judgeable
Fast BridgesGiven a k by k grid plus n bridges that cut travel time, find the sum of shortest distances over all cell pairs modulo 998244353.	Hard10	Shortest pathSorting+2	No attempts yet	2s	1024 MB	Judgeable
Huge TreeGiven a layered tree and query layers for A, B, and their LCA, find the optimal final score difference of the painting game modulo 1e9+7 for each query.	Hard10	Game theoryCombinatorics+1	No attempts yet	9s	1024 MB	Judgeable
Matrix nightmareGiven a multivariate integer polynomial, construct a small matrix of integers and variables whose weighted traversal sum equals that polynomial, or report that none exists.	Hard10	MatrixCombinatorics+2	No attempts yet	1s	1024 MB	Judgeable
Good and Lucky MatricesGiven an n x n binary matrix of one type (good or lucky), map it injectively to a matrix of the other type so the mapping is a bijection.	Hard10	CombinatoricsMath+1	No attempts yet	2s	1024 MB	Judgeable
Joint TrainingGiven N units with bus costs and dissatisfaction updates, check each lineup's validity, find the max feasible session cost, and count distinct costs per unit.	Hard10	GraphDynamic programming+1	No attempts yet	3s	1024 MB	Judgeable
ChatGPT's MasterpieceGiven intervals [L[i], R[i]], find an x where f(x) is false and f(x+1) is true, with f defined by repeated exponentiation modulo 2^64.	Hard10	ImplementationMath+1	No attempts yet	1s	1024 MB	Judgeable
Monthly Advisory MatchGiven a functional graph with two tokens, decide whether the first or second player wins the vertex-deletion and token-move game, or whether it is a draw.	Hard10	GraphGame theory+1	No attempts yet	1s	1024 MB	Judgeable
Two RingsGiven n integer points, find two non-penetrating rectangular rings covering all points that minimize the larger of their widths, and print that width.	Hard10	GeometryBinary search+1	No attempts yet	2s	2048 MB	Judgeable
Edges and DivisorsGiven a weighted DAG and weights a_1 to a_(n-1), choose a chain of paths whose lengths are multiples of i+1 in round i, maximizing the weighted average score.	Hard10	GraphDynamic programming+1	No attempts yet	1s	2048 MB	Judgeable
Huge SequencesGiven three arrays, answer queries asking for the sum over all subintervals of a range of the product of AND of a, OR of b, and GCD of c, modulo 2^32.	Hard10	Divide and conquerBit manipulation+2	No attempts yet	1s	2048 MB	Judgeable
Master of Both VAfter each insertion or deletion, report whether some convex polygon exists that has every segment in the multiset lying on one of its edges.	Hard10	GeometrySegment tree+1	No attempts yet	5s	2048 MB	Judgeable