Math and counting

Number theory, combinatorics, and geometry

Under construction

Still being built. Things may change

Total results13,153 problems

Ring Out
Hard8
Probability, Combinatorics+2
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
Colored Rectangles and Queries
Hard8
Geometry, Segment tree+1
No attempts yet
Time limit
3s
Memory limit
512 MB
Judgeable
Champernowne Subsequence
Hard8
String, Greedy+2
No attempts yet
Time limit
2s
Memory limit
2048 MB
Judgeable
Free Solo
Hard8
Geometry, Graph+1
No attempts yet
Time limit
5s
Memory limit
2048 MB
Judgeable
Fences Make Good Neighbors
Hard8
Dynamic programming, Geometry
No attempts yet
Time limit
4s
Memory limit
2048 MB
Judgeable
Great Plain
Hard8
Shortest path, Graph+2
No attempts yet
Time limit
3s
Memory limit
1024 MB
Judgeable
Glued Grid
Hard8
Math, Graph+1
No attempts yet
Time limit
3s
Memory limit
2048 MB
Judgeable
It's a Kind of Magic
Hard8
Number theory, Combinatorics+1
No attempts yet
Time limit
4s
Memory limit
2048 MB
Judgeable
Capybara Cozy Carnival
Hard8
Math, Graph+1
No attempts yet
Time limit
4s
Memory limit
2048 MB
Judgeable
Recurrence and Queries
Hard8
Math, Matrix+1
No attempts yet
Time limit
3s
Memory limit
1024 MB
Judgeable
Candles and shadows 2
Hard8
Geometry, Greedy+1
No attempts yet
Time limit
2s
Memory limit
1024 MB
Judgeable
Legacy Screensaver
Hard8
Math, Number theory+1
No attempts yet
Time limit
3s
Memory limit
2048 MB
Judgeable
East 2 Will Not Come to This Match! 9
Hard8
Combinatorics, Dynamic programming+1
No attempts yet
Time limit
5s
Memory limit
1024 MB
Judgeable
Lighting
Hard8
Geometry, Two pointers+1
No attempts yet
Time limit
4s
Memory limit
1024 MB
Judgeable
Robot Upgrades
Hard8
Dynamic programming, Combinatorics+1
No attempts yet
Time limit
1s
Memory limit
2048 MB
Judgeable
Intensive Training
Hard8
Math, Greedy+1
No attempts yet
Time limit
1s
Memory limit
2048 MB
Judgeable
Primal Collection
Hard8
Combinatorics, Tree+1
No attempts yet
Time limit
1s
Memory limit
2048 MB
Judgeable
Narrower Passageway
Hard8
Stack, Probability+2
No attempts yet
Time limit
1s
Memory limit
2048 MB
Judgeable
Flowers
Hard8
Game theory, Tree+1
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
Largest Triangle
Hard8
Geometry, Divide and conquer+1
No attempts yet
Time limit
1s
Memory limit
2048 MB
Judgeable
Double Radars
Hard8
Simulation, Math+1
No attempts yet
Time limit
1s
Memory limit
2048 MB
Judgeable
Cetinska Road Construction
Hard8
Shortest path, Geometry
No attempts yet
Time limit
1s
Memory limit
2048 MB
Judgeable
Building Marble Tracks
Hard8
Geometry, Greedy+1
No attempts yet
Time limit
4s
Memory limit
2048 MB
Judgeable
Let's Play Games!
Hard8
Geometry, Implementation+1
No attempts yet
Time limit
5s
Memory limit
2048 MB
Judgeable
Coin Game
Hard8
Game theory, Geometry+1
No attempts yet
Time limit
90s
Memory limit
2048 MB
Judgeable
Counting Is Not Fun (Hard Version)
Hard8
Combinatorics, Math+1
No attempts yet
Time limit
3s
Memory limit
2048 MB
Judgeable
Even-dominant Numbers
Hard8
Dynamic programming, Math
No attempts yet
Time limit
3s
Memory limit
2048 MB
Judgeable
Series Sum
Hard8
Math, Combinatorics+1
No attempts yet
Time limit
2s
Memory limit
2048 MB
Judgeable
Fischer's Chess Guessing Game
Hard8
Combinatorics, Implementation
No attempts yet
Time limit
2s
Memory limit
2048 MB
Judgeable
Crossing the Border
Hard8
Dynamic programming, Bit manipulation+1
No attempts yet
Time limit
15s
Memory limit
2048 MB
Judgeable
Fortune Wheel
Hard8
Dynamic programming, Math+2
No attempts yet
Time limit
1s
Memory limit
2048 MB
Judgeable
Abstract
Hard8
Graph, Topological sort+2
No attempts yet
Time limit
2s
Memory limit
2048 MB
Judgeable
Lost Table
Hard8
Combinatorics, Math+1
No attempts yet
Time limit
2s
Memory limit
2048 MB
Judgeable
A Tree Game
Hard8
Tree, Game theory+1
No attempts yet
Time limit
1s
Memory limit
2048 MB
Judgeable
Generating the Sequence
Hard8
Number theory, Bit manipulation+1
No attempts yet
Time limit
10s
Memory limit
2048 MB
Judgeable
Festival Decorating
Hard8
Math, Array
No attempts yet
Time limit
9s
Memory limit
2048 MB
Judgeable
Count the Orders
Hard8
Sorting, Greedy+1
No attempts yet
Time limit
1s
Memory limit
2048 MB
Judgeable
Simple Math Problem
Hard8
Combinatorics, Math
No attempts yet
Time limit
1s
Memory limit
2048 MB
Judgeable
Neutral Spectator
Hard8
Binary search, Geometry+1
No attempts yet
Time limit
2s
Memory limit
2048 MB
Judgeable
Old Solution Methods
Hard8
Geometry, Math+1
No attempts yet
Time limit
1s
Memory limit
2048 MB
Judgeable
Immensely Long Expressions
Hard8
Dynamic programming, Probability+1
No attempts yet
Time limit
1s
Memory limit
2048 MB
Judgeable
Sequences, Queries, and Probability 2
Hard8
Probability, Math+1
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
Sum Sequence
Hard8
Math, Number theory+1
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
Good Numbers
Hard9
Combinatorics, Math+2
No attempts yet
Time limit
2s
Memory limit
128 MB
Judgeable
Dominoes
Hard9
Graph, Combinatorics+2
No attempts yet
Time limit
2s
Memory limit
128 MB
Judgeable
Folded Paper Painting
Hard9
Geometry, Simulation+2
No attempts yet
Time limit
2s
Memory limit
128 MB
Judgeable
Cactus Graph Automorphisms
Hard9
Tree, Combinatorics+2
No attempts yet
Time limit
2s
Memory limit
128 MB
Judgeable
Coloring Rectangles
Hard9
Geometry, Dynamic programming+2
No attempts yet
Time limit
2s
Memory limit
128 MB
Judgeable
Goal Celebration
Hard9
Geometry, Sorting+2
No attempts yet
Time limit
2s
Memory limit
128 MB
Judgeable
Robot Arm
Hard9
Geometry, Intervals+2
No attempts yet
Time limit
5s
Memory limit
128 MB
Judgeable
Queen and Two Kings
Hard9
Game theory, BFS+2
No attempts yet
Time limit
2s
Memory limit
128 MB
Judgeable
Wake Up!
Hard9
Geometry, Divide and conquer+2
No attempts yet
Time limit
1s
Memory limit
128 MB
Judgeable
Shot
Hard9
Segment tree, Binary search+2
No attempts yet
Time limit
2s
Memory limit
256 MB
Judgeable
Coprime Products from Six Indices
Hard9
Number theory, Combinatorics+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Matrix Swaps
Hard9
Graph, Shortest path+2
No attempts yet
Time limit
2s
Memory limit
128 MB
Judgeable
Hyungtaek's Candy Bags
Hard9
Combinatorics, Number theory+1
No attempts yet
Time limit
5s
Memory limit
128 MB
Judgeable
Shom Language
Hard9
Graph, Combinatorics+2
No attempts yet
Time limit
2s
Memory limit
128 MB
Judgeable
All Closed-Walk Lengths
Hard9
Graph, Matrix+2
No attempts yet
Time limit
2s
Memory limit
128 MB
Judgeable
Maximum Matching in an Almost Bipartite Graph
Hard9
Graph, Dynamic programming+2
No attempts yet
Time limit
2s
Memory limit
128 MB
Judgeable
Small Squares
Hard9
Game theory, Dynamic programming+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Pro Gamer Youngsik
Hard9
Dynamic programming, Greedy+2
No attempts yet
Time limit
2s
Memory limit
128 MB
Judgeable
Choosing Points
Hard9
Geometry, Combinatorics+2
No attempts yet
Time limit
2s
Memory limit
128 MB
Judgeable
Woodpeckers
Hard9
Tree, Graph+2
No attempts yet
Time limit
10s
Memory limit
128 MB
Judgeable
Counting Multiples by Divisor Count
Hard9
Number theory, Combinatorics+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Travel Guide
Hard9
Brute force, Binary search+2
No attempts yet
Time limit
2s
Memory limit
128 MB
Judgeable
Candy Jars
Hard9
Greedy, Bit manipulation+2
No attempts yet
Time limit
2s
Memory limit
128 MB
Judgeable
Orchard
Hard9
Geometry, Matrix+2
No attempts yet
Time limit
2s
Memory limit
64 MB
Judgeable
Cowboys
Hard9
Game theory, Dynamic programming+2
No attempts yet
Time limit
2s
Memory limit
128 MB
Judgeable
Hangul-Missing Numbers
Hard9
Dynamic programming, Combinatorics+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Mail Carrier
Hard9
Graph, Greedy+1
No attempts yet
Time limit
2s
Memory limit
128 MB
Judgeable
Fence
Hard9
Geometry, Sorting+1
No attempts yet
Time limit
2s
Memory limit
128 MB
Judgeable
Matrix and Fibonacci Sum
Hard9
Matrix, Math+2
No attempts yet
Time limit
5s
Memory limit
512 MB
Judgeable
Square and Points
Hard9
Geometry, Math+1
No attempts yet
Time limit
2s
Memory limit
128 MB
Judgeable
Hard Matching
Hard9
String matching, Prefix sum+2
No attempts yet
Time limit
30s
Memory limit
1536 MB
Judgeable
FPS
Hard9
Combinatorics, Math+2
No attempts yet
Time limit
5s
Memory limit
128 MB
Judgeable
Waiting for the Dog
Hard9
Geometry, Shortest path+2
No attempts yet
Time limit
1s
Memory limit
256 MB
Judgeable
Chip Routing
Hard9
Dynamic programming, Greedy+2
No attempts yet
Time limit
1s
Memory limit
128 MB
Judgeable
BEARs
Hard9
Graph, Game theory+2
No attempts yet
Time limit
1s
Memory limit
128 MB
Judgeable
L Game
Hard9
Game theory, Brute force+2
No attempts yet
Time limit
1s
Memory limit
128 MB
Judgeable
Farm and Factory
Hard9
Shortest path, Graph+2
No attempts yet
Time limit
5s
Memory limit
128 MB
Judgeable
Beasts
Hard9
Geometry, Binary search+1
No attempts yet
Time limit
3s
Memory limit
128 MB
Judgeable
Casting Spells
Hard9
String matching, String+2
No attempts yet
Time limit
1s
Memory limit
128 MB
Judgeable
Fields and Farmers
Hard9
Geometry, Combinatorics+1
No attempts yet
Time limit
1s
Memory limit
128 MB
Judgeable
Hanging Hats
Hard9
Geometry, Segment tree+2
No attempts yet
Time limit
3s
Memory limit
128 MB
Judgeable
Origami Axiom Six: Counting Folds
Hard9
Geometry, Math+1
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Asteroids
Hard9
Geometry, Math+1
No attempts yet
Time limit
1s
Memory limit
128 MB
Judgeable
Exclusive Access 2
Hard9
Graph, Combinatorics+2
No attempts yet
Time limit
1s
Memory limit
128 MB
Judgeable
Grand Theft Auto Wheel
Hard9
Geometry, Simulation+1
No attempts yet
Time limit
3s
Memory limit
256 MB
Judgeable
Fibonacci Base
Hard9
Math, Number theory+2
No attempts yet
Time limit
1s
Memory limit
128 MB
Judgeable
Ground Works
Hard9
Geometry, Simulation+2
No attempts yet
Time limit
3s
Memory limit
256 MB
Judgeable
Fool's Game
Hard9
Game theory, DFS+2
No attempts yet
Time limit
1s
Memory limit
128 MB
Judgeable
Tantrix
Hard9
Simulation, Geometry+2
No attempts yet
Time limit
1s
Memory limit
128 MB
Judgeable
Road Planner
Hard9
Graph, Math+1
No attempts yet
Time limit
1s
Memory limit
128 MB
Judgeable
RSA Factorization
Hard9
Number theory, Math+1
No attempts yet
Time limit
1s
Memory limit
128 MB
Judgeable
Cubic Colonies
Hard9
Geometry, Graph+2
No attempts yet
Time limit
5s
Memory limit
128 MB
Judgeable
Periodic Points
Hard9
Math, Geometry+1
No attempts yet
Time limit
2s
Memory limit
128 MB
Judgeable
Origami Through-Hole
Hard9
Geometry, Simulation+1
No attempts yet
Time limit
1s
Memory limit
128 MB
Judgeable
Lowest Pyramid
Hard9
Geometry, Math+1
No attempts yet
Time limit
30s
Memory limit
128 MB
Judgeable
Polygons on the Grid
Hard9
Geometry, Math+1
No attempts yet
Time limit
5s
Memory limit
128 MB
Judgeable
Crossing Prisms
Hard9
Geometry, Math+1
No attempts yet
Time limit
1s
Memory limit
128 MB
Judgeable

Title	Level	Topics	Solved	Time limit	Memory limit	Judge
Ring OutFor each staff member, sum over rounds the probability that two or more of their balls come out consecutively when all balls in the round's range are shuffled and drawn.	Hard8	ProbabilityCombinatorics+2	No attempts yet	1s	1024 MB	Judgeable
Colored Rectangles and QueriesGiven N non-touching axis-aligned rectangles with colored sides, answer each query with the fewest distinct side colors that any path between two points must pass through.	Hard8	GeometrySegment tree+1	No attempts yet	3s	512 MB	Judgeable
Champernowne SubsequenceGiven a digit string, find the smallest k such that the string is a subsequence of the Champernowne word formed by concatenating 1 through k.	Hard8	StringGreedy+2	No attempts yet	2s	2048 MB	Judgeable
Free SoloFind the shortest path Alex's body point can travel while keeping at least three of four limbs on holds, until a limb touches the target hold.	Hard8	GeometryGraph+1	No attempts yet	5s	2048 MB	Judgeable
Fences Make Good NeighborsTriangulate a convex polygon so that exactly two fences separate the two brothers' parcels, avoiding fences through their houses, and minimize total fence length.	Hard8	Dynamic programmingGeometry	No attempts yet	4s	2048 MB	Judgeable
Great PlainGiven axis-parallel rectangles with per-km travel costs, find the least time for an ant to move from the start point to the destination.	Hard8	Shortest pathGraph+2	No attempts yet	3s	1024 MB	Judgeable
Glued GridDecide whether a sliding puzzle with glued tiles can be sorted into row-major order with the empty square at the bottom right.	Hard8	MathGraph+1	No attempts yet	3s	2048 MB	Judgeable
It's a Kind of MagicCount the 3x3 grids of positive integers whose row, column, and diagonal products are all equal and at most n, for up to 1e5 values of n.	Hard8	Number theoryCombinatorics+1	No attempts yet	4s	2048 MB	Judgeable
Capybara Cozy CarnivalCount proper k-colorings of an n-corner polygon's vertices, where sides and non-crossing diagonals are edges, modulo 998244353.	Hard8	MathGraph+1	No attempts yet	4s	2048 MB	Judgeable
Recurrence and QueriesGiven x_n = ax_(n-1) + bx_(n-2) + n^k with initial terms x_0 and x_1, answer up to 50,000 queries for x_n mod 100003 where n is up to 10^18.	Hard8	MathMatrix+1	No attempts yet	3s	1024 MB	Judgeable
Candles and shadows 2Find the fewest points in the ring between a convex red polygon and a blue polygon inside it, so every point of the ring is visible from a candle.	Hard8	GeometryGreedy+1	No attempts yet	2s	1024 MB	Judgeable
Legacy ScreensaverTwo bouncing rectangles move around a W by H screen; find the long-run fraction of seconds in which their interiors overlap.	Hard8	MathNumber theory+1	No attempts yet	3s	2048 MB	Judgeable
East 2 Will Not Come to This Match! 9Count the ways to pick 14 of the N wall tiles, by position, that can form a dragon of one head and four bodies or seven distinct heads, modulo 998244353.	Hard8	CombinatoricsDynamic programming+1	No attempts yet	5s	1024 MB	Judgeable
LightingGiven a zigzag road built from segments of lengths a_i, find the fewest line segments that describe the light trace as Rabbit Math walks along the road.	Hard8	GeometryTwo pointers+1	No attempts yet	4s	1024 MB	Judgeable
Robot UpgradesCount the ways to set each of N parts to an upgrade level from 0 to M so that, for each i, at most A_i parts reach level i or higher, modulo 998244353.	Hard8	Dynamic programmingCombinatorics+1	No attempts yet	1s	2048 MB	Judgeable
Intensive TrainingGiven N days, find the maximum sum of k_i times r_i, where k is nonincreasing, r is nondecreasing, sum of k is K, and sum of r is R.	Hard8	MathGreedy+1	No attempts yet	1s	2048 MB	Judgeable
Primal CollectionCount the primal arrays over values 1 to N+1 (missing S) for which inserting S at position N+1 and sifting it up takes exactly K swaps.	Hard8	CombinatoricsTree+1	No attempts yet	1s	2048 MB	Judgeable
Narrower PassagewayEach column is fogged with probability 1/2; find the expected total strength, where each unfogged segment adds min of its two row maxima (0 if equal), modulo 998244353.	Hard8	StackProbability+2	No attempts yet	1s	2048 MB	Judgeable
FlowersGiven a rooted tree of N pots with water needs A_i, decide whether the first player wins the watering game when both players play optimally.	Hard8	Game theoryTree+1	No attempts yet	1s	1024 MB	Judgeable
Largest TriangleGiven an x-monotone terrain polyline from y=0 to y=0, find the largest-area triangle inside the terrain that has one vertex at one of the interior points p2 to p(n-1).	Hard8	GeometryDivide and conquer+1	No attempts yet	1s	2048 MB	Judgeable
Double RadarsPick a start house and move at speed v around a circle of k houses to collect the most coin value without meeting either of two bouncing radars.	Hard8	SimulationMath+1	No attempts yet	1s	2048 MB	Judgeable
Cetinska Road ConstructionFind the minimum cost of a road between the two ends of a south-to-north river polyline, where each meter of road costs 1 and each river crossing costs T.	Hard8	Shortest pathGeometry	No attempts yet	1s	2048 MB	Judgeable
Building Marble TracksGiven n non-vertical segments in priority order, scan them and keep each one that crosses none of the already kept segments, then print the kept indices.	Hard8	GeometryGreedy+1	No attempts yet	4s	2048 MB	Judgeable
Let's Play Games!Given a table of game ratings, build an ASCII yes/no decision diagram that always leads to a game with the smallest maximum rating difference.	Hard8	GeometryImplementation+1	No attempts yet	5s	2048 MB	Judgeable
Coin GamePlayers alternately turn a coin by one of four angles and step it 1 unit forward for 500 moves; you win if the final x is negative.	Hard8	Game theoryGeometry+1	No attempts yet	90s	2048 MB	Judgeable
Counting Is Not Fun (Hard Version)Given n clues that each force a good pair in a balanced bracket sequence with n pairs, count the matching sequences before and after each clue, modulo 998244353.	Hard8	CombinatoricsMath+1	No attempts yet	3s	2048 MB	Judgeable
Even-dominant NumbersFor each query, count the integers x in [l, r] whose even digit count, together with the digits of floor(sqrt(x)), exceeds the odd digit count.	Hard8	Dynamic programmingMath	No attempts yet	3s	2048 MB	Judgeable
Series SumGiven k and p, compute the infinite sum of C(n, k)^p / 2^n for n from k to infinity, modulo 998244353.	Hard8	MathCombinatorics+1	No attempts yet	2s	2048 MB	Judgeable
Fischer's Chess Guessing GameJill picks one of the 960 Fischer Random starting positions, and Jack must identify it in at most six guesses, each returning how many white pieces match.	Hard8	CombinatoricsImplementation	No attempts yet	2s	2048 MB	Judgeable
Crossing the BorderPack n weighted items into knapsacks of capacity W so that the sum of each knapsack's maximum tax is minimal, and count the optimal packings.	Hard8	Dynamic programmingBit manipulation+1	No attempts yet	15s	2048 MB	Judgeable
Fortune WheelGiven a wheel with n sectors, a start sector x, and K power spins, find the minimum expected number of spins to land on sector 0, as an irreducible fraction.	Hard8	Dynamic programmingMath+2	No attempts yet	1s	2048 MB	Judgeable
AbstractValues in a DAG pass along edges each second, and the sink keeps half of its own value. Find the first moment all values reach 0, modulo 998244353.	Hard8	GraphTopological sort+2	No attempts yet	2s	2048 MB	Judgeable
Lost TableCount the n by m tables of positive integers whose row maxima are a and column maxima are b, modulo 1e9+7.	Hard8	CombinatoricsMath+1	No attempts yet	2s	2048 MB	Judgeable
A Tree GameGiven a tree, decide whether Little I can move a chip from vertex 1 to a leaf (degree 1) while Little J closes one open edge per round. Print 1 if I wins, else 0.	Hard8	TreeGame theory+1	No attempts yet	1s	2048 MB	Judgeable
Generating the SequenceGiven an array of odd numbers, add an even value to a range and query the product of a range modulo 2^20.	Hard8	Number theoryBit manipulation+1	No attempts yet	10s	2048 MB	Judgeable
Festival DecoratingFor each distance d, find the lowest-index lamp that has a lamp at x plus d with a different color, or print 0 if none exists.	Hard8	MathArray	No attempts yet	9s	2048 MB	Judgeable
Count the OrdersPlace n distinct integers on a circle to maximize the sum of adjacent absolute differences, then count the arrangements that reach that maximum modulo 1e9+7.	Hard8	SortingGreedy+1	No attempts yet	1s	2048 MB	Judgeable
Simple Math ProblemGiven positive integers m and n, compute a double sum of squared binomial products modulo 998244353 for up to 100000 test cases.	Hard8	CombinatoricsMath	No attempts yet	1s	2048 MB	Judgeable
Neutral SpectatorEach query picks x consecutive good mages and y consecutive evil mages, and asks for the largest possible minimum of (a_i + c_j) / (b_i + d_j) over all cross pairs.	Hard8	Binary searchGeometry+1	No attempts yet	2s	2048 MB	Judgeable
Old Solution MethodsThree lines through fixed points A, B, C are rotated by a common angle, and the task is to find the largest area of the triangle formed by their pairwise intersections.	Hard8	GeometryMath+1	No attempts yet	1s	2048 MB	Judgeable
Immensely Long ExpressionsFor each odd length n, find the expected value of a uniformly random valid arithmetic expression of that length, modulo 998244353.	Hard8	Dynamic programmingProbability+1	No attempts yet	1s	2048 MB	Judgeable
Sequences, Queries, and Probability 2Given M random operations on a sequence, find the expected ratio of the final sum or product to the initial one, modulo 1e9+7.	Hard8	ProbabilityMath+1	No attempts yet	1s	1024 MB	Judgeable
Sum SequenceFor a given M, decide for each query N whether N appears in the sequence B_M formed by repeatedly summing the M smallest unused positive integers.	Hard8	MathNumber theory+1	No attempts yet	1s	1024 MB	Judgeable
Good NumbersGiven a set S of forbidden integers, rank positive integers by how many good intervals (ranges containing only non-S values) contain each one, then print the first n.	Hard9	CombinatoricsMath+2	No attempts yet	2s	128 MB	Judgeable
DominoesCount how many ways a given set of dominoes can be partitioned into one or more edge-disjoint cycles using every piece exactly once.	Hard9	GraphCombinatorics+2	No attempts yet	2s	128 MB	Judgeable
Folded Paper PaintingSimulate K rounds of folding a W by H rectangle along a vertical line and several horizontal folds, painting one rectangle each round through all layers, and report the unpainted area at the end.	Hard9	GeometrySimulation+2	No attempts yet	2s	128 MB	Judgeable
Cactus Graph AutomorphismsCount automorphisms modulo 1e9+3 of a given vertex cactus graph with up to 200 vertices.	Hard9	TreeCombinatorics+2	No attempts yet	2s	128 MB	Judgeable
Coloring RectanglesGiven N rectangles, choose exactly K of them to maximize the total visible union area under a max-index-wins overlap rule, picking the lexicographically smallest tie-break.	Hard9	GeometryDynamic programming+2	No attempts yet	2s	128 MB	Judgeable
Goal CelebrationGiven a point inside a field with polygonal obstacles, find the farthest boundary point reachable by a straight segment that avoids the obstacles' interiors.	Hard9	GeometrySorting+2	No attempts yet	2s	128 MB	Judgeable
Robot ArmGiven a rectilinear factory polygon and five candidate fixed points, decide for each whether an L-shaped two-segment robot arm confined to the polygon can reach every interior point.	Hard9	GeometryIntervals+2	No attempts yet	5s	128 MB	Judgeable
Queen and Two KingsGiven a queen and two kings on a 100x100 board playing optimally, compute the minimum number of queen moves needed to capture either king.	Hard9	Game theoryBFS+2	No attempts yet	2s	128 MB	Judgeable
Wake Up!Count the distinct points where any two of up to 20,000 line segments intersect, using an efficient computational geometry sweep.	Hard9	GeometryDivide and conquer+2	No attempts yet	1s	128 MB	Judgeable
ShotGiven columns of black/gray/white cans stacked in fixed color order, repeatedly shoot a height to remove one layer from every tall-enough column and report the collapsing score after each shot.	Hard9	Segment treeBinary search+2	No attempts yet	2s	256 MB	Judgeable
Coprime Products from Six IndicesGiven N integers, count ordered 6-tuples of indices whose three pairwise products mod 359999 = 599*601 have gcd 1, modulo 1e9+7.	Hard9	Number theoryCombinatorics+2	No attempts yet	2s	512 MB	Judgeable
Matrix SwapsGiven binary matrices A and B and a per-cell swap-count limit matrix C, find the minimum number of adjacent (including diagonal) cell swaps to turn A into B, or report impossibility.	Hard9	GraphShortest path+2	No attempts yet	2s	128 MB	Judgeable
Hyungtaek's Candy BagsGiven N, find the maximum sum-free subset size of {1,...,N}, count all such maximum subsets, and print every one of them.	Hard9	CombinatoricsNumber theory+1	No attempts yet	5s	128 MB	Judgeable
Shom LanguageGiven a sentence with alternating uppercase and lowercase letters, find the minimum number of distinct two-letter words needed to rebuild it via overlapping placements.	Hard9	GraphCombinatorics+2	No attempts yet	2s	128 MB	Judgeable
All Closed-Walk LengthsGiven a directed graph, decide for every length x whether a closed walk of that length exists, then print the eventually periodic 0/1 sequence in its shortest prefix-plus-period notation.	Hard9	GraphMatrix+2	No attempts yet	2s	128 MB	Judgeable
Maximum Matching in an Almost Bipartite GraphCompute the maximum matching size in a graph formed by two paths (A and B) joined by up to 50 extra cross edges.	Hard9	GraphDynamic programming+2	No attempts yet	2s	128 MB	Judgeable
Small SquaresDetermine the winner of an optimal-play coloring game on a grid where players color 1x1 or restricted 2x2 squares, using Sprague-Grundy analysis.	Hard9	Game theoryDynamic programming+2	No attempts yet	2s	512 MB	Judgeable
Pro Gamer YoungsikGiven time and resource budgets, compute the maximum number of top-tier units obtainable from a chain of unit upgrades where each unit can repeatedly spawn the next type.	Hard9	Dynamic programmingGreedy+2	No attempts yet	2s	128 MB	Judgeable
Choosing PointsGiven up to 1000 planar points, find the largest subset where every line through two chosen points also passes through a third chosen point, or report -1 if impossible.	Hard9	GeometryCombinatorics+2	No attempts yet	2s	128 MB	Judgeable
WoodpeckersCount ways to place N woodpeckers into two height-ordered trees so every visiting pair lands in different trees and their connecting segments never cross, modulo K.	Hard9	TreeGraph+2	No attempts yet	10s	128 MB	Judgeable
Counting Multiples by Divisor CountGiven N up to 10^18, count positive integers X that are multiples of N and have exactly N divisors, or report infinitely many.	Hard9	Number theoryCombinatorics+2	No attempts yet	1s	512 MB	Judgeable
Travel GuideFind the minimum time for a guide starting at the origin to intercept N moving tourists in some order and send them home, then return herself.	Hard9	Brute forceBinary search+2	No attempts yet	2s	128 MB	Judgeable
Candy JarsGiven N jars holding consecutive candy counts starting at K, find the minimum number of subset-subtraction operations needed to empty every jar and print the operations.	Hard9	GreedyBit manipulation+2	No attempts yet	2s	128 MB	Judgeable
OrchardGiven up to 2500 non-overlapping colored rectangles, find the maximum area axis-aligned rectangle fully covered by orchards of one fruit type.	Hard9	GeometryMatrix+2	No attempts yet	2s	64 MB	Judgeable
CowboysGiven N cowboys shooting in turns with hit probabilities and optimal target choice under strategic play, compute each cowboy's probability of being the sole survivor.	Hard9	Game theoryDynamic programming+2	No attempts yet	2s	128 MB	Judgeable
Hangul-Missing NumbersGiven which Hangul letters are forbidden, find the N-th positive integer up to 10^52-1 whose Korean numeral representation avoids all forbidden jamo, using digit DP over decomposed syllables.	Hard9	Dynamic programmingCombinatorics+2	No attempts yet	2s	512 MB	Judgeable
Mail CarrierFind an Euler tour of a multigraph that maximizes the sum of w[i] minus \|k - w[i]\| over the traversal order of edges, then print the resulting vertex sequence.	Hard9	GraphGreedy+1	No attempts yet	2s	128 MB	Judgeable
FenceGiven a square field with 4N fence posts and up to 30000 convex polygonal rocks blocking sight lines, count how many posts are visible from a given viewpoint using angular occlusion by polygon silhouettes.	Hard9	GeometrySorting+1	No attempts yet	2s	128 MB	Judgeable
Matrix and Fibonacci SumCompute the sum of Fibonacci numbers with linearly growing indices times increasing powers of a K×K matrix, modulo a prime, for N up to 10^1000.	Hard9	MatrixMath+2	No attempts yet	5s	512 MB	Judgeable
Square and PointsGiven points inside a unit square with 4 fixed corners, find where to move the points to minimize the Steiner-tree-like minimum spanning length, then among those optimal configurations minimize total movement of points.	Hard9	GeometryMath+1	No attempts yet	2s	128 MB	Judgeable
Hard MatchingGiven a text sequence and two number patterns, count positions where consecutive-sum grouping matches each pattern, then find the smallest glue value x maximizing matches of the concatenated pattern with x inserted between them and report that match count.	Hard9	String matchingPrefix sum+2	No attempts yet	30s	1536 MB	Judgeable
FPSGiven N players and Q candidate additions, count ways to pick K bots with distinct speeds/ranges each dominated by some human, modulo 10009.	Hard9	CombinatoricsMath+2	No attempts yet	5s	128 MB	Judgeable
Waiting for the DogGiven rectangular obstacles, entrance, exit, and a waiting time, compute the total area of points whose shortest-path distances from both entrance and exit sum to at most a bound, in an L1-like grid metric with obstacles.	Hard9	GeometryShortest path+2	No attempts yet	1s	256 MB	Judgeable
Chip RoutingAssign each marked point on a square chip a direction toward a side so that drawn segments never cross or pass through other points, minimizing the total segment length.	Hard9	Dynamic programmingGreedy+2	No attempts yet	1s	128 MB	Judgeable
BEARsDetermine the maximum guaranteed Chebyshev distance from the origin that a pursuer can force an evader to maintain on an infinite grid graph, given blocked main-street edges, using a game-theoretic reachability argument.	Hard9	GraphGame theory+2	No attempts yet	1s	128 MB	Judgeable
L GameGiven a 4x4 L-Game board, determine if the player to move has a forced win, output the lexicographically smallest winning resulting board, or report draw/loss under perfect play.	Hard9	Game theoryBrute force+2	No attempts yet	1s	128 MB	Judgeable
Farm and FactoryGiven a weighted graph with two special nodes, choose non-negative toll values for new edges from a virtual capital so every shortest path to farm and factory avoids it, minimizing average distance to all cities, expressed as an exact fraction.	Hard9	Shortest pathGraph+2	No attempts yet	5s	128 MB	Judgeable
BeastsGiven lines splitting the plane, compute the exact squared minimum distance as a reduced fraction between two convex regions containing two extremely distant fixed points, bounded by half-planes determined for each side.	Hard9	GeometryBinary search+1	No attempts yet	3s	128 MB	Judgeable
Casting SpellsGiven a string, find the maximum length of a substring of the form ww^R w w^R (a palindrome ww^R followed immediately by itself) across up to 40 large test cases.	Hard9	String matchingString+2	No attempts yet	1s	128 MB	Judgeable
Fields and FarmersGiven initial unit-square fields, count subsets whose repeated convex-hull-based expansion yields the same final parcel as the full set, modulo 1e9+7.	Hard9	GeometryCombinatorics+1	No attempts yet	1s	128 MB	Judgeable
Hanging HatsSimulate mages hanging triangular hats on a wall, tracking nail visibility and expulsion under coverage rules that require an advanced geometric data structure.	Hard9	GeometrySegment tree+2	No attempts yet	3s	128 MB	Judgeable
Origami Axiom Six: Counting FoldsGiven two point-line pairs, count the distinct fold lines (common tangents of two parabolas) satisfying Huzita's sixth origami axiom for up to 20000 test cases.	Hard9	GeometryMath+1	No attempts yet	1s	512 MB	Judgeable
AsteroidsGiven two convex polyhedra, find rotations and a touching translation that minimize the distance between their centers of mass without overlap.	Hard9	GeometryMath+1	No attempts yet	1s	128 MB	Judgeable
Exclusive Access 2Given process-resource pairs, choose lock acquisition order per process to avoid deadlock while minimizing the longest alternating wait chain, over at most 15 resource labels.	Hard9	GraphCombinatorics+2	No attempts yet	1s	128 MB	Judgeable
Grand Theft Auto WheelGiven star-shaped polar polygons for a bolt hole and several wrench lugs, determine which wrenches can be inserted but cannot fully rotate inside the bolt hole.	Hard9	GeometrySimulation+1	No attempts yet	3s	256 MB	Judgeable
Fibonacci BaseGiven N up to 10^15, count how many '1' characters appear among the first N characters of the string formed by concatenating Zeckendorf (Fibonacci base) representations of 1,2,3,... in order.	Hard9	MathNumber theory+2	No attempts yet	1s	128 MB	Judgeable
Ground WorksSimulate water filling inside the region enclosed by a rotated Hilbert curve fractal against a tilted ground line, accounting for trapped air pockets, and output the flooded area to four decimals.	Hard9	GeometrySimulation+2	No attempts yet	3s	256 MB	Judgeable
Fool's GameSimulate the full two-player card game 'Fool' with optimal play from both sides and determine which player ultimately wins.	Hard9	Game theoryDFS+2	No attempts yet	1s	128 MB	Judgeable
TantrixSimulate the hexagonal tile game Tantrix and count all legal placements of hand tiles given complex forced-space and controlled-side rules.	Hard9	SimulationGeometry+2	No attempts yet	1s	128 MB	Judgeable
Road PlannerGiven a DAG with linear latency functions per edge, distribute an integer number of cars from source to sink to reach Wardrop (selfish routing) equilibrium and output the floor of the equilibrium travel time.	Hard9	GraphMath+1	No attempts yet	1s	128 MB	Judgeable
RSA FactorizationGiven a huge n up to 10^120 and k, find primes p ≤ q with n = p*q and \|q - kp\| bounded by 10^5, requiring advanced factorization insight.	Hard9	Number theoryMath+1	No attempts yet	1s	128 MB	Judgeable
Cubic ColoniesGiven a 3x3x3 arrangement of unit cubic blocks (some missing) and two surface points, compute the length of the shortest path on the colony's outer surface between them, allowing passage through zero-width edge or vertex gaps.	Hard9	GeometryGraph+2	No attempts yet	5s	128 MB	Judgeable
Periodic PointsCount periodic points of period n for a piecewise linear map on [0,m] modulo a given value, detecting infinite solution cases.	Hard9	MathGeometry+1	No attempts yet	2s	128 MB	Judgeable
Origami Through-HoleSimulate repeated paper folds with layered segments and reflection/overlap propagation rules, then count how many layers a pin punch pierces.	Hard9	GeometrySimulation+1	No attempts yet	1s	128 MB	Judgeable
Lowest PyramidGiven an integer-coordinate base triangle, choose integer-coordinate apex points for its unfolded net so the folded tetrahedron has minimum positive height, or report impossibility.	Hard9	GeometryMath+1	No attempts yet	30s	128 MB	Judgeable
Polygons on the GridGiven up to six rod lengths, determine the maximum-area convex polygon whose edges are the rods with both endpoints on integer grid points.	Hard9	GeometryMath+1	No attempts yet	5s	128 MB	Judgeable
Crossing PrismsCompute the surface area of the solid formed by intersecting two identical prisms (one along the x-axis, one along the y-axis) whose cross section is a given simple polygon.	Hard9	GeometryMath+1	No attempts yet	1s	128 MB	Judgeable