Math and counting

Number theory, combinatorics, and geometry

Under construction

Still being built. Things may change

Total results13,164 problems

Vera and Modern Art
Hard8
Math, Bit manipulation+2
No attempts yet
Time limit
4s
Memory limit
1024 MB
Judgeable
Nemmo Nemmo (Hard)
Hard8
Dynamic programming, Bit manipulation+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Tile Flipping (Hard)
Hard8
Math, Greedy+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
God Game
Hard8
BFS, Graph+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Strange Solutions at Jeong Lab
Hard8
Geometry, Binary search+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Jerry and Tom
Hard8
Geometry, Graph+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Leftmost Segment
Hard8
Sorting, Binary search+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Studying for Exams
Hard8
Math, Greedy+2
No attempts yet
Time limit
3s
Memory limit
512 MB
Judgeable
Stable Neighbors
Hard8
Greedy, Implementation+2
No attempts yet
Time limit
5s
Memory limit
512 MB
Judgeable
Core Training (Small2)
Hard8
Dynamic programming, Greedy+2
No attempts yet
Time limit
5s
Memory limit
512 MB
Judgeable
Operation (Small)
Hard8
Brute force, Backtracking+2
No attempts yet
Time limit
5s
Memory limit
512 MB
Judgeable
Card Operation (Large)
Hard8
Greedy, Sorting+2
No attempts yet
Time limit
5s
Memory limit
512 MB
Judgeable
Smallest Graph with K Spanning Trees
Hard8
Graph, Dynamic programming+2
No attempts yet
Time limit
5s
Memory limit
512 MB
Judgeable
Omnicircumnavigation (Small)
Hard8
Geometry, Math+1
No attempts yet
Time limit
5s
Memory limit
512 MB
Judgeable
Coin Combinations and Queries
Hard8
Dynamic programming, Combinatorics+2
No attempts yet
Time limit
3s
Memory limit
512 MB
Judgeable
doju
Hard8
Math, Number theory+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Binomial coefficient 6
Hard8
Number theory, Combinatorics+1
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Grid paper and triangles
Hard8
Combinatorics, Math+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
GCD table and a contiguous subsequence
Hard8
Number theory, Math+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Product of GCDs
Hard8
Number theory, Math+2
No attempts yet
Time limit
5s
Memory limit
512 MB
Judgeable
Sum of least common multiples
Hard8
Number theory, Math+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Horse tied outside the castle
Hard8
Geometry, Math+1
No attempts yet
Time limit
0.1s
Memory limit
16 MB
Judgeable
Permutation Swaps
Hard8
Combinatorics, Dynamic programming+1
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
ACG
Hard8
Dynamic programming, Combinatorics+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Rectangle Coloring
Hard8
Dynamic programming, Combinatorics+1
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Number of good permutations
Hard8
Combinatorics, Math+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Sequence and Queries 19
Hard8
Segment tree, Linked list+1
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Who made the Christmas sound
Hard8
Dynamic programming, Tree+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Alien microbes
Hard8
Dynamic programming, Combinatorics+2
No attempts yet
Time limit
2s
Memory limit
256 MB
Judgeable
Rectilinear Regions
Hard8
Geometry, Two pointers+2
No attempts yet
Time limit
0.5s
Memory limit
512 MB
Judgeable
Vacation Plans
Hard8
Shortest path, Dynamic programming+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Making Lunch Boxes
Hard8
Math, Bit manipulation+1
No attempts yet
Time limit
8s
Memory limit
512 MB
Judgeable
Booming Business
Hard8
Dynamic programming, Combinatorics+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Flatland Fidget Spinner
Hard8
Geometry, Binary search+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Ghostbusters
Hard8
Graph, Dynamic programming+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Knight's Marathon
Hard8
Math, BFS+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Easter Eggs
Hard8
Binary search, Graph+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Hoarse Horses
Hard8
Geometry, Graph+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Jumping Choreography
Hard8
Math, Number theory+1
No attempts yet
Time limit
3s
Memory limit
512 MB
Judgeable
Airport Coffee
Hard8
Dynamic programming, Greedy+2
No attempts yet
Time limit
6s
Memory limit
512 MB
Judgeable
Hubtown
Hard8
Greedy, Sorting+2
No attempts yet
Time limit
10s
Memory limit
512 MB
Judgeable
Intergalactic Chords
Hard8
Segment tree, Implementation+2
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
Periodical cicadas
Hard8
Number theory, Math+1
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
Daunting device
Hard8
Segment tree, Implementation+2
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
Jumping Frog
Hard8
Number theory, Math+2
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
Keep it covered
Hard8
Graph, DFS+2
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
Abstract Art
Hard8
Geometry, Implementation+1
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
The Uncertainty of Politics
Hard8
Dynamic programming, Probability+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Distinct Distances
Hard8
Geometry, Math+2
No attempts yet
Time limit
3s
Memory limit
512 MB
Judgeable
Long Long Strings
Hard8
String, Math+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Spinning Up Palindromes
Hard8
Dynamic programming, Greedy+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Flipping Out
Hard8
String, Dynamic programming+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Dividing Marbles
Hard8
Math, Number theory+2
No attempts yet
Time limit
3s
Memory limit
512 MB
Judgeable
Joker's Card Trick
Hard8
Segment tree, Prefix sum+2
No attempts yet
Time limit
3s
Memory limit
512 MB
Judgeable
Hot Sand and Umbrellas
Hard8
Graph, Shortest path+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Haggling With a Witcher
Hard8
Dynamic programming, Math+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Dendroctonus
Hard8
Geometry, Brute force+2
No attempts yet
Time limit
8s
Memory limit
512 MB
Judgeable
Hilbert's Hash Browns
Hard8
Number theory, Math+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Painting polygon outlines
Hard8
Geometry, Implementation+1
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Pyramid
Hard8
Binary search, Combinatorics+2
No attempts yet
Time limit
2s
Memory limit
1024 MB
Judgeable
Power plants
Hard8
Geometry, Divide and conquer+2
No attempts yet
Time limit
3s
Memory limit
1024 MB
Judgeable
The Battle for Wesnoth
Hard8
Probability, Math+2
No attempts yet
Time limit
0.1s
Memory limit
1024 MB
Judgeable
Ironman
Hard8
Dynamic programming, Math+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Racetrack
Hard8
Simulation, Implementation+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Saturn Bees
Hard8
Math, Combinatorics+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
EvenOdd
Hard8
Math, Bit manipulation+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Islands of Weenesia
Hard8
Graph, Geometry+2
No attempts yet
Time limit
5s
Memory limit
512 MB
Judgeable
Lights Out
Hard8
Graph, Bit manipulation+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Boom!
Hard8
Dynamic programming, Combinatorics+1
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Mousetrap
Hard8
Tree, DFS+2
No attempts yet
Time limit
5s
Memory limit
512 MB
Judgeable
Building Bridges
Hard8
Dynamic programming, Greedy+1
No attempts yet
Time limit
3s
Memory limit
128 MB
Judgeable
Cumulative Code
Hard8
Math, Tree+2
No attempts yet
Time limit
7s
Memory limit
512 MB
Judgeable
Embedding Enumeration
Hard8
Tree, DFS+2
No attempts yet
Time limit
4s
Memory limit
512 MB
Judgeable
Faulty Factorial
Hard8
Number theory, Math+2
No attempts yet
Time limit
3s
Memory limit
512 MB
Judgeable
Gambling Guide
Hard8
Graph, Probability+2
No attempts yet
Time limit
3s
Memory limit
512 MB
Judgeable
Archery Tournament
Hard8
Geometry, Binary search+2
No attempts yet
Time limit
3s
Memory limit
512 MB
Judgeable
Box
Hard8
Geometry, Brute force+2
No attempts yet
Time limit
3s
Memory limit
512 MB
Judgeable
The Final Level
Hard8
Math, Greedy+2
No attempts yet
Time limit
3s
Memory limit
512 MB
Judgeable
Knapsack Cryptosystem
Hard8
Number theory, Brute force+2
No attempts yet
Time limit
3s
Memory limit
512 MB
Judgeable
Fence Invasion
Hard8
Geometry, Combinatorics+2
No attempts yet
Time limit
5s
Memory limit
512 MB
Judgeable
Mindol Tour
Hard8
Dynamic programming, Combinatorics+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Bang! Bang!
Hard8
Geometry, Combinatorics+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Directing the Tree
Hard8
Tree, DFS+2
No attempts yet
Time limit
2s
Memory limit
256 MB
Judgeable
Parallel Lines
Hard8
Bit manipulation, Dynamic programming+2
No attempts yet
Time limit
10s
Memory limit
512 MB
Judgeable
Medical Checkup
Hard8
Simulation, Math+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Making the Perimeter of the Convex Hull Shortest
Hard8
Geometry, Sorting+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Rendezvous on a Tetrahedron
Hard8
Geometry, Implementation+1
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Border Wall
Hard8
Geometry, Sorting+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Homotopic Paths
Hard8
Geometry, Implementation+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Winning Segments
Hard8
Bit manipulation, Prefix sum+2
No attempts yet
Time limit
4s
Memory limit
256 MB
Judgeable
K-summary
Hard8
Math, Number theory+2
No attempts yet
Time limit
0.5s
Memory limit
64 MB
Judgeable
Pictionary
Hard8
Union-find, Number theory+2
No attempts yet
Time limit
1.5s
Memory limit
64 MB
Judgeable
Multiple of a Squared Factorial
Hard8
Number theory, Math+2
No attempts yet
Time limit
3s
Memory limit
512 MB
Judgeable
The Grand Noi and ICPC Battle
Hard8
Segment tree, Divide and conquer+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
AdoraBalls
Hard8
Number theory, Math+2
No attempts yet
Time limit
6s
Memory limit
512 MB
Judgeable
Balloon Distribution
Hard8
Binary search, Sorting+2
No attempts yet
Time limit
6s
Memory limit
512 MB
Judgeable
Convex Quadrilateral
Hard8
Geometry, Greedy+2
No attempts yet
Time limit
9s
Memory limit
512 MB
Judgeable
Handbags
Hard8
Shortest path, Graph+1
No attempts yet
Time limit
11s
Memory limit
512 MB
Judgeable
Off the Rails
Hard8
Dynamic programming, Geometry+2
No attempts yet
Time limit
5s
Memory limit
512 MB
Judgeable
Cat and Mouse
Hard8
Tree, DFS+2
No attempts yet
Time limit
10s
Memory limit
512 MB
Judgeable

Title	Level	Topics	Solved	Time limit	Memory limit	Judge
Vera and Modern ArtEach of N paint drops covers a lattice of points with power-of-two steps; answer Q queries for the total colour sum at a given point.	Hard8	MathBit manipulation+2	No attempts yet	4s	1024 MB	Judgeable
Nemmo Nemmo (Hard)Count subsets of occupied cells in an N by M grid (N times M at most 300) that contain no full 2 by 2 square, modulo 1e9+7.	Hard8	Dynamic programmingBit manipulation+2	No attempts yet	2s	512 MB	Judgeable
Tile Flipping (Hard)Fill the free tiles so that flipping every black tile once leaves the whole board white, choosing the lexicographically smallest result or reporting impossibility.	Hard8	MathGreedy+2	No attempts yet	1s	512 MB	Judgeable
God GameFind the minimum time for a ball on an N by M grid to reach the goal while dodging obstacles that loop clockwise around small squares forever.	Hard8	BFSGraph+2	No attempts yet	1s	512 MB	Judgeable
Strange Solutions at Jeong LabGiven a growing set of (A,B) pairs, decide each day whether the new pair is dominated by or lies on the segment between two existing points.	Hard8	GeometryBinary search+2	No attempts yet	1s	512 MB	Judgeable
Jerry and TomDecide whether every mouse can be assigned to a visible hole on the polygon boundary, with each hole holding at most k mice.	Hard8	GeometryGraph+2	No attempts yet	1s	512 MB	Judgeable
Leftmost SegmentGiven n segments spanning two horizontal lines, answer m queries asking which segment meets a horizontal line at the leftmost point, breaking ties by the upper endpoint.	Hard8	SortingBinary search+2	No attempts yet	1s	512 MB	Judgeable
Studying for ExamsDistribute up to T hours among N subjects to maximize the average of concave quadratic grade functions, with continuous time and exact rounding.	Hard8	MathGreedy+2	No attempts yet	3s	512 MB	Judgeable
Stable NeighborsPlace given counts of six mane colors around a ring so that no two neighbors share a base hair color, and output the lexicographically smallest valid arrangement.	Hard8	GreedyImplementation+2	No attempts yet	5s	512 MB	Judgeable
Core Training (Small2)Distribute U training units among N cores, each unit adding 1 to a core's success probability (capped at 1), to maximize the chance that at least K cores succeed.	Hard8	Dynamic programmingGreedy+2	No attempts yet	5s	512 MB	Judgeable
Operation (Small)Given a start value S and up to 15 operation cards, order all cards to maximize the final rational result, printed as an irreducible fraction with positive denominator.	Hard8	Brute forceBacktracking+2	No attempts yet	5s	512 MB	Judgeable
Card Operation (Large)Order a set of arithmetic cards applied to a starting value to maximize the final rational result, printed as a reduced fraction.	Hard8	GreedySorting+2	No attempts yet	5s	512 MB	Judgeable
Smallest Graph with K Spanning TreesFind the smallest node count of a graph built by the move/attach process whose spanning tree count equals K, for K up to 10000.	Hard8	GraphDynamic programming+2	No attempts yet	5s	512 MB	Judgeable
Omnicircumnavigation (Small)Given points on a sphere visited in order, decide whether the closed path along shortest arcs meets every great circle (every hemisphere) on the sphere.	Hard8	GeometryMath+1	No attempts yet	5s	512 MB	Judgeable
Coin Combinations and QueriesFor each query, count the multisets of at most d_i coins of denomination c_i (i=1..4) that sum to exactly v; answers fit in 64-bit.	Hard8	Dynamic programmingCombinatorics+2	No attempts yet	3s	512 MB	Judgeable
dojuCount increasing sequences of distinct integers within bounds for which both wrong formulas a_n/g and a_n-n give the wrong parity, modulo q.	Hard8	MathNumber theory+2	No attempts yet	2s	512 MB	Judgeable
Binomial coefficient 6For up to 100,000 queries, compute the binomial coefficient C(N,K) modulo 142857 where N goes up to 1e9.	Hard8	Number theoryCombinatorics+1	No attempts yet	2s	512 MB	Judgeable
Grid paper and trianglesCount ordered triples of lattice points in a (w+1) by (h+1) grid whose triangle has positive integer area, modulo 1e9+7.	Hard8	CombinatoricsMath+2	No attempts yet	2s	512 MB	Judgeable
GCD table and a contiguous subsequenceGiven n, m, k and a sequence a, decide whether some row i of the GCD matrix G[i][j] = gcd(i, j) contains a as a contiguous run of columns.	Hard8	Number theoryMath+2	No attempts yet	2s	512 MB	Judgeable
Product of GCDsCompute the product of gcd(i, j) over all pairs 1<=i<=N, 1<=j<=M, modulo 1e9+7, with N and M up to 15 million.	Hard8	Number theoryMath+2	No attempts yet	5s	512 MB	Judgeable
Sum of least common multiplesSum lcm(x, y) over all pairs 1<=x<=n, 1<=y<=m that share no squared prime factor.	Hard8	Number theoryMath+2	No attempts yet	2s	512 MB	Judgeable
Horse tied outside the castleGiven a convex polygon and an exterior point with rope length L, compute the area reachable when the rope bends around polygon vertices and the two wrapping directions do not overlap.	Hard8	GeometryMath+1	No attempts yet	0.1s	16 MB	Judgeable
Permutation SwapsFor each k from 1 to n-1, count permutations reachable from A in exactly k swaps, modulo 1e9+7.	Hard8	CombinatoricsDynamic programming+1	No attempts yet	2s	512 MB	Judgeable
ACGCount assignments of N ordered problems to three solvers so A's count is a multiple of k, C never solves two in a row, and G solves at least one, modulo 10000007.	Hard8	Dynamic programmingCombinatorics+2	No attempts yet	2s	512 MB	Judgeable
Rectangle ColoringCount the black-or-white colorings of an N by M grid where every X by Y subrectangle contains both colors.	Hard8	Dynamic programmingCombinatorics+1	No attempts yet	2s	512 MB	Judgeable
Number of good permutationsCount permutations of 1..N that respect given fixed positions and contain at least one pair i<j with P[i]>j and P[j]>i, modulo 2000000011.	Hard8	CombinatoricsMath+2	No attempts yet	2s	512 MB	Judgeable
Sequence and Queries 19Maintain an array under range add, range floor-division by d, and report the minimum and sum over a range. The division step needs a segment tree with min and sum.	Hard8	Segment treeLinked list+1	No attempts yet	2s	512 MB	Judgeable
Who made the Christmas soundRoot the tree at socket 1 and count colorings with R, G, B bulbs, respecting the green and blue adjacency rules, whose total cost is divisible by K.	Hard8	Dynamic programmingTree+2	No attempts yet	1s	512 MB	Judgeable
Alien microbesCount the breeding patterns over H days starting from one microbe, where each day the microbes alive produce children with a total of at most W.	Hard8	Dynamic programmingCombinatorics+2	No attempts yet	2s	256 MB	Judgeable
Rectilinear RegionsGiven two unbounded staircase polylines L and U, count the closed regions they enclose with L below and U above, and sum their areas.	Hard8	GeometryTwo pointers+2	No attempts yet	0.5s	512 MB	Judgeable
Vacation PlansFind the minimum total cost for up to three people to each travel from city 1 to their airports across separate countries in the same number of days.	Hard8	Shortest pathDynamic programming+2	No attempts yet	1s	512 MB	Judgeable
Making Lunch BoxesGiven binary recipe vectors, choose the largest subset with every ingredient appearing in an even number of chosen recipes, meaning their XOR is zero.	Hard8	MathBit manipulation+1	No attempts yet	8s	512 MB	Judgeable
Booming BusinessCount ordered rooted trees with exactly w nodes and height exactly h, modulo 1e9+7, where children of each node are an ordered sequence.	Hard8	Dynamic programmingCombinatorics+2	No attempts yet	2s	512 MB	Judgeable
Flatland Fidget SpinnerGiven the pixel colors a camera recorded of a three-armed spinner, recover the camera's position and rotation angle.	Hard8	GeometryBinary search+2	No attempts yet	2s	512 MB	Judgeable
GhostbustersGiven independent button press probabilities, find the most likely set of pressed buttons that produces the observed row-to-column connectivity signals.	Hard8	GraphDynamic programming+2	No attempts yet	2s	512 MB	Judgeable
Knight's MarathonOn a huge rectangular board, find the minimum number of knight moves from one square to another while staying inside the board.	Hard8	MathBFS+2	No attempts yet	2s	512 MB	Judgeable
Easter EggsChoose a red egg set and a blue egg set from given plants, total N eggs, maximizing the minimum red-blue distance.	Hard8	Binary searchGraph+2	No attempts yet	2s	512 MB	Judgeable
Hoarse HorsesGiven line segments in the plane, count the maximum number of faces enclosed by them, i.e. bounded regions of their arrangement.	Hard8	GeometryGraph+2	No attempts yet	2s	512 MB	Judgeable
Jumping ChoreographyMaintain the minimum total number of jumps for frogs to gather at a tower that also moves, under insertions and deletions.	Hard8	MathNumber theory+1	No attempts yet	3s	512 MB	Judgeable
Airport CoffeeGiven spaced coffee carts along a corridor, choose where to buy cups so the total walking time with alternating slow and fast phases is minimized, output as a fraction.	Hard8	Dynamic programmingGreedy+2	No attempts yet	6s	512 MB	Judgeable
HubtownAssign citizens to one of their two angularly nearest train rays, respecting each ray's capacity, and maximize the number assigned.	Hard8	GreedySorting+2	No attempts yet	10s	512 MB	Judgeable
Intergalactic ChordsMaintain an array of N notes (0 to 8); for each chord [a,b] find the most frequent note in the range, break ties by largest, then add it modulo 9 to every note in the range.	Hard8	Segment treeImplementation+2	No attempts yet	1s	1024 MB	Judgeable
Periodical cicadasGiven cycle lengths that already coincide within L, choose the smallest extra cycle maximizing the next common multiple not exceeding L.	Hard8	Number theoryMath+1	No attempts yet	1s	1024 MB	Judgeable
Daunting deviceApply N range-recolor operations whose endpoints depend on the current count of a query color, then report the highest cell frequency.	Hard8	Segment treeImplementation+2	No attempts yet	1s	1024 MB	Judgeable
Jumping FrogGiven a circular string of rocks and ponds, count the step sizes K (1 to N-1) for which some rock's K-step cycle stays entirely on rocks.	Hard8	Number theoryMath+2	No attempts yet	1s	1024 MB	Judgeable
Keep it coveredDecide whether a grid of dots and empty cells can be tiled by four line-piece types so that lines match across shared sides and never touch the border.	Hard8	GraphDFS+2	No attempts yet	1s	1024 MB	Judgeable
Abstract ArtGiven up to 100 simple polygons with 3 to 20 vertices each, compute the sum of their areas and the area of their union, each rounded to six decimals.	Hard8	GeometryImplementation+1	No attempts yet	2s	512 MB	Judgeable
The Uncertainty of PoliticsEach hearing has a start time and a uniform integer length in [a,b]; pick hearings to attend fully so the expected count is maximized.	Hard8	Dynamic programmingProbability+2	No attempts yet	2s	512 MB	Judgeable
Distinct DistancesChoose any point q in the plane and minimize the number of distinct Euclidean distances from q to n given integer points.	Hard8	GeometryMath+2	No attempts yet	3s	512 MB	Judgeable
Long Long StringsDecide whether two sequences of insertions and deletions, applied to any sufficiently long string, produce identical results.	Hard8	StringMath+2	No attempts yet	1s	512 MB	Judgeable
Spinning Up PalindromesGiven a digit string of up to 40 wheels, find the minimum number of single-digit advances (with cascading carries) to reach a palindrome.	Hard8	Dynamic programmingGreedy+2	No attempts yet	1s	512 MB	Judgeable
Flipping OutCount the strings that, added to the given patterns, make the flip rule reproduce the given flip sequence, or -1 if infinitely many work.	Hard8	StringDynamic programming+2	No attempts yet	2s	512 MB	Judgeable
Dividing MarblesFour players each contribute a power of two marbles; splitting piles while merging equal sizes, find the fewest turns to leave exactly one marble.	Hard8	MathNumber theory+2	No attempts yet	3s	512 MB	Judgeable
Joker's Card TrickAfter each point update to a row of nonzero integers, find the smallest prefix index maximizing the running sum of values scaled by the total positive and total negative sums.	Hard8	Segment treePrefix sum+2	No attempts yet	3s	512 MB	Judgeable
Hot Sand and UmbrellasFind the minimum total time Kevin sprints on hot sand to go from the car to the ball and back, cooling at circular umbrellas, where each sun run is at most k seconds and the ball visit does not reset the limit.	Hard8	GraphShortest path+2	No attempts yet	2s	512 MB	Judgeable
Haggling With a WitcherGiven an unknown target fee uniform on [L,R], maximize expected gold by naming fees over time, where each attempt or save-reload costs 100 ms and time is capped by T.	Hard8	Dynamic programmingMath+2	No attempts yet	2s	512 MB	Judgeable
DendroctonusDecide whether the infected and non-infected points can be separated by a single circle centered anywhere, where boundary non-infected points are allowed but interior ones are not.	Hard8	GeometryBrute force+2	No attempts yet	8s	512 MB	Judgeable
Hilbert's Hash BrownsCount how many residues mod n are reachable as x^p + q mod n over all nonnegative integers x.	Hard8	Number theoryMath+2	No attempts yet	1s	512 MB	Judgeable
Painting polygon outlinesFor each polygon side, split it at intersections with later polygons, then sum over the pieces where the depth t counts how many later polygons contain the piece.	Hard8	GeometryImplementation+1	No attempts yet	1s	512 MB	Judgeable
PyramidFor each query Q, find the Q-th smallest positive integer divisible by at least one of up to 15 given numbers, with every answer at most 10^18.	Hard8	Binary searchCombinatorics+2	No attempts yet	2s	1024 MB	Judgeable
Power plantsColor n points with two colors so the closest same-color pair is as far apart as possible, and output that squared distance plus the lexicographically smallest optimal coloring.	Hard8	GeometryDivide and conquer+2	No attempts yet	3s	1024 MB	Judgeable
The Battle for WesnothChoose positive d and b with d*b <= m to maximize the chance that the total damage of b independent blows, each landing with probability p/100 and dealing d, kills a unit with h hitpoints; report the smallest-d, smallest-b optimum or 1 1 if impossible.	Hard8	ProbabilityMath+2	No attempts yet	0.1s	1024 MB	Judgeable
IronmanFind the fastest path across n horizontal layers with different speeds, entering and exiting each layer boundary at an optimal x position, and print the minimum travel time.	Hard8	Dynamic programmingMath+2	No attempts yet	2s	512 MB	Judgeable
RacetrackGiven ordered lap times and lap counts and the rule that passes happen only at the finish line, compute when each runner finishes the race.	Hard8	SimulationImplementation+2	No attempts yet	2s	512 MB	Judgeable
Saturn BeesOn a torus-like hexagonal grid, decide whether nm/4 vertices can each dominate a closed neighborhood of 4 vertices, covering every vertex.	Hard8	MathCombinatorics+2	No attempts yet	2s	512 MB	Judgeable
EvenOddSum f(X) for every X in [L, R], where f counts the steps of a process that halves even numbers and adds 1 to odd numbers until reaching 1. The bounds reach 10^18.	Hard8	MathBit manipulation+2	No attempts yet	2s	512 MB	Judgeable
Islands of WeenesiaFind the shortest tunnel between two circular islands whose entrance points sit at least 100 cm inside the rims, so that the reachability graph over islands becomes strongly connected.	Hard8	GraphGeometry+2	No attempts yet	5s	512 MB	Judgeable
Lights OutFind the shortest walk from room 1 to room 0 whose switches span exactly the set of reachable lamp states, counting repeated visits.	Hard8	GraphBit manipulation+2	No attempts yet	2s	512 MB	Judgeable
Boom!Count the ways to fold a strip of N segments so that no two chemically coated faces touch.	Hard8	Dynamic programmingCombinatorics+1	No attempts yet	2s	512 MB	Judgeable
MousetrapOn a tree, Dumbo blocks or cleans edges while an edge-averse mouse moves; find the minimum moves to force it into the trap.	Hard8	TreeDFS+2	No attempts yet	5s	512 MB	Judgeable
Building BridgesPick a subset containing the first and last pillars, pay (h_i-h_j)^2 for each bridge section and w_i for each skipped pillar, and minimize the total.	Hard8	Dynamic programmingGreedy+1	No attempts yet	3s	128 MB	Judgeable
Cumulative CodeFor the complete binary tree of depth k, answer q queries each summing m elements of its Prüfer code at positions a, a+d, ..., a+(m-1)d.	Hard8	MathTree+2	No attempts yet	7s	512 MB	Judgeable
Embedding EnumerationCount the ways to place a labeled tree's nodes into a 2 by n grid so node 1 sits at the top-left, edges touch, and no cell repeats, modulo 1e9+7.	Hard8	TreeDFS+2	No attempts yet	4s	512 MB	Judgeable
Faulty FactorialGiven n, prime p, and target r mod p, find the faulty factorial (one factor reduced below its index) with remainder r, printing the smallest such (index, value).	Hard8	Number theoryMath+2	No attempts yet	3s	512 MB	Judgeable
Gambling GuideOn an undirected graph, find the minimum expected number of random tickets (with rejection allowed) needed to travel from city 1 to city n.	Hard8	GraphProbability+2	No attempts yet	3s	512 MB	Judgeable
Archery TournamentMaintain a dynamic set of non-overlapping circles tangent to the ground, support insertions and point queries that remove the hit circle, and report which circle each arrow hits.	Hard8	GeometryBinary search+2	No attempts yet	3s	512 MB	Judgeable
BoxGiven a box with edges a, b, c and a w by h cardboard, decide whether some edge-aligned net of the box fits on the cardboard.	Hard8	GeometryBrute force+2	No attempts yet	3s	512 MB	Judgeable
The Final LevelFind the minimum number of L-shaped n-blocks needed to cover a connected path of squares from (0,0) to (a,b) on an infinite grid.	Hard8	MathGreedy+2	No attempts yet	3s	512 MB	Judgeable
Knapsack CryptosystemRecover the plaintext bits from a Merkle-Hellman knapsack instance where q = 2^64, exploiting the known modulus to invert the hidden superincreasing sequence.	Hard8	Number theoryBrute force+2	No attempts yet	3s	512 MB	Judgeable
Fence InvasionCount how many distinct convex polygons can be formed as the convex hull of some subset of at least 3 of the given points, modulo 1e9+7.	Hard8	GeometryCombinatorics+2	No attempts yet	5s	512 MB	Judgeable
Mindol TourCount Hamiltonian cycles starting and ending at trampoline 0 in a graph where node 0 connects to all and node i reaches nodes within distance A_i, with A_i at least i.	Hard8	Dynamic programmingCombinatorics+2	No attempts yet	1s	512 MB	Judgeable
Bang! Bang!Given lines and circles all passing through the origin, count how many regions the plane is divided into, treating duplicates as one shape.	Hard8	GeometryCombinatorics+2	No attempts yet	2s	512 MB	Judgeable
Directing the TreeCount the orientations of a tree's edges such that every given vertex pair has a directed path one way or the other, modulo 1e9+7.	Hard8	TreeDFS+2	No attempts yet	2s	256 MB	Judgeable
Parallel LinesGiven up to 16 distinct points, pair them up to maximize the number of parallel pairs among the drawn segments.	Hard8	Bit manipulationDynamic programming+2	No attempts yet	10s	512 MB	Judgeable
Medical CheckupGiven n students in a fixed queue and their per-item service times, report the item each student is on or waiting for at time t+0.5.	Hard8	SimulationMath+2	No attempts yet	2s	512 MB	Judgeable
Making the Perimeter of the Convex Hull ShortestGiven n points, find the largest decrease in convex hull perimeter achievable by removing exactly two of the points.	Hard8	GeometrySorting+2	No attempts yet	2s	512 MB	Judgeable
Rendezvous on a TetrahedronTwo worms start at vertex A of a regular tetrahedron, crawl straight across faces reflecting off edges, and stop after integer trail lengths; decide whether they end on the same face.	Hard8	GeometryImplementation+1	No attempts yet	1s	512 MB	Judgeable
Border WallGiven two colored point sets and a width d, find the minimum number of points to delete so that a strip of width d separates the remaining points by color.	Hard8	GeometrySorting+2	No attempts yet	2s	512 MB	Judgeable
Homotopic PathsDecide whether two polygonal paths from s to t in a plane with point obstacles are homotopic, that is, deformable into each other without crossing any tree.	Hard8	GeometryImplementation+2	No attempts yet	2s	512 MB	Judgeable
Winning SegmentsGiven a permutation of 0..2^M-1, count the nonempty subarrays whose XOR can be made equal to 2^M-1 by one mandatory swap of two elements.	Hard8	Bit manipulationPrefix sum+2	No attempts yet	4s	256 MB	Judgeable
K-summaryGiven segment lengths K_i, count how many array positions are pinned down by all the K_i-summaries.	Hard8	MathNumber theory+2	No attempts yet	0.5s	64 MB	Judgeable
PictionaryCities get roads on day i joining all pairs whose gcd is M-i+1; for each query, find the first day two given cities become connected.	Hard8	Union-findNumber theory+2	No attempts yet	1.5s	64 MB	Judgeable
Multiple of a Squared FactorialFor many queries N, find the smallest K such that K! is divisible by (N!)^2. The answer is always between N and 2N, and needs Legendre exponent checks.	Hard8	Number theoryMath+2	No attempts yet	3s	512 MB	Judgeable
The Grand Noi and ICPC BattleMaintain a sequence of N ones under range assignment and queries for the sum of A_i A_j A_k over all i<j<k in a range, modulo 10^8, with N up to 1e9 and Q up to 1e5.	Hard8	Segment treeDivide and conquer+2	No attempts yet	2s	512 MB	Judgeable
AdoraBallsGiven the counts of children in four colours and four bundle types, decide whether some non-negative number of each bundle can supply equal, positive balls to every child with none left over.	Hard8	Number theoryMath+2	No attempts yet	6s	512 MB	Judgeable
Balloon DistributionRank all ratios P_i/j from largest to smallest and count, for each contestant, how many ratios fall at rank N or above, with ties at the cutoff all counted.	Hard8	Binary searchSorting+2	No attempts yet	6s	512 MB	Judgeable
Convex QuadrilateralGiven n points, find the smallest-area convex quadrilateral whose four sides each pass through at least two of the points and that contains every point.	Hard8	GeometryGreedy+2	No attempts yet	9s	512 MB	Judgeable
HandbagsA grid of villages sets prices from s source prices; report the maximum price and how many villages reach it.	Hard8	Shortest pathGraph+1	No attempts yet	11s	512 MB	Judgeable
Off the RailsGiven n cities sorted by x, cover them with straight non-vertical segments so that the sum of squared vertical distances plus C per segment is minimized.	Hard8	Dynamic programmingGeometry+2	No attempts yet	5s	512 MB	Judgeable
Cat and MouseOn a tree with distinct edge weights, the mouse always moves to its heaviest incident edge (or second heaviest if the cat blocks it); find the minimum number of mouse moves for the cat to trap it.	Hard8	TreeDFS+2	No attempts yet	10s	512 MB	Judgeable