Math and counting

Number theory, combinatorics, and geometry

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Still being built. Things may change

Total results13,164 problems

Cunning Friends
Hard8
Game theory, Greedy+2
No attempts yet
Time limit
2s
Memory limit
64 MB
Judgeable
French Dinner
Hard8
Shortest path, Graph+1
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Blowing Candles
Hard8
Geometry, Brute force+2
No attempts yet
Time limit
4s
Memory limit
512 MB
Judgeable
Canonical Coin Systems
Hard8
Dynamic programming, Greedy+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Cat and Mice
Hard8
Binary search, Dynamic programming+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Umbral Decoding
Hard8
Geometry, Math+1
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Vera and the Engineering Buildings
Hard8
Tree, Dynamic programming+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Greedy Gift Takers
Hard8
Math, Simulation
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
A Simple Function
Hard8
Number theory, Combinatorics+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
K-Uniform String
Hard8
Dynamic programming, Combinatorics+2
No attempts yet
Time limit
1s
Memory limit
256 MB
Judgeable
Arranging game levels
Hard8
Tree, Combinatorics+2
No attempts yet
Time limit
1s
Memory limit
256 MB
Judgeable
Programming Duel Tournament
Hard8
Greedy, Tree+2
No attempts yet
Time limit
2s
Memory limit
256 MB
Judgeable
Making a Beautiful Puzzle
Hard8
Dynamic programming, Backtracking+2
No attempts yet
Time limit
3s
Memory limit
128 MB
Judgeable
Operation Optimization
Hard8
String, Greedy+2
No attempts yet
Time limit
2s
Memory limit
256 MB
Judgeable
Coin Slider
Hard8
Geometry, Bit manipulation+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Help the Princess!
Hard8
Graph, BFS+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Share the Ruins Preservation
Hard8
Geometry, Sorting+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Multisect
Hard8
Dynamic programming, Binary search+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Maximum Interval Sum 2
Hard8
Segment tree, Divide and conquer+2
No attempts yet
Time limit
1s
Memory limit
256 MB
Judgeable
Blocks 4
Hard8
Dynamic programming, Math+2
No attempts yet
Time limit
1s
Memory limit
256 MB
Judgeable
Big Number Multiplication (2)
Hard8
Math, Divide and conquer+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Sprinklers
Hard8
Combinatorics, Divide and conquer+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Connect the Dots
Hard8
Geometry, Greedy+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Factor-Free Tree
Hard8
Tree, Divide and conquer+2
No attempts yet
Time limit
6s
Memory limit
512 MB
Judgeable
Juggling Troupe
Hard8
Simulation, Greedy+2
No attempts yet
Time limit
3s
Memory limit
512 MB
Judgeable
Broken Gearbox
Hard8
Graph, Math+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Pillars
Hard8
Implementation, Simulation+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Drawing a Character Face
Hard8
Geometry, Math+2
No attempts yet
Time limit
0.1s
Memory limit
256 MB
Judgeable
Satan Game
Hard8
Probability, Math+1
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Catch the Plane
Hard8
Dynamic programming, Probability+2
No attempts yet
Time limit
10s
Memory limit
1024 MB
Judgeable
Gem Island
Hard8
Probability, Dynamic programming+2
No attempts yet
Time limit
3s
Memory limit
1024 MB
Judgeable
Getting a Jump on Crime
Hard8
Graph, BFS+2
No attempts yet
Time limit
2s
Memory limit
1024 MB
Judgeable
Panda Preserve
Hard8
Geometry, Binary search+2
No attempts yet
Time limit
10s
Memory limit
1024 MB
Judgeable
Single Cut of Failure
Hard8
Geometry, Sorting+2
No attempts yet
Time limit
6s
Memory limit
1024 MB
Judgeable
xor game
Hard8
Math, Combinatorics+2
No attempts yet
Time limit
0.5s
Memory limit
128 MB
Judgeable
Cow Gymnasts
Hard8
Number theory, Math+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Out of Sorts
Hard8
Sorting, Math+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Magic
Hard8
Hash map, Prefix sum+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Six
Hard8
Combinatorics, Math+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Camel
Hard8
Greedy, Implementation+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
System Call
Hard8
Math, Number theory+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Namje Adventure
Hard8
Dynamic programming, Greedy+1
No attempts yet
Time limit
3s
Memory limit
512 MB
Judgeable
Non-Interactive Guessing Number
Hard8
Binary search, Greedy+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Random Number Generator
Hard8
Probability, Dynamic programming+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Permutation
Hard8
Math, Combinatorics+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Sacred Scarecrows
Hard8
Dynamic programming, Bit manipulation+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Love Polygon
Hard8
Graph, Greedy+2
No attempts yet
Time limit
2s
Memory limit
1024 MB
Judgeable
IP over Avian Carriers
Hard8
Math, Implementation
No attempts yet
Time limit
2s
Memory limit
1024 MB
Judgeable
Mysterious Array
Hard8
Combinatorics, Sorting+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Pineapple Pizza
Hard8
Geometry, Sorting+2
No attempts yet
Time limit
1s
Memory limit
256 MB
Judgeable
Turf Wars
Hard8
Geometry, Brute force+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Split and Merge
Hard8
Dynamic programming, Combinatorics+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Full House
Hard8
Combinatorics, Greedy+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Matrix Multiplication
Hard8
Greedy, Sorting+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
A Simple Problem
Hard8
Number theory, Math+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Teleport Pads
Hard8
Graph, BFS+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Magic Necklace
Hard8
Math, Number theory+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Kakao Money
Hard8
Math, Number theory+2
No attempts yet
Time limit
5s
Memory limit
256 MB
Judgeable
Shootings
Hard8
Geometry, Sorting+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
POPA
Hard8
Divide and conquer, Tree+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Toys
Hard8
Number theory, Combinatorics+2
No attempts yet
Time limit
4s
Memory limit
512 MB
Judgeable
Triangles
Hard8
Geometry, Divide and conquer+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Playoff by all the teams
Hard8
Brute force, Backtracking+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Equilateral Triangular Fence
Hard8
Geometry, Binary search+1
No attempts yet
Time limit
8s
Memory limit
512 MB
Judgeable
Cut It Out!
Hard8
Geometry, Dynamic programming
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Zoning Houses
Hard8
Segment tree, Divide and conquer+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Battle Royale
Hard8
Geometry, Math+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Hyper Illuminati
Hard8
Math, Number theory+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Amateur Radio Network
Hard8
Geometry, Binary search+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Fair Share
Hard8
Geometry, Sorting+2
No attempts yet
Time limit
5s
Memory limit
512 MB
Judgeable
Last Casino
Hard8
Math, Probability+1
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
I'm a Fan
Hard8
Geometry, Math+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Office Relocation
Hard8
Tree, Dynamic programming+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Number Theory and Applications
Hard8
Number theory, Math+2
No attempts yet
Time limit
0.2s
Memory limit
16 MB
Judgeable
Number Theory and Applications: Recitation
Hard8
Number theory, Math+2
No attempts yet
Time limit
4s
Memory limit
512 MB
Judgeable
Peace Sign
Hard8
Geometry, Hash map+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Binary Tree and Sequence
Hard8
String matching, Hash map+2
No attempts yet
Time limit
3s
Memory limit
256 MB
Judgeable
Möbius Madness
Hard8
Math, Number theory+1
No attempts yet
Time limit
2.5s
Memory limit
512 MB
Judgeable
Liar Game
Hard8
Combinatorics, Dynamic programming+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Fake Plastic Trees
Hard8
Tree, Math+2
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
Game on Plane
Hard8
Game theory, Geometry
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
Balcony Repairs
Hard8
Dynamic programming, Combinatorics+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Finding Tricky Numbers
Hard8
Dynamic programming, Binary search+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Laziness
Hard8
Math, Greedy+1
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Build a Wall!
Hard8
Dynamic programming, Geometry+1
No attempts yet
Time limit
2.5s
Memory limit
1024 MB
Judgeable
Sorting Game
Hard8
Array, Math+1
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
We Live Forgetting the Truth
Hard8
Graph, Combinatorics+2
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
Slalom
Hard8
Dynamic programming, Combinatorics+1
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Red-Black Tree
Hard8
Dynamic programming, Tree+1
No attempts yet
Time limit
3s
Memory limit
512 MB
Judgeable
Nice Report
Hard8
Graph, Probability+1
No attempts yet
Time limit
5s
Memory limit
512 MB
Judgeable
Small Numbers
Hard8
Number theory, Math+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Folding the Figure
Hard8
Implementation, Geometry+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Eleventh Birthday
Hard8
Dynamic programming, Combinatorics+1
No attempts yet
Time limit
4s
Memory limit
512 MB
Judgeable
Eating Everything Efficiently
Hard8
Dynamic programming, Graph+1
No attempts yet
Time limit
3s
Memory limit
512 MB
Judgeable
KALLAX Construction
Hard8
Dynamic programming, Greedy+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Harry the Hamster
Hard8
Game theory, Dynamic programming+2
No attempts yet
Time limit
3s
Memory limit
512 MB
Judgeable
Intergalactic Bidding
Hard8
Greedy, Sorting+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
King's Colors
Hard8
Tree, Dynamic programming+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Broken Watch
Hard8
Math, Combinatorics+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Moving Furniture
Hard8
Geometry, Math
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable

Title	Level	Topics	Solved	Time limit	Memory limit	Judge
Cunning FriendsThree players take turns removing stones from piles; Ben and Chris cooperate to make Anthony lose, so decide whether Anthony can avoid defeat.	Hard8	Game theoryGreedy+2	No attempts yet	2s	64 MB	Judgeable
French DinnerDecide whether dishes can be assigned serving times satisfying simultaneity and precedence bounds while keeping the whole meal within K minutes.	Hard8	Shortest pathGraph+1	No attempts yet	2s	512 MB	Judgeable
Blowing CandlesGiven up to 200,000 points inside a disk, find the minimum width of a strip that can cover all of them.	Hard8	GeometryBrute force+2	No attempts yet	4s	512 MB	Judgeable
Canonical Coin SystemsGiven a sorted coin system, decide whether the greedy algorithm always makes change with the fewest coins, or whether some amount is a counterexample.	Hard8	Dynamic programmingGreedy+2	No attempts yet	2s	512 MB	Judgeable
Cat and MiceFind the smallest initial speed v so the cat can visit all points in some order, each arrival at or before its deadline, with speed multiplied by m after every meal.	Hard8	Binary searchDynamic programming+2	No attempts yet	2s	512 MB	Judgeable
Umbral DecodingGiven up to 100 safe points (x, y, b), count lattice points (p, q) in the square [0, n]^2 that are not covered by any region \|x-p\|^3 + \|y-q\|^3 <= b.	Hard8	GeometryMath+1	No attempts yet	2s	512 MB	Judgeable
Vera and the Engineering BuildingsGiven a tree of N nodes with distinct hidden values and inspection costs, find the minimum total cost of an adaptive strategy that is guaranteed to locate a local maximum.	Hard8	TreeDynamic programming+2	No attempts yet	2s	512 MB	Judgeable
Greedy Gift TakersEach cow takes a gift and reinserts herself c_i positions from the tail; count how many cows never reach the head.	Hard8	MathSimulation	No attempts yet	2s	512 MB	Judgeable
A Simple FunctionDefine f via a Pascal-like recurrence that resets to 0 whenever the sum is divisible by prime M, and answer up to 10^4 queries f(a, b, M) modulo 10^9+7.	Hard8	Number theoryCombinatorics+2	No attempts yet	1s	512 MB	Judgeable
K-Uniform StringCount binary strings of length N where, for each of M given intervals, every length-K substring inside it contains the same number of ones, modulo 1e9+7.	Hard8	Dynamic programmingCombinatorics+2	No attempts yet	1s	256 MB	Judgeable
Arranging game levelsCount rooted tree arrangements of N levels where each level's clear score S_i and the cumulative score K_i along the root-to-level path are given, and children must have larger S than parents.	Hard8	TreeCombinatorics+2	No attempts yet	1s	256 MB	Judgeable
Programming Duel TournamentChoose a duel schedule for N contestants, where the higher skill always wins and each contestant duels at most L_i times, to maximize total duel XOR interest minus fatigue.	Hard8	GreedyTree+2	No attempts yet	2s	256 MB	Judgeable
Making a Beautiful PuzzleFill each square of an N by M board with one of four colors so that orthogonal neighbors differ, maximizing total beauty and counting optimal placements modulo 1e9+7.	Hard8	Dynamic programmingBacktracking+2	No attempts yet	3s	128 MB	Judgeable
Operation OptimizationFind the shortest sequence of append-0, append-1, and self-doubling operations whose two-fold application to the empty string yields a given binary string S.	Hard8	StringGreedy+2	No attempts yet	2s	256 MB	Judgeable
Coin SliderChoose the largest subset of at most 16 coins and an order of moves so no moving coin ever collides with a stationary or already-moved coin.	Hard8	GeometryBit manipulation+2	No attempts yet	2s	512 MB	Judgeable
Help the Princess!Decide whether a princess can reach the single escape hatch on a grid while any number of soldiers chase her simultaneously and catch her by sharing a cell.	Hard8	GraphBFS+2	No attempts yet	2s	512 MB	Judgeable
Share the Ruins PreservationSplit points by a vertical line that avoids all points, build the minimum-area enclosing convex hull of each side, and minimize the total area.	Hard8	GeometrySorting+2	No attempts yet	2s	512 MB	Judgeable
MultisectGiven a hidden failing revision among n candidates and up to K simultaneous tests per round, find the strategy that minimizes expected total cost when a round with i failures costs T_i.	Hard8	Dynamic programmingBinary search+2	No attempts yet	2s	512 MB	Judgeable
Maximum Interval Sum 2For a sequence with point updates, answer range queries for the maximum of U times a subarray sum plus V times its length minus one.	Hard8	Segment treeDivide and conquer+2	No attempts yet	1s	256 MB	Judgeable
Blocks 4Count the tilings of an N by M rectangle using blocks of size k by N (rotatable) for k from 1 to N, modulo 1999, where M can be as large as 1e10.	Hard8	Dynamic programmingMath+2	No attempts yet	1s	256 MB	Judgeable
Big Number Multiplication (2)Multiply two integers of up to 300,000 digits each, too large for quadratic multiplication, and print the exact product.	Hard8	MathDivide and conquer+2	No attempts yet	2s	512 MB	Judgeable
SprinklersGiven a permutation of N sprinklers, count axis-aligned integer rectangles whose every point lies both northeast of some sprinkler and southwest of another, modulo 1e9+7.	Hard8	CombinatoricsDivide and conquer+2	No attempts yet	2s	512 MB	Judgeable
Connect the DotsGiven a 4 by 4 grid labeled 1 to 16, find the minimum number of straight segments a continuous polyline needs so that the dots are visited in numeric order.	Hard8	GeometryGreedy+2	No attempts yet	2s	512 MB	Judgeable
Factor-Free TreeGiven a sequence, decide whether it can be the inorder of a rooted binary tree where every node is coprime with all its ancestors, and if so output each node's parent index.	Hard8	TreeDivide and conquer+2	No attempts yet	6s	512 MB	Judgeable
Juggling TroupeSimulate balls thrown left and right simultaneously until every position holds at most one ball, then report the final configuration.	Hard8	SimulationGreedy+2	No attempts yet	3s	512 MB	Judgeable
Broken GearboxAssign each of n gear radii to a vertex of a connected graph so that every edge's distance equals the sum of its assigned radii, returning the lexicographically smallest assignment or impossible.	Hard8	GraphMath+2	No attempts yet	2s	512 MB	Judgeable
PillarsGiven a grid with 2x2 pillars spaced apart, construct the unique Hamiltonian circuit through all free cells defined by a fixed local rule.	Hard8	ImplementationSimulation+2	No attempts yet	2s	512 MB	Judgeable
Drawing a Character FaceGiven three circles, compute the area of their union, counting overlaps once, and print it to six decimal places.	Hard8	GeometryMath+2	No attempts yet	0.1s	256 MB	Judgeable
Satan GameOutput a board with N up to 100, M up to 20, and snakes and ladders so the expected number of dice rolls to finish is at least 5e18.	Hard8	ProbabilityMath+1	No attempts yet	2s	512 MB	Judgeable
Catch the PlaneChoose an adaptive strategy of buses to maximize the probability of reaching station 1 by time k, where each bus runs independently with a known probability.	Hard8	Dynamic programmingProbability+2	No attempts yet	10s	1024 MB	Judgeable
Gem IslandAt each of d steps a uniformly random gem splits in two; find the expected total held by the r largest holders after d splits.	Hard8	ProbabilityDynamic programming+2	No attempts yet	3s	1024 MB	Judgeable
Getting a Jump on CrimeGiven building heights on a grid, find the minimum number of jumps to reach each roof, where a jump is valid only if its parabola clears every building between the two roofs.	Hard8	GraphBFS+2	No attempts yet	2s	1024 MB	Judgeable
Panda PreserveGiven a simple polygon and receivers at its vertices with a common radius, find the smallest radius whose union of disks covers the whole polygon.	Hard8	GeometryBinary search+2	No attempts yet	10s	1024 MB	Judgeable
Single Cut of FailureWires cross a rectangle between boundary sides; find the fewest straight cuts connecting different sides that cross every wire, and output the lexicographically smallest such cut.	Hard8	GeometrySorting+2	No attempts yet	6s	1024 MB	Judgeable
xor gameCount sequences of n xor masks (each below 2^31) that carry a to b, modulo 1e9+7.	Hard8	MathCombinatorics+2	No attempts yet	0.5s	128 MB	Judgeable
Cow GymnastsCount circular stack-size assignments of length N (N up to 1e12) that stay unchanged after each stack falls clockwise, modulo 1e9+7.	Hard8	Number theoryMath+2	No attempts yet	2s	512 MB	Judgeable
Out of SortsGiven an array, count how many times the outer loop of a forward-backward bubble sort variant runs before the array becomes sorted.	Hard8	SortingMath+2	No attempts yet	2s	512 MB	Judgeable
MagicCount substrings of an N-character string in which all K distinct letters of the whole string appear an equal number of times, modulo 1e9+7.	Hard8	Hash mapPrefix sum+2	No attempts yet	2s	512 MB	Judgeable
SixN has at most six distinct prime divisors; count the sequences of divisors greater than 1 where each new divisor shares a factor with at most one earlier entry, modulo 1e9+7.	Hard8	CombinatoricsMath+2	No attempts yet	2s	512 MB	Judgeable
CamelConstruct a closed knight-like tour for a jumping camel piece on an N x N board where N is a multiple of 5, printing the visit order or NO.	Hard8	GreedyImplementation+2	No attempts yet	2s	512 MB	Judgeable
System CallChoose one buffer size K for all files to minimize sum over files of ceil(F_i/K) times (T+K).	Hard8	MathNumber theory+2	No attempts yet	1s	512 MB	Judgeable
Namje AdventureN people hang at depths 1 to N and must reach the bottom depths D-N+1 to D; only the highest person can move down 1 to L steps, find the least total energy.	Hard8	Dynamic programmingGreedy+1	No attempts yet	3s	512 MB	Judgeable
Non-Interactive Guessing NumberGiven N, K, and Theodora's answer string, output guess values that follow the rules, or -1 if impossible.	Hard8	Binary searchGreedy+2	No attempts yet	2s	512 MB	Judgeable
Random Number GeneratorGiven how many values from 1 to N have been seen zero or one time, find the expected number of draws until every value appears at least twice.	Hard8	ProbabilityDynamic programming+2	No attempts yet	2s	512 MB	Judgeable
PermutationGiven a permutation P and queries K, find the exponent T such that P^T is the K-th smallest among P^1 through P^(M-1) in lexicographic order.	Hard8	MathCombinatorics+2	No attempts yet	2s	512 MB	Judgeable
Sacred ScarecrowsCount subsets of empty cells in an R x C grid, modulo 1e9+7, such that every row has a scarecrow and every pair of consecutive columns has one.	Hard8	Dynamic programmingBit manipulation+2	No attempts yet	2s	512 MB	Judgeable
Love PolygonEach of N people loves exactly one person; rewrite the minimum number of love targets so that everyone ends up in a mutual pair.	Hard8	GraphGreedy+2	No attempts yet	2s	1024 MB	Judgeable
IP over Avian CarriersWrite an encoder that turns C×N bits into K strings of N bits, and a decoder that recovers the original bits from any C of those strings.	Hard8	MathImplementation	No attempts yet	2s	1024 MB	Judgeable
Mysterious ArrayCount permutations of 1..N consistent with Q range-minimum constraints, modulo 1e9+7, with contradictions giving 0.	Hard8	CombinatoricsSorting+2	No attempts yet	2s	512 MB	Judgeable
Pineapple PizzaGiven n points and a center Q, decide whether k rays from Q can split the plane so every sector holds exactly n/k points, with no point on a ray.	Hard8	GeometrySorting+2	No attempts yet	1s	256 MB	Judgeable
Turf WarsEach gang owns disjoint axis-aligned rectangles; pick exactly one rectangle to drop per gang so that no two kept rectangles from different gangs overlap, and report whether this is possible.	Hard8	GeometryBrute force+2	No attempts yet	2s	512 MB	Judgeable
Split and MergeGiven two tilings of a 1xL board by 1x1 and 1x2 pieces, find the minimum number of split/merge operations to transform one into the other and count the ways.	Hard8	Dynamic programmingCombinatorics+2	No attempts yet	1s	512 MB	Judgeable
Full HouseKnowing only how many cards were removed from a 52-card deck, find the minimum and maximum number of disjoint full houses (3 of one rank plus 2 of another) that can be formed from the remaining cards.	Hard8	CombinatoricsGreedy+2	No attempts yet	2s	512 MB	Judgeable
Matrix MultiplicationFor each prefix of n matrices, decide whether some multiplication order is valid, and if so report the largest possible area of the final product.	Hard8	GreedySorting+2	No attempts yet	2s	512 MB	Judgeable
A Simple ProblemFind positive integers B_i so that the product of (A_i + B_i)/B_i equals 1 + (2^m - 1)/n, or report that none exist.	Hard8	Number theoryMath+2	No attempts yet	1s	512 MB	Judgeable
Teleport PadsEach pad cycles through a fixed list of zones with its own period; find the earliest time Hyeonuk, starting on pad 1 at coordinate 0, can reach the exit zone by riding and switching pads.	Hard8	GraphBFS+2	No attempts yet	2s	512 MB	Judgeable
Magic NecklaceFor each of the N cut positions on a circular array, fuse contiguous segments into one bead equal to their gcd so that every resulting bead is 1, and report the maximum bead count.	Hard8	MathNumber theory+2	No attempts yet	2s	512 MB	Judgeable
Kakao MoneyGiven a log of deposits and withdrawals with resulting balances, find a minimum charge unit M that is consistent with every withdrawal, or report that none exists.	Hard8	MathNumber theory+2	No attempts yet	5s	256 MB	Judgeable
ShootingsGiven non-overlapping axis-aligned rectangles and shots that are vertical or 45-degree half-lines, compute for each shot the squared total length of its intersection with all rectangles.	Hard8	GeometrySorting+2	No attempts yet	1s	512 MB	Judgeable
POPABuild a binary tree on indices with inorder order 0..N-1 and parent weights dividing child weights, using at most Q gcd-equality queries on hidden subarrays.	Hard8	Divide and conquerTree+2	No attempts yet	1s	512 MB	Judgeable
ToysFor a given n, find every total toy count m whose partitions into type-quantities number exactly n.	Hard8	Number theoryCombinatorics+2	No attempts yet	4s	512 MB	Judgeable
TrianglesFind the number of vertices of the convex hull of n points using only clockwise or counterclockwise orientation queries on triples, with a query budget.	Hard8	GeometryDivide and conquer+2	No attempts yet	2s	512 MB	Judgeable
Playoff by all the teamsCount the ways to fill in the unplayed matches of a round-robin tournament so that every team ends with the same number of wins.	Hard8	Brute forceBacktracking+2	No attempts yet	2s	512 MB	Judgeable
Equilateral Triangular FenceGiven pear trees above a road, find the shortest perimeter of an equilateral triangle with a horizontal base that encloses all but at most k trees.	Hard8	GeometryBinary search+1	No attempts yet	8s	512 MB	Judgeable
Cut It Out!Given convex polygons A and B with B strictly inside A, find the minimum total length of cuts along B's edge lines that leave exactly B.	Hard8	GeometryDynamic programming	No attempts yet	2s	512 MB	Judgeable
Zoning HousesFor each query range of houses, find the side length of the smallest axis-aligned square covering all points in the range, with the option to drop one point.	Hard8	Segment treeDivide and conquer+2	No attempts yet	2s	512 MB	Judgeable
Battle RoyaleFind the shortest path between two points inside a circle while staying outside an inner red circle, touching boundaries only.	Hard8	GeometryMath+2	No attempts yet	2s	512 MB	Judgeable
Hyper IlluminatiGiven m up to 10^16, find n >= 3 and s >= 1 such that the block count of an n-dimensional hyper-step pyramid with s steps equals m, or report impossible.	Hard8	MathNumber theory+2	No attempts yet	2s	512 MB	Judgeable
Amateur Radio NetworkSplit at least 4 points into two groups of size at least 2 minimizing the largest same-group pairwise distance, and output that diameter rounded up to 0.01.	Hard8	GeometryBinary search+2	No attempts yet	2s	512 MB	Judgeable
Fair ShareGiven n weighted points around the origin, choose a line through the origin that splits them into two half-planes, minimizing the absolute difference of the two half-plane weight sums.	Hard8	GeometrySorting+2	No attempts yet	5s	512 MB	Judgeable
Last CasinoGiven n bins, pick a ball count from 1 to 10^6 and a red, black, or white coloring that makes Alice's and Britney's win probabilities as close as possible.	Hard8	MathProbability+1	No attempts yet	2s	512 MB	Judgeable
I'm a FanFind the smallest CCW rotation angle whose swept orbit of a star-shaped polygon around the origin is a full disk.	Hard8	GeometryMath+2	No attempts yet	2s	512 MB	Judgeable
Office RelocationGiven a weighted tree with marked query and leaf-coloured vertices, compute for every marked vertex the sum of squared weighted distances to coloured leaves (mod a prime).	Hard8	TreeDynamic programming+2	No attempts yet	2s	512 MB	Judgeable
Number Theory and ApplicationsGiven two Gaussian integers up to 10^9 in each coordinate, output every greatest common divisor in lexicographic order.	Hard8	Number theoryMath+2	No attempts yet	0.2s	16 MB	Judgeable
Number Theory and Applications: RecitationGiven n up to 1e9 and v up to 100, compute the sum over i=1..n and u=1..v of Jordan's totient function modulo 1e9+7.	Hard8	Number theoryMath+2	No attempts yet	4s	512 MB	Judgeable
Peace SignFind the similarity transform (translation, rotation, uniform scale) of the first segment set that matches the most segments of the second set, counting exact matches.	Hard8	GeometryHash map+2	No attempts yet	2s	512 MB	Judgeable
Binary Tree and SequenceFind the smallest tree depth where one concatenated leaf sequence occurs at least K times under a periodic leaf pattern.	Hard8	String matchingHash map+2	No attempts yet	3s	256 MB	Judgeable
Möbius MadnessGiven N, L, and K, compute the sum over d from 1 to N of mu(L*d) times floor(N/d) to the power K, modulo 1e9+7.	Hard8	MathNumber theory+1	No attempts yet	2.5s	512 MB	Judgeable
Liar GameFor N cards (one Joker) and R rounds, compute the probability of scoring K points, times (2*N)^R, modulo 1000003.	Hard8	CombinatoricsDynamic programming+2	No attempts yet	2s	512 MB	Judgeable
Fake Plastic TreesBuild at most 125 balanced binary trees, reusing earlier trees as subtrees, so that one of them has exactly N nodes.	Hard8	TreeMath+2	No attempts yet	1s	1024 MB	Judgeable
Game on PlanePlayers alternately draw non-crossing segments between vertices of a regular N-gon, and the one who completes a convex polygon wins. Decide who should move first to force a win.	Hard8	Game theoryGeometry	No attempts yet	1s	1024 MB	Judgeable
Balcony RepairsGiven a huge R by C grid with at most 1000 blocked cells, place horizontal dominoes on free cells to maximize the count, then report that maximum and the number of ways modulo 1e9+7.	Hard8	Dynamic programmingCombinatorics+2	No attempts yet	2s	512 MB	Judgeable
Finding Tricky NumbersGiven A and K up to 10^18, find the K-th positive integer whose adjacent digits differ by at least A, and print it modulo 10^9+7.	Hard8	Dynamic programmingBinary search+2	No attempts yet	1s	512 MB	Judgeable
LazinessCut a bar of total length into given pieces with cut cost xy and minimize total cost; the cost is fixed at (sum of squares differences)/2, so just read the lengths.	Hard8	MathGreedy+1	No attempts yet	1s	512 MB	Judgeable
Build a Wall!Given a convex N-gon and query points, find for each point the triangulation that maximizes how many diagonals must be crossed to reach it from outside.	Hard8	Dynamic programmingGeometry+1	No attempts yet	2.5s	1024 MB	Judgeable
Sorting GameAfter each swap of two positions, find the minimum rounds Aizan needs to sort the permutation while Ermac delays, or -1 if Ermac can always prevent sorting.	Hard8	ArrayMath+1	No attempts yet	1s	1024 MB	Judgeable
We Live Forgetting the TruthGiven a fixed n-vertex graph, find min and max pairs revealed in a random pair order before an online decision rule can prove it connected or not.	Hard8	GraphCombinatorics+2	No attempts yet	1s	1024 MB	Judgeable
SlalomCount the right-or-up paths from (1, 1) to (n, m) that avoid rectangular obstacles, where each obstacle is passed on either side, modulo 10^9 + 7.	Hard8	Dynamic programmingCombinatorics+1	No attempts yet	2s	512 MB	Judgeable
Red-Black TreeCount the colorings of a binary tree's vertices that satisfy the red-black rules, with fake leaves added at missing children, modulo 1e9+7.	Hard8	Dynamic programmingTree+1	No attempts yet	3s	512 MB	Judgeable
Nice ReportFor each vertex of a directed graph, estimate how many vertices it can reach, with each estimate within a factor of two of the exact count.	Hard8	GraphProbability+1	No attempts yet	5s	512 MB	Judgeable
Small NumbersGiven positive integers a and b, reduce their sum using common-divisor divisions and factor moves between them. Report the minimum sum and one minimizing pair.	Hard8	Number theoryMath+2	No attempts yet	2s	512 MB	Judgeable
Folding the FigureGiven a connected polyomino of n cells that results from folding a k-cell polyomino along one grid line, reconstruct any valid original k-cell figure and the fold line.	Hard8	ImplementationGeometry+2	No attempts yet	2s	512 MB	Judgeable
Eleventh BirthdayCount permutations of cards whose concatenation is divisible by 11, where cards count as distinct and equal numbers still give separate permutations.	Hard8	Dynamic programmingCombinatorics+1	No attempts yet	4s	512 MB	Judgeable
Eating Everything EfficientlyFollow a directed path from stall 0 and choose stalls to eat with halves 1, 1/2, 1/4, ..., maximizing the weighted satisfaction.	Hard8	Dynamic programmingGraph+1	No attempts yet	3s	512 MB	Judgeable
KALLAX ConstructionGiven a chain of companies that each combine previous pack sizes to reach target sizes, find the smallest advertised pack guaranteeing at least B bolts.	Hard8	Dynamic programmingGreedy+2	No attempts yet	1s	512 MB	Judgeable
Harry the HamsterOn a directed weighted graph, Max and Min alternately choose the outgoing edge, Max moving first; compute the total travel time from s to t under optimal play.	Hard8	Game theoryDynamic programming+2	No attempts yet	3s	512 MB	Judgeable
Intergalactic BiddingGiven up to 1000 bidders with huge distinct bids and a huge target s, find every bidder contained in a subset whose sum is exactly s.	Hard8	GreedySorting+2	No attempts yet	2s	512 MB	Judgeable
King's ColorsCount proper colorings of a rooted tree with n nodes using exactly k labeled colors, modulo 1000000007, where every color must appear at least once.	Hard8	TreeDynamic programming+2	No attempts yet	1s	512 MB	Judgeable
Broken WatchPlace three hands at distinct markings, form a triangle from their tips, and count the center-containing triangles modulo 2^64.	Hard8	MathCombinatorics+2	No attempts yet	1s	512 MB	Judgeable
Moving FurnitureGiven 4N leg hollow coordinates from N square tables, find the total area of all tables, which the points alone determine.	Hard8	GeometryMath	No attempts yet	2s	512 MB	Judgeable