Math and counting

Number theory, combinatorics, and geometry

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Still being built. Things may change

Total results13,153 problems

Cheating or Not
Hard9
Combinatorics, Probability+2
No attempts yet
Time limit
1s
Memory limit
128 MB
Judgeable
Once You Shoot, You Cannot Stop
Hard9
Combinatorics, Dynamic programming+1
No attempts yet
Time limit
1s
Memory limit
128 MB
Judgeable
Protein Identification
Hard9
Dynamic programming, Greedy+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
DNA Sequences
Hard9
Dynamic programming, Combinatorics+2
No attempts yet
Time limit
1s
Memory limit
128 MB
Judgeable
Nice Prefixes
Hard9
Dynamic programming, Combinatorics+2
No attempts yet
Time limit
1s
Memory limit
128 MB
Judgeable
Asteroid Rangers
Hard9
Minimum spanning tree, Geometry+2
No attempts yet
Time limit
1s
Memory limit
128 MB
Judgeable
Old Factory Plumbing
Hard9
Graph, Minimum spanning tree+2
No attempts yet
Time limit
5s
Memory limit
128 MB
Judgeable
Affine Mess
Hard9
Geometry, Math+2
No attempts yet
Time limit
2s
Memory limit
128 MB
Judgeable
Mummy Madness
Hard9
Binary search, Geometry+2
No attempts yet
Time limit
6s
Memory limit
128 MB
Judgeable
Spellcasting
Hard9
Math, Greedy+2
No attempts yet
Time limit
1s
Memory limit
128 MB
Judgeable
Cubic Rube
Hard9
Implementation, Geometry+2
No attempts yet
Time limit
1s
Memory limit
128 MB
Judgeable
A to Z Numerals
Hard9
Greedy, Math+2
No attempts yet
Time limit
1s
Memory limit
128 MB
Judgeable
Guard
Hard9
Geometry, Binary search+2
No attempts yet
Time limit
1s
Memory limit
128 MB
Judgeable
Triangle Cuts
Hard9
Geometry, Simulation+2
No attempts yet
Time limit
1s
Memory limit
128 MB
Judgeable
Potholes
Hard9
Geometry, Sorting+2
No attempts yet
Time limit
1s
Memory limit
128 MB
Judgeable
Congruent Partition of Chocolate
Hard9
Brute force, DFS+2
No attempts yet
Time limit
30s
Memory limit
128 MB
Judgeable
Twirl Around
Hard9
Geometry, Simulation+2
No attempts yet
Time limit
1s
Memory limit
128 MB
Judgeable
Around the Track
Hard9
Graph, Dynamic programming+2
No attempts yet
Time limit
1s
Memory limit
128 MB
Judgeable
ASCII Art
Hard9
Geometry, Implementation+2
No attempts yet
Time limit
1s
Memory limit
128 MB
Judgeable
Two Circles in a Convex Polygon
Hard9
Geometry, Binary search+2
No attempts yet
Time limit
4s
Memory limit
128 MB
Judgeable
Giant Cover
Hard9
Geometry, Math+2
No attempts yet
Time limit
1s
Memory limit
128 MB
Judgeable
Tables
Hard9
Dynamic programming, Geometry+2
No attempts yet
Time limit
1s
Memory limit
128 MB
Judgeable
Farmer John
Hard9
Geometry, Graph+2
No attempts yet
Time limit
1s
Memory limit
128 MB
Judgeable
Archery
Hard9
Math, Simulation+2
No attempts yet
Time limit
1s
Memory limit
128 MB
Judgeable
Success Probability of the Card-Pile Game
Hard9
Probability, Combinatorics+2
No attempts yet
Time limit
1s
Memory limit
128 MB
Judgeable
Apparent Twin Primes
Hard9
Number theory, Math+2
No attempts yet
Time limit
1s
Memory limit
128 MB
Judgeable
Ballroom Lights
Hard9
Geometry, Math+2
No attempts yet
Time limit
1s
Memory limit
128 MB
Judgeable
Not Too Convex Hull
Hard9
Dynamic programming, Geometry+2
No attempts yet
Time limit
1s
Memory limit
128 MB
Judgeable
The Ideal City
Hard9
Graph, BFS+2
No attempts yet
Time limit
1s
Memory limit
256 MB
Judgeable
Hyperspace Routes
Hard9
Shortest path, Graph+2
No attempts yet
Time limit
5s
Memory limit
64 MB
Judgeable
Tropical Garden
Hard9
Graph, Simulation+2
No attempts yet
Time limit
5s
Memory limit
256 MB
Judgeable
Tied Down
Hard9
Geometry, Graph+2
No attempts yet
Time limit
1s
Memory limit
128 MB
Judgeable
Simplifying the Farm
Hard9
Minimum spanning tree, Union-find+2
No attempts yet
Time limit
1s
Memory limit
128 MB
Judgeable
Taking Turns
Hard9
Dynamic programming, Greedy+2
No attempts yet
Time limit
1s
Memory limit
128 MB
Judgeable
Cow Hopscotch
Hard9
Dynamic programming, Segment tree+2
No attempts yet
Time limit
1s
Memory limit
128 MB
Judgeable
Largest Fence
Hard9
Geometry, Dynamic programming+2
No attempts yet
Time limit
2s
Memory limit
128 MB
Judgeable
Casting
Hard9
Geometry, Two pointers+2
No attempts yet
Time limit
1s
Memory limit
128 MB
Judgeable
Winmine (Minesweeper)
Hard9
Dynamic programming, Graph+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Servers
Hard9
Graph, Shortest path+2
No attempts yet
Time limit
1s
Memory limit
128 MB
Judgeable
Pendulum
Hard9
Geometry, Simulation+2
No attempts yet
Time limit
1s
Memory limit
128 MB
Judgeable
Cyclic Antimonotonic Permutations
Hard9
Combinatorics, Math+2
No attempts yet
Time limit
2s
Memory limit
128 MB
Judgeable
Alea iacta est
Hard9
Dynamic programming, Simulation+2
No attempts yet
Time limit
2s
Memory limit
128 MB
Judgeable
The Herbalists' Village
Hard9
Graph, Geometry+2
No attempts yet
Time limit
1s
Memory limit
128 MB
Judgeable
Downpayment
Hard9
Dynamic programming, Greedy+2
No attempts yet
Time limit
1s
Memory limit
256 MB
Judgeable
The Lights Going On and Off
Hard9
Bit manipulation, Math+2
No attempts yet
Time limit
1s
Memory limit
128 MB
Judgeable
Landing
Hard9
Geometry, Combinatorics+2
No attempts yet
Time limit
1s
Memory limit
128 MB
Judgeable
Move that Mouse AGAIN
Hard9
Segment tree, Geometry+2
No attempts yet
Time limit
3s
Memory limit
128 MB
Judgeable
Fast Food
Hard9
Geometry, Divide and conquer+2
No attempts yet
Time limit
1s
Memory limit
128 MB
Judgeable
Checker Board
Hard9
Game theory, Greedy+2
No attempts yet
Time limit
1s
Memory limit
128 MB
Judgeable
Joy of Mobile Routing
Hard9
Graph, Shortest path+2
No attempts yet
Time limit
1s
Memory limit
128 MB
Judgeable
Deformed Wheel
Hard9
Geometry, Simulation+2
No attempts yet
Time limit
1s
Memory limit
128 MB
Judgeable
Parallel Expectations
Hard9
Probability, Dynamic programming+1
No attempts yet
Time limit
1s
Memory limit
128 MB
Judgeable
Find the Border
Hard9
Geometry, Implementation+2
No attempts yet
Time limit
2s
Memory limit
128 MB
Judgeable
Illumination
Hard9
Geometry, Combinatorics+2
No attempts yet
Time limit
1s
Memory limit
128 MB
Judgeable
Exam
Hard9
Dynamic programming, String matching+2
No attempts yet
Time limit
2s
Memory limit
128 MB
Judgeable
Jogger
Hard9
Tree, Graph+2
No attempts yet
Time limit
1s
Memory limit
128 MB
Judgeable
Structural Isomers
Hard9
Dynamic programming, Combinatorics+2
No attempts yet
Time limit
1s
Memory limit
128 MB
Judgeable
Juggle with Criteria
Hard9
Combinatorics, Dynamic programming+2
No attempts yet
Time limit
1s
Memory limit
128 MB
Judgeable
Markov Trains
Hard9
Dynamic programming, Probability+1
No attempts yet
Time limit
1s
Memory limit
128 MB
Judgeable
Mirror Trap
Hard9
Math, Number theory+2
No attempts yet
Time limit
3s
Memory limit
512 MB
Judgeable
Dextrogyrate Camel
Hard9
Geometry, Dynamic programming+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Save the Dinosaurs
Hard9
Geometry, Sorting+2
No attempts yet
Time limit
1s
Memory limit
128 MB
Judgeable
Bank
Hard9
Greedy, Math+2
No attempts yet
Time limit
1s
Memory limit
128 MB
Judgeable
Sleepwalker
Hard9
Recursion, Divide and conquer+2
No attempts yet
Time limit
1s
Memory limit
128 MB
Judgeable
Ice rink
Hard9
BFS, Graph+2
No attempts yet
Time limit
1s
Memory limit
128 MB
Judgeable
Trees
Hard9
Array, Math+2
No attempts yet
Time limit
1s
Memory limit
128 MB
Judgeable
Axes of Symmetry
Hard9
String matching, Geometry+2
No attempts yet
Time limit
1s
Memory limit
128 MB
Judgeable
Toll
Hard9
Graph, Math
No attempts yet
Time limit
1s
Memory limit
128 MB
Judgeable
Isles in a Triangular Grid
Hard9
Geometry, Brute force+2
No attempts yet
Time limit
1s
Memory limit
128 MB
Judgeable
Island
Hard9
Graph, Shortest path+1
No attempts yet
Time limit
1s
Memory limit
128 MB
Judgeable
Ones
Hard9
Math, Combinatorics+2
No attempts yet
Time limit
3s
Memory limit
512 MB
Judgeable
Garbage
Hard9
Graph, DFS+2
No attempts yet
Time limit
1s
Memory limit
128 MB
Judgeable
Ski Rental
Hard9
Segment tree, Geometry+1
No attempts yet
Time limit
1s
Memory limit
128 MB
Judgeable
Binary Knockout
Hard9
Game theory, Math+1
No attempts yet
Time limit
1s
Memory limit
128 MB
Judgeable
Spider
Hard9
Geometry, Implementation+1
No attempts yet
Time limit
1s
Memory limit
128 MB
Judgeable
Fragments
Hard9
String matching, Dynamic programming+2
No attempts yet
Time limit
1s
Memory limit
128 MB
Judgeable
Army Training
Hard9
Geometry, Combinatorics+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Blindfold Nim
Hard9
Dynamic programming, Combinatorics+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Diamond
Hard9
Geometry, Brute force+1
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Fishes
Hard9
Graph, Geometry+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Programming Contest
Hard9
Greedy, Math+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Watchmen
Hard9
Geometry, Graph+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Questions
Hard9
Brute force, Simulation+2
No attempts yet
Time limit
1s
Memory limit
128 MB
Judgeable
Dragon Milkdrinker
Hard9
Probability, Math+2
No attempts yet
Time limit
1s
Memory limit
128 MB
Judgeable
Video Poker
Hard9
Brute force, Combinatorics+2
No attempts yet
Time limit
1s
Memory limit
128 MB
Judgeable
Microchips
Hard9
Graph, Number theory+2
No attempts yet
Time limit
1s
Memory limit
128 MB
Judgeable
Fibonacci Word
Hard9
String, Dynamic programming+2
No attempts yet
Time limit
1s
Memory limit
128 MB
Judgeable
Manhunt
Hard9
Graph, BFS+2
No attempts yet
Time limit
1s
Memory limit
128 MB
Judgeable
Minimum brackets
Hard9
String, Implementation+2
No attempts yet
Time limit
1s
Memory limit
128 MB
Judgeable
Palindromic Equivalence
Hard9
String, String matching+2
No attempts yet
Time limit
1s
Memory limit
128 MB
Judgeable
BARMAN
Hard9
Number theory, Math+2
No attempts yet
Time limit
1s
Memory limit
128 MB
Judgeable
Sets
Hard9
Math, Number theory+2
No attempts yet
Time limit
1s
Memory limit
128 MB
Judgeable
The Most Valuable Tower
Hard9
Number theory, Sorting+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Sequence
Hard9
Math, Binary search+1
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Land Tax
Hard9
Divide and conquer, Geometry+2
No attempts yet
Time limit
1s
Memory limit
128 MB
Judgeable
Plot of Land
Hard9
Geometry, Divide and conquer+1
No attempts yet
Time limit
1s
Memory limit
128 MB
Judgeable
Crystal
Hard9
Math, Geometry+2
No attempts yet
Time limit
1s
Memory limit
128 MB
Judgeable
Multiplication
Hard9
Number theory, Math+1
No attempts yet
Time limit
5s
Memory limit
128 MB
Judgeable
Roof
Hard9
Geometry
No attempts yet
Time limit
1s
Memory limit
128 MB
Judgeable
Aquarium Drainage
Hard9
Geometry, Sorting+2
No attempts yet
Time limit
1s
Memory limit
128 MB
Judgeable

Title	Level	Topics	Solved	Time limit	Memory limit	Judge
Cheating or NotGiven g groups, seeded teams, pots, and confederation constraints, compute the average total strength of a given team's group opponents over all valid draws.	Hard9	CombinatoricsProbability+2	No attempts yet	1s	128 MB	Judgeable
Once You Shoot, You Cannot StopGiven board dimensions and bead counts per color, arrange beads and clear groups to maximize the sum of squared group sizes.	Hard9	CombinatoricsDynamic programming+1	No attempts yet	1s	128 MB	Judgeable
Protein IdentificationGiven peaks from an imperfect MS2 experiment, find the minimum number of noise peaks over all P/Q proteins whose total mass equals the largest peak.	Hard9	Dynamic programmingGreedy+2	No attempts yet	1s	512 MB	Judgeable
DNA SequencesGiven a DNA pattern with wildcards and a rank R, find the R-th lexicographic matching string that decomposes into at most K non-decreasing runs.	Hard9	Dynamic programmingCombinatorics+2	No attempts yet	1s	128 MB	Judgeable
Nice PrefixesCount length-L strings over a K-letter alphabet where every prefix keeps all symbol counts within 2 of each other, modulo 1e9+7, with L up to 1e18.	Hard9	Dynamic programmingCombinatorics+2	No attempts yet	1s	128 MB	Judgeable
Asteroid RangersGiven n moving points, count how many times the minimum spanning tree over all future times changes, plus the initial build.	Hard9	Minimum spanning treeGeometry+2	No attempts yet	1s	128 MB	Judgeable
Old Factory PlumbingChoose a water height so the flooded region avoids open holes unless plugged or piped, minimizing pipe distances plus 0.5 per plug.	Hard9	GraphMinimum spanning tree+2	No attempts yet	5s	128 MB	Judgeable
Affine MessGiven three integer start points and three integer end points, decide whether a snapped integer rotation, integer scaling, and integer translation map one set onto the other, and if so whether all such maps agree on the whole plane.	Hard9	GeometryMath+2	No attempts yet	2s	128 MB	Judgeable
Mummy MadnessGiven mummy start positions on an infinite grid, compute how many time steps a fleeing player survives when both sides move on a king-step grid.	Hard9	Binary searchGeometry+2	No attempts yet	6s	128 MB	Judgeable
SpellcastingGiven element costs, power rates, and a support tree, find the minimum time for the spell's total power to reach the target, given starting energy and continuous accumulation.	Hard9	MathGreedy+2	No attempts yet	1s	128 MB	Judgeable
Cubic RubeGiven two connected 5x5 height maps of unit cubes, decide whether the pieces can be rotated and translated in 3D to assemble a full 5x5x5 cube.	Hard9	ImplementationGeometry+2	No attempts yet	1s	128 MB	Judgeable
A to Z NumeralsConvert each positive integer up to 7e17 into its unique A to Z numeral, where letters a to r and A to R stand for powers of ten and their quintuples.	Hard9	GreedyMath+2	No attempts yet	1s	128 MB	Judgeable
GuardPlace g guards on segments so every valuable point is seen, minimizing the largest value-times-distance risk, or report too few guards.	Hard9	GeometryBinary search+2	No attempts yet	1s	128 MB	Judgeable
Triangle CutsGiven a large triangle and four small triangles as angle triples in clockwise order, decide whether three straight cuts can produce exactly those four pieces.	Hard9	GeometrySimulation+2	No attempts yet	1s	128 MB	Judgeable
PotholesPlace a straight rope across a rectangular lot without crossing any pothole so the total pothole area is split as evenly as possible, with tie-breaking rules.	Hard9	GeometrySorting+2	No attempts yet	1s	128 MB	Judgeable
Congruent Partition of ChocolateGiven a connected polyomino of at most 36 unit squares, decide whether it splits into two connected pieces that are congruent under rotation, reflection, and translation.	Hard9	Brute forceDFS+2	No attempts yet	30s	128 MB	Judgeable
Twirl AroundA bar inside a simple polygon rotates clockwise, pivoting on the wall whenever a new contact point appears; report the final position of one end, or the position when it jams.	Hard9	GeometrySimulation+2	No attempts yet	1s	128 MB	Judgeable
Around the TrackFind the Eulerian circuit of a planar-ish graph whose total turning cost is minimized, where each degree-4 node requires choosing how to pair its incident edges.	Hard9	GraphDynamic programming+2	No attempts yet	1s	128 MB	Judgeable
ASCII ArtRender triangles with ASCII characters, projecting 3D vertices through a camera onto an S by S screen grid with depth-based visibility.	Hard9	GeometryImplementation+2	No attempts yet	1s	128 MB	Judgeable
Two Circles in a Convex PolygonFind the largest radius R so that two non-overlapping circles of radius R fit inside a given convex polygon with N vertices.	Hard9	GeometryBinary search+2	No attempts yet	4s	128 MB	Judgeable
Giant CoverGiven axis-aligned boxes on a rectangular campus, find the minimum surface area of a convex solid above the ground that covers all boxes and is anchored to the campus boundary.	Hard9	GeometryMath+2	No attempts yet	1s	128 MB	Judgeable
TablesCount the tilings of a polyiamond on a triangular grid by isosceles trapezoids made of three unit triangles, given the shape's boundary as a sequence of grid nodes.	Hard9	Dynamic programmingGeometry+2	No attempts yet	1s	128 MB	Judgeable
Farmer JohnGiven start, goal, and up to 100 disjoint line-segment fences, find the shortest path that cannot cross any fence, touching allowed, and print the length to six decimals.	Hard9	GeometryGraph+2	No attempts yet	1s	128 MB	Judgeable
ArcheryPlace Seungwon into one of 2N gaps so that after R tournament rounds his final target number is minimized, breaking ties by the largest starting target.	Hard9	MathSimulation+2	No attempts yet	1s	128 MB	Judgeable
Success Probability of the Card-Pile GameGiven n decks of k cards each shuffled into n piles, find the probability that the follow-the-number drawing game succeeds within m restarts, printed to r decimals.	Hard9	ProbabilityCombinatorics+2	No attempts yet	1s	128 MB	Judgeable
Apparent Twin PrimesFor each query (n, t), find the smallest n-digit p such that neither p nor p+2 has a prime factor at most t.	Hard9	Number theoryMath+2	No attempts yet	1s	128 MB	Judgeable
Ballroom LightsGiven point lightbulbs and disjoint circular columns inside a rectangle, compute the total length of the wall perimeter that some lightbulb can reach with a straight, unblocked ray.	Hard9	GeometryMath+2	No attempts yet	1s	128 MB	Judgeable
Not Too Convex HullPartition the nails into B convex polygonal groups, all sharing the origin nail, minimizing the total covered area, with the origin strictly inside the global hull.	Hard9	Dynamic programmingGeometry+2	No attempts yet	1s	128 MB	Judgeable
The Ideal CityGiven N cells forming a simply connected polyomino with no holes, compute the sum of grid shortest-path distances over all pairs, modulo 1e9.	Hard9	GraphBFS+2	No attempts yet	1s	256 MB	Judgeable
Hyperspace RoutesFor each query, find every possible value of the shortest A-to-B path length as the shared hyperspace edge weight x ranges over the positive integers, then report the count and sum, or inf when unbounded.	Hard9	Shortest pathGraph+2	No attempts yet	5s	64 MB	Judgeable
Tropical GardenCount starting ponds whose deterministic non-backtracking walk (prefer the most beautiful unused-at-previous-step walkway) reaches pond P after exactly K steps, for many K.	Hard9	GraphSimulation+2	No attempts yet	5s	256 MB	Judgeable
Tied DownGiven a closed polygonal rope loop and up to 10 collinear posts on its left, find the smallest set of posts to remove so the rope can be pulled free to the right.	Hard9	GeometryGraph+2	No attempts yet	1s	128 MB	Judgeable
Simplifying the FarmGiven a weighted graph where each edge length occurs at most three times, find the minimum spanning tree weight and count distinct minimum spanning trees modulo 1e9+7.	Hard9	Minimum spanning treeUnion-find+2	No attempts yet	1s	128 MB	Judgeable
Taking TurnsTwo players alternately take bales from a line, skipping any number of earlier bales; each plays optimally and takes the leftmost optimal bale. Find each player's total.	Hard9	Dynamic programmingGreedy+2	No attempts yet	1s	128 MB	Judgeable
Cow HopscotchChoose an outbound path of jumps (each at most K squares) and a return path that only lands on squares one less than an outbound square, maximizing collected values.	Hard9	Dynamic programmingSegment tree+2	No attempts yet	1s	128 MB	Judgeable
Largest FenceGiven N grid points with no three collinear, find the size of the largest subset whose points form the vertices of a convex polygon.	Hard9	GeometryDynamic programming+2	No attempts yet	2s	128 MB	Judgeable
CastingFor a convex polygon, count the vertex pairs whose connecting line splits it into two parts that can each be pulled out by translation.	Hard9	GeometryTwo pointers+2	No attempts yet	1s	128 MB	Judgeable
Winmine (Minesweeper)Count the ways to place the remaining mines on the unrevealed squares so that every revealed number matches its adjacent mine count, modulo 1000003.	Hard9	Dynamic programmingGraph+2	No attempts yet	2s	512 MB	Judgeable
ServersGiven a weighted connected graph with server ranks at most 10, count for each server the vertices W such that no vertex closer or equally close has a larger rank, then sum.	Hard9	GraphShortest path+2	No attempts yet	1s	128 MB	Judgeable
PendulumSimulate an idealized pendulum swinging around point hooks on a wall and print the length of the periodic orbit it eventually settles into.	Hard9	GeometrySimulation+2	No attempts yet	1s	128 MB	Judgeable
Cyclic Antimonotonic PermutationsFor each n, output the lexicographically smallest permutation of 1 to n that is both antimonotonic (every middle element is a local min or max) and a single cycle when read as a pointer mapping.	Hard9	CombinatoricsMath+2	No attempts yet	2s	128 MB	Judgeable
Alea iacta estGiven a linear congruential generator, compute the maximum Yahtzee score over eleven rounds by choosing which dice to keep and which combination to score each round.	Hard9	Dynamic programmingSimulation+2	No attempts yet	2s	128 MB	Judgeable
The Herbalists' VillageGiven a friendship graph, decide whether it has a planar straight-line drawing where every vertex reaches infinity without crossing an edge.	Hard9	GraphGeometry+2	No attempts yet	1s	128 MB	Judgeable
DownpaymentGiven future monthly interest rates for m mortgage plans, binding periods, and switch penalties, find the schedule of plan choices that minimizes the total money paid, with debt rounded down each month.	Hard9	Dynamic programmingGreedy+2	No attempts yet	1s	256 MB	Judgeable
The Lights Going On and OffGiven a light grid, pushing the button beside row k XORs it with the row above; count how many distinct bottom-row patterns can result from any subset and order of pushes.	Hard9	Bit manipulationMath+2	No attempts yet	1s	128 MB	Judgeable
LandingGiven up to 100000 integer points, find the largest circle whose boundary passes through at least three points and whose interior contains none, and output R^2 as a reduced fraction.	Hard9	GeometryCombinatorics+2	No attempts yet	1s	128 MB	Judgeable
Move that Mouse AGAINGiven up to 50,000 axis-aligned rectangles in a fixed bottom-to-top stacking order, process 50,000 point clicks, printing the topmost window at each point and moving it to the top of the stack.	Hard9	Segment treeGeometry+2	No attempts yet	3s	128 MB	Judgeable
Fast FoodGiven up to 50 points in a 10 by 10 square, compute for each point the area of its Voronoi cell within the square and report the percentage, rounded to nearest with halves up.	Hard9	GeometryDivide and conquer+2	No attempts yet	1s	128 MB	Judgeable
Checker BoardEach row holds at most one checker per color; players slide their pieces along rows and the one who cannot move loses. Decide whether White wins, Black wins, or the game can run forever.	Hard9	Game theoryGreedy+2	No attempts yet	1s	128 MB	Judgeable
Joy of Mobile RoutingGiven grid building heights and antennas, find the shortest path from a start to a destination intersection where every visited intersection has line-of-sight to some antenna.	Hard9	GraphShortest path+2	No attempts yet	1s	128 MB	Judgeable
Deformed WheelSimulate a convex polygon rolling down a piecewise-linear hill until it comes to rest, and print the final position of its center of gravity.	Hard9	GeometrySimulation+2	No attempts yet	1s	128 MB	Judgeable
Parallel ExpectationsGiven two programs run by randomly interleaving their instructions, find the expected final value of every shared variable.	Hard9	ProbabilityDynamic programming+1	No attempts yet	1s	128 MB	Judgeable
Find the BorderGiven a closed self-intersecting polyline, count the vertices of the border of its interior, the outer boundary enclosing all bounded regions.	Hard9	GeometryImplementation+2	No attempts yet	2s	128 MB	Judgeable
IlluminationAssign N fixed angular directions to N sources so their wedges cover the plane and the sum of projections is minimized, tie-broken lexicographically.	Hard9	GeometryCombinatorics+2	No attempts yet	1s	128 MB	Judgeable
ExamGiven each student's distribution over exam scores, find the exact probability that the sequence of European marks from all students avoids every listed unpleasant string.	Hard9	Dynamic programmingString matching+2	No attempts yet	2s	128 MB	Judgeable
JoggerGiven the distance matrix of a tree with houses as leaves, find the leaf pair whose weighted travel time (distance times r plus internal nodes crossed times t) is largest.	Hard9	TreeGraph+2	No attempts yet	1s	128 MB	Judgeable
Structural IsomersCount the number of distinct alkane carbon skeletons (free trees in which every node has degree at most 4) with n carbon atoms.	Hard9	Dynamic programmingCombinatorics+2	No attempts yet	1s	128 MB	Judgeable
Juggle with CriteriaFor each of n five-symbol relation patterns (<, =, >) and a fixed length l, decide whether two permutations of length l exist whose inversion count, local inversions, LIS, longest increasing substring, and fixed points match that exact pattern.	Hard9	CombinatoricsDynamic programming+2	No attempts yet	1s	128 MB	Judgeable
Markov TrainsFind the station list maximizing the chance of arriving by a deadline when each train may be cancelled and the traveler waits for the next one after a cancellation.	Hard9	Dynamic programmingProbability+1	No attempts yet	1s	128 MB	Judgeable
Mirror TrapFor each box [-x,x]x[-y,y]x[-z,z], find the maximum Manhattan distance a laser at the origin can travel before returning to the origin, avoiding edges and vertices.	Hard9	MathNumber theory+2	No attempts yet	3s	512 MB	Judgeable
Dextrogyrate CamelFind the longest closed camel route that starts at oasis 1 heading to oasis 2, always turns right by at most 180 degrees at each oasis, never crosses itself, and visits the most distinct oases.	Hard9	GeometryDynamic programming+2	No attempts yet	1s	512 MB	Judgeable
Save the DinosaursFor each vacant point, add it to the existing set and report the area protected by the soldiers (the region where every move gets closer to some soldier).	Hard9	GeometrySorting+2	No attempts yet	1s	128 MB	Judgeable
BankFind the lexicographically smallest four-currency reserve vector that lets a bank serve all clients in some order, where serving client i requires its remaining need in all four currencies to be covered at once.	Hard9	GreedyMath+2	No attempts yet	1s	128 MB	Judgeable
SleepwalkerA self-similar walk on a 3^k by 3^k grid is defined by a recursive rewrite; given a starting tile on the walk and a hole tile, find the number of steps until the walk reaches the hole.	Hard9	RecursionDivide and conquer+2	No attempts yet	1s	128 MB	Judgeable
Ice rinkA skater slides in straight lines across a square rink with rectilinear obstacles, stopping only at walls, and must reach the finish point in the fewest slides.	Hard9	BFSGraph+2	No attempts yet	1s	128 MB	Judgeable
TreesFor each tree, find the smallest adjacent-difference sum reachable by either keeping the row or swapping that tree with one other tree.	Hard9	ArrayMath+2	No attempts yet	1s	128 MB	Judgeable
Axes of SymmetryFor each simple polygon, count its axes of symmetry; n can reach 100000, so the check must run in near-linear time.	Hard9	String matchingGeometry+2	No attempts yet	1s	128 MB	Judgeable
TollEach selected town must charge on exactly one incident road, and no road may be charged by both endpoints. Maximize selected towns in a general graph, not necessarily the whole graph.	Hard9	GraphMath	No attempts yet	1s	128 MB	Judgeable
Isles in a Triangular GridEnumerate all non-congruent triangular-grid isles of up to ten triangles, canonicalizing each by the lexicographically smallest clockwise boundary-turn word.	Hard9	GeometryBrute force+2	No attempts yet	1s	128 MB	Judgeable
IslandGiven a convex polygon with towns on its vertices, all diagonals and sides drawn, and some segments blocked, find the shortest path from vertex n to vertex 1 using roads and their crossings.	Hard9	GraphShortest path+1	No attempts yet	1s	128 MB	Judgeable
OnesGiven run lengths of n in binary, output run lengths of the binary form of sks(n), the total UFO count over 1 to n.	Hard9	MathCombinatorics+2	No attempts yet	3s	512 MB	Judgeable
GarbageEach street needs its state flipped or not; a route is a simple cycle, and driving a street flips it. Find the minimum total length of cycles whose symmetric difference equals the set of streets needing a flip.	Hard9	GraphDFS+2	No attempts yet	1s	128 MB	Judgeable
Ski RentalGiven daily snowfall amounts with point updates, answer queries asking for the maximum average snowfall over a consecutive run starting at a given day, reported as an irreducible fraction.	Hard9	Segment treeGeometry+1	No attempts yet	1s	128 MB	Judgeable
Binary KnockoutA coin game on a line: each coin may double its position or move one step right; the player unable to move loses. Find the k-th value of n where the second player wins.	Hard9	Game theoryMath+1	No attempts yet	1s	128 MB	Judgeable
SpiderA walk on an infinite regular seven-legged web is given as turn directions; count the web nodes strictly inside the closed polygon it traces.	Hard9	GeometryImplementation+1	No attempts yet	1s	128 MB	Judgeable
FragmentsCount how many times each digit string appears as a contiguous substring across the decimal forms of all numbers in a union of disjoint integer intervals up to 10^18.	Hard9	String matchingDynamic programming+2	No attempts yet	1s	128 MB	Judgeable
Army TrainingGiven n points with no three collinear, answer m queries, each a simple clockwise polygon on those points, counting the points strictly inside it.	Hard9	GeometryCombinatorics+2	No attempts yet	2s	512 MB	Judgeable
Blindfold NimEach stack size is uniform on [0, a_i]; compute the probability that the first player wins a game of Nim with hidden positions where a player who overshoots a stack loses at once.	Hard9	Dynamic programmingCombinatorics+2	No attempts yet	2s	512 MB	Judgeable
DiamondGiven a convex polyhedron, choose one plane cut so that the two resulting pieces have the largest combined number of faces.	Hard9	GeometryBrute force+1	No attempts yet	2s	512 MB	Judgeable
FishesGroup recorded closed routes into the fewest fish, where two routes can follow on consecutive days if the start cells touch and every point is visible 24 hours earlier.	Hard9	GraphGeometry+2	No attempts yet	2s	512 MB	Judgeable
Programming ContestGiven each participant's skill per topic, decide whether we can choose n tasks (topic and difficulty) so Byteman is the unique winner under solve-count then points ranking.	Hard9	GreedyMath+2	No attempts yet	2s	512 MB	Judgeable
WatchmenCount, for each city gutter, how many Palace gutters a walker can reach while dodging rotating watchers' lines of sight.	Hard9	GeometryGraph+2	No attempts yet	2s	512 MB	Judgeable
QuestionsSimulate a logic puzzle where princes and a sorcerer reason about a system of variable constraints over time; answer what each prince or the sorcerer knows.	Hard9	Brute forceSimulation+2	No attempts yet	1s	128 MB	Judgeable
Dragon MilkdrinkerCompute the probability that the sum of n independent uniform [m, M] yields is strictly less than h, printed truncated to d decimals.	Hard9	ProbabilityMath+2	No attempts yet	1s	128 MB	Judgeable
Video PokerFor a given video poker payout table, count how many of the 2,598,960 dealt hands make the optimal expected-value strategy discard exactly 0, 1, 2, 3, 4, and 5 cards.	Hard9	Brute forceCombinatorics+2	No attempts yet	1s	128 MB	Judgeable
MicrochipsCount directed walks whose edge-impedance product equals I, allowing repeated vertices and edges, and report infinity when infinitely many such walks exist.	Hard9	GraphNumber theory+2	No attempts yet	1s	128 MB	Judgeable
Fibonacci WordCount occurrences of a given binary pattern in the Fibonacci word F_m and count distinct subwords occurring at least that many times, mod 20062006, with m up to 1e9.	Hard9	StringDynamic programming+2	No attempts yet	1s	128 MB	Judgeable
ManhuntGiven a connected undirected graph where the bandit moves to a different city each night, find the minimum number of days for a search schedule that guarantees capture, or report impossibility.	Hard9	GraphBFS+2	No attempts yet	1s	128 MB	Judgeable
Minimum bracketsGiven an arithmetic template with holes, delete as many brackets as possible while keeping the same value for every valid assignment of real numbers to the holes.	Hard9	StringImplementation+2	No attempts yet	1s	128 MB	Judgeable
Palindromic EquivalenceCount words of the same length that have palindromic substrings at exactly the same positions as the given word.	Hard9	StringString matching+2	No attempts yet	1s	128 MB	Judgeable
BARMANGiven orders m_i of hidden values modulo a hidden n, choose up to 2k range-multiply operations to maximize the worst-case guaranteed order of the final sum.	Hard9	Number theoryMath+2	No attempts yet	1s	128 MB	Judgeable
SetsGiven n arithmetic-progression sets of multiples of d_i, count elements in their union that share no prime factor with m.	Hard9	MathNumber theory+2	No attempts yet	1s	128 MB	Judgeable
The Most Valuable TowerFind the largest sum any single tower can reach by swapping top segments between towers of different heights.	Hard9	Number theorySorting+2	No attempts yet	1s	512 MB	Judgeable
SequenceFind the nth term of the nondecreasing sequence where each k appears exactly as many times as the kth term.	Hard9	MathBinary search+1	No attempts yet	1s	512 MB	Judgeable
Land TaxChoose a non-empty contiguous row and column range that maximizes combined row and column payments weighted by heights and widths.	Hard9	Divide and conquerGeometry+2	No attempts yet	1s	128 MB	Judgeable
Plot of LandGiven up to 3000 pine points and one million query rectangles, report the convex hull area of the points inside each rectangle.	Hard9	GeometryDivide and conquer+1	No attempts yet	1s	128 MB	Judgeable
CrystalSum the signed charges of all three-colored unit triangles in a hexagonal crystal filled row by row from a modular generator.	Hard9	MathGeometry+2	No attempts yet	1s	128 MB	Judgeable
MultiplicationGiven prime p and each query pair a and b, find the smallest k with a to the k-th power congruent to b modulo p, or print -1 when b never appears.	Hard9	Number theoryMath+1	No attempts yet	5s	128 MB	Judgeable
RoofCompute the maximum height of the 45-degree straight-skeleton roof built over a rectilinear polygon.	Hard9	Geometry	No attempts yet	1s	128 MB	Judgeable
Aquarium DrainageGiven an orthogonal aquarium floor with holes on its segments, compute the total drain time and the water left behind.	Hard9	GeometrySorting+2	No attempts yet	1s	128 MB	Judgeable