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Piet (Mondrian)'s Puzzle

For more information, watch this video, and go to A276523 for a related sequence.The Mondrian Puzzle (for an integer n) is the following:Fit non-congruent rectangles into a n*n square grid. What is the...

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Is my kids' alphabet mat properly grouped by colors?

My kids have an alphabet mat to play with, something like this:After months with the tiles of the mat randomly placed, I got tired and placed all the tiles of the mat grouped by sections according to...

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Arranging arbitrary rectangles to fill a space

Can these rectangles fill a rectangular space?Given a bunch of rectangles, you are asked whether or not they can be arranged to fill a rectangular space.SpecsGiven a bunch of arbitrary m x n...

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Random ASCII Art of the Day #5: Diamond Tilings

Mash Up Time!This is instalment #5 of both my Random Golf of the Day and Optimizer's ASCII Art of the Day series. Your submission(s) in this challenge will count towards both leaderboards (which you...

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Test a polyomino against Conway criterion

BackgroundConway criterion is a method to test if a given polygon can tile (i.e. cover without overlapping) an infinite plane. It states that a polygon can tile the plane if the following conditions...

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Number of tilings on a triangular board with triangular tiles

BackgroundConsider the shape \$T(n)\$ consisting of a triangular array of \$\frac{n(n+1)}{2}\$ unit regular hexagons:John Conway proved that \$n = 12k + 0,2,9,11\$ if and only if \$T(n)\$ can be tiled...

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Can this polyomino tile the toroidal grid?

Inspired by certain puzzles on Flow Free: Warps.BackgroundWe all know that L-triominos can't tile the 3x3 board, and P-pentominos can't tile the 5x5 board. But the situation changes if we allow the...

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Identify the smallest possible tile in the matrix

ChallengeGiven a matrix of digits (0-9), find the smallest (in terms of area) rectangular matrix of digits where one or more copies of itself, possibly rotated, can tile the original matrix. Reflection...

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Integers, Assemble!

Your task is to assemble the integers from 1 to N (given as input) into a rectangle of width W and height H (also given as input). Individual numbers may be rotated by any multiple of 90 degrees, but...

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ASCII Exact Cover with Rectangles

ChallengeGiven a rectangular area arrange a group of rectangles such that they cover the rectangular area entirely.InputAn integer denoting the height.An integer denoting the width.The dimensions of...

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Simplest Tiling of the Floor

You should write a program or function which receives a string describing the floor as input and outputs or returns the area of the simplest meta-tiling which could create the given pattern of the...

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Number of domino tilings

Write a program or function that given positive n and m calculates the number of valid distinct domino tilings you can fit in a n by m rectangle. This is sequence A099390 in the Online Encyclopedia of...

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Generate valid Fibonacci tilings

BackgroundThe Fibonacci tiling is a tiling of the (1D) line using two segments: a short one, S, and a long one, L (their length ratio is the golden ratio, but that's not relevant to this challenge)....

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Is this a robbery?

BackstoryYou own a tiny jewellery shop in the suburbs of the city. The suburbs are too much overpopulated, so your shop has a thickness of only one character to fit in the busy streets.Recently, there...

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Maximal saturated domino covering of a rectangle

Inspired by this OEIS entry.BackgroundA saturated domino covering is a placement of dominoes over an area such thatthe dominoes are completely inside the area,the dominoes entirely cover the given...

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How should I tile my kitchen?

I recently ordered some new and colorful tiles to replace my boring old white tiling for my kitchen. However, when the tiles arrived, they were all in a weird shape! Therefore, I need a program to...

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Tiling a staircase with staircases

BackgroundA staircase polyomino is a polyomino made of unit squares whose shape resembles a staircase. More formally, a staircase polyomino of size \$n\$ is defined as follows:A staircase polyomino of...

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Concentric rings on a snub square tiling

This challenge takes place on the snub square tiling.Start by choosing any triangle, and color it \$c_1\$.Next, find all tiles which touch this triangle at any vertex, and color them \$c_2\$. Next,...

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Domino Recurrence Generator

ChallengeWe once had a challenge to count domino tilings of m by n grid, and we all know that, for any fixed number of rows, the number of domino tilings by columns forms a linear recurrence. Then why...

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Counting polydominoes

BackgroundA polyomino of size \$n\$ is a contiguous shape made from joining \$n\$ unit squares side by side. A domino is a size-2 polyomino.A polydomino of size \$2n\$ is defined as a polyomino of size...

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The number of tilings of a grid

Setup:A block is any rectangular array of squares, specified by its dimensions \$(w,h)\$. A grid is any finite ordered list of blocks. For example, \$\lambda = ((3,2),(3,1),(1,2))\$ defines a grid.Let...

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Is it a checkered tiling?

BackgroundA checkered tiling of a rectangular grid is a tiling using some polyominoes, where each region can be colored either black or white so that no two polyominoes sharing an edge has the same...

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Triangular domino tiling of an almost regular hexagon

BackgroundAn almost regular hexagon is a hexagon whereall of its internal angles are 120 degrees, andpairs of the opposite sides are parallel and have equal lengths (i.e. a zonogon).The following is an...

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Counting maximal domino placements

BackgroundA maximal domino placement (MDP) on a rectangular grid is a non-overlapping placement of zero or more dominoes, so that no more dominoes can be added without overlapping some existing...

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Game of Life, but on a 4-8-8 tiling

BackgroundThe 4-8-8 tiling looks like this:For the purpose of this challenge, we take the orientation of the tiling as exactly shown above. In plain English words, we take the tiling so that it can be...

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AoCG2021 Day 25: Stitching maps together

Part of Advent of Code Golf 2021 event. See the linked meta post for details.Related to AoC2020 Day 20, Part 1. (This day is a dreaded one for many of you, I know :P)Obligatory final "but you're not...

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Draw the GKMS aperiodic tile

Chaim Goodman-Strauss, Craig Kaplan, Joseph Myers and David Smith found the following simple (both objectively and subjectively) polygon that tiles the plane, but only aperiodically:Indeed they found a...

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Complete the landscape

Carcassonne is a tile-based game, where the objective is to construct Roads, Cities and Monasteries, in order to score points. The game works by players taking turns to draw and place tiles to...

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Extending OEIS: Counting Diamond Tilings

I promise, this will be my last challenge about diamong tilings (for a while, anyway). On the bright side, this challenge doesn't have anything to do with ASCII art, and is not a code golf either, so...

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Seamless conversion from square to hexagon

For many games played on a grid, hexagons are the Clearly Superior Choice™. Unfortunately, many free game art sites only have seamless tile sets for square maps. On a past project, I used some of...

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