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...
View ArticleClik here to view.
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...
View ArticleClik here to view.
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...
View ArticleClik here to view.
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...
View ArticleClik here to view.
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...
View ArticleCan 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...
View ArticleIdentify 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...
View ArticleIntegers, 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...
View ArticleASCII 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...
View ArticleSimplest 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...
View ArticleNumber 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...
View ArticleGenerate 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)....
View ArticleIs 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...
View ArticleMaximal 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...
View ArticleHow 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...
View ArticleTiling 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...
View ArticleClik here to view.
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,...
View ArticleDomino 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...
View ArticleCounting 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...
View ArticleClik here to view.
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...
View ArticleIs 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...
View ArticleClik here to view.
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...
View ArticleCounting 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...
View ArticleClik here to view.
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...
View ArticleAoCG2021 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...
View ArticleClik here to view.
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...
View ArticleClik here to view.
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...
View ArticleClik here to view.
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...
View ArticleClik here to view.
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...
View ArticleClik here to view.
Index into a Fibonacci tiling
The Cartesian plane can be tiled with increasingly large squares like so:This tiling can be generated by starting with a square of side length 1, placed at the origin 0, 0, and then repeatedly adding a...
View Article