# Questions tagged [tiling]

A geometric packing puzzle in which a number of shapes have to be assembled into a larger shape, generally without overlaps or gaps.

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### Tiling a rectangle with an odd number of Y pentomoes

Follow-on from Tiling a rectangle with just the Y pentomino Two questions: Find the smallest rectangle that can be tiled with an odd number of Y pentominoes, or prove it impossible Find the smallest ...
229 views

### Challenging 15 rectangle tiling problem

This will test you, a computer will definitely help. Just one set of $1:2$ aspect ratio rectangles this time, but $15$ of them. Short side only is listed. The challenge is to arrange them into a ...
667 views

### The Pentomino Snake

The premise of the puzzle is quite simple. Here's how to set it up. Draw a 5x5 grid of squares. Write the number 1 in the middle. Make a "snake" of numbers up to 25 so that each number is ...
1k views

### Building a Tetromino Tower [duplicate]

So, I just bought a Tetris Light like this one. With all 7 unique tetrominos, I can build a tower whatever I like and then turning them on at night to give me a good sleep, mm hm. (What a geek!) I ...
236 views

### Tiling rectangles with Heptomino plus rectangle #6

Inspired by Polyomino T hexomino and rectangle packing into rectangle See also series Tiling rectangles with F pentomino plus rectangles and Tiling rectangles with Hexomino plus rectangle #1 ...
324 views

### Fill up a tetris field where bordering tiles have different colors

Is it possible to completely fill the infinite tetris field $\mathbb Z^2$ with tetrominoes such that no tetromino borders another one of the same type? Assume that two tetromiones border each other ...
643 views

### Planning an Archipelago

We can place S and Z tetromino shaped islands on an 8x8 grid of water in such a way that no two islands are touching by their edges, because then they would not be two islands. Two islands may touch ...
486 views

### Perfectionist Pete's Perfect Pain: Even Tilings

Pete's room has a rectangular floor with dimensions $15 \times 20$. He wants to tile the floor of his room with black and white coloured tiles. Each tile is an unit square (ie. $1 \times 1$ square). ...
206 views

### Professor Halfbrain and the wonderful rectangles

Professor Halfbrain calls a rectangle wonderful, if it is similar to the rectangle with side lengths $1$ and $2-\sqrt[3]{5}$. The professor claims to have a proof for the following theorem: ...
145 views

### Fit as many overlapping generators as possible

Rimworld is a tile-based videogame. One of its constructibles in the wind generator: The wind generator itself occupies a space of 7x2 and can be placed facing the 4 cardinal directions. In order ...
231 views

### Tiling rectangles with Hexomino plus rectangle #1

Inspired by Polyomino T hexomino and rectangle packing into rectangle See also series Tiling rectangles with F pentomino plus rectangles and Tiling rectangles with Hexomino plus rectangle #1 Next ...
187 views

### Cover 3*2.6 rectangle with the least number convex polygons cut from sheets of given size 1.2*2.4

I want to cover a rectangle of given dimensions ($3\times2.6$) with a minimal number of convex polygons cut from rectangular sheets of material of given size ($1.2\times2.4$). These polygons don't ...
382 views

### Unfair tiling puzzle

Your goal is to make two squares of the same size from a set of rectangles. Each of the rectangles has an aspect ratio of $1:2$. Select two sets of rectangles from the list: ...
267 views

### Tiling a 6x6 board with an equal number of horizontal and vertical dominoes

Can you tile a 6x6 chessboard with dominoes, without overlaps or gaps, so that the number of dominoes oriented horizontally is equal to the number of dominoes oriented vertically? Why or why not?
195 views

### Five graded difficulty isosceles right triangle into square tilings

Similar to: Unlucky tiling: Arrange thirteen right isosceles triangles into a square Two difficult "Seventeen right isosceles triangles into a square" tilings V.hard problem, 20 right ...
220 views

### 20 right isosceles triangles into a square

Similar: Unlucky tiling: Arrange thirteen right isosceles triangles into a square Five graded difficulty isosceles right triangle into square tilings Two difficult "Seventeen right isosceles ...
176 views

### A minor rearrangement of the one sided hexominoes in 12 simultaneous shapes

Here are the one sided hexominoes arranged into 12 congruent shapes. But there are one or two flaws: The dark blue hexominoes, which are the symmetric ones, may not occur more than once each in a ...
1k views

### Is there an efficient algorithm for solving tiling puzzles?

As an example of the type of problem, consider Stewart Coffin's Cruiser puzzle: Let R be a 48 × 31 rectangle. Let T be a 30°-60°-90° triangle with hypotenuse 34.565 (so legs are 17.2825 and 29....
1k views

### Fitting rectangles into square (optimal/perfect rectangle packing)

I gave the puzzle you can see on the image below to a friend of mine for christmas last year. I thought it would be fun to dump it out in front of him so he would not know the solution. Unfortunately ...
535 views

### Largest Complete Scrabble Block

Let's define a Complete Scrabble Block as an arrangement of Scrabble tiles such that: The four edges are all flat. All words are words. There is an order in which the tiles can be played in a game of ...
263 views

### Trickier hand tiling

This should be a little trickier. Using $20$ rectangles of aspect ratio $1:2$, make two squares. Use sizes 2,3,7,12,16 in both squares. And split this list among ...
436 views

### Puzzle that consists of all possible combinations of pieces containing 5 squares

When I was a child my father gave me a wooden puzzle that consisted of pieces that represented every possible combination of 5 squares. The goal was to arrange the pieces in various rectangular ...
189 views

### Two similar hand tiling puzzles

Make a square from each of these lists of aspect ratio $1:2$ rectangles 1, 4, 5, 6, 7, 9, 11, 12, 13, 14, 15, 17 ...
337 views

### Hard tiling puzzle

Your goal is to make two squares of the same size from a set of rectangles. Each of the rectangles has an aspect ratio of 1:2. Select two sets of rectangles from the list: ...
166 views

### Slightly bigger 1:2 hand tiling, getting a little harder

Pretty sure an expert hand tiler would be able to find this. Please post a spoiler only if you hand tile it... Tile a $60\times60$ square with $1:2$ rectangles of sizes ...
339 views

### Make me a room-filling pattern!

So I need a new knitting pattern, but I figured this might be a nice puzzle. I'm looking for a pixelated 2D-shape that can be used in a room-filling pattern (rotation and flipping allowed). The ...
435 views

### Square Room Tiles

The square floor of a square room was covered with colored 1 square unit tiles.The covering tiles were designed to have different (solid) colored tiles that forms rectangular areas but none of these ...
192 views

### Tiling rectangles with U pentomino plus rectangles

Inspired by Polyomino Z pentomino and rectangle packing into rectangle Also in this series: Tiling rectangles with F pentomino plus rectangles Tiling rectangles with N pentomino plus rectangles ...
147 views

### Tiling rectangles with Hexomino plus rectangle #3

Inspired by Polyomino T hexomino and rectangle packing into rectangle See also series Tiling rectangles with F pentomino plus rectangles and Tiling rectangles with Hexomino plus rectangle #1 ...
120 views

### Hand tiling puzzle 2

Here's another set of polyominoes (sizes 4,5,6,7,8,9,10) that you can print and cut out. As before, the two smallest (same pieces as previous version) make a 3x3. The rest of the pieces are different. ...
153 views

### Is it possible to build this out of soma cube parts?

For those of you who dont know, these are soma cube parts: They can be assembled into a 3x3x3 cube. Is it possible to build a hollow cube with the extra little cube being on top, in the middle of ...
84 views

### Max 4x1 pattern fit within 11x11 area

Rimworld is a tile-based videogame. There is a constructible called a sun lamp, which provides light for indoor farming: . As you can see, the area covered by the lamp is 11 * 11, minus 1 for the ...
130 views

### Tiling rectangles with Heptomino plus rectangle #4

Inspired by Polyomino T hexomino and rectangle packing into rectangle See also series Tiling rectangles with F pentomino plus rectangles and Tiling rectangles with Hexomino plus rectangle #1 ...
114 views

### Dissect a square into 1:2 non-congruent integer-sided rectangles

(Similar to the recent 3:1 and my 3:2 rectangle question) Tile a square completely with rectangles which have aspect ratio 1:2, integral side lengths and all different sizes. In other words selected ...
89 views

### Tiling rectangles with Hexomino plus rectangle #2

Inspired by Polyomino T hexomino and rectangle packing into rectangle See also series Tiling rectangles with F pentomino plus rectangles and Tiling rectangles with Hexomino plus rectangle #1 ...
326 views

### Packing an Efficient 9 Pack

This is sorta like How to ship the new Slurm 7-pack efficiently by Matt Malone but instead of 7, it's the 9 pack! It's basically a 2 by 4 pack with a piece sticking out, like in the above link. What's ...
190 views

### Tiling rectangles with a Heptomino plus 2x2 square

Inspired by Polyomino T hexomino and rectangle packing into rectangle See also series Tiling rectangles with F pentomino plus rectangles and Tiling rectangles with Hexomino plus rectangle #1 ...
141 views

### Two difficult “Seventeen right isosceles triangles into a square” tilings

Similar to: Unlucky tiling: Arrange thirteen right isosceles triangles into a square Five graded difficulty isosceles right triangle into square tilings V.hard problem, 20 right isosceles triangles ...
135 views

### Tile a square with five rectangles with 10 distinct edges

The baby brother of: Cutting a square into seven rectangles Tile a square with five rectangles. Select the lengths of the edges of the rectangles from the set $1$ through $10$, with no length ...
128 views

### Tiling rectangles with Heptomino plus rectangle #3

Inspired by Polyomino T hexomino and rectangle packing into rectangle See also series Tiling rectangles with F pentomino plus rectangles and Tiling rectangles with Hexomino plus rectangle #1 Next ...