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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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2answers
227 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 ...
5
votes
2answers
664 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 ...
5
votes
1answer
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 ...
5
votes
2answers
231 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 ...
5
votes
2answers
311 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 ...
5
votes
2answers
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 ...
5
votes
1answer
484 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). ...
5
votes
1answer
203 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: ...
5
votes
3answers
142 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 ...
5
votes
1answer
227 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 ...
5
votes
1answer
186 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 ...
5
votes
1answer
378 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: ...
5
votes
1answer
265 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?
5
votes
2answers
193 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 ...
5
votes
2answers
213 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 ...
5
votes
1answer
172 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 ...
4
votes
1answer
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....
4
votes
3answers
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 ...
4
votes
3answers
528 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 ...
4
votes
2answers
262 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 ...
4
votes
2answers
411 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 ...
4
votes
1answer
188 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 ...
4
votes
1answer
329 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: ...
4
votes
1answer
165 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 ...
3
votes
3answers
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 ...
3
votes
4answers
427 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 ...
3
votes
3answers
191 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 ...
3
votes
2answers
145 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 ...
3
votes
1answer
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. ...
3
votes
1answer
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 ...
3
votes
1answer
79 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 ...
3
votes
2answers
128 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 ...
3
votes
1answer
113 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 ...
2
votes
2answers
87 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 ...
2
votes
2answers
321 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 ...
2
votes
2answers
183 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 ...
2
votes
2answers
139 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 ...
2
votes
1answer
134 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 ...
2
votes
1answer
124 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 ...
1
vote
2answers
141 views

Tiling rectangles with Heptomino plus rectangle #7

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 ...
-1
votes
1answer
359 views

Dominoes on a Chess Board [duplicate]

Imagine an 8x8 chessboard has two opposite corners taken out, with 62 squares left over. Is it possible to lay 31 dominoes with the size 2x1 so they cover all of the empty, left over, squares?