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.
228 questions
14
votes
3
answers
652
views
A "crappy" pentagon puzzle
Lately, we've had plenty of puzzles based on the regular pentagon and its geometric properties. So I propose one that literally brings it all together.
Use eleven copies of the larger (left) piece ...
- 2,694
11
votes
2
answers
779
views
Is it possible to fill a 2x2x15 volume with 12 non-flat pentacubes?
I am playing with non flat pentacubes (i.e. 5-cube non-flat puzzle pieces), trying to fill all possible volumes of 60 cubes (then using 12 different ones of the 17 possible pieces).
Up to now, I made ...
- 119
5
votes
1
answer
640
views
Is there a perfect squared square made entirely of squares of prime edge?
There are infinitely many sets of distinct primes whose squares add up to a square number and, presumably, sets of any size (https://mathoverflow.net/questions/501745/primes-whose-squares-add-up-to-...
23
votes
4
answers
1k
views
Covering a rectangular floor with prime tiles
At my local store the only tiles sold are size 1 x p, p any of the first twenty five primes. What is the area of the largest rectangular floor, with width and height greater than 1, that I can ...
9
votes
2
answers
957
views
Tiling a rectangle with heptominoes [duplicate]
An n-omino is a two-dimensional polygon composed of n congruent squares glued together via the edges. For instance, the 4-ominoes are the Tetris shapes.
It is famously known that one can tile a 6-by-...
- 1,101
6
votes
1
answer
246
views
How many two-coloured tilings of the plane are there using F-pentominos?
I looked at finding two-coloured F-pentomino tilings of the plane today. I have a program that tiles rectangles and also handles wrapping of each axis, ie tiling a torus. Tiling a 10x10 torus I get ...
- 4,505
15
votes
1
answer
646
views
Maximize the number of triangular tiles that can fit inside a hexagon after three tiles are placed
While traveling in Europe recently, I bought a tiling puzzle for my daughter. (It is a Grimm’s wooden puzzle, exactly like the one in this link.) The puzzle contains 18 congruent tiles, each of which ...
- 19.8k
9
votes
1
answer
471
views
Find the smallest odd rectangle tiled using equal number of trapeziums and pentagons
Using right trapeziums of area 1.5 and irregular pentagons of area 3.5, whose shapes are shown in figure below, your task is to find the smallest rectangle with odd area covered by these trapeziums ...
- 1,730
21
votes
2
answers
1k
views
Tetris Perfect Clear puzzles
The aim of each puzzle is to completely clear each field, using the listed pieces in order from top to bottom.
"But wait, ApexPolenta," you say, "isn't this just a tiling puzzle?"
...
- 4,674
10
votes
3
answers
781
views
Coverable and Non-Coverable?
Handmade Puzzle!
1. Notation
Covarable - If a figure A can be covered with figure B, without double (or more)-covered areas, allowing rotations and flips, then A is coverable with B.
Non-Coverable - ...
- 5,168
8
votes
2
answers
354
views
Ten-T puzzle. Place nine sets of the ten given T-shapes in a 20x36 rectangle
This set of T-shapes was devised by Jim Kerley who asked whether 1,2,3, or 4 sets would tile a rectangle (they will probably not, search nearly complete, tilings can be found for five sets or higher).
...
- 4,505
8
votes
3
answers
933
views
Dissect shape into as few pieces as possible that can be reassembled into a square
Dissect the following shape into as few pieces as possible so that those pieces can be reassembled (without rotations or reflections) into a square.
Attribution:
This puzzle is a slight variant of ...
- 31.9k
10
votes
3
answers
946
views
Tiling Quandary
Mo Demir is a master tiler, but he knew this task would be challenging - his friend, the famous mathematician Roger P. has asked him to tile the new bathroom. The customer has given him a full plan - ...
- 1,049
19
votes
1
answer
1k
views
Cover the 7x7 square with the 12 L-shaped pieces
Cover the 7x7 square on the left with the 12 L-shaped pieces on the right. You are not allowed to turn over any of the pieces, but you may rotate them in the plane.
Attribution: Nob Yoshigahara
- 31.9k
1
vote
1
answer
362
views
Smallest square with pentominoes
I created a puzzle by myself for the first time and this is it:
Using all the pentominoes from the figure at least once, what is the least size of square (or rectangle, whichever comes first) that we ...
- 125
11
votes
2
answers
763
views
Use all eight of the given polygons to tile a parallelogram
The goal of this puzzle is to use all eight of the given polygons to tile a parallelogram without gaps or overlaps. Rotations and reflections are allowed.
Description of the polygons:
The triangles ...
- 31.9k
2
votes
1
answer
438
views
How many of the 16 cells of the grid could contain the black dot?
Beginner puzzle
This puzzle is intended to be suitable for people who are new to puzzle solving.
Clarification: Both experienced solvers and new solvers are welcome to post solutions to this puzzle.
...
- 31.9k
19
votes
2
answers
2k
views
7x10 floor and a 8x8 and a 6x1 carpet, only one cut allowed
We have a 8x8 carpet, we can do only one cut of any complexity and also we have an uncuttable 6x1 carpet. We need to fill a 7x10 space using those 2. The 8x8 can only be cut into two pieces.
We have ...
- 193
5
votes
3
answers
828
views
Is it possible to arrange the free n-minoes of orders 2, 3, 4 and 5 into a rectangle?
To be explicit, the shapes pictured below, with reflections permitted.
Can these be packed into a rectangle?
This puzzle arose from discussion on r/mathmemes. No solution was posted (and I don't know ...
- 4,674
0
votes
1
answer
307
views
Tile dominoes in a 3x10 space [closed]
How many ways are there to tile 1x2 (unmarked) dominoes in a 3x10 space?
This is a harder version of Tile dominoes in a 2x10 space, since that was too easy.
- 1,029
9
votes
3
answers
2k
views
Tiling a 16x16 square with 1x4 rectangles
Consider a 16x16 square subdivided by grid lines into unit squares. It is easy to completely tile (no overlaps, no gaps) this square with 64 1x4 rectangles. Each 1x4 rectangle in the tiling (no ...
- 31.9k
32
votes
5
answers
5k
views
Can you tile a 25x25 square with a mixture of 2x2 squares and 3x3 squares?
Can you tile a 25x25 square (no overlaps, no gaps) with a mixture of 2x2 squares and 3x3 squares?
This puzzle is by David A. Klarner.
Clarification: The number of 2x2 squares and 3x3 squares can be ...
- 31.9k
9
votes
1
answer
859
views
Tile a square as small as possible using two different sizes of square tiles
There are two types of square tiles. One type has a side length of 1 cm and the other has a side length of 2 cm.
What is the smallest square that can be made with equal numbers of each type of tile?
...
- 31.9k
9
votes
2
answers
436
views
How do I constrain a puzzle and keep a singular solution?
I am tinkering with a puzzle framework that has the following rules:
In a 6x6 grid of squares, arrange 8 strips of connected squares such that there exists exactly one strip of every length (i.e. a ...
- 571
21
votes
1
answer
2k
views
Which heptomino is it obvious can't tile the plane?
A polyomino is a collection of equal-sized squares joined edge-to-edge in the plane (think Tetris pieces, but with an arbitrary number of squares instead of just four). A heptomino is a polyomino ...
- 672