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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Can you use triangular tiles to form a rectangle of size 2016 cm by 2021 cm?
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.
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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 ...
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Filling a rectangular grid with holes using tetrominoes
There is a rectangular grid of $R$ rows and $C$ columns. $R \times C \bmod 4$ of the cells are painted black, and all other cells are white. In other words, there are at least 0 and at most 3 black ...
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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.
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Packing 25 three-dimensional N pentominoes into a 5x5x5 cube
The puzzle contains 25 identical pieces that look like this:
To be explicit, the piece is composed of five cubes. In the picture, three cubes form the base, and two cubes form the overhang.
The goal ...
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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 ...
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Can you tile a 15x16 rectangle using eight rectangles whose sizes are 1x2, 2x3, 3x4, ... 8x9?
Can you tile a 15x16 rectangle using eight rectangles whose sizes are 1x2, 2x3, 3x4, ... 8x9?
No two rectangles can be the same size.
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Can you tile a 25 x 25 square with a mixture of 2 x 2 squares and 3 x 3 squares?
Can you tile a $25 \times 25$ square (no overlaps, no gaps) with a mixture of $2 \times 2$ squares and $3 \times 3$ squares?
This puzzle is by David A. Klarner.
Clarification: The number of $2 \times ...
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Recursive rhombic dodecahedron tiling
Say you have a single rhombic dodecahedron, call it "layer p0". If you then tile identical dodecahedrons around it so that it gets completely covered, the number of dodecahedrons on the ...
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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?
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Gimme five (Pentomino puzzle)
A pentomino is a tile made of five unit squares joined edge to edge. Divide this grid into five pentominoes, each containing the five letters A,B,C,D,E. The regions are not necessarily the same ...
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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 ...
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Tiling a 5-by-5 bathroom with L-shaped triomino tiles
The following puzzle appeared in the Cambridge, UK February 2024 MathsJam Shout:
Tiling with Triominoes
Imagine tiling a 5-by-5 bathroom with L-shaped triomino tiles.
Clearly, not every square can be ...
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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 ...
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Tiling a square with right-angled triangles
Tile a square with twenty congruent right-angled triangles. For each triangle, one leg is of length 1 and the other leg is of length 2.
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