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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.

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

186 questions
24
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3 answers

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.
Will Octagon Gibson
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Find a heptagon with mirror symmetry that can tile a flat plane

A seven-sided flat shape of fixed size in which all angles are equal and all sides of the same length, called a regular heptagon, cannot tile a flat plane. The only regular shapes that can are the equilateral triangle, the square, and the regular…
h34
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1 answer

Hexomino Puzzle

First, draw out a 10x10 grid. Take the shape below and see how many you can fit in the 10x10 grid. It should take up 6 grid squares. Also, it can be rotated. 1) How many can you fit in the grid? 2) Can you prove that this is the most possible? …
user41716
11
votes
2 answers

Fit small squares in a large square

Fit the given square pieces in a larger square! Warmup In a 10x10 square, fit 5 1x1 squares, 8 2x2 squares, and 7 3x3 squares. Solution Puzzles In an 11x11 square, fit 3 1x1 squares, 12 2x2 squares, 5 3x3 squares, and 1 5x5 square. In a 12x12…
Pontus von Brömssen
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2 answers

Occupy a field with your choice of tetromino

You have an 8x8 board, and you must partially cover it with a single kind of tetromino in such a way that it is impossible to place any additional tetrominoes of that kind in the empty spaces. Additionally, no two tetrominoes may touch by their…
Ben Frankel
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9
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2 answers

Tiling a diamond-shaped grid with tetrominoes

You have a grid like this: (The entire grid isn't shown as it would be too large, but the number of squares in each row are as follows: $2, 4, 6, \ldots, 96, 98, 100, 100, 98, 96, \ldots, 6, 4, 2$.) We define this grid as $G(100)$, as it is 100…
Doorknob
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1 answer

Surely they can fit?

Suppose you have a grid of squares that has even dimensions, with at least one dimension greater than or equal to 4 squares, and from one corner you remove a 1x4 rectangle of those squares for example: □□□□□□ □□□□□□ □□□□□□ XXXX□□ Can you fill in…
micsthepick
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6
votes
1 answer

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?
Tyler Seacrest
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3 answers

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 for it to work optimally, it is required that it has…
George Menoutis
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4
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2 answers

Double tiling congruent triangles with little else in common

When you really want to tile more than one layer but triple tiling is just too much of a good thing, surely the happy medium is double tiling. How may a mosaic of more than 900 sections be double tiled with congruent triangles along the…
humn
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