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.
235 questions
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Given six hexagons, cut three of them and reassemble into an equilateral triangle
Six congruent regular hexagons are given. Cut three of them into two parts such that the nine parts obtained (three hexagons and six "halves") can be used to compose an equilateral triangle.
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Grouping and routing puzzle: can these circles be partitioned into triples and connected by a single non-crossing path?
I’m interested in whether the following puzzle has a valid solution.
You are given a fixed arrangement of circles in a plane (see attached image). The task is to:
Partition all circles into groups of ...
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How many ways to tile this shape with dominoes?
In how many different ways can this shape be tiled with dominoes? This is one of the possible ways:
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Halving a 6×6 Grid into Two Identical Shapes
Find the number of ways to cut a 6x6 grid of unit squares along the grid lines into two connected pieces that are identical in shape.
Here is one example.
Note that two solutions are considered the ...
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Minimize the number of pieces to form a square.
The figure depicted in the picture (a 6x6 square, in which the top row is moved by 1 square), was cut along the grid lines into identical parts which could be put together to form a 6x6 square (the ...
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Cut and rearrange regular polygons with no overlap with original positions
Consider a regular n-gon. The goal is to cut it up into a finite number of pieces and rearrange them, without flipping, into the same shape, but none of the pieces should overlap with their original ...
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Tile a 9x9 grid with trominoes while avoiding the black lines
Beginner puzzle (suitable for people who are new to puzzle solving).
To allow new users to solve this puzzle and earn reputation points, I encourage all users whose reputation is 200 or more to not ...
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Can a 10*10 square be paved with 1*4 rectangular stone plates?
Can a 10 * 10 square be paved with 1*4 rectangular stone plates?
I seek a very intuitive and simple answer to this puzzle.
P.S. Will post the source later. The source contains the answer but it is not ...
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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 ...
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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 ...
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The slanted blocks box problem
Woody Woodcutter is preparing his special slanted wooden blocks box. His nephew likes to put slanted roofs on every construction, so he made a special box with many slanted blocks to add to his ...
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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-...
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Good old Ministeck
Wth Ministeck you can create some nice patterns and images, such as the following:
There are 5 basic pieces:
Because the dots (1-pieces) are very scarce (and you easily lose them because they're so ...
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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 ...
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Tiling 7×107 rectangle with heptominoes
Is it possible to tile a 7×107 rectangle with the 107 heptominoes that do not have a hole?
Obviously, the heptomino with a hole cannot be used to tile, and there are 107 remaining heptominoes?
Rules:
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