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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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?"
...
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Build two squares by joining tetrominoes
Move, rotate and flip tetrominoes in order to get two squares, note: one square is inside the other.
The following image shows all the 25 tetrominoes (5 of type I and 20 of type L) to be arranged in a ...
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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 - ...
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Tiling a 4 x 4 grid with 16 colored tiles (4 red, 4 black, 4 green and 4 yellow)
Beginner puzzle (suitable for people who are new to puzzle solving).
A 4 x 4 grid is to be covered with 16 square tiles. There are four tiles in each of the colours red, black, green, and yellow. Each ...
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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).
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Can these squares fit? Partridge packing puzzle
You have 1 1×1 square, 2 2×2 squares, 3 3×3 squares, 4 4×4 squares, 5 5×5 squares, 6 6×6 squares, 7 7×7 square and 8 8×8 squares.
Is it possible to fit them in a 36×36 square grid without overlaps?
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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 ...
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Poly and Omino play a rectangle tiling game
A polyomino is a two-dimensional shape formed by putting together some unit squares fully along their edges. An N-omino is a polyomino formed with exactly N unit squares. Two N-ominoes are the same if ...
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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 - ...
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Make a square with the fewest number of pieces
Neat shearing:
You have to make one square out of the three squares (2x2, 3x3 and 6x6) as shown in the figure. How can you do this, cutting the squares into the smallest possible number of pieces?
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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
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What is Jules’ shape (with 10 copies of it a rectangle can be tiled)?
Jules is playing with a pentomino set and suddenly shouts out in excitement. (A pentomino is any shape made from five identical squares by joining them along the full lengths of their edges.) “I have ...
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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 ...
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One number grid, two ways to divide it (Part 2)
Find a rectangular grid of the smallest area that satisfies the following:
Each cell contains an integer between 1 and 4 inclusive.
The grid follows the Fillomino rule:
When the cells are divided ...
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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 ...
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