Questions tagged [polyomino]
A geometric puzzle centered around geometric figures formed from unit-squares, or a puzzle that uses polyominoes as an integral part.
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Do solutions exist for 3D tiling with Pentaminos/Pentacubes?
To make a long story short, I have developed an IOS App running the classic game with Pentaminos and Pentacubes (see my profile for details). I am now considering the tiling option game with the same ...
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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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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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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-...
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Dividing both the interior and the boundary of a square into equal parts using polyominos
We want to cover an m×m square with n non-overlapping axis-parallel polyominos such that both the interior and the boundary of the square are divided into n equal areas and n equal lengths, ...
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Covering a Rubik's Cube Pattern with Pentominoes
Given a Rubik's Cube pattern:
And using each of the following 12 pentominoes at least once:
Can you cover entirely the Rubik's Cube?
The answer is obviously yes!
However, given that the Rubik's Cube ...
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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 ...
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Largest area enclosed by pentominoes
What is the most number of empty cells that you can enclose by placing each of the 12 pentominoes on a grid? Pentominoes can be flipped and rotated. An empty cell is considered enclosed if there is no ...
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Largest area enclosed by tetrominoes
What is the most number of empty cells that you can enclose by placing each of the 5 tetrominoes on a grid? Tetrominoes can be flipped and rotated. An empty cell is considered enclosed if there is no ...
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Kissing number for tetrominoes
The kissing number of a circle is the greatest number of non-overlapping unit circles that can be arranged to touch a common unit circle.
We now extend this definition to polyominoes. The kissing ...
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Two Geometric Magic Squares
The following is a traditional 3x3 magic square:
8 1 6
3 5 7
4 9 2
In a traditional magic square, the sum of the numbers in each row, each column and both ...
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Use the given L-shaped polyominoes to tile a 5x10 rectangle.
Goal:
Use all nine L-shaped polyominoes shown below (each exactly once) to tile a 5x10 rectangle. The polyominoes can be rotated and reflected.
The colors are purely decorative and can be ignored.
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Smallest possible pentomino farm
A pentomino farm is an arrangement of the 12 pentominoes (each of area 5) that satisfies all of the following conditions:
All 12 pentominoes must be used exactly once
Pentomioes must be grid-aligned
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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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Solving strategies for a hexagonal polyomimo-ish tiling wooden puzzle
I have this wooden puzzle. It consists of a couple of pieces that need to be arranged inside the box. The hexagonal pattern makes it so that each piece can go in the puzzle in one of three possible ...
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