Questions tagged [polyomino]
For challenges that involve polyominoes of some sort. Polyominoes are shapes made of concatenating the edges of equally sized squares to create a form of square tiling. Tetris is a well known example of something involving polyominoes. This tag also refers to challenges that relate to polyominoes formed with shapes other than squares (also known as polyforms)
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Generate all polyiamonds
A polyiamond of size \$n\$ is a contiguous shape formed by joining \$n\$ equilateral triangles side by side.
Your output should consist of two distinct characters, plus whitespace as necessary (▲ and ▼...
- 1,995
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3
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Pretty print a grid of polyominoes
Write a function that accepts a rectangular grid of ids in any reasonable format, for example a multi-line string:
IIILOO
ILLLOO
and a string or list of box ...
- 5,830
14
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3
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Counting uniquely solvable polylinks
Related: Counting polystrips
Background
Link-a-Pix is a puzzle on a rectangular grid, where the objective is to reveal the hidden pixel art by the following rules:
Connect two cells with number N ...
- 62.2k
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3
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Sticky polyhexes
Background
A polyhex of size \$n\$ is a contiguous shape made from joining \$n\$ unit regular hexagons side-by-side. As an example, the following image (from Wikipedia) contains all 7 distinct ...
- 62.2k
9
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2
answers
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Counting polydominoes
Background
A polyomino of size \$n\$ is a contiguous shape made from joining \$n\$ unit squares side by side. A domino is a size-2 polyomino.
A polydomino of size \$2n\$ is defined as a polyomino of ...
- 62.2k
25
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14
answers
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Is this an L-shape?
Background
An L-shape is defined as a polyomino which can be made by extending two rectangular legs in orthogonal directions from a full square (called a pivot). The size of the square should be at ...
- 62.2k
16
votes
1
answer
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Gluing tetrahedra together
(This challenge exists to extend sequence A276272 in the On-Line Encyclopedia of Integer Sequences, and perhaps create a new OEIS sequence1.)
This is a code-challenge, which will have you write code ...
- 8,097
19
votes
2
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Tiling a staircase with staircases
Background
A staircase polyomino is a polyomino made of unit squares whose shape resembles a staircase. More formally, a staircase polyomino of size \$n\$ is defined as follows:
A staircase polyomino ...
- 62.2k
13
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3
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Can this polyomino tile the toroidal grid?
Inspired by certain puzzles on Flow Free: Warps.
Background
We all know that L-triominos can't tile the 3x3 board, and P-pentominos can't tile the 5x5 board. But the situation changes if we allow the ...
- 62.2k
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votes
1
answer
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Test a polyomino against Conway criterion
Background
Conway criterion is a method to test if a given polygon can tile (i.e. cover without overlapping) an infinite plane. It states that a polygon can tile the plane if the following conditions ...
- 62.2k
11
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Counting hypercube Tetris pieces
Consider the Tetris pieces, but made out of some number of (hyper)cubes instead of four squares, where two blocks are considered the same if one is a rotation, reflection, or translation of another. ...
- 8,097
11
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Counting polyominoes on (hyper-)cubes
This challenge like some of my previous challenges will have you counting free polyforms, which are generalizations of Tetris pieces.
This code-golf challenge will have you count polyomino-like ...
- 8,097
22
votes
3
answers
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Impress Donald Knuth by counting polyominoes on the hyperbolic plane
This challenge is inspired by a talk about Schläfli symbols, etc that I gave in a Geometry seminar. While I was putting together this challenge, I saw that Donald Knuth himself was interested in (some ...
- 8,097
11
votes
4
answers
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L tromino tiling
Inspired by this challenge from puzzling.SE.
Polyominoes are fun - you can fill all sorts of shapes with them. But as soon as you have limits on what polyominoes you can use, you sadly start running ...
- 3,585
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2
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Number of distinct tilings of an n X n square with free n-polyominoes
The newest "nice" OEIS sequence, A328020, was just published a few minutes ago.
Number of distinct tilings of an n X n square with free n-polyominoes.
This sequence counts tilings up to ...
- 8,097
14
votes
2
answers
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Counting generalized polyominoes
This challenge will have you count pseudo-polyforms on the snub square tiling.
I think that this sequence does not yet exist on the OEIS, so this challenge exists to compute as many terms as possible ...
- 8,097
14
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8
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Rotation invariant fingerprinting
Imagine we have some polyomino and would like to uniquely identify them, however the polyominos can be rotated, so blindly hashing them won't give us the same fingerprint for a piece and a rotation ...
- 16.4k
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2
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Drawing convex polyiamonds
Description
OEIS sequence A096004 gives the
Number of convex triangular polyominoes [polyiamonds] containing n cells.
It begins:
...
- 8,097
29
votes
4
answers
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Smallest region of the plane that contains all free n-ominoes
On Math Stack Exchange, I asked a question about the smallest region that can contain all free n-ominos.
I'd like to add this sequence to the On-Line Encyclopedia of Integer Sequences once I have ...
- 8,097
20
votes
2
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Counting polystrips
Polystrips are a subset of polyominoes conforming to the following rules:
each piece consist of 1 or more cells
no cell can have more than two neighbours
the cells should not enclose a hole
Free ...
- 20.5k
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Compute the polyomino capacity of a rectangle
Write a program or function that takes as input three positive integers x, y, and a and ...
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