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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 ▼...
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23 votes
3 answers
1k views

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 ...
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14 votes
3 answers
304 views

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 ...
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22 votes
3 answers
530 views

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 ...
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9 votes
2 answers
280 views

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 ...
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25 votes
14 answers
4k views

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 ...
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  • 62.2k
16 votes
1 answer
363 views

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 ...
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  • 8,097
19 votes
2 answers
650 views

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 ...
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13 votes
3 answers
590 views

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 ...
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8 votes
1 answer
485 views

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 ...
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11 votes
1 answer
219 views

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. ...
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  • 8,097
11 votes
1 answer
196 views

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 ...
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  • 8,097
22 votes
3 answers
1k views

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 ...
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  • 8,097
11 votes
4 answers
693 views

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 ...
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17 votes
2 answers
841 views

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 ...
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  • 8,097
14 votes
2 answers
760 views

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 ...
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  • 8,097
14 votes
8 answers
2k views

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 ...
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7 votes
2 answers
252 views

Drawing convex polyiamonds

Description OEIS sequence A096004 gives the Number of convex triangular polyominoes [polyiamonds] containing n cells. It begins: ...
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  • 8,097
29 votes
4 answers
1k views

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 ...
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  • 8,097
20 votes
2 answers
523 views

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 ...
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8 votes
1 answer
192 views

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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