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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14
votes
3answers
295 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 ...
22
votes
3answers
434 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 ...
9
votes
2answers
273 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 ...
24
votes
14answers
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 ...
13
votes
1answer
305 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 ...
19
votes
2answers
639 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 ...
13
votes
3answers
561 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 ...
8
votes
1answer
461 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 ...
10
votes
1answer
213 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. ...
11
votes
1answer
186 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 ...
22
votes
3answers
974 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 ...
11
votes
4answers
657 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 ...
16
votes
2answers
769 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 ...
14
votes
2answers
730 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 ...
14
votes
8answers
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 ...
7
votes
2answers
247 views

Drawing convex polyiamonds

Description OEIS sequence A096004 gives the Number of convex triangular polyominoes [polyiamonds] containing n cells. It begins: ...
27
votes
4answers
968 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 ...
19
votes
2answers
473 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 ...
8
votes
1answer
190 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 ...