Questions tagged [polyomino]

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13
votes
3answers
527 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
388 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 ...
9
votes
1answer
190 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. ...
10
votes
1answer
159 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 ...
17
votes
1answer
624 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
517 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 ...
17
votes
2answers
635 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 ...
13
votes
2answers
653 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 ...
15
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
232 views

Drawing convex polyiamonds

Description OEIS sequence A096004 gives the Number of convex triangular polyominoes [polyiamonds] containing n cells. It begins: ...
27
votes
4answers
866 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 ...
18
votes
2answers
435 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 ...
7
votes
1answer
183 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 ...