Questions tagged [polyomino]
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15
questions
10
votes
1answer
250 views
Gluing tetrahedra together
(This challenge exists to extend sequence A267272 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 ...
20
votes
2answers
617 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
543 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
429 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
205 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
177 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
854 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
572 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
712 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
690 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
240 views
Drawing convex polyiamonds
Description
OEIS sequence A096004 gives the
Number of convex triangular polyominoes [polyiamonds] containing n cells.
It begins:
...
27
votes
4answers
928 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
450 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
188 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 ...
