Busy Bricklayer Problem
The Busy Bricklayer Problem is a polyomino tiling problem for which its decidability is unknown.
Definition
The order of a polyomino is the minimum number of copies required to tile a rectangle (of any finite size with no gaps or overlaps, allowing for rotation and reflection) or zero if it doesn't tile any rectangles. Let the sequence a(n) be the maximum over the orders of all polyominoes of size n.
For example, a(5) = 10. Pentominoes F, N, T, U, V, and W have order 0, pentomino I has order 1, pentominoes L and P have order 2, and the Y pentomino has order 10 (with the following tiling).
Values
| a(n) | Value | Champion |
|---|---|---|
| 1 | 1 | |
| 2 | 1 | |
| 3 | 2 | |
| 4 | 4 | |
| 5 | 10 | |
| 6 | 92 | |
| 7 | 76 | |
| 8 | 246 | |
| 9 | 4 | |
| 10 |