MathDB
Polyomino Caterpillar

Source:

March 24, 2021
combinatorics

Problem Statement

A polyomino PP occupies nn cells of an infinite grid of unit squares. In each move, we lift PP off the grid and then we place it back into a new position, possibly rotated and reflected, so that the preceding and the new position have nāˆ’1n-1 cells in common. We say that PP is a caterpillar of area nn if, by means of a series of moves, we can free up all cells initially occupied by PP.
How many caterpillars of area n=106+1n=10^{6}+1 are there?
Proposed by Nikolai Beluhov, Bulgaria