Polyomino Caterpillar
Source:
March 24, 2021
combinatorics
Problem Statement
A polyomino occupies cells of an infinite grid of unit squares. In each move, we lift 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 cells in common. We say that is a caterpillar of area if, by means of a series of moves, we can free up all cells initially occupied by .How many caterpillars of area are there?Proposed by Nikolai Beluhov, Bulgaria