MathDB

A polyomino

P

occupies

n

cells of an infinite grid of unit squares. In each move, we lift

P

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

n-1

cells in common. We say that

P

is a caterpillar of area

n

if, by means of a series of moves, we can free up all cells initially occupied by

P

.
How many caterpillars of area

n=10^{6}+1

are there?
Proposed by Nikolai Beluhov, Bulgaria

A. 794