Problem A. 794. (February 2021)

A. 794. A polyomino \(\displaystyle P\) occupies \(\displaystyle n\) cells of an infinite grid of unit squares. In each move, we lift \(\displaystyle P\) 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 \(\displaystyle n-1\) cells in common. We say that \(\displaystyle P\) is a caterpillar of area \(\displaystyle n\) if, by means of a series of moves, we can free up all cells initially occupied by \(\displaystyle P\).

How many caterpillars of area \(\displaystyle 10^6 + 1\) are there?

Submitted by Nikolai Beluhov, Bulgaria

(7 pont)

Deadline expired on March 10, 2021.

Statistics:

2 students sent a solution.
1 point:	2 students.

Problems in Mathematics of KöMaL, February 2021