For an integer
, we consider partitions of a
chessboard into rectangles consisting of cells of chessboard, in which each of the
cells along one diagonal forms a separate rectangle of side length
. Determine the smallest possible sum of rectangle perimeters in such a partition.
Proposed by Gerhard Woeginger, Netherlands
![m\geq 1](/media/m/1/7/1/1714fc0f740ba6df5a1a63ab4b83e195.png)
![2^m\times 2^m](/media/m/9/c/f/9cf61511b9907480b93858e7730de47d.png)
![2^m](/media/m/9/f/d/9fd21b1dfc0b1a705cfdb123862acd4f.png)
![1](/media/m/a/9/1/a913f49384c0227c8ea296a725bfc987.png)
Proposed by Gerhard Woeginger, Netherlands