Question 133
At each node of the checkered $n \times n$ board sat a beetle. At midnight, each beetle crawled into the center of a cell. It turned out that the distance between any two beetles sitting in adjacent (along a side) nodes did not increase.
Prove that at least one beetle crawled into the center of a cell at a vertex of which it sat initially.
(A. Voidelevich)
Prove that at least one beetle crawled into the center of a cell at a vertex of which it sat initially.
(A. Voidelevich)