Question 52
Given an $n \times n$ square table. Exactly one beetle sits in each cell of the table. At 12.00 all beetles creep to some neighboring cell (two cells are neighboring if they have the common side).
Find the greatest number of cells which can become empty (i.e. without beetles) if
a) $n = 8$;
b) $n = 9$.
(Problem Committee of BMO 2011)
Find the greatest number of cells which can become empty (i.e. without beetles) if
a) $n = 8$;
b) $n = 9$.
(Problem Committee of BMO 2011)