Question 119
Given a $(2n + 1) \times (2n + 1)$ table, all its unit cells being white. Per move it is allowed to change the color of any three consecutive cells in any row or in any column (white cell is replaced by black one and vice versa).
a) Prove that for any positive integer $n$ one can obtain the chess coloring of the given table with white corner cells (the example of such coloring is shown in the figure for $n = 3$).
b) Find the minimum number of the moves one needs to obtain the chess coloring of the given table with white corner cells if $n = 3$. (E. Barabanov)
a) Prove that for any positive integer $n$ one can obtain the chess coloring of the given table with white corner cells (the example of such coloring is shown in the figure for $n = 3$).
b) Find the minimum number of the moves one needs to obtain the chess coloring of the given table with white corner cells if $n = 3$. (E. Barabanov)