MathDB

On an infinite white checkered sheet, a square

Q

of size

12

12

is selected. Petya wants to paint some (not necessarily all!) cells of the square with seven colors of the rainbow (each cell is just one color) so that no two of the

288

three-cell rectangles whose centers lie in

Q

are the same color. Will he succeed in doing this? (Two three-celled rectangles are painted the same if one of them can be moved and possibly rotated so that each cell of it is overlaid on the cell of the second rectangle having the same color.)
(Bogdanov. I)

1

Problems(1)