Will Petya Succeed ? , P1
Source: Silk Road Mathematical Competition 2017, P1.
May 25, 2017
combinatoricssrmc
Problem Statement
On an infinite white checkered sheet, a square of size × 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 three-cell rectangles whose centers lie in 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)