Question 18
Let $Q$ be a square of size $12 \times 12$ given on an infinite cell grid. Student wants to paint some (not necessary all!) cells with seven colors (each cell with one color), such that no two three-cell rectangles (out of 288) with centers in $Q$ are colored identically. Is this possible?
(Two three-cell rectangles are colored identically, if it is possible to shift and/or rotate so that each cell of a rectangle matches the same color cell of the other rectangle.)
(Two three-cell rectangles are colored identically, if it is possible to shift and/or rotate so that each cell of a rectangle matches the same color cell of the other rectangle.)