MathDB

In a

50 \times 50

checkered square, each cell is painted in one of

100

given colors so that all colors are present and it is impossible to cut a single-color domino from the square (i.e. a

1 \times 2

rectangle). Galiia wants to recolor all the cells of one of the colors into another color (out of the given

100

colors) so that this condition is preserved (i.e., it is still impossible to cut out a domino of the same color). Is it true that Galiia will definitely be able to do this?

Problem Statement