MathDB
Coloring of a board without monochromatic dominoes

Source: Kvant Magazine No. 11-12 2023 M2774

March 16, 2024
combinatoricsboardColoringdominoes

Problem Statement

In a 50×5050\times 50 checkered square, each cell is colored in one of the 100 given colors so that all colors are used and there does not exist a monochromatic domino. Galia wants to repaint all the cells of one of the colors in a different color (from the given 100 colors) so that a monochromatic domino still won't exist. Is it true that Galia will surely be able to do this
Proposed by G. Sharafutdinova