MathDB

The cells of a square

100 \times 100

table are colored in one of two colors, black or white. A coloring is called admissible if for any row or column, the number

b

of black colored cells satisfies

50 \le b \le 60

. It is permitted to recolor a cell if by doing so the resulting configuration is still admissible. Prove that one can transition from any admissible coloring of the board to any other using a sequence of valid recoloring operations.

Problem Statement