MathDB

Ana and Bruno have an

8 \times 8

checkered board. Ana paints each of the

64

squares with some color. Then Bruno chooses two rows and two columns on the board and looks at the

4

squares where they intersect. Bruno's goal is for these

4

squares to be the same color. How many colors, at least, must Ana use so that Bruno can't fulfill his objective? Show how you can paint the board with this amount of colors and explain because if you use less colors then Bruno can always fulfill his goal.

Problem Statement