Can We Use Parity?

Discrete Mathematics Level 2

Consider an \(8 \times 8\) grid of squares. We color every square blue or green such that 3 of the 4 squares on the corners of the grid are blue and the fourth is green.

Will there always exist a \(2 \times 2\) square inside this grid such that there are an odd number of squares of each color inside?

Bonus: Generalize this for the \(n \times n\) grid.

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, interactive explorations.

Used and loved by over 6 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.