Mounting A Defense Against Sheldon

Discrete Mathematics Level 4

We say that a set of rooks dominate the chessboard if each square is either occupied by a rook, or can be directly attacked by a rook. Obviously the smallest number of rooks which can dominate a \( 12 \times 12 \) chessboard is 12, which we can achieve by placing them along the main diagonal.

In 3-dimensional chess, rooks can attack in a straight line in the direction of the coordinate axis. What is the minimum number of rooks which can dominate a \( 12 \times 12 \times 12 \) chessboard?

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.