Problem
COM-B1-M06-P022 Knight Returns
#22
★★★★☆ Level 4 of 5
A knight stands on a black square. Prove that it cannot return to the same square in exactly \(15\) moves.
The color changes after each move.
Every knight move changes the square color. After \(15\) moves, since \(15\) is odd, the knight is on the opposite color. The starting square is black, so it cannot return to it.
Short but important return idea.