Problem
COM-B1-M07-P011 A Knight Path on \(4\times4\)
#11
★★☆☆☆ Level 2 of 5
A knight starts in a corner of a \(4\times4\) board, makes \(15\) moves, and visits a new cell each time. Can it finish in the opposite corner?
Compare the colors of the corners and the parity of the number of moves.
Opposite corners of a \(4\times4\) board have the same color. But every knight move changes color, so after \(15\) moves, an odd number, the knight must be on the opposite color. Therefore it cannot finish in the opposite corner.
No need to know whether a full tour exists.