# Another Knight On The Tiles

**Discrete Mathematics**Level 5

This chessboard has a "safe zone," consisting of the four central squares. The knight starts its journey on one of the squares in the safe zone. The expected number of moves it must make until it returns to any square in the safe zone can be written as \(\tfrac{a}{b}\), where \(a\) and \(b\) are coprime positive integers. What is the value of \(a + b\)?