Check Mate Solution!
All squares that are on the edge of the chessboard can hit 21 squares; there are 28 such squares. Now consider the 6x6 chessboard that is obtained by removing these bordering squares. The squares on the edge of this board can hit 23 squares; there are 20 of these squares. Now we consider the 12 squares on the boundary of the 4x4 chessboard left; each of these squares can hit 25 squares. The remaining 2 can hit 27 squares. The probability then follows as:
(21 × 28 + 23 × 20 + 25 × 12 + 27 × 4) / (64 × 63) =13/36
Check Mate Problem Check Mate Hints