Final Answer:
The maximum number of moves a knight and a bishop can make to capture all pieces on an n times n) chessboard is (
- 1) moves.
Explanation
In a chessboard scenario where a knight and a bishop aim to capture all pieces, their combined movement capabilities yield a maximum of (
- 1) moves for an (n times n\) board. This maximum count is achieved by employing an optimized strategy.
The knight's unique L-shaped movement restricts it to capturing pieces from various positions across the board. By carefully navigating the knight to cover every cell, it touches (
- 1) squares in a sequence that avoids revisiting any space.
The bishop's diagonal movement complements the knight's actions. It captures pieces along diagonals inaccessible to the knight. Combining these movements ensures comprehensive coverage of the entire board, maximizing the capture count while adhering to the rules of chess.
This strategy exhausts the potential moves of both the knight and the bishop, culminating in the capture of all pieces except one. The single leftover piece is safeguarded in a corner inaccessible to the bishop's diagonal or the knight's L-shaped moves.