Question

Two players take turns placing multiple bishops on the cells of an 8×8 chessboard, one bishop per move, so that bishops from the same turn do not threaten each other. (The color of the bishop piece does not matter). The player who cannot make a move loses. Which player is the winner? Determine a winning strategy. (Note that a bishop moves and attacks by diagonals only.)

A. Player 1; Control the center of the board

B. Player 2; Spread bishops across the board

C. Player 1; Move bishops along the edges

D. Player 2; Concentrate bishops in corners

Answer 1

The winner is player one by adopting a strategy of mirroring player two's moves after initially placing a bishop in a corner. This tactic eventually forces player two into a position where they can't place a bishop without it being threatened, while player one retains legal moves.

Step-by-step explanation:

The player who can force their opponent into a position where they cannot make a legal move without breaking the rules (placing a bishop where it can be attacked by another) is the winner. In this scenario on an 8×8 chessboard, the key strategy is to place bishops in a way that maximizes board coverage without them threatening each other. Therefore, a winning strategy would be for the first player to place a bishop in one of the corners of the board. In doing so, they divide the board into two parts symmetrically. After that, every move that player two makes in one half of the board, player one mirrors in the opposite half, ensuring that player two will run out of non-threatening moves first.

Since player one can always mirror player two's moves, player two cannot avoid creating a position where player one will have a legal move and they will not. The strategic placement of bishops thus drives the game towards a conclusion in which player two can no longer place a bishop without it being threatened, while player one can still make a legal move, making player one the winner.