Alice and Bob take turns placing bishops on

empty squares of a 2026×2026 chessboard, with

Alice moving first. At all times, no diagonal

may contain four bishops. The game ends when

no legal move is possible; the player who makes

the last move wins.

Questions.

A. Assuming both players make optimal moves,

who would win the game? Explain.

B. Would the answer for part A change if the

chess board was of size 2025×2025?

C. After the game, they decide to put bishops on

the empty 2026×2026 board in a way that no

diagonal contains more than three bishops.

Maximum how many bishops they can put on

the board? Describe a pattern that

corresponds to the maximum number of

bishops on the board.

asked by guest
on Mar 17, 2026 at 3:15 pm



MathBot Answer:

MathBot is working on a solution to your problem.

Loading bar