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.
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