MathDB

M2595

Part of Kvant 2020

Problems(1)

Covering chessboard with crosses and dominoes

Source: Kvant Magazine No. 3 2020 M2595

3/10/2023
Kolya and Dima play a game on an 8×88\times 8 board, making moves in turn. During his turn, Kolya must put one cross in any empty cell (i.e., in a cell in which a cross has not yet been drawn and which has not yet been covered with a domino). Dima must cover two adjacent cells with a domino (which are not yet covered with other dominoes), in which there are an even number of crosses in total (0 or 2). The one who can't make a move loses. Which of does the player have a winning strategy, if
[*]Dima makes the first move? [*]Kolya makes the first move?
Proposed by M. Didin
gameboardcombinatorics