Covering chessboard with crosses and dominoes
Source: Kvant Magazine No. 3 2020 M2595
March 10, 2023
gameboardcombinatorics
Problem Statement
Kolya and Dima play a game on an 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