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Omni-MATH / Kolya and Dima play a game on an 8×8 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 dra…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

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 [list=a] [*]Dima makes the first move? [*]Kolya makes the first move? [/list] [i]
Plain-text mathematical notation (without MathML)
Kolya and Dima play a game on an 8×8 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
[list=a]
[*]Dima makes the first move?
[*]Kolya makes the first move?
[/list]
[i]
Original LaTeX notation
Kolya and Dima play a game on an $8\times 8$ 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
[list=a]
[*]Dima makes the first move?
[*]Kolya makes the first move?
[/list]
[i]

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Source and history

task_id
390858f5-ba1b-5e6d-b231-2fe1f671217f
task_key
test--390858f5-ba1b-5e6d-b231-2fe1f671217f
task_revision_id
1
config / split
/ test

Official source

initial import