MHB John & Peter's Chessboard Game: Minimal Moves for Victory

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In the chessboard game between John and Peter, John selects 8 squares on the board, ensuring no two are in the same row or column. Peter places 8 rooks on the board, aiming to avoid attacks among them. Peter wins if the number of rooks on John's chosen squares is even; otherwise, he must reset and try again. The challenge is to determine the minimal number of moves required for Peter to guarantee a win. The optimal strategy involves careful placement of rooks to manipulate the outcome and achieve victory in a minimal number of moves.
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John and Peter play the following game using a regular chessboard. John thinks of 8 squares so that no two squares lie in the same row or in the same column. During each move Peter puts 8 rooks on the board so that they don't attack each other, and John points out all rooks that are located on the squares he has chosen. If the number of rooks pointed out by John during this move is even (i.e., 0, 2, 4, 6 or 8), then Peter wins; otherwise all pieces are taken off the board and Peter makes the next move. What minimal number of moves are necessary for Peter to have a guaranteed victory?

Note: John thinks of 8 squares only once per game.
 
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Evgeny.Makarov said:
John and Peter play the following game using a regular chessboard. John thinks of 8 squares so that no two squares lie in the same row or in the same column. During each move Peter puts 8 rooks on the board so that they don't attack each other, and John points out all rooks that are located on the squares he has chosen. If the number of rooks pointed out by John during this move is even (i.e., 0, 2, 4, 6 or 8), then Peter wins; otherwise all pieces are taken off the board and Peter makes the next move. What minimal number of moves are necessary for Peter to have a guaranteed victory?

Note: John thinks of 8 squares only once per game.

Please post the solution you have ready.
 
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