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

[Evgeny.Makarov]

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.

 

[MarkFL]

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.