MathNet 2017-part-05 — 176 problems (EN–VI) Question 133

Initially, Bazil thinks of eight cells on a chessboard, no two of which are in the same row or in the same column. Then Pete makes a series of guesses. By a guess, he places 8 rooks onto the chessboard, and Bazil indicates all the rooks that stand on the cells he thought of. If Bazil indicates an even number of rooks, Pete wins. Otherwise, the rooks are removed from the board, and then Pete makes the next guess.

Find the least number of guesses at which Pete can win for sure.