Mowing a Chessboard

Logic Level 4

Imagine that you're mowing an \(8\times8\) chessboard pattern into your lawn. Here's how you plan to do it:

  • Your mower is wide enough to only mow one row or column at a time.

  • You proceed by choosing a row or column and mowing the entire thing. Once you start mowing a row or column you must continue mowing it until you reach the other side of the board.

  • You can mow over squares that you've already mowed over as long as at least one square in that row/column has yet to be mowed.

If \(A\) is the minimum number of times you must cross the board and \(B\) is the maximum number of times, what is \(A+B\)?


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