Mowing a Chessboard
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 \(A+B\)?