# 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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