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Modified checkerboard destruction



@CaptainEd brilliantly answered a puzzle that I mis-worded into a much tougher one. Nice job.

Here's the puzzle I had intended to post:

You have just lost your 143rd straight game of checkers and have vowed never to play another game. To confirm your vow you decide to saw your wooden checkerboard into pieces that contain no more than a single (red or black) square. With each use of the saw you may pick up a piece of the board and make one straight cut, along boundaries of individual squares, completely through to the other side. You wish to inflict as much damage as possible with each cut, so you first calculate the minimum number of saw cuts needed to finish the job. And that number is ... (spoilers appreciated.)

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4 hours ago, CaptainEd said:

Thank you for the kind words, Bonanova. I fear my answer to this one is not so brilliant. 


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63 is the lowest I can get. 

7 vertical cuts of length 8, 

56 horizontal cuts of length 1

i get the same result if I divide the board into 4 quarters, divide those into quarters(16), and divided THOSE into quarters(64).



Can you think of a reason?

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