Modified checkerboard destruction

[bonanova]

@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 143^rd 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.)

[Molly Mae]

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Every cut increases the number of separate pieces by 1.  Since you can't cut more than one piece at a time, you will always need n-1 cuts to separate every square.  EDIT: You'll also never be able to do it in more than n-1 cuts.

Edited February 26, 2018 by Molly Mae

[CaptainEd]

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).

[bonanova]

  On 2/23/2018 at 3:42 PM, 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).

 

 

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Can you think of a reason?