Thread: Problem 37
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Old September 20th, 2007, 04:34 AM
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Quote:
Originally Posted by ThePerfectHacker View Post
3)Given an 8\times 8 checkerboard what is the maximum number of checkers which can be placed so that no two are adjacent. Prove your answer. "Adjacent" means either horizontally or veritcally next to eachother not diagnolly.
That simply means that all the pieces should either be on the white squares or black squares only. Seeing as the amount of black squares is equal to the amount of white squares, then that means the maximum amount of pieces which can be placed is: \frac{1}{2} (8 \times 8) = 32 \ pieces
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