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Turkey NMO 2007 1st Round - P32 (Combinatorics)

Source:

October 5, 2012

Problem Statement

We are writing either 00 or 11 to unit squares of an 8×88\times 8 chessboard. If the sum of numbers is even vertically, horizontally, or diagonally, what is the greatest possible value of the sum of the all numbers on the board?
<spanclass=′latex−bold′>(A)</span> 32<spanclass=′latex−bold′>(B)</span> 48<spanclass=′latex−bold′>(C)</span> 52<spanclass=′latex−bold′>(D)</span> 56<spanclass=′latex−bold′>(E)</span> 64 <span class='latex-bold'>(A)</span>\ 32 \qquad<span class='latex-bold'>(B)</span>\ 48 \qquad<span class='latex-bold'>(C)</span>\ 52 \qquad<span class='latex-bold'>(D)</span>\ 56 \qquad<span class='latex-bold'>(E)</span>\ 64
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