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How can you show the sum is 260 if a chessboard is filled with numbers from 1 to 64 from top left to the bottom right row wise and 8 squares are chosen among them exactly one from each row and column?
Wiki User
∙ 14y ago
The first column, which is the first entries of each row, is 1, 9, 17, 25, 33, 41, 49, 57.
The second column is each of these numbers plus 1, the third column is each number plus 2, and so on until the eighth column which is each number plus 7.
By picking one square from each row and column, you are essentially getting each of the numbers from the first column as well and one of each +0, +1, +2, ... +7.
When you add that all together, you get 260:
1 + 9 + 17 + 25 + 33 + 41 + 49 + 57 + 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 = 260.
Wiki User
∙ 14y ago
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