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2008 OIM Problems/Problem 1

Revision as of 15:28, 14 December 2023 by Tomasdiaz (talk | contribs) (Created page with "== Problem == Numbers <math>1, 2, 3, \cdots , 2008^2</math> were distributed on a <math>2008 \times 2008</math> board, such that in each box there is a different number. For e...")
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Problem

Numbers $1, 2, 3, \cdots , 2008^2$ were distributed on a $2008 \times 2008$ board, such that in each box there is a different number. For each row and each column of the board, the difference between the largest and smallest of its elements is calculated. Let $S$ be the sum of the 4016 numbers obtained. Determine the largest possible value of $S$.

~translated into English by Tomas Diaz. ~orders@tomasdiaz.com

Solution

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See also

OIM Problems and Solutions

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