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Pairwise differences of numbers

Source: AMC 10 2011 b Problem 21

February 24, 2011
AMC

Problem Statement

Brian writes down four integers w>x>y>zw > x > y > z whose sum is 4444. The pairwise positive differences of these numbers are 1,3,4,5,6,1,3,4,5,6, and 99. What is the sum of the possible values for ww?
<spanclass=′latex−bold′>(A)</span> 16<spanclass=′latex−bold′>(B)</span> 31<spanclass=′latex−bold′>(C)</span> 48<spanclass=′latex−bold′>(D)</span> 62<spanclass=′latex−bold′>(E)</span> 93 <span class='latex-bold'>(A)</span>\ 16 \qquad <span class='latex-bold'>(B)</span>\ 31 \qquad <span class='latex-bold'>(C)</span>\ 48 \qquad <span class='latex-bold'>(D)</span>\ 62 \qquad <span class='latex-bold'>(E)</span>\ 93
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