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P04 [Algebra] - Turkish NMO 1st Round - 2004

Source:

November 16, 2013
inequalitiesrearrangement inequality

Problem Statement

What is the difference between the maximum value and the minimum value of the sum a1+2a2+3a3+4a4+5a5a_1 + 2a_2 + 3a_3 + 4a_4 + 5a_5 where {a1,a2,a3,a4,a5}={1,2,3,4,5}\{a_1,a_2,a_3,a_4,a_5\} = \{1,2,3,4,5\}?
<spanclass=′latex−bold′>(A)</span> 20<spanclass=′latex−bold′>(B)</span> 15<spanclass=′latex−bold′>(C)</span> 10<spanclass=′latex−bold′>(D)</span> 5<spanclass=′latex−bold′>(E)</span> 0 <span class='latex-bold'>(A)</span>\ 20 \qquad<span class='latex-bold'>(B)</span>\ 15 \qquad<span class='latex-bold'>(C)</span>\ 10 \qquad<span class='latex-bold'>(D)</span>\ 5 \qquad<span class='latex-bold'>(E)</span>\ 0
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