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Turkish NMO First Round - 2012 Problem - 20 {Combinatorics}

Source:

July 1, 2012

Problem Statement

For each permutation

(a_1,a_2,\dots,a_{11})

of the numbers

1,2,3,4,5,6,7,8,9,10,11

, we can determine at least

k

of

a_i

s when we get

(a_1+a_3, a_2+a_4,a_3+a_5,\dots,a_8+a_{10},a_9+a_{11})

.

k

can be at most ?

<span class='latex-bold'>(A)</span>\ 11 \qquad <span class='latex-bold'>(B)</span>\ 6 \qquad <span class='latex-bold'>(C)</span>\ 5 \qquad <span class='latex-bold'>(D)</span>\ 2 \qquad <span class='latex-bold'>(E)</span>\ \text{None}

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