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Removing n numbers from {1,...,2n-1} to leave maximal sum

Source: Vietnam NMO 1990 question 2

October 26, 2008
combinatorics unsolvedcombinatorics

Problem Statement

At least n−1 n - 1 numbers are removed from the set {1,2,…,2n−1}\{1, 2, \ldots, 2n - 1\} according to the following rules: (i) If a a is removed, so is 2a 2a; (ii) If a a and b b are removed, so is a \plus{} b. Find the way of removing numbers such that the sum of the remaining numbers is maximum possible.
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