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base subsets -- Bulgaria MO

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September 21, 2010
inductioncombinatorics unsolvedcombinatorics

Problem Statement

Let MM be the set of the integer numbers from the range [āˆ’n,n][-n, n]. The subset PP of MM is called a base subset if every number from MM can be expressed as a sum of some different numbers from PP. Find the smallest natural number kk such that every kk numbers that belongs to MM form a base subset.
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