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A seqence of 51 terms

Source: 2019 Danube

October 29, 2019
number theorycombinatoricsSequence

Problem Statement

Let be a sequence of 51 51 natural numbers whose sum is 100. 100. Show that for any natural number 1≤k<100 1\le k<100 there are some consecutive numbers from this sequence whose sum is k k or 100−k. 100-k.
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