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Putnam 1995 A4

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July 1, 2014
Putnamcollege contests

Problem Statement

Suppose we have a necklace of nn beads. Each bead is labelled with an integer and the sum of all these labels is n−1n-1. Prove that we can cut the necklace to form a string whose consecutive labels x1,x2,⋯ ,xnx_1, x_2,\cdots , x_n satisfy \sum_{i=1}^{k}x_i\le k-1  \forall \;\;1\le k\le n
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