MathDB
2n integers arbitrarily assigned to 2n numbered boxes

Source: JBMO 2008 Shortlist C3

October 14, 2017
JBMOcombinatoricsremainder

Problem Statement

Integers 1,2,...,2n1,2, ...,2n are arbitrarily assigned to boxes labeled with numbers 1,2,...,2n1, 2,..., 2n. Now, we add the number assigned to the box to the number on the box label. Show that two such sums give the same remainder modulo 2n2n.
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