MathDB
Transposing numbers arranged in a circle

Source: XV Rioplatense Mathematical Olympiad (2006), Level 3

August 10, 2011
combinatorics unsolvedcombinatorics

Problem Statement

The numbers 1,2,…,20061, 2,\ldots, 2006 are written around the circumference of a circle. A move consists of exchanging two adjacent numbers. After a sequence of such moves, each number ends up 1313 positions to the right of its initial position. lf the numbers 1,2,…,20061, 2,\ldots, 2006 are partitioned into 10031003 distinct pairs, then show that in at least one of the moves, the two numbers of one of the pairs were exchanged.
Back to ProblemsView on AoPS