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Coins on number line

Source: Swiss Math Olympiad 2010 - final round, problem 1

March 16, 2010
combinatorics proposedcombinatoricsinduction.

Problem Statement

Three coins lie on integer points on the number line. A move consists of choosing and moving two coins, the first one 1 1 unit to the right and the second one 1 1 unit to the left. Under which initial conditions is it possible to move all coins to one single point?