IMO Shortlist 2000 problem A5

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Dodao/la: arhiva
2. travnja 2012.
Let n \geq 2 be a positive integer and \lambda a positive real number. Initially there are n fleas on a horizontal line, not all at the same point. We define a move as choosing two fleas at some points A and B, with A to the left of B, and letting the flea from A jump over the flea from B to the point C so that \frac {BC}{AB} = \lambda.

Determine all values of \lambda such that, for any point M on the line and for any initial position of the n fleas, there exists a sequence of moves that will take them all to the position right of M.
Izvor: Međunarodna matematička olimpijada, shortlist 2000