2000 IMO Problems/Problem 3
Let be a positive integer and a positive real number. Initially there are fleas on a horizontal line, not all at the same point. We define a move as choosing two fleas at some points and to the left of , and letting the flea from jump over the flea from to the point so that .
Determine all values of such that, for any point on the line and for any initial position of the fleas, there exists a sequence of moves that will take them all to the position right of .
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