IMO 2000 Problem 3

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 $M$ .