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2000 IMO Problems/Problem 3

Revision as of 23:12, 18 November 2023 by Tomasdiaz (talk | contribs)

Problem

Let $n \ge 2$ 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 $B$ 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 $M$.


Solution

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See Also

2000 IMO (Problems) • Resources
Preceded by
Problem 2 		1 • 2 • 3 • 4 • 5 • 6 Followed by
Problem 3
All IMO Problems and Solutions
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