Difference between revisions of "2000 IMO Problems/Problem 3"
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Latest revision as of 16:01, 30 December 2024
Problem
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 .
Solution
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See Also
| 2000 IMO (Problems) • Resources | ||
| Preceded by Problem 2 |
1 • 2 • 3 • 4 • 5 • 6 | Followed by Problem 4 |
| All IMO Problems and Solutions | ||
