# Ants on a rod puzzle [closed]

Hi everybody,

Kindly forgive me if this question is too trivial for this forum. But I am just curious to find the right solution.

There are n ants ( of negligible width ) on 1m rod. They move at 1m/s and if they collide they reverse their direction without any delay. The ants fall off when they approach the end of the rod.

What will be the maximum time required for all ants to fall off ?

Intuitively an answer can be arrived at.

But is there a formal proof or solution for this ? How does one approach this problem for a mathematical proof ?

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## closed as too localized by Steve Huntsman, Reid Barton, Yemon Choi, Scott Morrison♦Mar 15 '10 at 21:11

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Answer is 1 sec. You may think that ants freely pass, without any colliding. – Petya Mar 15 '10 at 17:50
Imagine that colliding ants switch hats. Then the hats ignore each other and fall off within 1 second. – Douglas Zare Mar 15 '10 at 17:50
Those are extremely fast ants! – Harald Hanche-Olsen Mar 15 '10 at 17:53
Instead of "Intuitively an answer can be arrived at" it would be much better to say "I think the answer is ___, because ..." – Reid Barton Mar 15 '10 at 18:04
Douglas, when I first read your comment I thought you were saying something about the hats falling off of the ants and got terribly confused. – Qiaochu Yuan Mar 15 '10 at 19:27