Bouncy Ants...

Algebra Level 3

One hundred ants are dropped on a 1 meter long stick. Each ant is traveling either to the left or the right with constant speed 1 meter per minute. When two ants meet, they bounce off each other and reverse direction. When an ant reaches an end of the stick, it falls off.

Over all possible starting configurations of the ants, what is the longest amount of time (in SECONDS) that you would need to wait to guarantee that the stick has no more ants ?

The problem is not original.

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