Puzzle round.
Ants on a pole
The question
Ants are placed at random points on a one-metre pole, each facing a random direction, all walking at one metre per minute. When two meet they reverse. How long until the pole is clear?
Have a go before you open the solution. If you are stuck after a few minutes, the first paragraph below is usually enough of a nudge.
Show the worked solution
The answer
At most one minute.
When two ants collide and reverse, the picture is identical to the two ants passing through each other and swapping identities.
Under that relabelling every ant walks in a straight line and leaves the pole within one minute.
Since the set of positions is the same in both pictures, the pole is clear within one minute in the original problem too.
The worst case is exactly one minute, achieved by an ant starting at one end walking the full length.
What it is testing
Finding the change of view that removes the interaction entirely.
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