A bunch of ants are left inside a very, very, tight tube, and they keep colliding with each other and turning around. How long will it take them to escape?

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Problem statement

Suppose you have a very thin pipe. The pipe is the exact width of an ant, so that ants can travel inside the pipe, but they can't cross paths because the pipe isn't wide enough for that. Assume an ant takes exactly 1h to travel through said pipe.

I will now place several ants along the pipe, facing different directions, and all ants will start walking in a straight line. When two ants collide, they both turn around and continue walking in the opposite direction they were walking in. When an ant reaches the end of the pipe, the ant just leaves the pipe.

What is the shortest amount of time that ensures all ants have left the pipe?

Solution

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