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500 ants are placed on a 1-foot string without any order. Assume independent uniform distribution for each ant.
Each ant will move randomly towards either end of the string at a constant speed of 1 foot per minute.
The ants will keep moving until they reach the end of the string, and if two ants collide head-on, they will both immediately turn around and continue moving.
Assuming that the size of the ants is infinitely small, what is the expected time for all 500 ants to fall off the string?