More riddles

Following my own riddle post (OK, not really), Gil Kalai posted two math riddles. I would like to offer a variation on the ant riddle, which also appears in Peter Winkler’s book (it has a whole chapter on ants riddles):

24 ants are randomly placed on a a circular track, each in a random direction. Whenever 2 ants collide they each reverse direction. The track is 1 meter long and ants walk at 1 meter per minute. After one minute, what is the probability that Alice, a randomly chosen ant, finds herself in the place she began?

And if I might add:

Would the answer change significantly, if there were 25 ants, instead of 24?

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~ by Ori on October 24, 2008.

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