## 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?*