An ant is walking on a hexagon. At each step, he moves from the vertex on which he is standing to an adjacent vertex. After 6 steps, what is the probability that he is standing on the same vertex on which he began?

Guest Nov 4, 2020

#3**0 **

*An ant is walking on a hexagon. At each step, he moves from the vertex on which he is standing to an adjacent vertex. After 6 steps, what is the probability that he is standing on the same vertex on which he began?*

If the ant is allowed to backtrack any time he wants to, my guess is the odds are 50-50. In other words, he might or he might not.

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Guest Nov 4, 2020

#5**0 **

This question is about an ant, and there's a comment by Pangolin.

How many of you knew that a pangolin is ... wait for it ... an anteater!

What I meant by 50-50 is that, if the ant is allowed to move either direction, then for each step, there'd be just as much chance that he would go backward as forward, therefore his probability of landing where he started would be 50%.

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Guest Nov 5, 2020