Question 1197385
Image is here: https://latex.artofproblemsolving.com/d/0/4/d04c14a38efb837151549f4b864fde841fa50f95.png
*[illustration d04c14a38efb837151549f4b864fde841fa50f95.png].
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Answer(since I originally answered the question in Latex, and since It's almost time to sleep, I will edit it tomorrow.)(The original post is here: https://artofproblemsolving.com/texer/yglroond)


Color the dots red and blue shown below.. Notice that whenever the ant moves, it moves from a red dot to a blue dot or a blue dot to a red dot. So since *[tex A] is a red dot, it must move to a blue dot, then a red dot, then a blue dot, then a red dot, and end up on a blue dot. There are only four blue dots, and the ant is equally likely to end up on any one of these four, since the diagram is symmetric to a *[tex 90^\circ] rotation. The probability that the ant ends on *[tex B] after five minutes is therefore *[tex \fbox{\frac{1}{4}].
*[illustration d6e224fa2ed11f3b16d2e15a0a8d8709847d7326.png].

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Note: @Ikleyn is not correct unlike the other times I saw her answer questions. The correct ones are me and @greenstamps.