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AoPS Math Contest

 
 
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AoPS Math Contest
by Aric Zhang - Monday, 31 July 2023, 6:28 PM
 

Call two units squares neighboring if they share a side.Pablo will start on the center unit square on a 3-by-3 grid of squares,and each second,given that he is  on Square d,he will move to a square neighboring d,each of the possible neighboring squares with equal probability.Find the expected value of the number of seconds he will take to move back to the center square.