Random walk in Ring City puzzle

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Ring City has 100 houses arranged in a circle. Alice starts at her own house, and every day she randomly moves to one of the two adjacent houses, each with 50% probability.She repeats this until she has visited all of the houses.

Which house(s) is/are the most likely to be visited last?

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  • 3 Answer(s)

    her own

    TimSpence Starter Answered on 9th March 2017.

    she starts from her house daily.

    on 19th June 2018.
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    now 99 houses are remaining
    let her house be 1st one. 99/2=49.5 for integer term that’s 49.
    so her house + 49 =50 .so in 99 houses left 51th is going to be the last one.

    silento Scholar Answered on 15th June 2018.
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    The riddle is not formulated clearly. I think that "she randomly moves to one of the two adjacent houses" means that she moves to one of the two adjacent houses she went
    during the last two days. For example: If we had only 6 houses then on day 1 she can go to number 1 or 6 and if she went to 1 then on day 2 she can go to 2 or 6 and if she
     went to 6 then on day 3 she can go to 3 or 5 and so on. So if one day she goes left and on the other right the last one will be 1+(100/2)=51
    Moshe Expert Answered on 10th August 2022.
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