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?
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.
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
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