One hundred people are standing in a line and they are required to count off in fives as "one, two, three, four, five" and so on
from the first person in the line. Anyone who counts "five" walks out of the line. Those remaining repeat this procedure until only
four people remain in the line. What was the original position in the line of the last person to leave?
Solution
In each pass, remove every fifth person from the current list and retain the others in their order. Near the end, the successive survivor lists become $$\{1,2,3,4,52,64,79,98\}$$, then $$\{1,2,3,4,64,79,98\}$$, then $$\{1,2,3,4,79,98\}$$ and then $$\{1,2,3,4,98\}$$. The next person removed is therefore the person originally in position $$98$$.
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