Question 74
Find the smallest positive integer $n$ such that, if there are initially $2n$ townspeople and $1$ goon, then the probability the townspeople win is greater than $50\%$.
Official shared context (supplement): Each morning jail a uniformly chosen remaining player; stop if either side is gone. Each evening jail a uniformly chosen townsperson; then goons win if their number is at least the townspeople’s. Start in the morning.
Official preamble: https://hmmt-archive.s3.amazonaws.com/tournaments/2014/nov/thm/problems.pdf
Official shared context (supplement): Each morning jail a uniformly chosen remaining player; stop if either side is gone. Each evening jail a uniformly chosen townsperson; then goons win if their number is at least the townspeople’s. Start in the morning.
Official preamble: https://hmmt-archive.s3.amazonaws.com/tournaments/2014/nov/thm/problems.pdf