In every round of a certain game show, votes are cast by the public to decide which contestants out of contestants continue to the next round. The contestant with the lowest amount of votes in every round is eliminated. The next round proceeds with contestants, and so on. What is the minimum number of votes needed to guarantee that a contestant will proceed to the next round, assuming that he/she does not forfeit?
is updated at the start of every round to represent the number of remaining contestants.
may vary with each round.
Every round, one contestant must be eliminated by voting, forfeit, or tiebreaker.