# Surviving elimination

In every round of a certain game show , $$v$$ votes are cast by the public to decide which contestants out of $$c$$ contestants continue to the next round. The contestant with the lowest amount of votes in every round is eliminated. The next round proceeds with $$c - 1$$ 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?

• $$c$$ is updated at the start of every round to represent the number of remaining contestants.

• $$v$$ may vary with each round.

• Every round, one contestant must be eliminated, by voting, forfeit or tiebreaker.

• $$c \geq 2$$

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