Surviving elimination

In every round of a certain game show, v v votes are cast by the public to decide which contestants out of c 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 c1 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 c is updated at the start of every round to represent the number of remaining contestants.

  • v v may vary with each round.

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

  • c2. c \geq 2.


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