in a certain club with 29 members, there are 3 candidates for club president. If all 29 club members vote and each member votes for exactly 1 candidate, what is the least number of votes a candidate can receive and still be sure in all cases of receiving the most votes?

Question

anonymous · Answer

@Kainui

kainui · Answer

Well, reason through it a little bit. What do you think?

kainui · Answer

Just like, throw ideas out and I'll give you useful advice on what direction to think in.

anonymous · Answer

@Kainui Someone told me to use permutation, and I have no clue @Kainui

kainui · Answer

No permutations needed here at all. You know that you must have the majority of the votes to win right? What's the majority of the people?

kainui · Answer

So for example, if it was him versus the other 2 people, he can get all 29 votes and they can both get 0. He wins, but this isn't the least amount of votes, because he will still always win if he gets 26 votes and one of the other guys gets 1 and the other gets 2 or one other guy gets all 3 other votes and the other gets 0, right?

anonymous · Answer

The majority? That's not stated, is it?

kainui · Answer

Yep, that's what the question is saying. What's the least amount of votes that guy can get while being sure that he won the election no matter what. So for example, he could win with 11 votes and the other guys could each have 9 votes (11+9+9=29) but that doesn't guarantee he's going to win because he could get 11 votes and one guy could get 0 votes while the other gets all 18 other votes (11+0+18=29). So he could win, but not unless the other votes are split a special way.