Class President Election
Adam, Bernice, and Carl are candidates in the class president election. Including them, a total of 40 students will vote in this election. In order to win, a candidate must get more votes than any other candidate.
What is the fewest number of votes Bernice needs to secure her victory with certainty?
Details and Assumptions:
- Each of the 40 students casts a single vote.
- All votes are valid.
- Every candidate will vote for himself or herself.
The answer is 20.
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1 solution
In order to win Bernice needs at least half of total votes. The problem say that each candidate will receive at least a single vote.
4 0 − 3 = 3 7 votes must be distributed in a way that Bernice wins. The half of 3 7 is 1 8 and will be left one vote. If Bernice receive more 1 8 votes, and other candidate receive the other 1 8 will be a draw. Then Bernice need to receive the last vote to tie break the election. In total she needs to receive at least 1 8 + 1 + 1 = 2 0 votes to assure her victory.
Notice that if she receive 2 0 votes the maximum number of votes that any other candidate can receive is 1 9 . Why not 2 0 ? It is because the third candidate will receive the last vote (his own vote).