4
$\begingroup$

In an award show, there are 12 jury members and 12 candidates to be selected as nominees. Out of 12 candidates, the jury has to pick 4 nominees for the award. So they decided that each jury member will vote for 4 of the candidates and the top 4 voted candidates will be selected as nominees.

What will be the minimum number of votes required for a candidate to confirm his/her nomination?

$\endgroup$
2
$\begingroup$

I believe it's

9 (At worst you will tie with someone for 4th place) or 10 (Guaranteed clean win)

Because

There are 12*4 = 48 votes in total. If you receive 8 or less votes, then there are still at least 40 remaining ones - more than enough for 4 other people get at least 9.

Here's an example on how you can still lose with 8 votes:
Let there be candidates A (you), B, C, D, and E. Assume the remaining candidates are utterly terrible and thus out of the consideration.
2 Juries vote A, B, C, D
2 Juries vote A, B, C, E
2 Juries vote A, B, D, E
2 Juries vote A, C, D, E
The remaining 4 Juries vote B, C, D, E
A (you) get 8 votes, while B, C, D, and E gets 10.

If you got 9 votes, however, there are only 39 votes remaining. Worst case scenario is that 3 other people got 10 votes and someone ties with you for 4th place with 9 votes.

To visualize this, imagine that in the example above one of the last 4 juries decided against voting one of B/C/D/E and voted for you instead. Then there will be 3 people with 10 votes, and you will tie at 9 votes with the person whose vote got taken.

If a clean win is a must, then 10 votes are necessary.

$\endgroup$
2
$\begingroup$

I'd say

2 (to reach a tied 4th place) or 3 (to be alone in the 4th place).

because

the jury has a total of 48 votes. When the top three candidates collect 12 votes each, there are 12 votes remaining for the other 9 candidates. If three of them get 2 votes and the rest 1, the three are tied for 4th place.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.