16. The pupils in Year 8 are holding a mock election. A candidate receiving more votes than any other wins. The four candidates receive 83 votes between them. What is the smallest number of votes the winner could receive?
A 21
B 22
C 23
D 41
E 42
Solution: B
Since $\frac{1}{4}(83)=20.75$, the winner must get at least 21 votes. If one candidate gets 21 votes there are 62 votes to be shared between the other three candidates, and so, as $3 \times 20<62$ one of these candidates must get at least 21 votes. So a candidate with 21 votes cannot be the winner.

However if one candidate gets 22 votes and the others 21,20 and 20 votes respectively, all 83 votes have been used, and the winner receives only 22 votes.