Problem

Source: 2000 Estonia National Olympiad Final Round grade 10 p1

Tags: combinatorics



There are three candidates in the Hundilaane forest governor elections: $A, B$ and $C$. For each of the $20$ forest dwellers, the names of all three candidates were written on the ballot paper in the order of their preference. Examination of the ballots revealed that $11$ forest dwellers prefer $A$, $12$ $B$ and $14$ $C$. Which of the candidates will be marked first on the largest number of ballot papers when it is known that each possible the order of the candidates appears on at least one ballot?