The math club at Rocky Mountain High used ranked voting in its most recent election. The candidates for
president were Abby, Bart, and Carol. The 32 members of the club ranked their first, second, and third choices.
The voters' preferences sorted out as follows:
1. Abby had the smallest number of first-choice votes, but was ranked third by none of the voters.
2. Bart garnered both the largest number of first-choice votes as well as the largest number of third-choice votes.
3. Each candidate was ranked second by a positive even number of voters.
Can you determine the number of members who chose each possible order of the three candidates for president?
Or can you figure out how many 1st, 2nd, and 3rd place votes each candidate received?
Solution to the Problem:
13 voters chose Bart, Abby, Carol.11 voters chose Carol, Abby, Bart.
6 voters chose Abby, Carol, Bart.
2 voters chose Abby, Bart, Carol.
No one chose Bart, Carol, Abby.
No one chose Carol, Bart, Abby.
Here are the votes that each received:
| 1st | 2nd | 3rd | |
|---|---|---|---|
| Abby | 8 | 24 | 0 |
| Bart | 13 | 2 | 17 |
| Carol | 11 | 6 | 15 |
Correctly solved by:
| 1. James Alarie | Flint, Michigan |
| 2. Chelsea Anglen |
Mountain View High School, Mountain View, Wyomng |