Rolla HS and Central HS duelled through all 12 questions, so we went to a tie-breaker. Rolla won the contest and Central received very honorable mention.

1. What is the degree measure of an interior angle of a regular 30-sided polygon?
2. Find the next most likely term in the following sequence: 0, 1, 6, 20, 50, 105, 196, ...?
3. If the polynomial x⁴ + kx³ + 5x² + k has x − 2 as a factor, what must k be?
4. Find all solutions to |log₃|log₃x|| = 1.
5. A group consists of 8 Americans and 7 Canadians. How many ways are there to choose a committee of 3 people from this group if at least one committee member must be Canadian?
6. If a fair coin is tossed 8 times, what is the probability that exactly 4 of the tosses are heads? Please give your answer as a reduced fraction.
7. Find the first three digits of 2019²⁰¹⁹.
8. A car travels up a hill at an average speed of 36 mph and down the same hill at an average speed of 45 mph. What is the average speed for the round trip?
9. A spherical snow ball is melting. If its surface area decreases by 19%, by what percentage does its volume decrease?
10. Find the total number of squares (of any size) in the figure shown.
    

11. Find the last three digits of 1! + 2! + 3! + ... + 100!.
12. In the figure shown, AP/PB = BQ/QC = CR/RA = 1/2. Find the ratio of the area of triangle ABC to the area of triangle PQR.
    

TIE BREAKER: The partition number of an integer n is the number of ways of writing n as a sum of positive integers where the order of the integers does not matter. For example the partition number of 5 is 7 since 5 = 5, 4 + 1, 3 + 2, 3 + 1 + 1, 2 + 2 + 1, 2 + 1 + 1 + 1, or 1 + 1 + 1 + 1 + 1. What is the partition number of 50?

The team getting closest to the correct answer wins.

Here are the answers.