## Annual Chris Nash Mathematics Competition

In 2023, the Department of Mathematics & Statistics is hosting the annual Chris Nash math competition on Saturday, March 25.

The competition will be held in MSPB 370 from 10am to noon. Afterwards, free pizza will be provided. The event is open to all USA undergraduates and the problems should be accessible to anyone familiar with Calculus I.

Please email Dr. Straub at straub@southalabama.edu if you are interested in participating. You will then receive a copy of a previous contest. (And we will have an idea of how much pizza to get.)

Prizes of $500,$200 and $100 are awarded to the top three contestants who will still be enrolled in Fall (math/stats majors are eligible for the main prize of$500, any major is eligible for the $200 and$100 prizes).

When?
Saturday, March 25, 2023
10am - noon

Where?
MSPB 370

Who?

If you are interested, please send an email to Dr. Straub at straub@southalabama.edu.
You will then receive a copy of a previous contest.

### Example problems

The problems on the contest are of varying difficulty. They are meant to be fun challenges, and it is typical for the winner to only solve a subset of them.

The first few problems are usually designated as warm-up problems to indicate that they require less work. All of the problems should be accessible to anyone familiar with Calculus I, and the problems are crafted so that having taken advanced math classes should not provide an unfair advantage.

Below are three example problems from past contests.

Example (warm-up):
A recipe for a certain mixed drink calls for $$1$$ ounce of $$1$$-$$1$$ simple sirup (meaning the sirup is $$1$$ part sugar and $$1$$ part water). Suppose you only have $$2$$-$$1$$ simple sirup at hand ($$2$$ parts sugar and $$1$$ part water). For use in the recipe, how much of your simple sirup do you mix with how much water?

Example (challenging):
$$60$$ candidates run for the position of mayor in the town of Hogsface. $$500$$ inhabitants show up for the election and cast one vote each for a single candidate. What is the smallest number $$d$$ such that there must be at least $$d$$ candidates with the same number of votes?

Example (challenging):
We start with an eight-sided polygon (you can think of the shape of a stop sign) and cut it into successively smaller pieces. Specifically, during each step, we cut every piece into two smaller pieces (via a straight cut), so that after 10 steps the initial polygon has been cut into $$2^{10}$$ pieces. Let $$m$$ be the total number of vertices of these $$2^{10}$$ pieces. What is the minimum possible value for $$m$$? What is the maximum possible value for $$m$$?

### Past winners

Congratulations to all the past prize winners!

 2022 Mirza Helms Daniel Hodgins Alex Jin Felicity Bryant 2021 Daniel Hodgins Dylan Johnson Mirza Helms 2020 Audrey Palmore Ashlyn Stahly Dylan Johnson 2019 John Pomerat Samuel Formichella Martin Piff Harley McCardle 2018 Samuel Formichella Kevin Ingles Donald Bethea Rachel Chai