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1. Take three coins of radius 2 and arrange them in a triangle touching each other. What is the area of the region left in between the coins?
2. Find, with proof, the smallest possible sum of six distinct prime numbers which form an arithmetic progression.

These questions are from the 2017 High School Mathematics Competition (HSMC), held on April 15, 2017, at Georgia Tech. Close to 300 students from 30 schools participated in the day-long event.

The competition comprised four exams covering algebra, geometry, combinatorics, number theory, and basic calculus. The School of Mathematics hosted the event, thanks to an army of volunteer Georgia Tech faculty, staff, and students, led by School of Mathematics Academic Professional Christopher Jankowski

Participating schools sent up to five teams of five students each. The fierce competition, held in the Clough Undergraduate Learning Commons, culminated in team and individual winners.

The top five teams, listed alphabetically, scored 835-1,000 points out of a possible perfect score of 1,600 points:

The highest individual scorers, listed alphabetically, scored 33-41 points out of a possible perfect score of 50 points:

According to Jankowski, questions 1 and 2 above are, respectively, one of the easier and one of the harder questions. Here are the answers:

1. 4 √ 3 − 2π. For the solution, go to http://hsmc.gatech.edu/sites/default/files/2017cypher_0.pdf
2. 492. For the solution, go to http://hsmc.gatech.edu/sites/default/files/2017proof_0.pdf

Problems and solutions from the competition in 2017 and earlier years are available at http://hsmc.gatech.edu/exams.

“The sheer energy and brain power of these students is inspiring for all of us,” says School of Mathematics Professor and Chair Rachel Kuske. "Throughout the day of competition, there was plenty of opportunity for camaraderie and sharing ideas.”

“It was a day of fun and mathematics for the students and volunteers,” Jankowski adds. “We hope to make it even better next year.”

In the group pictured above are hosts, volunteers, and guests. Standing (from left) are Rachel Kuske, Sharon McDowell, and Christopher Jankowski, from the School of Mathematics (SoM); Debbie Poss and Don Slater, Lassiter High School; Prasad Tetali, SoM; Angelique Allen, Greater Atlanta Christian School; Carol Sikes, South Forsyth High School; and Tom Morley, SoM. Seated are student participants (from left) Ella Zhou, Andrea Zheng, and Bryn Evans.

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Published
• Created By:
A. Maureen Rouhi
• Created:
04/27/2017
• Modified By:
A. Maureen Rouhi
• Modified:
05/01/2017

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