March 26, 2014 — There are infinitely many triples of
unequal positive integers (a,b,c) in geometric progression
in which every term is the square of an integer. What is the least possible value of a+b+c?
Glens Falls High School Mathletes have solved problems like these (the answer is 21, by the way) to finish in fifth place out of seven area schools in this year’s Math League competition. Senior Ethan Katz was the season's top scorer, with Emma Conrick, Jon White, Hannah Morrissey, and Brian Dwyre finishing as the top five.
Glens Falls' 32 Mathletes were coached this year by GFHS math teacher Tom Barrows. "The questions are very difficult," says Mr. Barrows, who describes the material as "outside-the-box." "Ethan did a great job coming up with the solutions. These questions are not the type that you just plug something into a formula or the calculator. Ethan showed great reasoning skills to be the team’s top scorer."
The season consisted of five math meets which started in November and went through March. At the meets, students work individually on the questions and are given 17 minutes to complete the first set of three questions. Papers are then collected and graded by the team's math coach while students work on the second set of questions.
Students do not know the questions in advance of a meet, and they look like this:
GFHS Mathlete team members include: Evan Abess, Annie Botch, Jacob Center, Bri Collins, Emma Conrick, Patty Corey, Ethan Cronquist, Liz deAvila, Scarlett Dewitt, Noah Duell, Brian Dwyre, Stephanie Eddy, Caroline Forbes, Alee Hayes, Joe Hill, Tom Jenkins, Ethan Katz, Logan Kunst, David Mauro, Hannah Morrissey, Ayumi Ogiwara, Emily Parent, Nate Plocharczyk, Adair Pruner, Tanner Sax, Lauren Stamatel, Allison Stanley, Demi Vanderheyden, Caleb Vaughan, Jon White, Clark Wooley, and Evan Yavner.
Emily Parent designed the team’s T-shirts for 2013-14.