Ten people meet in a room.  Each person shakes hands once with everyone else in the room.  How many handshakes take place?

You have 30 seconds to answer, no calculator, and an anxious audience of nearly two-hundred parents, peers, and teachers.  Such were the challenges presented by Florida Engineering Society’s 29th annual MATHCOUNTS competition, held February 25 at the FAMU/FSU College of Engineering in Tallahassee.

Riversprings Middle School placed fifth among top mathematicians from twelve competing middle schools around the Big Bend area in the regional competition.  The challenges included timed Sprint, Target, and Team round competitions, as well as an entertaining Cipher round in the afternoon that was open to parents, coaches and spectators.

Mattias Gunnarsson placed 18th among all competitors and was the team’s top individual scorer, followed by Kyle Pearson, Nic Samlal and Isaac Kent.  Riversprings Middle School Team members were eighth-grade students Gunnarsson, Kyle Pearson, Samlal, Kent, John Ahrendt, Blakeleigh Bolton, Maria Parmer and Jenna Franck, and seventh-grade student, Paige Pearson.  The team is coached by John Kane.

The day-long event featured team photos, competitions, a pizza luncheon, and closed with a Mathlete awards ceremony.  The MATHCOUNTS meet was hosted by the FAMU/FSU College of Engineering and sponsored by the Florida Engineering Society, the Big Bend Chapter of the Florida Engineering Society, and numerous local supporters.  A special thank you to Mr. Patrick Becker (Riversprings Middle School) and Mrs. Ro Samlal (Shadeville Elementary) for their time and effort supporting the Team and for making the competition possible.

The solution to the sample problem is 45 handshakes.  The first person shakes hands with nine other people.  The second person, having already shaken with one person, shakes hands with the eight remaining people, the third person shakes hands with the seven remaining people, and so forth.  So the total number of handshakes is determined by the sum 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1, which is 45.

Pictured (left to right) front row:  Jenna Franck; second row:  Isaac Kent, Nic Samlal, and Paige Pearson; third row:  John Ahrendt, Maria Parmer, and Blakeleigh Bolton; back row:  Kyle Pearson and Mattias Gunnarsson.

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