Fabian has a deck of 25 cards. Each card has an integer between 1 and 5, inclusive, printed on it in one of five colors: red, orange, green, blue, or violet. Each number-color combination appears on exactly one card in the deck. Fabian draws four cards at random, without replacement, from the deck. What is the probability that exactly two different numbers and exactly three different colors appear on his four cards? Express your answer as a common fraction.

This was one of the easier questions in the recent 2017-18 MATHCOUNTS competition.

Despite daunting questions such as these, the TBS MATHCOUNTS team placed ninth out of 18 schools at the county competition on February 10, 2019, and enjoyed the experience of competing, which was the goal of MATHCOUNTS Faculty Advisor Mrs. Cathryn Hansen.

“I want people to have a passion for math, and also for science, engineering, and technology,” said Hansen. “Math is the foundation of all those lovely subjects. They unite everything. [Math] also opens different doors and opportunities for you.”  

The following students were part of the 2019 Benjamin Mathletes team: eighth graders Sean Collins, Darren Dharia, Jessica Holland, Skyler Malmberg, Aadi Patel, Joie Rodin, Darian Salehi, and Jonathan Skatoff, as well as seventh graders Tyler Kelly, Wilson Stewart, and Addie Vining.  

To determine the team, Hansen advertises the opportunity to the entire Middle School before whittling it down to the best math students in the division.

“We find out who’s interested [in Mathcounts] in school, and we take the top ten people who are interested in it,” said Hansen who is also chair of the middle school math department. “Usually, [the team consists of] Algebra I kids, Geometry kids, and Algebra II kids because you have to have the exposure [to those concepts]. From there, we progress to the county chapter and we have fun.”

Many of the students joined because they enjoy math and they want to be challenged in new ways.

“I joined because I liked doing it last year,” said eighth-grader Jonathan Skatoff. “It’s something that you don’t get to do on a regular day of school, and I like math, so it makes it fun. I learn stuff and become more challenged than I normally [am] during class.

“I am good at math and I have really good grades, so I decided to try,” added seventh-grader Tyler Kelly, a new member of the team this year.

To prepare for the competition, the team met twice a week either in the morning at 7:30, during lunch, or during study hall in Mrs. Hansen’s room beginning four weeks prior to the competition. The students practiced different kinds of math and the different categories of challenges each mathlete would need to know before going into the competition.

“We each completed a series of packets for about a month,” said Skatoff. We also met in the mornings to discuss and check the packets.”

At the county competition, which took place at the Gulf Stream School, there were five parts to the competition. The sprint round was individual and consisted of competitors trying to answer 30 questions in 40 minutes. In the target round, students had to answer four pairs of questions and had six minutes to complete each pair. In the team round, a group of four contestants on each team had to complete 10 questions in 30 minutes. The cipher round was a friendly individual round where four students from each school compete to answer the questions the fastest. Finally, the countdown round pitted the top 10 individual competitors from the previous three rounds against one another. This final portion of the competition had students battle head-to-head in a test of speed and accuracy. Once a student raised his or her hand in an attempt to answer the problem, he or she had three seconds to answer it correctly.

Out of the ten Benjamin mathletes who competed, the top-scoring competitor was seventh-grader Addie Vining who placed 25th overall out of 186 students, earning her a certificate.

“I think since I was on the team before, I knew what was coming since I had the experience,” said Vining. “ I also love math, [which] was the reason I joined MATHCOUNTS. I felt accomplished when they called me up for the award. Our team last year did better, but the difference is the experience of each Benjamin contender.”

Last year’s TBS MATHCOUNTS team earned second place overall out of 15 competing schools at the county competition. In addition, former seventh-grader Kiran Spencer finished first out of the 150 students in the individual competition, earning him and the team a trip to the state tournament.

“Every year it just depends on what the competition is and what the strengths [are], and how much everyone is involved,” said Hansen. “Our whole point is to get more and more people involved.”

Despite the short amount of time Hansen had to put the team together and prepare them for the competition, she feels this year’s group did a great job.

“I expect much from the students, and I am always proud of the team each year, so yes, I am proud of this team,” she said.