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Calvin Wins Statewide Mathematics Contest
May 10, 2005

For the 14th time in 29 years a team from Calvin College has won the annual Lower Michigan Mathematics Competition.

The event was held April 2 at the University of Michigan-Flint (it is held every spring at an institution in the lower peninsula of the state of Michigan) and the results were just recently released.

Calvin led a quartet of West Michigan schools in the top 10 (a total of 27 teams were entered in the competition).

The three-man Calvin squad of John Engbers (Grand Rapids/GR Christian), Kyle Glashower (Hudsonville/Unity Christian) and Matt Voorman (Thousand Oaks, CA) topped all 27 teams with 75 points. Albion was second with 66 points, while Grand Valley State's squad was third with 62 points. Aquinas College was fifth overall, while Hope College was sixth.

The annual competition is pretty simple: undergraduate students from four-year colleges and universities from the state of Michigan gather to challenge themselves on 10 interesting problems.


Find, with proof, the largest whole number that cannot be written as the sum of two composite whole numbers. (Recall that a whole number greater than 1 is "prime" if its only divisors are itself and 1; otherwise the number is "composite". Some small prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19, 23. Some small composite numbers are: 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22.)

Suppose there are 3 lines in 3-dimensional space, no two of which are parallel. Prove or disprove: there is a fourth line that passes through each of the other three lines.

Students compete in teams of up to three members, and each team has three hours to write solutions to the problems without the assistance of calculators, computers or books.

Calvin mathematics professor Gary Talsma notes that the school represented by the winning team takes possession of the Klein Bottle trophy, an honor Calvin has secured 14 times since the competition began (Hope has won the event 10 times, Kalamazoo four times and Albion once).

That trophy is a wooden pedestal with brass plates on which name of winning school is engraved annually. It is topped by a three-dimensional cross-section of a glass Klein bottle (a Klein bottle is a four-dimensional object having neither inside nor outside that is named for German geometer Felix Klein).