For most college students, the following math problem would probably produce serious head scratching and more than a little frustration:
“Players 1, 2, 3 …, n are seated around a table and each has a single penny. Player 1 passes a penny to Player 2, who then passes two pennies to Player 3. Player 3 then passes one penny to Player 4, who passes two pennies to Player 5, and so on, players alternately passing one penny or two to the next player who still has some pennies. A player who runs out of pennies drops out of the game and leaves the table. Find an infinite set of numbers n for which some player ends with all n pennies.”
For a four-member team from the College of Science’s Department of Mathematics and Statistics, such a problem during the recent 67th annual William Lowell Putnam Mathematical Competition was reason to feel challenged and motivated. The Nevada students, hoping for a strong placing for the University, tackled problems such as the one listed above, as well as many others.
Their effort led the University to a 77th place finish in the competition, which pitted 3,753 undergraduates from 516 colleges and universities from across the United States and Canada.
The University’s team consisted of mathematics undergraduates William Taylor, Michael Gallaspy and Alexander Lang. Alex Dussaq was a team alternate.
The examination was both challenging and grueling, with two three-hour sessions, and about half of the entrants only scored 0, 1, or 2 points out of 120. The examination consists of 12 questions, worth a maximum of 10 points each. All four Nevada students scored well above the median scores, however, with Taylor and Gallaspy finishing in the top 20 percent with 12 points, and Lang and Dussaq close behind with 10 and 9. High score for the competition is usually about 90 points.
The students prepared for the Dec. 1 competition by participating in weekly problem-solving sessions in the fall, taught by Department of Mathematics and Statistics faculty Valentin Deaconu and Don Pfaff. A problem-solving course Math 419 taught by Birant Ramzan also proved helpful.
The competition is held each year to stimulate a healthy rivalry in mathematical studies in the colleges and universities of the United States and Canada. It is administered under the administration of the Mathematical Association of America.