The Barge Mathematics Competition

Each semester, the Lafayette College Department of Mathematics holds the Barge Competition. Each week (on Friday), a new problem is posted in the Math Department and on the Barge Team Competition Moodle site. Teams hand in their solutions to the department on the following Friday. The contest lasts for 8 weeks, and the problems vary in difficulty.

The Rules

 Form a team with other Lafayette students. Each team must have 3, 4 or 5 members.

You can consult with inanimate objects (books, computers and the like), but you may not consult with people not on your team. This prohibition includes both consulting faculty members and help via internet communication.

Solve the Problem of the Week with your team. The weekly problem is posted in the Math Dept and is available on the Moodle site to all known participants in that semester's competition. Contact Professor Gordon for access to the Moodle site.

There will be 8 problems during the semester.

Get your solution to Professor Gordon (Pardee 229) by the weekly deadline, which is 5:00 pm on Friday. is posted. Submissions after 4 p.m. Friday should be sent electronically to gordong@lafayette.edu

Don't Quit! Keep turning in problems, even if your team isn't 100% sure of your solution.

Fall 2009 Problems

 The problems usually involve some ingenuity or insight and generally not lots of background information from previous courses. The topics range over all areas of mathematics: probability, geometry, number theory, combinatorics, algebra, calculus and more.

Sample Problem

A jail has 1000 cells, all of which are initially unlocked. Each time the jailer turns the key in a cell, the cell becomes locked if it was previously unlocked and becomes unlocked if it was previously locked. The jailer begins by turning the key in every cell. When she finishes, she turns the key again in every other cell (beginning at cell number 2 and ending at cellnumber 1000). Next she turns the key in every third cell, beginning at cell number three. Then every fourth cell, every fifth cell, and so on until she is done. Which cells will be locked at the end of this process? (Answer at end of page.)

PAST WINNERS

Spring 2009 Results

First Place - $750 for the team

Jorge Sawyer
Katie Sokolowsky
Xing Yan

Second Place - $600 for the team

Farhan Abedin
Shelvean Kapita
Ed Karasiewicz
Khine Lin
Peter McGrath

Third Place - $450 for the team

Zhukan Ding
Miao Wang
Shuang Zhao

Answer to sample problem: The cells which will be locked are the perfect squares; cells 1, 4, 9, 16, ...

If you are interested in the Barge Competition, contact Professor Gordon.