The Barge Team Competition

Each semester, the Lafayette College Department of Mathematics holds the Barge Competition. Each week (on Friday), the Math department posts a new problem. Teams turn their solutions into the department on the following Friday. The contest lasts for 8 weeks, and the problems vary in difficulty.

This Week's Problem (Problem 7)

Previous problems from this semster

Problems From Previous Competitions

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 appears on this web site as the current problem, is also posted in the Math Dept, and is emailed to all known participants in that semester's competition.

There will be 8 problems during the semester.

Get your solution to Professor Yuster (Pardee 234) by the weekly deadline, which is actually Saturday, 6 a.m. the week after the problem is posted. Submissions after 4 p.m. Friday should be sent electronically to yustert@lafayette.edu

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


The 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. See the Barge Archives for problems from previous semesters. The current problem is also available during the semester. Check it out!!!

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

Fall 2007 Results

First Place – $750 for the team

Xue Ji
Keming Liang
Jordan Tirrell

Second Place – $600 for the team

Shiliang Cui
Jinjin Qian
Xing Yan

Third Place – $450 for the team

Chak Man Chan
Jorge Sawyer
Katie Sokolowsky

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 Yuster.