The mathematics department holds the Barge Competition each semester.

Each week (on Friday), a new problem is posted in the math department and on the Barge Team Competition Moodle website. Teams hand in their solutions to the department on the following Saturday morning. The contest lasts for eight weeks, and the problems vary in difficulty.

## The Rules

Form a team with other Lafayette students. Each team must have three, four or five members.

You can consult with inanimate objects (books, computational devices, 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. In particular, no internet sources or searches may be used during the process of solving the problem and/or submitting a solution.

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

There will be eight problems during the semester.

Get your solution to Professor Yuster (Pardee 234) by the weekly deadline, which is 6 a.m. Saturday. Electronic submissions are preferred, as Professor Yuster has no intention of ever being in his office at 6 a.m. Saturday. You can submit an electronic version of your solution to yustert@lafayette.edu.

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

Jorge, Katie, and Xing’s solution to the 6th problem from the Fall ’09 competition was featured on the cover of the MAA journal FOCUS. Katie’s handwriting made this feasible.

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. Have fun!

## Sample Problem

As you enter the Math Common Room, you see the Calculus Bunny seated at a table, with what appears to be a balance scale and some colored coins. She sees you and beckons you over. “Where did you get the balance scale?” you ask. “It’s on loan from the Vector Viper,” she responds. You decide you don’t want to know where he got it, so you don’t ask. Instead, you ask, “What’s up with the colored coins?” She responds, “I thought you might like a Barge warm-up problem. There are six colored coins, two are blue, two are red, and two are green. One of the green coins weighs exactly 10 grams, the other weighs exactly 10.01 grams. The same is true about the two blue coins and the two red coins. So there’s no way you can tell a heavy coin from a light coin by hand – you have to use the balance scale. You put some of the coins on the right tray, the same number on the left tray, and then the scale will either tip left, tip right, or balance. The problem is to find all three heavy coins using the balance scale only twice.” (Answer at end of page.)

## Past Winners

### Fall 2016 Results

First Place: $750.00 for the team Ben Adenbaum, John Jamieson, Martin Segall Second Place:$600.00 for the team
Pierrette Umwali Dushime, Andrej Ilievski, Saeed Malami, Eunkyung Park

Third Place: $450.00 for the team: Xiaonan Chen, Tianman Huang, Xiaoshi Wang ### Spring 2016 Results First Place:$750.00 for the team
Hoa Duong, Joaquin Font, Huy Nguyen, Qi Yu

Second Place: $600.00 for the team Ben Adenbaum, John Jamieson, Martin Segall Third Place:$450.00 for the team
Ha My Bui, Linh Le, Lanxin Zhang

### Fall 2015 Results

First Place – $750.00 for the team Hoa Duong, Joaquin Font and Huy Nguyen Second Place –$600.00 for the team
Xiaoyu, Linqing Zhou and Zhiwei Zhu

Third Place – $450.00 for the team Xiaonan Chen, Sheng Miao and Qi Yu ### Spring 2015 Results First Place –$750.00 for the team
Blake Bortnick, Samantha Miller-Brown and Martin Segall

Second Place – $600.00 for the team John Jamieson, Josh Nolan, Bryan Sherril, Chris VanBlargan and Thomas Williams Third Place –$450.00 for the team
Josh Arfin, Noah Breininger, Vincent DeMarco and Benjamin Draves

### Fall 2014 Results

First Place – $750.00 for the team Bach Nguyen, Huy Nguyen, Oanh Doan, and Thanh Vu Second Place –$600.00 for the team
Anni Gao, Juan Posso, and Jason Saied

Third – Tie for Third Place – $225.00 for the team Wah Loon Keng, Brandon Strickland, and Atanas Angelov Third – Tie for Third Place Team Prize –$225.00 for the team
Sheng Miao, Yuxiang Shen, and Samantha Miller-Brown.

### Spring 2014 Results

First Place – $750.00 for the team Anni Gao, Rachel Gordon, Juan Posso, and Jason Saied Second Place –$600.00 for the team
Atanas Angelov, Wah Loon Keng, Dana Lapides, and Brandon Strickland

Third Place – $450.00 for the team Recep Celebi, Ivan Evtimov, Bach Nguyen, and Dantong Zhu ### Fall 2013 Results First Place –$750.00 for the team
Anni Gao, Juan Posso, and Jason Saied

Second Place – $600.00 for the team Linh Nguyen, Long Nguyen, and Mai Nguyen Third Place –$450.00 for the team
Ha My Bui, Linh Le, and Hong Ha Vu

### Spring 2013 Results

First Place – $750.00 for the team Linh Nguyen, Long Nguyen, and Mai Nguyen Second Place –$600.00 for the team
Anni Gao, Rachel Gordon, and Juan Posso

Third Place – $450.00 for the team [tie] Andrew Brady, Chris Miles, Stephanie Roebelen, and Chao Wang and Atanas Angelov, Wah Loon Keng, and Brandon Strickland ### Fall 2012 Results First Place –$750.00 for the team
Andrew Brady, Chris Miles, Stephanie Roebelen, and Chao Wang

Second Place – $600.00 for the team Eric Gallant, Haley Garrison, Helen Hutchins, and Jason Sheng Third Place –$450.00 for the team
Dan Bolognini, Grant Kempski, and Brandon Ross

Solution to the sample problem: Label the six coins B1, B2, R1, R2, G1, and G2, where B stand for blue, R for red, and G for green. First weighing: Put B1 and R1 on the left, B2 and G1 on the right. If the scale balances, either R1 is light and G1 is heavy, or the reverse is true. Once you know which is the case, you can work everything else out, so weigh R1 against G1. If on the first weighing the scale tips left, B1 must be heavy and R1 cannot be lighter than G1. Now weigh B1 and B2 against R1 and G1. Balance: R1 is heavy and G1 is light. Tip left: Both R1 and G1 are light. Tip right: Both R1 and G1 are heavy. You can work the rest of the weights out from there. The case where the first weighing results in a tip right is handled in a similar fashion.

If you are interested in the Barge Competition, contact Professor Yuster (yustert@lafayette.edu).