Problem of the Week

Due Wednesday, October 20, 2021 at 5:00 pm via email to

Suppose that we find sentient life things on another planet, and learn to communicate with them. It turns out that some of the things always lie, and the others always tell the truth. The things also come from one of two tribes, either tribe A or tribe B. Thus, there are 4 types of things: LA, LB, TA, and TB. (For example, a TB thing always tells the truth, and comes from tribe B.) However, we cannot tell what type a thing is from looking at them.

We get two things together in a room. Thing 1 says “We are both liars.” Thing 2 says “We are both from tribe A.”

What types are Thing 1 and Thing 2?

Rules for Problem of the Week

The contest is open to all undergraduates at Northern Arizona University.

Send your submissions or questions to Jim Swift at by the due date and time. Please include the subject “potw”. You may attach a pdf to the email. Please do not send jpegs, pngs, MS Word documents, etc. There are many free aps to make a pdf with your phone camera. I like Adobe scan. To answer some problems, you don't need a scan. You can use the “TeX for Gmail” extension to get nice equations within email.

The answers should be clearly and logically explained. The goal is to write mathematics, not to to write down the answer and draw a box around it.

If your instructor gives you credit for submissions to problem of the week, please include their name and the class (e.g. Swift, MAT 239).

Problems will be graded on a scale of 1 to 3. A model solution is posted each week. A ladder listing the points earned is posted in the lobby of the Adel Math Building (across from the MAP room). Your name will be printed on the ladder, but no names will be published on the web. Let me know if you want to remain anonymous on the posted ladder.