Problem of the Week

Due Wednesday, November 30, 2022 at midnight submitted to this Google form. You must be logged into your NAU gmail to submit via this form.

Twelve members of a family are sitting on two opposite sides of a rectangular dining table for dinner. There are 6 chairs on each of the long sides of the table. In row 1, Rita, Andrew, Pablo, Jiang, Sonia and Quinn are seated but not necessarily in the same order and all of them are facing south. In row 2, Tycho, Kiran, Daria, Cameron, Vivek and Martin are seated but not necessarily in the same order and all of them are facing north. Each of them has a different favorite Thanksgiving food among, turkey, stuffing, gravy, mashed potatoes, sweet potatoes, rolls, cranberries, green bean casserole, creamed corn, salad, mac and cheese and pumpkin pie, but not necessarily in the same order. Their favorite food is directly in front of them.

1. Pablo, who likes sweet potatoes, sits third to the left of Andrew.
2. Pablo is not an immediate neighbor of either Sonia or Rita.
3. Tycho, who likes mac and cheese, sits third to the right of Cameron.
4. Neither Tycho nor Cameron sits at the extreme ends.
5. Sonia, who likes turkey, faces the one who likes green bean casserole.
6. Quinn, who likes gravy, faces Martin, who sits second to the left of Vivek and does not like mashed potatoes.
7. Vivek is not an immediate neighbor of Cameron.
8. Only two people sit between Kiran and Vivek, who like pumpkin pie and creamed corn respectively.
9. Jiang likes neither stuffing nor mashed potatoes and sits on the immediate right of the person who likes sweet potatoes.
10. Rita, who likes rolls, does not face Daria.
11. The one who likes salad sits second to the left of the person who faces the one who likes gravy.

Rules for Problem of the Week

The contest is open to all undergraduates at Northern Arizona University. Solutions are due at midnight of every Wednesday.

Submit your solutions to this Google form as a pdf or jpg of either typed or neatly handwritten and scanned work. If you don't have access to a scanner use a phone app like CamScanner or Adobe Scan.

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.

Send your questions to Rachel Neville at Rachel.Neville@nau.edu. If your instructor gives you credit for submissions to problem of the week, please include their name and the class in the form (e.g. Swift, MAT 239) the first time you submit a solution. (After that I have the information in my spreadsheet.)

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.