Due Wednesday, October 27, 2021 at 5:00 pm via email to jwswift@gmail.com.
Glue 27 standard dice to form a big $3 \times 3 \times 3$ cube, sort of like a Rubik’s cube. Both faces in each pair of faces that are glued together have the same number of pips. How many pips are showing on the outside of the big cube?
Hints: Pips are the small dots on each face of a die. Standard dice are in the shape of a cube, with these pips denoting the numbers one through six. The sum of pips on opposing faces adds up to seven.
The contest is open to all undergraduates at Northern Arizona University.
Send your submissions or questions to Jim Swift at jwswift@gmail.com by the due date and time. Please include the subject “potw” so I can find it in my often overflowing inbox. You may be able to answer the question with a plain email, but for most problems you will want to include a scan of your solution. 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.
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) 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.