Due Wednesday, January 12, 2022 at 5:00 pm via email to jwswift@gmail.com.
Alice and Bea are playing a game. They decide together on an integer $n \geq 3$. Then Alice thinks of a number from the set $\{1, 2, 3, \ldots, n\}$. Then Bea guesses the number. Alice only tells Bea yes or no. If the answer is yes, the game ends. If the answer is no then Alice will choose a new number that differs from the previous number by 1. The new number must be positive, but it can be larger than $n$. Then Bea guesses the new number. The game continues until Bea guesses the number.
Give a strategy that Bea can use to end the game in at most $(3n-5)$ guesses.
Note: This problem of the break is more challenging than usual. We will have a new competition with a new ladder of scores, starting with the next problem, due 2022-01-19.
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.