### Problem of the Month

#### October 2021

**Fibonacho Numbers**

Two children eat nachos in turns, taking the next number in the Fibonacci sequence: 1, 1, 2, 3, 5, 8, 12, 21, …, restarting from the beginning if the next number is greater than the remaining nachos. What is the smallest number of nachos less than 500 that requires the most restarts?

### Prizes

- First place will get $15
- Second place will get $10.
- Correct solutions for each problem will also be acknowledged in the weekly Mathematics Newsletter.

### Rules

- You must be an undergraduate enrolled in coursework at UofSC.
- Solutions will be judged primarily on correctness, clarity of work, and speed of submission. The highest ranking students will receive the prizes for that month.
- Answers should be given in the form of mathematical proofs unless otherwise stated.
- Type or write your solution clearly and show all of your work. This should be your solution and not a solution posted online or copied from another source.
- Submit your solutions to Dr. Dunn at dunnsm@math.sc.edu before 11:59 pm on the last day of the month.

### Previous Problems

In a certain dice game, a player scores the total of a series of rolls of a six-sided die, provided a one is never rolled. The player is allowed to roll as many times as they like and stop whenever they like. What is the probability that they will score 6 or more points in a single turn if that is their goal?