# Department of Mathematics

## Math Problem of the Month

Enter the contest each month! The Problem of the Month contest starts at the beginning of the academic year and runs through April. New mathematics problems are posted at the beginning of each month.

### 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?

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### Prizes

1. First place will get $15 2. Second place will get$10.
3. Correct solutions for each problem will also be acknowledged in the weekly Mathematics Newsletter.

### Rules

1. You must be an undergraduate enrolled in coursework at UofSC.
2. 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.
3. Answers should be given in the form of mathematical proofs unless otherwise stated.
4. 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.
5. 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?

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