This week's brain potion is a version of a classic puzzle adapted to honor Mario Day (MAR10, i.e. March 10th).
The seven Koopalings (youngest to oldest) are named:
They were tired of working for Bowser without getting paid, so they decided to steal $100$ of Mario's coins and escape in their airship.
They agreed that they would divide the coins as follows:
- Ludwig, as the oldest, would suggest a number of coins to give to everyone.
- The others (not including Ludwig) would then vote on whether or not to accept the proposed distribution of the coins.
- If $\geq 50\%$ of them vote to accept, then they give out the coins according to the disposal.
- If $< 50\%$ of them vote to accept, they throw Ludwig from the airship and then repeat the procedure with the next oldest suggesting a distribution.
Assume that each of the Koopalings is rational, good at logical thinking, and, in order of importance,
- Would not like to be thrown overboard.
- Would like as many coins as possible.
- Enjoys throwing someone else overboard.
How many coins can Ludwig get? Explain your reasoning and include how many coins each of the Koopalings will receive.
Please share any thoughts or questions you have below. We'll monitor the responses and give our thoughts as well!