This riddle was originally posted on the MA375 Rhea website for the class of Fall 08. Here is the original link. Special thanks to Michael Burgess for posting the riddle; however, it was left unanswered on the page so I thought I'd bring it here for all to see. I included the solution that I came up with in case you are stumped. Enjoy!
Original:
So, there is this Carnie (small hands, smells of cabbage) that devised this new game at the carnival and wants to cheat you out of your money. You go to play this game. The game works as such:
You pay him a certain amount before you start flipping the coin.
The first round you flip a fair coin. If it comes up heads, you get paid $2. However, if it lands tails, you are allowed to go to the next round.
The second round works the same as the first. If it comes up heads, you get paid *$4*. But if it lands tails, you go on to the next.
The third round pays $8 dollars and so on.
If you were allowed to play this game as many time as you wanted, what is the maximum you would pay to start the game? (What is the average payout?)
You have to pay him a certain amount (like 1000 dollars) to start. The goal is to figure out the most you would pay--Norlow 10:32, 6 December 2008 (UTC)
-Just a clarification, this was mkburges's riddle last semester, and Nate amended to it.
Some clarification:
The goal of this riddle is to find out the maximum amount of money you could "bet" or "pay" to play the game and still at least break even with your winnings. I solved the problem two different ways since the original poster did not clarify if a person had to pay before each round of coin tossing or if one payment allowed a player to take an unlimited amount of turns.
One "turn" of coin tossing is every coin flip from the first flip of the coin (or the first flip of the coin following a payment for finishing the previous turn) until the result is a "Heads" and the turn ends. At that point the player is paid as described by the original poster for his play. A single player can partake in multiple consecutive "turns" should he so choose.
That said,
1) What is the maximum amount of money a person could "pay" to play this game and still break even if he only had to pay one time and was then allotted an infinite amount of turns?
2) What is the maximum amount of money a person could "pay" to play this game and still break even if he had to pay his decided dollar amount before each (EVERY) "turn" of coin tossing?
--Msstaffo 18:06, 26 January 2009 (UTC)
