An interesting probability problem
 

You are one of three prisoners. You cannot communicate with your compatriots in any way, but may assume that the other two are brilliant, i.e. they will do the right thing. You are each outfitted with a hat - which you cannot see. The warders have an infinite supply of red and black hats, so you know your hat must be one of those two colors. The three of you are led to a courtyard, to view each other's hats (sort of like that poker game where everyone holds a card to their own forehead). You are led back to your cells, and asked to state what color hat you are wearing. You may choose red, black, or "abstain." Warning, if all three abstain you will all be killed. Also, if any one of you guesses your color incorrectly, you will all be killed. You do not know beforehand the purpose of going to the courtyard, and you are all questioned simultaneously while separated from one another. What is the best strategy?

doormat

Re: An interesting probability problem
 

I'll take a stab at this. If you see your fellow prisoners have different color hats you abstain. If you see 2 of them with the same color hat (such as black) you guess the other color (red).

Re: An interesting probability problem
 

I must be missing something. If you are not given the game until after you return from your walk, the info is basically useless. The fact that there is an infinite supply of each color means the probability does not change based on the color hats they are wearing.

Now I do not think you can do better then have me guess (always black, always red or flip a coin) and have the other two always abstain. That will give us a 50% chance of living. However, this is not really plausible. How genius are the other two. Do they know they should abstain so that I can make the guess? If they do not you may all want to guess which means that you live only (1/8) of the time.

I am sure that this makes no sense but what can I say.

Re: An interesting probability problem
 

Congrats, Jimbo! If I ever get thrown in the clink I want you there with me, we might get out alive. I will leave it open as to why all the prisoners should logically reach the same conclusion.
doormat

Re: An interesting probability problem
 

gilly, sorry but they cannot confer and decide to make you the guesser. They can however come up with a better strategy through logic. See Jimbo's reply and you may figure out why.
doormat

Re: An interesting probability problem
 

I liked that one. Got any more like it?

Oh, and by following Jimbo's solution, the prisoners have a 75% chance of living, which is the best they can get. They're screwed if they all have the same color though.

Re: An interesting probability problem
 

Hello. Your puzzle is very interesting and I admit I cannot solve it. However, I know one that is very similar.

A king has three genius advisors and wants to marry one of them off to his daughter, who is ridiculously hot and tolerant of boyfriends spending large amounts of time playing poker with their buddies. The three advisors have their eyes blindfolded and hats put on their heads. They are told that their hats were chosen from a group of two red and three black hats, and then their blindfolds are removed. The first one to correctly guess the color of his hat gets the girl, but an incorrect guess means death. After a while, the first advisor says he passes, followed closely by the second one. Immediately the third advisor says "I'm wearing a black hat". He was correct and was able to explain why he was certain and a date was set. How did he know?

Re: An interesting probability problem
 

Raymundo,
That is a good puzzle but I have heard it before, so in the spirit of fun I will leave it for someone else to solve. I do have another puzzle that is somewhat difficult and that took a bit of time for me to solve that I will put up soon.

doormat

Re: An interesting probability problem
 

LB, right you are. I do have another one that drove me crazy for a couple of hours - I will post it soon.

doormat

Re: An interesting probability problem
 

I will leave it open as to why all the prisoners should logically reach the same conclusion.

Who do you think you are? Sklansky?



rJ