1. ## Prisoner Hat Riddle

Not really heavy into the math, but a challenge in logic.
I found it puzzling, but the answer is surprisingly simple.

Thought I would share it here.

The Prisoner Hat Riddle by Alex Gendler on TED Ed.
http://ed.ted.com/lessons/can-you-solve-the-prisoner-hat-riddle-alex-gendler

2. ## Re: Prisoner Hat Riddle

Quite a well-know riddle, along with others that are similar....

Here's another one you'll enjoy:
http://puzzles.nigelcoldwell.co.uk/seven.htm

3. ## Re: Prisoner Hat Riddle

A king has three prisoners. He decides to give them a chance to earn their freedom. The king says he will blindfold all three prisoners and place a white or black hat on the first prisoner's head, a red or green hat on the second's and a yellow or cyan hat on the third's.
He will then remove the blindfolds so that each prisoner can see the other two hats but not his own.
He will then ask them to simultaneously write on a piece of paper the color of the hat that each of them thinks he has on his head. The only choices that are permitted are, either a color, or "I don't know". The prisoners will win their freedom if at least one of them correctly guesses his own color, but with the restriction that no one must give a wrong answer (for example, if 2 of the 3 prisoners reply "I don't know" and the 3rd one guesses correctly, they go free). The king allows the prisoners to discuss and coordinate for a few minutes, before the placement of the hats, in order to decide a strategy. What is the optimum strategy that will give them the biggest chance to go free?

4. ## Re: Prisoner Hat Riddle

Originally Posted by Alderamin
A king has three prisoners. He decides to give them a chance to earn their freedom. The king says he will blindfold all three prisoners and place a white or black hat on the first prisoner's head, a red or green hat on the second's and a yellow or cyan hat on the third's.
He will then remove the blindfolds so that each prisoner can see the other two hats but not his own.
He will then ask them to simultaneously write on a piece of paper the color of the hat that each of them thinks he has on his head. The only choices that are permitted are, either a color, or "I don't know". The prisoners will win their freedom if at least one of them correctly guesses his own color, but with the restriction that no one must give a wrong answer (for example, if 2 of the 3 prisoners reply "I don't know" and the 3rd one guesses correctly, they go free). The king allows the prisoners to discuss and coordinate for a few minutes, before the placement of the hats, in order to decide a strategy. What is the optimum strategy that will give them the biggest chance to go free?
Answer was done by brute force. Couldn't prove if chances of losing could be pared down further.
Spoiler:

1,2,3 are Prisoners. WB, RG, YC, colors of hats. "RY - W" means if the prisoner sees a Red and Yellow Hat, write White.

The result was generated by enumerating along every possibility of what each prisoner could see. I then took a forced starting point that if 1 saw RY, then W R Y is a win, and B R Y is a loss (a 50/50 split). I then 'stacked' upon the B R Y loss as much as possible (ex. if 2 sees BY, say G, because B R Y is a loss anyway) and sealed the W R Y win (ex. if 2 sees WY, Don't Know). After elimination, make another 50/50 win/lose split and proceed again. I think both losses are forced.

Prisoner 1
RY - W
RC - Don't Know
GY - Don't Know
GC - B

Prisoner 2
WY - Don't Know
WC - R
BY - G
BC - Don't Know

Prisoner 3
WR - Don't Know
WG - Y
BR - C
BG - Don't Know

Result
W R Y - win
W R C - win
W G Y - win
W G C - lose
B R Y - lose
B R C - win
B G Y - win
B G C - win

Chance of being freed = 6/8 = 75% chance.