School-Safe Puzzle Games

Prisoner Puzzle: HARD

Thanks to Suineg for submitting this interesting (and hard!) prisoner puzzle.

20 prisoners are going to face the death penalty tomorrow. The  pacifist mayor, however, has decided to give them a second chance (but they are going to have to earn it!):

We are going to play a little game to see if you can give your life the value it deserves. Tomorrow you will be put in a line. I am going to put you a hat over your head that could be black or white, and then I will  ask you to tell me the color of your hat. If you guess correctly, you are free to go.  If not prepare to pay for your sins.

Premises:

• The prisoners can talk the night before and make a plan to survive
• On judgment day, the prisoners can only answer the mayor’s question by saying ‘black’ or ‘white’.  They can not give clues such as altering the tone of their voice or giving a little kick in the back, etc…
• The mayor will ask from the last person to the first person. The last person sees every hat of the other prisoners but not his own. This applies to every subsequent prisoner.

Some hints:

• This can be solved with pure logic
• Remenber that the mayor asks from the last person to the first person (very important)
• Would you prefer to be the first prisoner, who does not see any hat? or the last prisoner, who sees all hats but  his own?
• How many people can survive with total certainty following your  plan? Do you think you could save them all?
• What about playing a  game the night before-with the loser having to take a particular position in the lineup come  judgment day? Would you like to be that person?

If you can figure this out, feel free to enter your answer into the comment section below. Will unmask submissions after the 1st of the year.