All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars
 perplexus dot info

 Hats and alligators (Posted on 2006-07-15)
A group of prisoners is under sentence of death and the warder decides to give them a test to gain their freedom. He tells them, "I will place a red or blue hat on each of your heads and then I'm going to arrange you in random order in a row so that no prisoner will be able to see his own hat but each one will see all the hats in front of him. Starting with the guy at the back each of you in turn must loudly say what color hat you think you have. Correct answers will go free, incorrect ones will be thrown to the alligators in the moat. I will give you time for a brief meeting before we start, so you can plan your optimum strategy."

What strategy can the prisoners - there are N of them - adopt to improve their odds above 50:50?

Hint: They need to agree on a strategy which allows each person to identify his/her own hat while simultaneously providing as much information as possible for all those in front.

 No Solution Yet Submitted by JayDeeKay Rating: 4.4000 (5 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
 re: Solution (fixed) | Comment 5 of 19 |
(In reply to Solution by Old Original Oskar!)

Oskar:

Your idea, a great one, only works as stated if there are an odd number of prisoners.  If there are an even number of prisoners.  The last prisoner will always say "BLUE", and no information is transmitted.

Here's how to fix it.  The last prisoner calls out "RED" if he sees an odd number of red hats and  "BLUE" if he sees an even number of red hats.  Now all remaining prisoners can figure out their hat color, no matter how many prisoners there are.

 Posted by Steve Herman on 2006-07-15 14:10:37

 Search: Search body:
Forums (0)