A place for Ryans, sealions, and other things that bark.

Thursday, November 03, 2005

My Hat Is Off To You, Sir

Today's puzzle:


Four guys are in prison. Let's call them prisoners. The guard in charge of watching them decides to play a game with them. He puts one of the prisoners in one cell, and the other three in an adjacent cell. He then lines up the three in the one cell so that they are all facing the same direction. Next, he then takes four beanies, (two white and two black) and randomly puts them on all of their heads. The guy in the back of the three person line can see the color of the two beanies in front of him, (but not his own), the guy in the middle of the line can see the color of the guy in front of him, (but neither his own nor the guy behind him), and the guy at the front of the three person line, and the solo prisoner in the other cell, cannot see anyone's beany. The guard then tells them there are two white beanies and two black beanies, and if anyone can guess the color of his beany within the hour, he can go free, but if he guesses incorrecly, he will be shot. They are allowed to answer in any order, (as soon as they know, they can shout it out). If they say anything other than black or white within the hour, they will also be shot, (so no cheating). They only have 1 year left in jail, so assume that unless they know for sure, they won't guess, (they'd prefer to stay in jail for a year rather than get shot). Sooooooo...assuming they are all logical people, who, if anyone, will ALWAYS go free, (not matter what the distribution of hats is). The correct answer could range from no one to everyone. Good luck.

4 Comments:

Blogger FrannyD said...

if the guy in the back of the three (we'll hereforth call him #3, the guy in the middle #2, and the guy in the front #1, and the loner next door #4) sees either 2 whites or 2 blacks, he will immediately call out the color of his hat and be freed. If he does not call out immediately, #2 will know that #3 is unsure because he sees 2 colors, and then will know that he, himself is the opposite of what #1 is, and then can call out his own color (whatever opposite of #1 is), and then #2 would be the one to be freed. However, this is all assuming that they would want to be released as soon as possible.

8:58 PM

 
Blogger Ryan said...

Yes, we must assume they all want to go free immediately, (and will guess as soon as they know). However, your answer is incomplete, so I can't award you the win.

9:11 AM

 
Blogger FrannyD said...

oh. i get it now, but i will not post it here because i had to discuss parameters with ryry, so i feel a little cheaty.

10:05 AM

 
Blogger Ryan said...

Eh, I'll give it to both Paula and Fran. Hooray for them.

1:05 PM

 

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