The Guilty Party

Wednesday, February 4, 2009

A King, Three Prisoners and Five Hats

June 22, 2009: Welcome! According to the info I get from Statcounter, this entry is the most popular one on my blog. Seems like everybody, all around the globe, is searching for the answer to this question about hats and kings and incarcerated folks. Interesting question.

While I've got you here, I would like to let you know about Boomerang, my recently released novel. You can read the first chapters right here on my blog and of course it is available through Amazon, Barnes and Noble and all those other places that sell books. Not a lot of hats, and no kings, but it's a comic novel of international intrigue and those who have read it love it!

Boomerang on Amazon

And now, the hat entry that brought you here in the first place!

Our son is in his final year of college, on his way to becoming a teacher. Yesterday he came home with a problem his "How To Teach Math" professor had given his class as an example of a long term problem they could give their students to ponder. According to this professor, this question usually takes most people quite a while to solve. Our son said he got the answer in less than a minute.

Here 'tis:

A king has three prisoners brought before him. He has their eyes covered and a hat placed on each of their heads. Then he has the eye coverings removed. He tells them,

"I have five hats, three black and two white. Three of those hats have been placed on your heads. If you can tell me which color hat is on your own head I will set you free. If you say wrong, however, you will be put to death. You may look at your fellow prisoners to see what they are wearing, but of course may not look at the hat on your own head."

The first prisoner looks at the other two, ponders as best as he can, and finally says,"I have no idea."

The second prisoner looks at numbers one and three and shakes his head, discouraged. "Heck if I know."

The third prisoner, who is blind, says, with nary a bit of hesitation. "I am wearing a black hat."

The king says, "Correctomundo! Off you go." And sets the fellow free after first restoring his cane and seeing-eye iguana and pointing him in the direction of the nearest Tastee-Freeze.

The question is: Did the blind man know or guess? And if he knew, how did he know?

My first response was that the blind man had a monkey on his shoulder who tapped out the answer in Morse Code. This did not satisfy my son.

My next answer was that the blind man was so despondent over his condition and the fact that the prison had no soft serve ice cream that he did not care if he guessed right or wrong and simply lucked into the right answer. My son tells me I am mistaken and the ice cream reference was inserted by me without his permission.

Any answers out there?

Go Ye Forth and Do Likewise.


Timberati said...

Not a clue. My first inclination is he has a 33% probability with black and 20% with black.

On another topic, how are you liking Boomsday? I stopped when he went into sooo much backstory, I wanted to go forward he wanted to go backward. I left. I thoroughly enjoyed Supreme Courtship.

plumboz said...

I read Boomsday a few weeks ago. I enjoyed it, but not quite as much as No Way to Treat a First Lady. I noticed the backstory stuff but it didn't seem to get in the way for me.

Almost finished with ,Thud. It's not as tight as most of the other Pratchett I've read but it's still a pageturner and I do like Commander Vimes. I think of all the Discworld characters Vimes must be the most Pratchett-like.


Lexi said...

I have no idea.

But I proudly assert that my daughter, were she here, could do it in a trice.

Lexi said...

Okay, I have now heard from my mathematics correspondent as follows:

'Hmm, a mildly interesting problem.

The answer is that if the blind man is quick-witted and has confidence in his fellow prisoners' intelligence, then no, he wasn't guessing. Call the men (1) (2) and (3), with (1) being the first man to speak, (2) the second and (3) the blind man. Then:

(1) would only be able to answer correctly if both men had white hats, therefore (2) and (3) are not both wearing white.
(2) knows this; knows that him and (3) must either be both wearing black, or each have a different colour hat.
If (3) was wearing a white hat, then (2) would know he must be wearing black (otherwise (1) could have answered), and so (3) must be wearing black, otherwise (2) would be able to answer.
(3) cleverly works this all out and tells the king the correct answer.

Pretty easy if you just reason through it, but quite fun nonetheless.


A Bit About Me

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I am a writer with a longtime interest in photography. I'm a dad, husband, photographer, and not very good guitarist. My first novel, Boomerang, is available in both paperback and ebook form at Amazon, Barnes and Noble and As a matter of fact, my second novel, The Baer Boys, can be found at exactly the same places.