mental_floss magazine
SUBSCRIBE >
GIFT SUBSCRIPTIONS >
DIGITAL SUBSCRIPTIONS >
subscriber services >
Answer: Remember: Davis is in front, Jones is behind him, and Smith is behind Jones. And the warden has two yellow hats and three blue hats. Here’s how they figured it out.
If Smith (in the back) sees two yellow hats in front of him, he knows he’s wearing a blue hat and says so immediately. If he says nothing, then it becomes apparent that Davis and/or Jones are wearing blue hats. If Smith is silent, Jones looks at Davis’s hat. If it’s yellow, he knows his own hat is blue and says so. (If his hat were yellow as well, Smith would have spoken up.) But if Davis’s hat is blue, Jones is uncertain about the color of his own hat.
If neither Smith nor Jones speaks up, Davis immediately knows that his hat is blue and says so before the 10 seconds are up.
Comments (18)
Comment
- Follow mental_floss
I’m a little confused. If Smith doesn’t speak up, how does that mean that the other two have different color hats?
If Smith is silent, it means that at least one of the other two has a blue hat. But it doesn’t mean the other two are different.
posted by CSter on 6-17-2008 at 7:08 am
Nice one. For those who want to see the more difficult variant, click my name.
posted by emit on 6-17-2008 at 7:21 am
The link from the first page that says Click “here” for the answer takes you to the quarter answer from yesterday.
posted by Amy on 6-17-2008 at 7:22 am
Cool – I got it! Though I guess it was not clear (at least to me) if they could turn around at all, but I guess they don’t need to
posted by Dan on 6-17-2008 at 7:22 am
at least one of them has to be wearing a blue hat, so if they all answer “blue,” then at least one prisoner will be right.fron
posted by Gran on 6-17-2008 at 7:29 am
You’re right, C Ster – I’ve corrected the text to indicate that if Smith doesn’t speak up, either Jones or Davis (or perhaps both) are wearing a blue hat.
Amy, I’ve fixed the link – thanks for the heads up.
And Gran, if the first guess is wrong, they ALL go before the firing squad. And they sure don’t want that!
posted by Sandy on 6-17-2008 at 7:46 am
They took off the hats to check the color.
posted by Shaina on 6-17-2008 at 7:49 am
I agree with Gran–the text implies that if any of them are right before 10 secs, then they are pardoned, and only if they are all wrong do they get the firing squad. So everyone guessing blue would make at least one of them right.
posted by Amanda on 6-17-2008 at 7:51 am
How can they see the hats in front of them if they are blindfolded before the hats are placed on their heads?
posted by Lindsay on 6-17-2008 at 8:01 am
How can they see anything in front of them if they are blindfolded before the hats are placed on their heads?
posted by Lindsay on 6-17-2008 at 8:04 am
Lindsay – the text says that the blindfolds are removed after they’re fitted with the hats.
Amanda – I see what you’re saying; I’ll try a slight rephrase to make it clearer. Thanks!
posted by Sandy on 6-17-2008 at 8:24 am
Thanks Amanda for the backup!
The rephrase definitely cleared it up Sandy.
posted by Grant on 6-17-2008 at 10:03 am
I just figured they cheated. They are convicted criminals, after all.
posted by Miss Cellania on 6-17-2008 at 10:20 am
Dang… interesting system of punishment going on at this prison. :D
Great puzzle!
posted by Allison on 6-17-2008 at 8:10 pm
You’re solution is over-complicated.
If the guy in the back sees two hats of the same color, he says the opposite color.
If he says nothing, the second person’s hat must be the other color than the person’s in front of him, so he says that color.
Two stops – not three.
posted by PartiallyDeflected on 6-17-2008 at 8:45 pm
Or they just cover their mouths.
posted by Benjamin Baxter on 6-18-2008 at 3:06 am
Sorry PartiallyDeflected, not true. The guy in the back may be stymied if he sees two blue hats, or one of each. If #2 then confidently speaks the opposite of what he sees, he’s still running the risk of being strung up.
posted by Bob on 6-18-2008 at 6:57 am
In fact, they *are* cheating. The rules clearly state that they are not allowed to communicate in any way. A timed sequence of silence is communication.
There is no way to solve this without communication.
posted by Joe on 6-24-2008 at 3:24 pm