Pick your brain
Adam came home from Switzerland for the summer. I was ecstatic to see him, since I haven't seen him since Christmas. My parents and he came out yesterday and we went out to dinner at Nakama. For you Pittsburgers who enjoy fine sushi, theirs is awesome! If you like your food actually warmed and cooked, they have hibachi grills where they cook in front of you as well. There’s a little bit for everyone!
Today we went to the Cheesecake factory- more aesthetics than fine food, but it was still abundant and tasty. While waiting on our food to arrive, we killed some time by mapping out a hiking route and solving some brainteasers. Here's one:
As a form of torturous death, a central American native tribe buries its captives in the sand with only their heads exposed. They die an unpleasant death in the heat. Upon capturing four intruders, "Bob", a restless native decided to present his victims with a puzzler. If they solve it, then they may go free. Bob buries all four in the sand, with only their heads exposed. Three, he places on one side of a large wall, and one he places on the opposite wall. The three on the same side are buried facing the wall, one behind the other, all in the same direction. He has four hats, two white, and two black. He places one hat on each head of his Easter Island imitators. He tells them that without talking, motioning, or using any other form of communication, they must tell him, with absolute certainty, what color hat he or she is wearing.
After five minutes, one of the talking heads pipes up and declares the color of his hat. He is correct and they are all free.
How does he know the color of his hat?
A few disclaimers:
The wall does NOT have any windows, it is not transparent, and they cannot see over/around it
No one can see his or her own hat; It is too small. Lets pretend its a yamica.
If you know the answer, post it, I'll let you know sooner or later how the hat color is determined.
posted by Jen @ 6:47 PM
10 Comments:
So I would say that if the guy in the back on the side with three people sees two white hats, he will declare that he has black. If he sees two black, he will know he is white. Since he doesn't speak up immediately, the picture must look like:
x | W B x
or
x | B W x
where | is the wall and x is irrelevant. So the guy in the middle of the three knows that he is whatever color the guy in front of him is not. If he see black, he declares white. Otherwise, he says his hat is black.
Although usually these sorts of puzzles end with the guy with no information stating the answer, so I'm ready to be set straight for some oversight :-)
I suspect that the guy in the middle sneeze, therefore losing his hat and seeing what color it was when it dropped to the ground. Otherwise, I think stephen is on the right track.
If he isnt, then I'd figure that the guy who spoke up figured they were definitely fucked if they did nothing, so he took a 50-50 stab at it.
Further speculations, one of the tribeswomen thought he was hot, and tipped him off.
Brain teasers are retarded. Mom always made Dave, Jesse and I do these stupid 'lateral thinking problems.' I think that's what inspired me to hate math and become a writer. They aren't hard, they're just annoying. Tip: The simplest explanation is usually the correct one.
Ben,
I'm not superb at math, however brain teasers usually involve thinking outside the box. This is why I like them. There is usually a simple answer, that you want to kick yourself for, for not getting. I do that often...
My dad and Justin are exceptional at these; both of whom are strong in math.
However, I still like your tribeswomen theory.
That's what I'm saying, Jen. They're all logic-based, and don't require much time "outside the box." That's just how they advertise it, and why people who are good in math are good at them. I'm really good in math, and really good at brain teasers, but I just think they are dumb.
If it wasn't for these things growing up, likely I would be an engineer like Jesse. Thankfully, they ruined any chance of loving mathematics. I'm pretty sure that they utterly stunt creativity.
I have to disagree about the stunting creativity bit. But then there are different kinds of logic puzzles. The formulaic ones, like those that used to be in the GRE analytical section and I believe are also on the LSAT are not as fun. "If Sally can only sit next to Bob and no two boys can sit next to each other..." whatever. You just draw a grid, and work through the inferences. However the puzzles that involve creativity are useful. The first ten or so puzzles on my website are of this flavor, many of them requiring the reader to develop a mathematical proof, which, if you've done any sort of proving, you know requires a good deal of creativity and insight.
The puzzles such as those here, or the one on my site about the prisoners, require the development of an algorithm that solves a problem within some bounded time or other constraint (and often a proof that the algorithm is correct and satisfies the constraints). This is also a creative endeavor.
Stephen, you got the puzzler Jen posted without much trouble. I'm going to go ahead and assume you're a pretty smart guy.
That said, I'll also assume that the links to the puzzles were for other people that might read this blog, not the guy who just emphatically proclaimed twice that they ruined any enjoyment he ever had in mathematics.
ok, since the only two people leaving comments are stephen and ben it's time to change. Yes, stephen is right, and Ben I'm glad you agree, even though you hate "these kinds of problems". I was going to post a few more, however I feel that they may get old rather fast, and Ben, I don't want to lose your blogging patronage. Although I'm sure Stephen would like to keep going with these, I'll just drop some off on his doorstep to solve.
I'd just turn on all three, since the other two don't do anything.
This teaser reeks of logic though, so I still suspect it's math.
PS--David posted this just because I said it aggravates me.
PPS--Jen, you're not going to lose my readership, nor should it concern you. For instance, I demonstrated how concerned I am with losing readers yesterday by posting about a porn spam I received.
Dave!!!!!!!
That was going to be my next brain teaser!!! Seriously... Adam just told 2 at dinner the other night. The first one was about the guys with hats, and the second on was about the light switches.
Ben, I don't know if i would consider that losing readers, or just weeding out the boring and easily offended ones.
Anyone see that commercial with the guy turning the switch on and off, complaining it doesn't do anything? Meanwhile, down the street, his neighbor's garage door is going up and slamming down on her hood over and over again? Good stuff.
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