RAY: Hi, we're back. You're listening to Car Talk with us Click and Clack, the Tappet brothers, and we're here to talk about cars, car repair, and the answer to last week's puzzler.
TOM: Yeah, this was very good.
RAY: Yeah, I thought so. This was another in my series of black hat, white hat puzzlers, and this one was inspired by an email I got from a fellow named Jim Guilford. Seems that there's this penal colony on an island in the South Pacific and it's administered by a twisted little prison warden, who likes to play mind games with the prisoners. He likes to present difficult challenges, and if they solve the challenge, they're set free. And if they don't solve it, they're fed to the sharks that are constantly circling the island.
TOM: When they're set free, they just throw them in the water?
RAY: You have to swim to safety.
TOM: It sort of doesn't matter whether you get set free or not. The sharks are going to get you.
RAY: Anyway, he finds five prisoners who are breaking rocks together, and he says, "Here's the deal, guys. I'm going to stand you against a wall, but not in the manner that you usually think, you know firing squad manner. The first guy is going to face the wall with his hands and toes touching the wall. The next one's going to stand behind him about five feet away." The next one behind him etc., etc., so that each prisoner can see the guys in front of him, except for the first guy, who can see only the wall. So you've got the scenario.
TOM: I've got it.
RAY: So the twisted warden says, "Now, fellows, I'm going to come up from behind you, starting with the last guy in line and place either a white hat or a black hat on each of your heads. I can put all black hats on if I want, or all white hats, or any combination, and your job is to identify the color of your hat correctly. And if you fail to do so, sharks."
TOM: It's the sharks.
RAY: "Now, we're going to do this tomorrow, so you guys can think about it over night and plot and moan and groan all you want." Now obviously the guy at the back of the line would be able to see everyone in front of him, but the only words he can use are either black or white in guessing his own hat color. So he can only utter one word.
TOM: Gotcha.
RAY: You got it?
TOM: Yeah.
RAY: So they scheme over night. Obviously, the luck of the draw --
TOM: And they decide to tunnel instead.
RAY: Prison riot. Obviously, you know, if they leave it to luck, it's a 50/50 chance for each man. It's too big a chance to take. But then Crusty, who's been on the island for 19 years for overcharging for Valtop? says, "I have a plan that will improve our odds beyond 50/50." However, he says, "We must draw straws." So the question was what is Crusty's plan, and why must straws be drawn?
TOM: This is way up there in the white hat, black hat series.
RAY: Really?
TOM: This is way up there.
RAY: Let's say that we stand the guys against the wall, and we'll just pick an order. Say the guy closest to the wall has a black hat. The next guy has a black hat. The next guy has a black hat. The third guy is white. Then black, and then the last guy in line has a white hat. Here's what Crusty devised, and I think it was pretty smart.
TOM: I think so too. He should get out just because he thought of it.
RAY: And here's the reason they had to draw straws. By the way, he drew the short straw.
TOM: That's all right.
RAY: Too bad. What can you do? The guy at the back of the line obviously can see all the other hats, but, of course, he can't see his. So he's going to guess, but he's not going to guess. He's going to declare his hat as either black or white based on what he sees. And they've determined in advance that if he sees an odd number of white hats in front of him, he's going to call out his hat as black. If he sees an even number of white hats in front of him, he's going to call his hat out as white. So he looks ahead and he sees what? An odd number of white hats in front of him. He sees one white hat, in fact. So he says, I have a black hat. You with me?
TOM: Yeah.
RAY: He goes to the sharks, but because he's declared his hat as black, OK, the fellow who's directly in front of him knows that Crusty, or who was ever at the back of the line, must have seen an odd number of white hats. Well, looking ahead, he's see what? An odd number of white hats --
TOM: Exactly.
RAY: Therefore --
TOM: He sees a white, a black, and a black.
RAY: Therefore, he knows he has a black hat. Similarly, the guy in front of him who has a white hat knows that the guy behind him declared his hat black, and because he had to have seen an odd number of white hats, he knows that his hat is white, because the only two hats he can see are black. Etc., etc. And everyone gets out, except for the last guy, whose chances are still 50/50. Pretty cute huh? Do we have a winner?
TOM: The winner, get this, get this, if you will. Lieutenant Colonel Susan Robbins, United States Air Force, from of all places, Papillion, Nebraska.
RAY: You made that up!
TOM: I didn't make it up. I know it's Papillion, but wasn't Papillion the name of the movie on Devil's Island?
RAY: I believe so.
TOM: What are the chances of this? Holy cow! Lieutenant Colonel. You know how far above an E-2 that is?
RAY: Yeah, we do.
TOM: We all do, don't we? Well, congratulations to Lieutenant Colonel Susan Robbins, United States Air Force, from Papillion, Nebraska. And for having your answer selected at random from the white hat full of correct answers that we had, you're going to get a $25 gift certificate to the Shameless Commerce Division at the Car Talk section of cars.com.
RAY: You can buy a hat with that 25 bucks.
TOM: Whoopee! Whoopeee! And with that gift certificate, you can get a copy of our new CD, "Car Talk Car Tunes," which you can pop into the CD player in your F-16. Doesn't it have the optional six-CD changer in the dashboard of the thing?
RAY: Oh, absolutely.
TOM: Can you listen to CDs on an F-16?
RAY: Oh yeah, well --
TOM: You can't hear anything anyway.
RAY: Actually, the truth is they're not really flying the planes.
TOM: They don't fly them?
RAY: Oh no, they're all doing it with simulators. It's DVDs, your own DVD players.
TOM: Oh, that's it.
RAY: Yeah, they're just pretending. Anyway, we'll have a brand-new, you ready for this, automotive puzzler coming up in the third half of the show.
TOM: Get out.
RAY: But if you have a question about your car right now, you can give us a call at 888-CARTALK, which is also 888-227-8255. Hello, you're on Car Talk.
[ Car Talk Puzzler ]
