RAY: Hi. We're back. You're listening to Car Talk with us, Click and Clack, the Tappet Brothers, and we're here to discuss cars, car repair, and, duh, the answer to last week's Puzzler.
TOM: I'm not into the mode of answering the Puzzler questions. It seems like the Puzzler's been on vacation for so long, I'm not into the mode that it's back.
RAY: Really?
TOM: That's why I can't remember the Puzzler every week.
RAY: So, if it went away, like, you wouldn't miss it.
TOM: I wouldn't miss it. I don't think anybody would miss it.
RAY: Well, if you remember from last week, this was sort of an anthropological, geological, algebraic, and above all, obfuscational Puzzler.
TOM: Oh, yeah?
RAY: Yeah, I think so.
TOM: I don't remember anything about it.
RAY: Yeah. This was from the "Blind 'Em with Footwork" Collection.
TOM: Yeah? Those are the best.
RAY: Yeah.
TOM: Those are good.
RAY: This wasn't really cricket, but, hey, tough. In the little Asian country of Tuvaniska, there are two small towns separated by a mountain, and we'll call the towns Abba and Babba. And the preferred footwear in both of these little towns is the combat boot. Now, Abba has a population of 20,000. You need a pencil for this, so you've got to get it.
TOM: Oh, I remember this, yeah. They have 20,000 and one feetÉone foot.
RAY: So, of the 20,000 people in Abba, 1 percent have only one foot.
TOM: Yeah. Yeah. Got that.
RAY: So 1 percent wear only, what?
TOM: One boot.
RAY: One boot. Of the remaining population, half of them wear no boots, and the rest wear two boots, like you would expect.
TOM: Yeah.
RAY: In Babba, on the other side of the mountain, 20 percent of the people have one foot.
TOM: Mmm-hmm.
RAY: Of the remaining people, half wear no boots, and half wear two boots. Twenty thousand boots are worn in Babba. So, what's the population of Babba?
TOM: I have no idea. I can just guess.
RAY: Go ahead.
TOM: Zero.
RAY: How could it be zero? Who's wearing the boots?
TOM: I don't know. Maybe visitors. It's not...it's not...it's not zero.
RAY: Let's go to Abba for a second.
TOM: Yeah, we go to Abba.
RAY: OK. One percent of the population wear...is one...
TOM: Has one foot.
RAY: Is one-booted. Half of the remaining population wear no boots.
TOM: Yeah.
RAY: Right?
TOM: Right.
RAY: And obviously, the other half of the remaining population wear the conventional two boots.
TOM: Two boots.
RAY: OK. And if you go and if you figure that out, you'll find out that there are 20,000 boots worn in Abba.
TOM: Oh!
RAY: OK? And it turns out that it doesn't make any difference what percentage of the population has one leg.
TOM: No kidding?
RAY: And so, when you go to Babba, even though 20 percent of the population has one foot, because they have one foot, that's also equivalent to being, like, half the population, is it not?
TOM: Oh, of course.
RAY: So every person that has one boot is just like the other part of the population where half of the people wear no boots.
TOM: Don't wear any boots.
RAY: So, the average is that half the people wear a boot. Therefore, one boot per person comes out to 20,000. So, if there are 20,000 boots worn in Babba, the population must be 20,000. Or zero.
TOM: Well, that's very...that was...
RAY: Well, it was.
TOM: That was obfuscated. That was beautiful.
RAY: Yeah. It was very simple math.
TOM: Yeah?
RAY: But I had to blind you with the footwork.
TOM: Well, you had to, because it eluded me.
RAY: Yeah. For example, if I asked you what's half of 20,000 multiplied by two, you would have known the answer right off.
TOM: I would have known the answer, yeah.
RAY: Yeah, OK. Do we have a winner?
TOM: You bet we have a winner! The winner is Debra Garcia from Tuc-son, Arizona.
RAY: I think it's Tucson, but I'm not sure.
TOM: No. I call it Tuc-son.
RAY: OK.
TOM: I like it. And for having her answer selected at random from among all the correct answers that we got, Debra, Debra Garcia from Tucson, Arizona, will get a $25 gift certificate to the store at the Car Talk section of cars.com.
[ Car Talk Puzzler ]
