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. This is from my coin series.
TOM: I'm dying to hear the answer to this.
RAY: Here it is.
TOM: I'm dying to hear the question.
RAY: You're sitting at a table, you're blindfolded and you're wearing mittens. On the table is a bunch of pennies. You don't know how many pennies. It's unimportant. OK? But I did tell you that a number of them is facing heads up. Let's say its ten.
TOM: OK. So you're telling me there are a bunch of pennies in front of you and ten of them are heads up.
RAY: Now with your mittens on, you can move the pennies around. You're blindfolded, and you're wearing mittens. You can move the pennies around. You can pick them up. You can put them down again. You can listen to them. You can shake them. You can do whatever you want. See if Abe Lincoln talks to you --
TOM: Yeah.
RAY: -- and the question is, is it possible to separate those pennies into two groups so that each group has the same number of pennies facing heads up?
TOM: I got it.
RAY: OK?
TOM: All right.
RAY: Now the reason that you're wearing mittens is that you can't feel the, you know, if we could trust you, we wouldn't have you --
TOM: You can trust me!
RAY: Well, I don't trust you. You're wearing the mittens. Well, here's how you do it --
TOM: Yeah. Go ahead. I can hardly wait.
RAY: I'm going to tell you. Like I said, you don't know how many coins are on the table. Well, I'm going to tell you there are ten coins facing heads up. From that big group, take ten coins. Slide them over --
TOM: I can do, I can do that.
RAY: -- to you, now you have in front of you a little group of ten coins --
TOM: Got them right here.
RAY: -- and the larger group, OK, is off somewhere on the rest of the table.
TOM: And some of the heads could be in my little group and some not.
RAY: That's right. Now, I always like using limit theory when solving this kind of a problem.
TOM: Yeah. Go ahead.
RAY: What if you had, by luck, chosen all tails?
TOM: Yeah.
RAY: OK? Where would all the heads be?
TOM: In the other pile.
RAY: OK. They would be in the other pile. So how would you make the two piles so the same number--
TOM: I would flip over every single one that I just had, except I can't do it because I've got the stupid mittens on.
RAY: For this part, once you've gotten to this point, we'll allow you to remove the mittens.
TOM: OK.
RAY: And it turns out that no matter which, no matter what number of heads you manage to ?? out of that bigger group, you're going to flip over all your coins because as it turns out that the number of tails that you pull out always equals the number of heads remaining in the larger group.
TOM: Say that again? The number of --
RAY: Well, let's say for example that you pull out your ten coins, nine of them are tails, and one of them is a head.
TOM: Right.
RAY: How many heads are left in the big group?
TOM:: Nine.
RAY: Nine. Let's say it's eight and two. How many heads are left in the big group?
TOM: Eight.
RAY: How many tails do you have?
TOM: Two.
RAY: No, eight. And when you flip those eight tails over, you have eight heads and your group and eight heads --
TOM: So the way you do it is you take out ten coins --
RAY: Or whatever number of coins you are told are facing heads up.
TOM: Right, and in this case it's ten, and I, and I flip those over --
RAY: And you're done.
TOM: And I'm done.
RAY: Pretty good, huh?
TOM: Wow. That's very good.
RAY: Do we have a winner?
TOM: You bet we do. William Innes from Missoula, Montana. By the way, this only works if it's a two-sided coin. Three-sided coins, it wouldn't work.
RAY: No.
TOM: The winner this week is William Innes from Missoula, Montana, and for having his correct answer selected at random from all the correct answers that we got this week, William is going to get a $25 gift certificate to the Shameless Commerce division at the Car Talk section of Cars.com, with which I might add he can get our father's CD collection "Why you should never listen to your father when it comes to cars". And if you order it now, William, we guarantee you'll have it for Father's Day. If not this year's Father's Day, definitely next year's Father's Day.
RAY: Indeed. Anyway, we'll have a new, I guess you'd have to call it, automotive or semi-automotive puzzler coming up in the third half of the show.
TOM: ??
RAY: So, don't touch that dial. In the meantime, if you have a question about your car or anything else, give us a call at 888 Car Talk. That's 888, 227, 8255.
[ Car Talk Puzzler ]
