RAY: Hi! We're back. You're listening to Car Talk with us, Click and Clack, the Tappett Brothers, and we're here to talk about cars, car repair, and, duh, the answer to last week's Puzzler.
TOM: Yeah.
RAY: This came in from a listener named Scott Crass. You ready?
TOM: I actually remember the Puzzler.
RAY: I know you do.
TOM: Yeah.
RAY: Yeah. You've been placed on a medication regime in which you are to take the following medications once a day. You are to take one tablet of medicine A and one tablet of medicine B.
TOM: That would be like Valium and Prozac.
RAY: There you go. In your case, right.
TOM: In my case.
RAY: So, you've got two little boxes of pills, and you must be careful, because taking two or more Bs can have unpleasant side effects, like severe hemorrhoidal flare-ups. And taking an A and not a B, or vice versa, can also be very serious.
TOM: Mmm-hmm.
RAY: So, in order for B to be effective, it must be accompanied by the A pill, so you must take exactly one A and one B. Got it?
TOM: I'm with you.
RAY: So, you open up the A bottle, and you tap it, and one A pill falls into your hand.
TOM: Got it.
RAY: You put that bottle aside and you take the B bottle. You do the same, but by mistake, two Bs fall into your hand. Now, here's the problem. The pills look identical.
TOM: Oh, bummer!
RAY: Same size, same weight, same color, same everything. And they don't have As and Bs written on them, and they're both identical, so what are you gonna do? You can't tell which is which, but if you go eenie, meenie, minie, moe.
TOM: You could throw them away and start over again.
RAY: But, ah! They're a hundred bucks apiece. Did I mention that?
TOM: You can't throw them away and start over again.
RAY: So, here's the question. How do you get your daily dose of exactly one A and exactly one B without wasting any of the pills?
TOM: Wow!
RAY: And here's how you do it. You know that you have one A and two Bs. You just can't tell which are which. So let's add another A to the mix. So now, you have two As and two Bs, so you lay the four pills out in a row. But you don't know which are which.
TOM: No.
RAY: Now, you could again go, eenie, meenie, minie, moe. And your chances of getting the right thing are improved by having done this, but not good enough.
TOM: No, because you might die.
RAY: You could die. However, if you take each pill and cut it in half and without mixing up the halves, in other words, the first pill you cut in half, you leave those two halves near each other.
TOM: Yeah.
RAY: And the same thing with the second, the third, and the fourth pill. And then you take one from each of the cut pills.
TOM: A half a pill from each of the pairs.
RAY: Right. So, by definition, because you know you have two As and two Bs in the mix, you'll take a half an A from one of the cut pills, and a half a B, and then another half an A, and then another half a B, and you'll have two half Bs and two half As, making one A and one B, and then the remaining pills, cut pieces, will be tomorrow's dose.
TOM: Man.
RAY: Who's our winner, Tommy?
TOM: I have to say that that is not intuitively obvious.
RAY: No?
TOM: No.
RAY: Well, the only thing that made me a little bit discouraged about the Puzzler was that Berman got it.
TOM: He did, huh?
RAY: He did, yeah. Anyway, do we have a winner?
TOM: Yeah, we have a winner. The winner is Tom Mallon from Santa Clara, California. Tom, for having your answer selected at random from among the thousands of correct answers that we got, you're going to get a $25 gift certificate to the Car Talk Shameless Commerce Division, and with that $25, you can buy about five eighths of a Car Talk T-shirt. Which five eights will he get? Maybe he's got a short torso. It might work out for him.
[ Car Talk Puzzler ]
