Popping Pills

Feb 19, 2000

RAY: Hah! 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 new Puzzler.

TOM: I can hardly wait!

RAY: Well, I think you'll like this. This is a recent submission from a guy named Scott Crass, and I like it because my brother didn't get it. Here it is.

TOM: Yeah.

RAY: Pay careful attention. You're placed on a medication regime in which you are to take daily one tablet of A and one of B.

TOM: Got it.

RAY: You got it. So, you have two little pill, what do they call them, containers.

TOM: Yeah.

RAY: One says "Pill A," and one says "Pill B." You must be careful. Taking two or more B's can have unpleasant side effects, or can even be fatal. In order for the B to be effective —

TOM: Does my wife know?

RAY: In order for the B to be effective, it must be accompanied by the A pill.

TOM: Yeah. So, you gotta take one A and one B. That's it.

RAY: So, you open up the A bottle and you, as people do, you tap the bottle, and one A pill kind of jumps out into your palm.

TOM: Yeah.

RAY: You open the B bottle, and you accidentally get two Bs falling out of the bottle. But here's the problem. They look exactly the same.

TOM: Oh, they don't have little As and Bs on them?

RAY: Just on the container. But they're both —

TOM: Bummer!

RAY: They're both blue, they're the same size, they're the same weight. And as soon as they fell in there, they got mixed up, so now you have three pills, but you can't tell what the heck you got. How can you make... now, of course, you could just throw these pills away.

TOM: That was my first thought. My first thought was don't make this into a Puzzler; throw the pills away and start again.

RAY: But the pills cost a hundred bucks apiece, and you can't throw them away.

TOM: Yeah.

RAY: But how can you make sure that you get your daily dose of A and B without wasting any of the pills?

 
Answer: 

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.

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