Popping Pills

Feb 21, 2015

RAY: You're on a medication regime in which you are to take daily one tablet of A and one of B. So, you have two little pill containers. 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, it must be accompanied by the A pill.

TOM: So, you gotta take one A and one B. Got it.

RAY: Right. You open up the A bottle and one A pill kind of jumps out into your palm. 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. Both kinds of pills are blue, they're the same size, they're the same weight. And as soon as they fall in there, they get mixed up, so now you have three pills, but you can't tell what the heck you’ve got. The pills cost a hundred bucks apiece, and you can't throw them away.

How can you make sure that you get your daily dose of A and B without wasting any of the pills?

RAY: You know that you have one A and two Bs. You just can't tell which is which. So let's add another A to the mix. Now you have two As and two Bs. You lay the four pills out in a row.
Take each pill and cut it in half without mixing up the halves. In other words, the first pill you cut in half, you leave those two halves near each other. 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 cut pieces will be tomorrow's dose. Who's our winner, Tommy?

TOM: Congratulations to Tom Mallon from Santa Clara, California!                                                   

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