Buying House Number Letters

Oct 27, 2001

RAY: Remember last week's Puzzler?

TOM: Of course I do. It was about... it was about...

RAY: Right. House numbers. And so is this week's Puzzler. Here it is. A man is waiting in line at a hardware store to buy letters that make up the number of his house. You know. For example --

TOM: T, H, R, E, E.

RAY: There you go. But, by luck, there were three other guys ahead of him in line all doing the same thing. The first customer buys the number one. O, N, E. He pays two bucks. The next guy buys the number TWO, and pays three bucks. The third guy buys the number ELEVEN, and he pays five bucks.

Our protagonist is buying the number twelve. Here's my question: How much does he pay?


TOM: Let's see. If he beats up the first two guys, he can have the T and the E and he'll only have to buy, oh, 12. The T and the W --

RAY: Don't you notice --

TOM: -- and the E, oh.

RAY: All the letters in 12 are in the first three --

TOM: I was just thinking he'd only have to buy three letters.

RAY: Well, in fact, let's look at the word 12. Let's look at it. OK, and then let's look at --

TOM: He's got to buy all of them.

RAY: And then let's look at the word 11.

TOM: Eleven.

RAY: They share four letters.

TOM: Yeah.


TOM: Yeah.

RAY: OK? So if you take that away from the 12, you get T-W left over.

TOM: T-W and --

RAY: If you take those same four letters away from 11, you have N-E left over. Now, let's go back to the first two guys.

TOM: Yeah.

RAY: One cost two dollars, and two cost three dollars. What have we learned? Now we don't know the cost of any of the letters individually.

TOM: No, we don't, but we do know --

RAY: But we do know that a T and a W costs a dollar more than an N and an E.

TOM: Yeah. We do know that. I do know that. I see it right here.

RAY: We do know that. And as luck would have it, the T and W in 12 are going to cost a dollar more than the N and the E in 11. We know the whole of 11 costs five bucks, so 12 must cost six bucks. Pretty good. Huh?

TOM: Wow.

RAY: And you could use higher mathematics to solve this.

TOM: Well, I was writing a series of simultaneous equations.

RAY: You could do that.

TOM: Could I?

RAY: No.

TOM: Will I be able to play the piano?

RAY: My wife broke her finger recently. It was a little industrial accident, and whilst we were at the hospital waiting endlessly, I decided I had to ask the doctor when it was all over if she would be able to play the violin. And he was a young guy. I figured he'd go for it. He didn't.

TOM: He didn't go for it?

RAY: No. He said could she play the violin before? I told him he ruined my whole day. Anyway, who is our winner?

TOM: The winner this week is Meg Schneider from Boise, Idaho.

Get the Car Talk Newsletter