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, duh, the answer to last week's Puzzler.

RAY: You said you remembered it!

TOM: I was lying.

RAY: Well, anyway, this Puzzler came from my Fewest Number of Moves series.

TOM: Oh, that's, that crazy little thing.

RAY: No. I thought this was great little Puzzler.

TOM: Yeah, yeah, OK.

RAY: It was sent in by Bruce Robertson, who's a professor at the University of Tennessee. Anyway, here it is. There are 25 jealous people who live on one floor of a very strange apartment building. On this floor are 25 apartments laid out in a five by five grid.

TOM: Yeah.

RAY: Got it? So, if you draw this grid, the square in the upper left-hand corner we could say is one, and the one next to it is two, three, four, five, and then the line below that is six, seven, eight, nine, 10, 11, 12, right? All the way to 25. Got it?

TOM: I got it.

RAY: Now, each person who lives on the floor aspires to move into the apartment of one of his adjacent neighbors. So number one can move to square number two, or number six, for example.

TOM: But not diagonally.

RAY: Not diagonally. Number two can move to number one.

TOM: Or number three, or number seven.

RAY: There you go.

TOM: I can visualize all that.

RAY: So, here's the question. Why would anyone live in such a stupid building? No, the question is, what is the fewest number of total moves that will allow every person to move to an adjacent square.

TOM: All right. I see --

RAY: I know Doug Mayer has been, did you get the answer, Mayer? He says, no, I didn't get the answer.

TOM: Well, unencumbered by the thought process, I concluded right away when you gave this problem --

RAY: It had to be one or zero, right?

TOM: -- that the answer was, it was either going to be 26 --

RAY: Ah! Very good!

TOM: -- or millions.

RAY: Well, millions is close.

TOM: Millions is closer, huh?

RAY: If you don't number them one through 25, but instead, letter them.

TOM: Yeah.

RAY: And not A, B, C, D, E. Let's letter the first one A.

TOM: Yeah.

RAY: The next one B, the next one A, the next one B, et cetera, et cetera.

TOM: Oh, oh, oh.

RAY: Then, everyone who's on an A square must, by definition, move to what?

TOM: A B square.

RAY: Right.

TOM: And then, vice versa.

RAY: And everyone who's on a B square must move to an A square. It's pretty obvious if you draw it out.

TOM: Yeah. That's true.

RAY: Yeah. Now, if you add them up, by some stroke of bad luck, you got 13 A squares and only 12 B squares.

TOM: Someone's got to move out of the building.

RAY: They've got them mixed up, like. So, there are no fewest number of moves. It is impossible for this to happen. I know, it was a little sneaky.

TOM: No, no. Impossible is a good answer.

RAY: Impossible is a good number of moves. So, who's our winner, anyway?

TOM: That's very good, you know? I like that question.

RAY: Well, you're going to love this week's if you --

TOM: Yeah.

RAY: Poor Mayer just threw a waste basket at me! He was up to 26,215 moves, and he almost had it!

TOM: Ah, the winner is Martha Lozzanno from Richmond, Virginia. Richmond, Virginia.

RAY: Good work, Martha.

TOM: And for having her answer selected at random from the both of the correct answers that we got, Martha's going to get a $25 gift certificate to the store at the Car Talk section of cars.com, and with that 25 bucks, she can buy the better part of a Car Talk CD gift set.

RAY: What's the better part?

TOM: The carrying case. Actually, that's the best part. And by the way, if you'd like to learn more about any of the status lowering items that we mention on the show, you can always visit the store at the Car Talk section of cars.com yourself, or you can call 888-CAR-JUNK, and this is known as shameless commerce, what we just did.

[ Car Talk Puzzler ]