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 the answer to last week's puzzler. You don't remember this, Tom?

TOM: Well, I remember something about the stone but, oh he's going to break the stone up into pieces.

RAY: I'll repeat it .

RAY: A farmer had a 40 pound stone that he used to weigh 40 pounds of feed with, you know, he had a balanced scale, you put the stone on one side and the feed on the other side, and when it balanced, he knew he had 40 pounds of feed on the one side. You with me?

TOM: Yeah. If it wasn't 40 pounds of feed than the cows would get mad and get mad cow disease. And say hey it's only 38 pounds, what the hell is going on here, McDonald!

RAY: A neighbor of his, Frank Staples, I think, borrows the stone and when he returns it, he says I'm terribly sorry, I dropped the stone and it broke into four pieces. The farmer says don't worry, you actually did me a favor and he explains that the pieces of the broken stone could now be used to weigh any item, assuming those items were at one pound increments from one pound to 40 pounds. So, if he wants to weigh something that's one pound, two pounds, three pounds, four pounds, five pounds, he can do it with those four stones, four pieces and the balance scale.

TOM: And the sum of which obviously is 40 pounds.

RAY: Obviously he can't weigh anything heavier than 40 pounds because when he puts the stones altogether they weigh --

TOM: Well, he can stand on it.

RAY: So, the question is what are the weights of the four individual stones? And how does the farmer system work? And I think the hint I gave is how would you weigh two pounds?

TOM: Yeah, that was the hint that you gave.

RAY: Clearly, one of the pieces has to be one pound. I think we all agree on that.

TOM: And I think the next one will be three.

RAY: That's good. Why do you think so?

TOM: Put one on one side and three on the other and that's two.

RAY: Huh? You put the one pound weight on one side to weigh a two pound piece, the two pound thing on that same side and the three pound weight on the other side.

TOM: Exactly. Three pounds is obvious now because he's got the three pound thing. Four pound is easy, he puts the two together --

RAY: He's got three in one and --

TOM: And now we're in a lot of trouble.

RAY: Well, you're not. And the only way I came to the answer --

TOM: Well, I'm going to go one, three, five and whatever's left, 29 or something.

RAY: Well, that's close but it's wrong.

TOM: 31. No we don't need five because we can play around to get five with a bigger number. We could have an eight and we could do five --

RAY: Ooh, you're so close!

TOM: And we could have a six and have --

RAY: Well, the way I stumbled upon the answer by figuring there has to be --

TOM: By tripping over the book that the answer is in!

RAY: That's what it was, it was in the Math group. That somehow I figured out it had to be powers of three, because if it broke into four pieces, there are four powers of three between one and 40 -- three to the zero which is one, three to the one which is three, three squared which is nine and three cubed which is 27.

TOM: They don't add up to 40 by any chance?

RAY: They do!

TOM: Oh, my God! So they do.

RAY: And that's what they are.

TOM: Nine.

RAY: One, three, nine and 27.

TOM: Or nine if you put four on one side and nine on the other, that gives you the five.

RAY: Trust me it works. It works. I don't think they're are any other four sides that will allow you to do this, but I know one, three, nine and 27 do and I think those are the only ones that work.

TOM: This is like the Lou Gehrig thing.

RAY: Well, actually this is similar to the -- similar to but not quite like the puzzler that we had about the necklace some time ago. Taking pieces of the necklace --

TOM: Ah, yes, it's very similar.

RAY: It's very similar. Requires the same kind of thought process, except this required turning to page 18 where the answer was. And who's our winner this week, Tommy?

TOM: Oh, we got a winner?

RAY: Yeah!

TOM: Let me look on this little piece of paper. The winner is John Hengesbach from Windham, New Hampshire.

[ Car Talk Puzzler ]