Stone Temple Farmers
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 pounds 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.
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?
TOM: Let me look on this little piece of paper. The winner is John Hengesbach from Windham, New Hampshire.
[ Car Talk Puzzler ]