RAY: Hi, we're back. You're listening to Car Talk with us, Click and Clack, the Tappet brothers, and we're here to discuss cars, car repair, and the answer to last week's very, very good puzzler.

TOM: I didn't make it up!

RAY: No, this was top drawer, man.

TOM: I like it, I like it! Here it is. Three guys go out fishing, and they decide they're going to split whatever catch there is. This is in a boat. They're deep-sea fishing. They collect a bunch of fish; they throw them on the deck. They decide they're going to divvy up everything the next morning. So, they pull into the dock, they sit there, and they have a few beers. They sleep the night away in the boat. However, in the middle of the night, one of the guys has severe cramps and decides he's not going to stay the night. He's going to go home, and he wants some Pepto Bismol. So, he says, "I'll take my third." He goes onto the deck; he counts the fish, and says, "Hmm, not divisible by three." He throws one of the fish overboard, takes his third, and he leaves. An hour later, one of the other guys wakes up and realizes that he's got to be up real early tomorrow morning to go to a meeting. He can't stay on the boat all night. He says, "I'll take my third, and I'll go home." So, he counts the fish. He says, "Oops, they're not divisible by three," throws one fish overboard, takes his third, and leaves. The other guy wakes up at seven o'clock in the morning. He doesn't know the other two guys have gone, but he decides, well, it's time to leave. He looks at the fish, he counts them, throws one overboard and says, "Here's my third," and he leaves also.

RAY: And no fish are left except the two thirds?

TOM: No, the fish that are left, he's figuring he's leaving the other guys their two-thirds.

RAY: A third apiece?

TOM: Yeah.

RAY: Got it.

TOM: So, everyone did the same thing. The question simply was, what is the smallest number, the fewest number of fish by which this could happen? That each guy does the same thing and blah blah blah.

RAY: Yeah, yeah, yeah.

TOM: And? And, now what? Now, I give the answer? Just as simple as that? Well, I mean, you could do it simply by trial and error. Just keep trying numbers. The original littlest equation, which was in the book that I read, and I can't remember where I got this puzzler because I lost the book, but I did remember the equation. It was very simple. It was: Y=2/3(X-1), so that Y is what you end up with, X is what you start with, and you keep plugging in numbers for X, what you start with, until you can solve that equation three times without running into non-integers. That doesn't happen until you get to 25.

RAY: Wow! So, they caught 25 fish?

TOM: They caught 25 fish. The first guy tosses one overboard because you can't divide 25 by three. That's 24. He takes his third, which is eight, that leaves 16 fish. The next guy comes; you can't divide 16 by three.

RAY: Throws one overboard?

TOM: Throws one overboard. That's 15.

RAY: I can see it's beginning to play out.

TOM: Right! He takes five. That leaves 10 fish. The third guy shows up in the morning, there's 10 fish. He thinks he's dividing it again into threes. He can't divide it by three, he throws one fish overboard, takes his three, leaving six fish on the deck to rot.

RAY: To rot and attract flies!

TOM: And attract flies and god knows what kind of evil vermin. But the answer is that they caught 25 fish. Who's our winner, Raymie!

RAY: Our winner this week...

TOM: Wait, is this some kind of a sneaky plot to get me to do more work?

[ Car Talk Puzzler ]