##### Feb 26, 2000

**TOM:** Ha! We're back! You're listening to Car Talk with us, Click and Clack, the Tappet Brothers. And we are here to discuss cars, car repair, and, duh, my new Puzzler, which I stole out of a book, and I can't remember what book it was.

**RAY:** So, you don't know the answer.

**TOM:** I don't know the answer.

**RAY:** But you know the question.

**TOM:** I think I know the question.

**RAY:** That's as good as I can ever say.

**TOM:** Here's the question. Three guys go out fishing. They decide in advance that whatever they catch, they're going to divvy it up equally.

**RAY:** Was this a motorized boat or a sailboat?

**TOM:** This was a sailboat, because this is a non-automotive question.

**RAY:** OK. All right. So they go all fishing.

**TOM:** Yeah.

**RAY:** Was this during the week?

**TOM:** Stop interrupting! Is this what you have to...

**RAY:** Go ahead.

**TOM:** What a pain in the butt this is!

**RAY:** I'm sorry. I'll try to be good.

**TOM:** So, they decide in advance that whatever fish they catch, they're going to divvy them up three ways evenly.

**RAY:** As they catch them?

**TOM:** No.

**RAY:** OK.

**TOM:** When they get back to port.

**RAY:** All right.

**TOM:** So, they finish fishing for the day. They pull back into port, and they're going to sleep on the boat overnight. They're going to get up in the morning, divvy up the fish, and go home. In the middle of the night, however, one of the guys has a severe hemorrhoidal flare-up, and he's got to get to the drugstore right away to buy some stuff, Preparation Whatever-it-is.

**RAY:** Yeah.

**TOM:** G, B. So, he goes to take his third of the fish, and he notices that the number that they caught is not divisible by three, unless he throws one of the fish overboard. So, he does. He throws one of the fish overboard, takes his...

**RAY:** So like if there were 100 fish, he threw one away and...

**TOM:** And took 33.

**RAY:** And took 33. I got it.

**TOM:** Leaving 66.

**RAY:** Got it.

**TOM:** But it's not the right answer.

**RAY:** No?

**TOM:** No. So, he takes his third, and he leaves. Somehow, a few hours later, in the middle of the night, another guy wakes up with horrible stomach pains. Gotta have the Kaopectate. Gotta have it. So, they're going to bump into each other at the drugstore. He says, "I'll take my third of the fish, and then I'll go home, because I can't stay here like this." So, he goes to take his third, and he notices, interestingly, the same thing, that he can't take a third unless he throws one fish overboard. So, he throws one fish overboard, takes his third, and goes home.

**RAY:** Got it.

**TOM:** Third guy, whose stomach is fine, whose hemorrhoids have not flared up, he gets up in the morning, and he realizes that he hasn't taken his third of fish, but he's got to go home anyway. He figures the other guys are still sleeping.

**RAY:** Got it. Got it.

**TOM:** So, he says, I'll just take my third, and I'll go. When they wake up, they can take their third.

**RAY:** And they'll get stuck paying the fuel bill.

**TOM:** Right. However, he realizes that he can't take a third.

**RAY:** Let me guess! Not divisible by three.

**TOM:** It's not divisible by three.

**RAY:** Sonja Henie's...! What are the chances of that?

**TOM:** He throws one fish overboard, takes his third, and leaves.

**RAY:** Got it.

**TOM:** Question: What is the smallest number of fish by which this little scenario could have taken place? Not the smallest fish.

**RAY:** No.

**TOM:** That would be like minnows. The smallest number that they...

**RAY:** That they started out with.

**TOM:** That they caught.

**RAY:** Right.

**TOM:** That they started with when they pulled into port.

**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?

**RAY:**Well, we tried and it's hopeless. Our winner this week is Constantine Russos.