Going Fishing!

Jul 21, 2008

TOM: We're changing things up a bit and I've got the new puzzler this week. I stole it 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 but 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 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. Then they'll 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 Preparation Whatever-it-is.

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 and takes his share.

RAY: So for example, if there were 100 fish, he threw one away and took 33.

TOM: Right, leaving 66. 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. 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, gets up in the morning, and he realizes that he hasn't taken his third of fish. He figures the other guys are still sleeping. 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 because it's not divisible by three. He throws one fish overboard, takes his third, and leaves.

So the question is, what is the smallest number of fish by which this little scenario could have taken place? The smallest number that they started out with.
RAY: Here's the answer, and it was a big hint that there are nine numbers here.

TOM: Yeah.

RAY: If you went ahead and you spelled out the numbers, one, two, three, four, five, the number one has three letters, the number two has three letters, the number three has five letters.

TOM: Ohhh.

RAY: And the tenth term would be the number ten, which has --

TOM: Three letters.

RAY: And of course, the answer is three. Three is the next number in the sequence.

TOM: Wow, I have to say, that stunk.

RAY: Thanks for the brotherly support!

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