TOM: Three guys go out fishing. They decide in advance that whatever they catch, they’re going to divvy it up equally.

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.RAY: Right.TOM: 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 throws one of the fish overboard, takes his third and leaves. A few hours later, in the middle of the night, another guy wakes up with horrible stomach pains. He’s gotta have the Kaopectate. So he goes to take his third of the fish, and he notices, interestingly, the same thing — he can’t take a third unless he throws one fish overboard. He throws one fish overboard, takes his third, and goes home.

Third guy gets up in the morning and figures the other guys are still sleeping. So he figures, “I’ll just take my third, and I’ll go. When they wake up, they can take their third.” However, he realizes that he can’t take a third.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. Question: What is the smallest number of fish by which this little scenario could have taken place?

Can this happen with 4 people? 5? 6? n?

3 – 25, x = 9

4 – 253, x = 104

5 – 3,121, x = 1275

6 – 46,651, x = 18,744

I am still figuring out how to express in terms of n… I am using google spreadsheet with x as final number of fish just before the last person takes his portion. I can’t see people in pain counting the 46,651 fish, 3,121 maybe, but not 46,651.

Bill Brown

I was able to figure out the formula, but not sure WHY it’s the formula. If there are x people, I believe the minimum number of fish required are (x^x) – x + 1.

I figured it out when I found that, for three people, it works starting at 25 and then goes up by 27 from there, which is 3^3.