Feb 28, 2015
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.
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?
TOM: You could do it simply by trial and error. Just keep trying numbers. Or you can do a very simple equation: 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 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. Throws one overboard. That's 15. 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. So who's our winner, Raymie?
RAY: Our winner this week is Constantine Russos from Arlington, Virginia. Congratulations!