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Every Saturday, a gang of us play some kids from Brooklyn at baseball, but the other day, because of the flu, it looked like we'd have to miss a game. Then Chuck pointed out that, because some of us were better players than the rest, we'd still be able to pull together two evenly matched teams, though it would mean mixing up the two groups.
As I was getting ready to go to bat, who should walk up but the guy who's running for Mayor this year, saying we kids all looked so cute we could be brothers and sisters.
He patted my head for the benefit of the TV crew with him, so I told him we might look alike, but actually we belonged to four different families.
"There's my family," I explained. "Ours is the largest. Then there's the Browns, they're a smaller family. The Greens are smaller still, and the Black family is the smallest of all.
He wanted to know how many kids there were in each family, but I was in the mood to be difficult, so I told him, as it happens, you could multiply together the numbers of kids in each family and come out with the same number as was the number of fools who were going to vote for him this coming November. Then I told him how many votes I figured he'd get!
That should have been enough to persuade him to take a hike, but instead he said: "Well, let me see if I can work out the number of children in each family." After a moment, he said: "Tell me one thing, sonny: do the Blacks have more than one child?"
I didn't see how knowing that would help him much, so I answered. But I figured I'd out fox him by just saying Yes or No. Then the wise guy looked straight at the TV cameras and announced how many kids each family had!
How did I answer his question, and what did the wise guy say? (For the baseball-ignorant: there are 9 players on a team.)
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The reason we figured we might have to skip the game was that, thanks to the flu, fewer than 18 kids showed up at the park that Saturday. There are only fourteen different combinations of numbers that add up to 17 or less and still allow each of our four families to have a different number of kids. Eleven of the fourteen possible combinations give you different totals if you multiply the numbers together, the other three all give you the same total...120. Thats how many votes I told the wiseguy he was going to get on election day, thats why he had to ask his question about the Blacks. The three combinations that give you 120 when the numbers are multipled are, 8, 5, 3, 1..... 6, 5, 4, 1, and 5, 4, 3, 2. So when the would-be mayor asked me Do the Blacks have more than one child? I must have answered Yes, otherwise he wouldnt have been able to figure out how many kids each of our families had, 5,4,3 and 2.
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