#### Jonny K

##### Second Unit

- Joined
- Dec 18, 2002

- Messages
- 375

Anyway:

"

Jane goes to her friends house for a barbecure. Her friend greets her at the door and Jane responds "What a nice group of children playing in your yard". Her friend answers "They actually came from 4 families - mine is largest, my sisters smaller, my brothers smaller still, and my cousin's the smallest. The product of the numbers is my house number. But there were not enough people to play baseball.

Jane asks "could you tell me if you cousin's family has only one child?". Her friend answers, and Jane then responds by telling her the number of people in each family.

How many children in each family?

"

Note that we don't know the house number or the answer to the question. I confirmed this with the prof.

Here's the math translation (as given by our prof):

X1 > X2 > X3 > X4 >= 1

X1 + X2 + X3 + X4 < 18

X1*X2*X3*X4 = House #

X1 represents the largest family, while X4 is the smallest. 18 is the number of people you need to play baseball.

Now here's what I have so far...

X4 can either be 1 or 2. If it's greater than 2, then the minimum you'd get would be:

6 > 5 > 4 > 3

And 6 + 5 + 4 + 3 = 18 which is not less than 18, so you can't have this case.

Looking at the remaining two cases (X4 = 1 or 2), I get many possible combinations!

X4 = 1:

4 + 3 + 2 + 1 = 10

5 + 3 + 2 + 1 = 11

...

11 + 3 + 2 + 1 = 17

etc etc.

X4 = 2:

5 + 4 + 3 + 2 = 14

6 + 4 + 3 + 2 = 15

...

8 + 4 + 3 + 2 = 17

etc etc.

So without knowing the house number, how in the WORLD do I solve this darn problem! I know a guy who's on the DEAN'S list at the University (he's super smart), and he has no clue either...

Any idea?

Thanks.

Jonny K.