##### Oct 29, 2007

**RAY:**This is nice and short and it was sent in fairly recently by a fellow named Richard Rarridan. And I'm using it because a lot of people have complained that some of our puzzlers are a little difficult to grasp (i.e. boooogus)!

In a certain family each daughter has the same number of brothers and sisters. Each son has twice as many sisters as brothers. How many sons and daughters are there in the family? Now there are two ways to do this obviously, you can do it the hard way or the easy way.

Answer:

**RAY:**Well, the easy way to solve this puzzler was with algebra. If each daughter has the same number of brothers and sisters, it's obvious then that this family has one more girl than it has boys.

**TOM:**Yeah.

**RAY:**So we could write a very simple expression. If we let G equal girls, and B equals boys --

**TOM:**G equals B plus one.

**RAY:**Right, or G minus one equals B.

**TOM:**Same way.

**RAY:**Now, the second part of it, each son has twice as many sisters as brothers. Let's say B minus one equals the number of brothers that each son has, right?

**TOM:**Yah.

**RAY:**Then it says that each son has twice as many sisters as brothers. Then two times that amount, two times B minus one has got to equal G.

**TOM:**I got it.

**RAY:**It could be 14 girls and 13 boys, nine girls, eight boys.

**TOM:**It's not three to one then.

**RAY:**No. It's four girls and three boys. Pretty good.

**TOM:**Yah. Four and three.

**RAY:**Do we have a winner?

**TOM:**We do have a winner. The winner is Robert Stucker, from Kansas City, Missouri, and for having his answer selected at random from among the pile of correct answers that we got, Robert is going to get a 26-dollar gift certificate to the Shameless Commerce Division at cartalk.com. With which he can get our four show CD collection called Four Perfectly Good Hours. These are four shows that we picked because there was something particularly funny, and memorable on each one of them.

**RAY:**And they ain't half bad either.

**TOM:**Anyway this collection of four classic Car Talk shows can be yours Robert, if you want it, for being this week's Puzzler winner, and I have to say congratulations to you.