# The Family Jewels?

RAY: Now, we already know she needs one for day one. And she needs two. Well, it turns out that every integer could be expressed as the sum of powers of two. Right.

TOM: Yeah.

RAY: Right. And between one and thirty-one how many powers of two are there?

TOM: There are four, plus the fifth one.

RAY: Well, there's two to the zero which is one. There's two to the first which two. There's two to the second which is four. There's two to the third which is eight. And there's two to the fourth which is 16, and then two to the fifth is 32, but she doesn't need 32 pieces.

TOM: That's what I just said. There's four plus the fifth one which would be 32.

RAY: So how many pieces does the chain have to be cut in?

TOM: Four. Five.

RAY: Five. Four is close enough. If you're not really paying attention, four's good.

TOM: Yeah, I mean she might come into money around the 18th of the month.

RAY: You never know. And the hint I gave was that twenty years ago people would have had a more difficult time solving this, because people were not binary literate as much as they are today. I mean everyone knows -

TOM: I still don't get the binary thing. What's that got to do with it.

RAY: It's all powers of two. You know, base.

TOM: Yeah. So she's going to have one.

RAY: Oh, I knew this was going to be a problem.

TOM: Two, four, eight and sixteen.

RAY: 16. And you can make every number between 1 and 31 with those five pieces.

TOM: Of course you can, can't you.

RAY: Yes you can.

TOM: Isn't that good?

RAY: OK. Who's our winner this week?

TOM: The winner this week is Suzanne Boening.

RAY: Oh, they make great planes up there at Boenings, don't they.

TOM: Boning, yeah. From Tuscaloosa, Alabama.

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