##### Mar 10, 2001

**RAY: **I'm going to give you a thousand $1 bills. You come up with 10 envelopes.

Here's your assignment: Figure out a way to configure those 10 envelopes, that is, to put various numbers of dollar bills in those 10 envelopes, so that no matter what amount of money I ask you for, you can hand me some combination of envelopes and always be assured of giving me the correct amount of cash.

**TOM: **Let me get this straight. If you say, "Give me $637," I can say, "Oh, that will be envelope number one, envelope number six, and envelope number two."

**RAY:** You got it.

**RAY:** All right. Here it is.

**TOM:** Go ahead.

**RAY:** I gave Tommy a thousand $1 bills, and his assignment was, first, come up with 10 envelopes, and once he did that he had to figure out a way to put various numbers of dollar bills in those 10 envelopes so that no matter what amount of money I asked him for, he could hand me some combination of envelopes and always be sure of giving me the exact right amount. The question is: How did he do it?

**TOM:** That's the question? I thought the question was, What was going on in your mind that you gave me 1,000 $1 bills?

**RAY:** I could've given a hint last week and said one of the envelopes has $489 in it. I could have given that hint.

**TOM:** Really?

**RAY:** Well, yeah, and the other envelopes...the other nine have $1...

**TOM:** I like that.

**RAY:** $2.

**TOM:** Yeah.

**RAY:** Four dollars, $8, $16, $32, $64, $128, and the ninth envelope has $256. If you add those up -- 256, 128, 64, 32 -- you come up with 511, because in base 2, the next number would be...

**TOM:** 512.

**RAY:** 512, OK? Two to the tenth would be 512, but he couldn't put 512 because you don't have it in there.

**TOM:** No.

**RAY:** So you could put 489. So you can get any possible number between one and 511 by using the first nine envelopes, and then anything beyond 511 up to a 1,000 using 489 plus one gives you 490, 490 plus two gives you, and da-da-da.

**TOM:** Man.

**RAY:** Pretty good, huh? Give me my thousand bucks back. It was only a loan.

**TOM:** Give me my envelopes back.

**RAY:** A further demonstration of the power...

**TOM:** Of two.

**RAY:** Of two.

**TOM:** Man.

**RAY:** You can't do it unless the number is two. There you go, see? The power of two. Right?

**TOM:** They just won't leave you alone. I'm almost feeling sorry now. I'm going to have to stick up for my little brother. Lay off the guy!

**RAY:** I know, relentless. Everybody too.

**TOM:** I told him to do it. We have a winner. The winner is Betty Benson from Houston, Texas.