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A Thousand Dollars And a Bunch of Envelopes

The Puzzler


RAY: In the first nine envelopes, you're going to put one dollar, 2 dollars, then 4, 8, 16, 32, 64,128, and 256. That's nine envelopes.

If you add all those up, that's 511 dollars.

So if I ask you for any amount up to 511 dollars, you would give me some combination of those envelopes, and if I asked you for 511

TOM: I'd give you all of them.

RAY: Right. So, what do I put in the next envelope?

TOM: Everything else.

RAY: Exactly. 489 bucks. And if you do that, you can give me any amount of money that I ask for. For example, if I ask for say, 671 dollars, you would give me the envelope that's 489 dollars, plus you'd give me another 182 dollars. But we know that you can give me 182 dollars.

TOM: You could do that combination with the other envelopes. I like it.

RAY: Cute, eh? So who's our winner?

TOM: The winner is Linda Williams from Ann Arbor, Michigan. And for having her answer selected at random from among all the correct answers that we got, Linda gets a 26-dollar gift certificate to the Shameless Commerce Division at Car Talk.com with which she can get one of our fine -- you know when something is really junk, that's when you use the adjective "fine" to describe it -- anyway Linda, you can get one of our fine 'Best of Car Talk' collections on CD.

That's a fine product isn't it?

RAY: Oh yes. The finest!

[ Car Talk Puzzler ]

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