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Another puzzle

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Post by Hellsangel Mon Jan 21, 2013 12:11 am

From car talk.
Hellsangel
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Post by bw Mon Jan 21, 2013 12:20 am

oh, someone asked my kids this question just y'day. it's a nice one.

i know the answer and so won't try.

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Post by MaxEntropy_Man Mon Jan 21, 2013 12:25 am

Hellsangel wrote:From car talk.

good one! i started to think about it and will continue after i finish this infernal report.
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Post by Idéfix Mon Jan 21, 2013 12:30 am

1, 2, 4, 8, 16, 32, 64, 128, 256, 489.

Here is my rationale. You need to have an envelope with a single bill in it so you can meet a request for $1. To meet a request for $2, you might have another envelope with a single bill in it, but that would be inefficient. So you need an envelope with 2 bills in it. With those two, you can meet requests for any amount up to $3. You need a third envelope with 4 bills in it; this lets you meet any request up to $7. And so on. Your ninth envelope will have 256 bills in it, and with those nine envelopes, you can meet any request between $1 and $511. You are left with 489 bills and one envelope, so stuff them in the last envelope. If you get a request for $512, you hand out the tenth envelope, and the combination of envelopes 1-9 that would have added up to $23.
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Post by MaxEntropy_Man Mon Jan 21, 2013 10:01 am

haven't looked at anyone's solution yet. but i think i figured it out:

1,2,4,8,16, etc.?

now the question is if the information in the problem too much. i think for example they needn't have stated that the number of required envelopes is 10. they could have asked for the amounts and the minimum number of envelopes required.
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Post by Hellsangel Mon Jan 21, 2013 11:08 am

MaxEntropy_Man wrote:haven't looked at anyone's solution yet. but i think i figured it out:

1,2,4,8,16, etc.?

now the question is if the information in the problem too much. i think for example they needn't have stated that the number of required envelopes is 10. they could have asked for the amounts and the minimum number of envelopes required.

Yes. But I guess they were testing people on the binary concept.
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