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 Subject: Simple Math Puzzle Category: Miscellaneous Asked by: caseykangas-ga List Price: \$5.00 Posted: 22 Mar 2006 09:58 PST Expires: 21 Apr 2006 10:58 PDT Question ID: 710590
 ```Math puzzle: If you are a car dealer, and know that sometimes people will pay cash for a car using federal reserve note denominations of 1000, what amounts of money must you seal into 10 marked envelopes so that you can guarantee that no matter what the vehicle purchase price, you will be able to give exact change without having to open an envelope? Assume that the sale price is rounded to the nearest dollar and cents are not used. This is important, because you may have a less than savory sales staff that might dip into the envelopes if they weren't sealed, marked, and carefully accounted for.```
 Subject: Re: Simple Math Puzzle Answered By: websearcher-ga on 22 Mar 2006 10:10 PST Rated:
 ```Hi caseykangas: The answer is quite straightforward. The amounts that should be in the 10 sealed envelopes are: \$1 \$2 \$4 \$8 \$16 \$32 \$64 \$128 \$256 \$512 This is basically 2^0 through 2^9. With those 10 amounts, you can add to make any dollar amount between \$1 and \$1000. How to figure out which envelopes to give for change: * Use the following online decimal to binary conversion tool to find the binary representation. http://acc6.its.brooklyn.cuny.edu/~gurwitz/core5/nav2tool.html * Read the digits from right to left. If there's a 0 in the rightmost spot, then the \$1 envelope is not given as change. If there's a 1 in the rightmost spot the \$1 envelope is given as change. Similarly, the second digit from the right corresponds to whether the \$2 envelope is given. And so on. Example: Change = \$754 754 (decimal) = 1011110010 (binary) Therefore, you give the \$2, \$16, \$32, \$64, \$128, and \$512 envelopes. 2+16+32+64+128+512 = 754 Search Strategy (on Google): * convert decimal binary Hope this helps. websearcher```
 caseykangas-ga rated this answer: `Excellent! Thank you very much.`

 Subject: Re: Simple Math Puzzle From: atk-ga on 22 Mar 2006 12:19 PST
 ```Hey! Wasn't this a "Puzzler" on NPR's show "Car Talk" recently? (websurf, websurf, websurf...) Yep, it was: http://www.cartalk.com/content/puzzler/transcripts/200609/index.html http://www.cartalk.com/content/puzzler/transcripts/200609/answer.html```
 Subject: Re: Simple Math Puzzle From: roxrox-ga on 22 Mar 2006 12:24 PST
 `websearcher- You are really smart!`
 Subject: Re: Simple Math Puzzle From: harobed-ga on 22 Mar 2006 13:10 PST
 ```Actually, the 10th envelope can't have \$512 in it -- that would bring the total of the envelopes to \$1023. The largest amount in an envelope should be \$489.```
 Subject: Re: Simple Math Puzzle From: frankcorrao-ga on 22 Mar 2006 13:29 PST
 ```The question doesn't say that the values in the envelope can't add up beyond 1000, only that you be able to make all values up to 1000. Thus, websearcher's answer seems fine to me. This question is fairly obvious to anyone with any kind of programming background, but I can see how it would be tricky otherwise. It just goes to show that there are 10 kinds of people in this world: those who understand binary and those who don't :D```
 Subject: Re: Simple Math Puzzle From: nelson-ga on 22 Mar 2006 19:27 PST
 `Notes larger than \$100 are not in general circulation.`