Google Answers Logo
View Question
Q: Simple Math Puzzle ( Answered 5 out of 5 stars,   5 Comments )
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:5 out of 5 stars
Hi caseykangas:

The answer is quite straightforward. The amounts that should be in the
10 sealed envelopes are:


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.

* 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. 

caseykangas-ga rated this answer:5 out of 5 stars
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:
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.

Important Disclaimer: Answers and comments provided on Google Answers are general information, and are not intended to substitute for informed professional medical, psychiatric, psychological, tax, legal, investment, accounting, or other professional advice. Google does not endorse, and expressly disclaims liability for any product, manufacturer, distributor, service or service provider mentioned or any opinion expressed in answers or comments. Please read carefully the Google Answers Terms of Service.

If you feel that you have found inappropriate content, please let us know by emailing us at with the question ID listed above. Thank you.
Search Google Answers for
Google Answers  

Google Home - Answers FAQ - Terms of Service - Privacy Policy