Every week we feature a Brain Teaser or a thought-provoking question.

If you have one that you would like to share with fellow engineers please email it to info@engineeringdaily.net.

So, here is this week’s,

A gang of 17 thieves steals a bag of gold coins. In trying to share the coins equally, there are three coins remaining. In the ensuing fight over these three coins, one of the gang members is killed. In the next attempt to equally distribute the coins, there are 10 coins remaining. Again the gang fights, and another member dies. The third attempt is successful.

**What is the smallest number of coins stolen?**

The correct answer will be posted a week following this posting.

Good luck.

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Posted by Ken.Kabaki
on Apr 20th, 2009 and filed under Discussions.
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(x-3)/17 = (x-10)/16 = 122

How can you divide 122 in between 15 remaining thieves

3,930

Tom:

I guess great minds do think alike. I had not seen your answer when I struggled with this problem. I couldn’t find an algebraic solution either and independently came up with the same Excel ‘brute force’ approach with one exception, instead of using an “If” discriminator I just scanned down the three columns until I found the first row with three integers – which, of course, was 3930. The reason that Einstein would not have used that approach is because the operating system of the Babbage mechanical ‘computer’ of the period couldn’t run the Excel software.

Just FYI, the algebraic solution is obtained with the chinese remainder theorem [thousands of years old, I bet Einstein knew about it :-)]. If you ever had a math course involving modulo (finite field) arithmetic you probably had to solve a very similar problem in your exam.