Comments on: Weekly brain teaser | A gang of 17 thieves steals a bag of gold coins

By: dr

dr — Tue, 22 Nov 2011 15:58:06 +0000

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.

By: jon

jon — Tue, 22 Nov 2011 11:36:29 +0000

(x-3)/17 = (x-10)/16 = 122

By: Answer

Answer — Tue, 22 Nov 2011 04:30:35 +0000

3,930

By: Heinz Rosen

Heinz Rosen — Fri, 22 May 2009 22:47:24 +0000

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.

By: RSanders

RSanders — Wed, 20 May 2009 17:27:28 +0000

Of course, that 16th guy was certainly not minding his comparative values, deciding to fight and die rather than simply pony up 5 of his 245 coins to ensure his own safety.

If someone is going to die over that last batch of 10 leftovers, and once it has been established that the others are willing to turn on and kill off any one of the others over only 3 coins, it would have been much better for him to have determined which of the others was the least likely to assist him in future endeavors and ‘volunteer’ that individual as the scapegoat, netting him 486 gold (out back) for his initial investment of 5, and ensuring it is not the other 15 that split his own take…and head…hmmm

By: Tom

Tom — Thu, 07 May 2009 18:03:03 +0000

Even with the admin answer I could not see a mathematical substitution method to answer the question using the 3 equations available. So I cheated, using an EXCEL data base with three columns, one for each equation, with the values then placed in one column in ascending order will yield 3 consecutive 3930 values. To “spot” it, a simple IF-AND equation like =IF((H2-H1=0)*AND(H3-H1=0),”yes”,”"), identifies where the three equations will all yield the same value. Knowing the 3930 answer we can simply solve for the admin’s “a, b, & c” values. Not the way Einstein would solve it, but it works.

By: admin

admin — Wed, 06 May 2009 14:38:24 +0000

Thanks.

By: Allan Ropski

Allan Ropski — Mon, 04 May 2009 22:03:12 +0000

Dont’ forget the last part that the total is equally divisible among 15 thieves. The 272 is strictly a multiplier between 16 and 17. I found the solution by finding the least common multiple of 15x, 16x+10, and 17x+3. This way the remainers (10 and 3) are accounted for according to the the number of thieves.

By: Kevin

Kevin — Mon, 04 May 2009 20:10:26 +0000

16×17 is actually 272 but it looks like its just a typo. the solution works

By: Leslie Carter

Leslie Carter — Mon, 04 May 2009 19:59:02 +0000

16 * 17 = 272, is there a typo in the answer?

By: admin

admin — Mon, 04 May 2009 15:12:39 +0000

3930. The number of coins. X = 17a + 3 = 16b + 10 = 15c. By inspection, the first two criteria are met when a=b=7 and x=122. They are subsequently met at increments of x of 16×17 or 272. The first number in this series divisible by 15 is 3930.