Solution to Puzzle #144: Pirates and Gold Once Again

Many correct responses to this puzzle, but the I was happiest to see was Danny from Washington DC, an 8th grader – well done Danny. Other people who sent the right answer included Suman Saraf, Vivek Rai and Pratik Poddar. Thank you all!

The answer is that both Jack and Will will have the same number of coins at the end of the game. The reason is that they pass on the same number of coins to each other in every turn. Here is how this works (copying the answer from Pratik as well as Danny):

(J,W) = (2015!, 2015!) –> (2015!/2, 3/2*2015!) –> (2015!, 2015!) –> (2015!3*/4, 5/4*2015!) –> (2015!, 2015!) and so on

In other words, say Jack and Will have X amount of gold.  Jack gives Will X/n amount of gold, so Will ends up with X +X/n  OR (n+1)X/n amount of gold. Now Will gives Jack the amount he has divided by (n+1)  back , which equals X/n. 

Note that if instead of 2015, we had an even number, the answer would not be same!

Hope you all enjoyed the puzzle!

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