This is a beauty of a puzzle taken from the recent internet puzzle series on Ramanujan going on. Several great puzzles, this one of them.
Jack and Will are very successful pirates who have become very wealthy from their years of pillaging. They each start with 2015! gold coins. (This exclamation point is a factorial symbol as introduced in the previous problem and means 1x2x3x4x…..x2014x2015) Jack gives Will one-half of his gold. Will then gives Jack one-third of his gold. Jack then gives Will one-fourth of his gold. They repeat this back and forth process, ending with Will giving Jack 1/2015 of his gold. How much more gold does Will have than Jack at the end of these exchanges?
As always, please send your answers as comments within the blog (preferred), or send an e-mail to firstname.lastname@example.org. Please do share the puzzle with others if you like, and please also send puzzles that you have come across that you think I can share in this blog.
Happy gold juggling!