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> There is a pile of $n$ items. Every time you divide a pile into two piles, you get a score being the product of the number of items in the two piles. Show that the sum of your scores at the end is always $\binom{n}{2}$.
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My question: What are some (preferably well-known) books/articles that discuss or at least mention this puzzle? Is there a name to the puzzle? I guess it's quite famous, and as I want to mention it in an article, I would like to cite it properly instead of just saying that it is "a famous puzzle". Searching Google for "pile product score" doesn't yield useful results.



Reference for puzzle on dividing piles and scoring products
This [entry](http://www.cut-the-knot.org/proofs/piles.shtml) on *Cut the Knot* gives a proof and the reference to the book *Exploring Mathematics with Your Computer* by A. Engel. I am not sure if the puzzle was invented by Engel, but hopefully the book will have an earlier reference if that's not the case (unfortunately I do not have access to the book at the moment). 


