Here is the problem:

Proof

Tie each chip to every other chip by a thread. In all, there are going to be (n-1)n/2 threads. When you split a pile into two parts of x and y chips each, you have to cut xy threads connecting chips from the two parts. Which is exactly the number you will add to the total. To reach the stage of no nontrivial piles you will have to cut all the original threads.

Reference

1. A.Engel, Exploring Mathematics with Your Computer, MAA, 1993

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