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Balls in a box

Posted on: August 28th, 2013 by
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There are n balls in a box. Each ball is of a different color. At each iteration, you draw 2 balls at random, and paint the second ball so that it's the same color as the first; then you replace the balls. You keep repeating this until all the balls in the box are of the same color. What is the expected number of iterations?
- Via Quora

Spoiler alert:
There is a nice thread on math overflow to discuss this problem here. Thanks to Sudeep Kamath for pointing this out.

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