There is an urn of N balls, each of a unique color. In each step one takes out 2 balls without replacement, changes the color on the 2nd ball to that of the first ball and returns them back to the urn. What is the expected number of steps until all the balls in the urn are of the same color?
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As @ShaiCovo mentions in a comment above, this question is a duplicate of http://mathoverflow.net/questions/41939/a-balls-and-colours-problem and has been answered there.