Pick up sticks

Break a ruler of length n inches with indentations at each inchmark into n sticks of length one by repeatedly picking up all the fragments which are still of length greater than one and throwing them down all at once until all the sticks are of length one. Assume that each stick breaks into exactly two sticks uniformly at the inchmarks. What is the expected number of throws needed to complete the n− 1 breaks? We show that the answer to this question is (4.31107 . . . ) · lnn · (1 + o(1)) by, as mathematicians are fond of doing, reducing it to an already solved problem. The problem that we reduce it to-or rather show that it is almost trivially equivalent tois the problem of finding the asymptotic average height of a binary search tree. The latter problem was first solved by Luc Devroye[D], with a later refinement by Bruce Reed[Re].