Optimal Bin Packing of Items of Sizes Uniformly Distributed over [0, 1]

Consider n independent random variables uniformly distributed over [0, 1] and consider the minimum number Bk of unit size bins needed to pack these items under the restriction that no bin can accept more than k items. We prove that EB2 − EB3 is of order √n. But in sharp contrast, we show that EB3 − EBn is of a smaller order.