Suppose that we vary the balls-and-bins process as follows. For convenience let the bins be numbered 1 answer below »

Suppose that we vary the balls-and-bins process as follows.
For convenience let the bins be numbered from 0 to n − 1. There are log2
n players. Each player randomly chooses a starting location  uniformly from [0,
n − 1] and then places one ball in each of the bins numbered  mod n, + 1
mod n,…,+ n/ log2 n − 1 mod n. Argue that the maximum load
in this case is only O(log log n/ log log log n) with probability that
approaches 1 as n → ∞.

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