Optimal sequencing of a set of positive numbers with the variance of the   sequence's partial sums maximized
  We consider the problem of sequencing a set of positive numbers. We try to find the optimal sequence to maximize the variance of its partial sums. The optimal sequence is shown to have a beautiful structure. It is interesting to note that the symmetric problem which aims at minimizing the variance of the same partial sums is proved to be NP-complete in the literature. 
Li Wei, Wangdong Qi, Dingxing Chen, Peng Liu and En Yuan
math.CO