Consider the following problem that we call the "min-max interval sum" problem. The input consists of a sequence A[1..n] E R of numbers, and an integer k. The goal is to partition A[1..n] into k sub-intervals I1, ..., Ik that minimizes the maximum sum over all the intervals. In other words, the goal is to partition such that max; Si is minimized, where si = Leel; e is the sum of numbers in the interval I. Decide if either: (a) A polynomial time algorithm for min-max interval sum implies a polynomial time algorithm for SAT. O (b) There is a polynomial time algorithm for min-max interval sum