For a sequence x1,x2,…,xn of real numbers, we define its <spanclass=′latex−italic′>price</span> as 1≤i≤nmax∣x1+⋯+xi∣. Given n real numbers, Dave and George want to arrange them into a sequence with a low price. Diligent Dave checks all possible ways and finds the minimum possible price D. Greedy George, on the other hand, chooses x1 such that ∣x1∣ is as small as possible; among the remaining numbers, he chooses x2 such that ∣x1+x2∣ is as small as possible, and so on. Thus, in the i-th step he chooses xi among the remaining numbers so as to minimise the value of ∣x1+x2+⋯xi∣. In each step, if several numbers provide the same value, George chooses one at random. Finally he gets a sequence with price G. Find the least possible constant c such that for every positive integer n, for every collection of n real numbers, and for every possible sequence that George might obtain, the resulting values satisfy the inequality G≤cD.Proposed by Georgia IMO Shortlistalgebraalgorithmcombinatorics