MathDB

4

Part of 1974 Canada National Olympiad

Problems(1)

Sum of reals

Source: Canada 1974/4

1/13/2007
Let nn be a fixed positive integer. To any choice of real numbers satisfying 0\le x_{i}\le 1,  i=1,2,\ldots, n, there corresponds the sum ∑1≤i<j≤n∣xi−xj∣.\sum_{1\le i<j\le n}|x_{i}-x_{j}|. Let S(n)S(n) denote the largest possible value of this sum. Find S(n)S(n).