Known conditions: Two sets of positive number arrays A and B have the same average: (a(1) + a(2) + ... + a(N)) / N = (b(1) + b(2) + ... + b(N)) / N The minimum value in array A is less than the minimum value in array B: min(A) < min(B) The maximum value in array A is greater than the maximum value in array B: max(A) > max(B)
Prove that S_A is greater than S_B, where: Sum of the cubes of array A: S_A = a(1)^3 + a(2)^3 + ... + a(N)^3 Sum of the cubes of array B: S_B = b(1)^3 + b(2)^3 + ... + b(N)^3