max no of inversions in a sequence of positive integers whose sum is 2014
Source: New Zealand NZMOC Camp Selection Problems 2013 p7
September 19, 2021
number theoryDigits
Problem Statement
In a sequence of positive integers an inversion is a pair of positions such that the element in the position to the left is greater than the element in the position to the right. For instance the sequence has five inversions - between the first and fourth positions, the second and all later positions, and between the third and fourth positions. What is the largest possible number of inversions in a sequence of positive integers whose sum is ?