Question 51
In a sequence of positive integers, an inversion is a pair of positions in which the element in the leftmost position is greater than the element in the rightmost position. For example, the sequence $2,5,3,1,3$ has $5$ inversions: between the first and the fourth positions, between the second and all the others to its right and, finally, between the third and the fourth. Among all sequences of positive integers whose sum of elements is $n$, what is the largest possible number of inversions if
a) $n=7$ ?
b) $n=2019$ ?
Remark: The sequences of positive integers considered in this problem may have more than $5$ elements.
a) $n=7$ ?
b) $n=2019$ ?
Remark: The sequences of positive integers considered in this problem may have more than $5$ elements.