Problem
ALG-B2-M04-P006 Arbitrary permutation
#6
★★★☆☆ Level 3 of 5
Let \(a\le b\le c\le d\) and \(x\le y\le z\le t\). Prove that for any permutation \(p,q,r,s\) of \(x,y,z,t\), \[ap+bq+cr+ds\le ax+by+cz+dt.\]
Hint. If two elements are in the wrong order, an adjacent swap does not decrease the sum.
If for \(i
This is the first problem where the student proves the inequality for any permutation, not just for one displayed permutation.