Problem

Source: Australia MO 2024 P3

Tags: algebra



Let a1,a2,,an be positive reals for n2. For a permutation (b1,b2,,bn) of (a1,a2,,an), define its score to be n1i=1b2ibi+1.Show that some two permutations of (a1,a2,,an) have scores that differ by at most 3|a1an|.