lean_workbook_plus_58814

Given $a{1}$ , $a{2}$ ...... $a{7}$ , $b{1}$ , $b{2}$ ...... $b{7}$ are positive real numbers satisfying $a{i}$ + $b{i}$ < 2. Prove that there exist two positive integers k, m (k, m = 1, 2, ..., 7) such that | $a{k}-a{m}$ |+| $b{k}-b{m}$ |<1.