Problem Let a1,a2,…,a11a_1, a_2, \dots, a_{11}a1,a2,…,a11 be integers chosen from the set {1,2,3,…,20}.\{1, 2, 3, \dots, 20\}.{1,2,3,…,20}. Show that there exist two distinct indices i≠ji \neq ji=j such that ∣ai−aj∣≤1.|a_i - a_j| \le 1.∣ai−aj∣≤1.