Question 75
Given a finite sequence with terms belonging to the set $A = \{0, 1, \ldots, 121\}$, an allowed operation consists in replacing each term by a number of the set $A$ so that equal terms are replaced by equal numbers, and different terms are replaced by different numbers. (Some terms may remain unreplaced.) The goal is to obtain, from a given sequence and by means of the allowed operation, a new sequence the sum of which is divisible by $121$. Show that it is possible to achieve the goal for any given sequence.