Problem

Source: Balkan BMO Shortlist N7

Tags: number theory, Digits, decimal representation, IMO Shortlist



Positive integer $m$ shall be called anagram of positive $n$ if every digit $a$ appears as many times in the decimal representation of $m$ as it appears in the decimal representation of $n$ also. Is it possible to find $4$ different positive integers such that each of the four to be anagram of the sum of the other $3$? (Bulgaria)