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1 positive integer anagram of the sum of 3 other positive integers

Source: Balkan BMO Shortlist N7

August 5, 2019

number theoryDigitsdecimal representationIMO Shortlist

Problem Statement

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)