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sum of digits of 3n if sum of digits of n is 100 and of 4n is 800

Source: 2020 Dürer Math Competition Finals Day2 E4 https://artofproblemsolving.com/community/c1622639_2020_

January 7, 2022
sum of digitsnumber theory

Problem Statement

We have a positive integer nn, whose sum of digits is 100100 . If the sum of digits of 44n44n is 800800 then what is the sum of digits of 3n3n?
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