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numbers satisfying s(n) < s(2n), are as many as ...s(n) > s(2n) [sum of digits\

Source: Dutch IMO TST 2016 day 3 p3

August 30, 2019
number theorysum of digitsDigits

Problem Statement

Let kk be a positive integer, and let s(n)s(n) denote the sum of the digits of nn. Show that among the positive integers with kk digits, there are as many numbers nn satisfying s(n)<s(2n)s(n) < s(2n) as there are numbers nn satisfying s(n)>s(2n)s(n) > s(2n).
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