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Number Theory + Combinat

Source: Cono sur Olympiad 1997 P5

October 11, 2017
combinatoricsnumber theorycono sur

Problem Statement

Let nn be a natural number n>3n>3. Show that in the multiples of 99 less than 10n10^n, exist more numbers with the sum of your digits equal to 9(n−2)9(n - 2) than numbers with the sum of your digits equal to 9(n−1)9(n - 1).
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