2023 OIM Problems/Problem 1

Problem

Let $n$ be a positive integer. The following 35 multiplications are performed:

\[1 \cdot n,2 \cdot n,\cdots ,35 \cdot n\]

Show that in at least one of these results the digit 7 appears at least once.

Solution

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See also

https://sites.google.com/associacaodaobm.org/oim-brasil-2023/pruebas