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Distinct 7-Digit Non-Multiples

Source: Mathematics Regional Olympiad of Mexico Southeast 2023 P1

October 8, 2023
MexicoDigits

Problem Statement

Victor writes down all 7āˆ’7-digit numbers using the digits 1,2,3,4,5,6,1, 2, 3, 4, 5, 6, and 77 exactly once. Prove that there are no two numbers among them where one is a multiple of the other.
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