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1,2,...,2011 around circle such that 8 of 25 successive multiples of 5 and/or 7

Source: 2011 Belarus TST 2.1

November 8, 2020
combinatoricsnumber theorymultipledivisible

Problem Statement

Is it possible to arrange the numbers 1,2,...,20111,2,...,2011 over the circle in some order so that among any 2525 successive numbers at least 88 numbers are multiplies of 55 or 77 (or both 55 and 77) ?
I. Gorodnin
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