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subset of 1-2007, one divides another

Source: Switzerland - 2007 Swiss MO Final Round p8

December 26, 2022
combinatoricsnumber theorydivisible

Problem Statement

Let MāŠ‚{1,2,3,...,2007}M\subset \{1, 2, 3, . . . , 2007\} a set with the following property: Among every three numbers one can always choose two from MM such that one is divisible by the other. How many numbers can MM contain at most?
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