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Special and superspecial sets

Source: Finland 2013, Problem 4

May 2, 2013
combinatorics unsolvedcombinatorics

Problem Statement

A subset EE of the set {1,2,3,…,50}\{1,2,3,\ldots,50\} is said to be special if it does not contain any pair of the form {x,3x}.\{x,3x\}. A special set EE is superspecial if it contains as many elements as possible. How many element there are in a superspecial set and how many superspecial sets there are?
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