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Part of 2005 Czech And Slovak Olympiad III A

Problems(1)

2^{15} subsets X of {1,2,...,47}, min m in X, x in X, either x+m in X or x+m>47

Source: Czech and Slovak MO, III A, 2005 p2

1/12/2020
Determine for which mm there exist exactly 2152^{15} subsets XX of {1,2,...,47}\{1,2,...,47\} with the following property: mm is the smallest element of XX, and for every x∈Xx \in X, either x+m∈Xx+m \in X or x+m>47x+m > 47.
Subsetscombinatoricsminimum