Mathegoras

Combinatorics › Combinations and selections › Choosing with gaps

Subsets with smallest element m

University · ●●●●○ 100 pts

Determine all values of mm with 1≤m≤471 \leq m \leq 47 for which there are exactly 2152^{15} subsets XX of the set {1,2,3,…,47}\{1,2,3,\ldots,47\} such that 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.

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counting subsetsremainderspowers of two