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2012 PUMaC Combinatorics B4

Source:

October 5, 2019
combinatorics

Problem Statement

For a set SS of integers, define max⁡(S)\max (S) to be the maximal element of SS. How many non-empty subsets S⊆{1,2,3,...,10}S \subseteq \{1, 2, 3, ... , 10\} satisfy max⁡(S)≤∣S∣+2\max (S) \le |S| + 2?
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