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UKMT Senior Kangaroo, 2017

Combinatorics Difficulty 2.0 Junior Prove it United Kingdom

The set $S$ is given by $S = \{1, 2, 3, 4, 5, 6\}$ . A non-empty subset $T$ of $S$ has the property that it contains no pair of integers that share a common factor other than 1. How many distinct possibilities are there for $T$ ?

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