Prove that for every positive integer
![n,](/media/m/5/f/2/5f26ebab144fee216fbc733cb1fa2f2b.png)
the set
![\{2,3,4,\ldots,3n+1\}](/media/m/d/1/e/d1ebeb0544f48ba0a1d91a4518ba2066.png)
can be partitioned into
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
triples in such a way that the numbers from each triple are the lengths of the sides of some obtuse triangle.
Proposed by Canada
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Prove that for every positive integer $n,$ the set $\{2,3,4,\ldots,3n+1\}$ can be partitioned into $n$ triples in such a way that the numbers from each triple are the lengths of the sides of some obtuse triangle.
Proposed by Canada