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COMMENTS
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For n=1,2 there are numerous ways, while for each of n=3 and n=4 there is only one way: n=3:{1,4,6,7,10,11,13,16},{2,3,5,8,9,12,14,15} (see A133483-A133484), n=4: {1,2,3,4,8,9,10,11,12,16},{5,6,7,13,14,15}.
Presumably for n >= 4 there are no solutions.
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