Let S be a subset of {1, 2, 3, ... 100}, containing 50 elements. How many such sets have the property that every pair of numbers in S has a common divisor that is greater than 1?
I can only think of 1 subset that will meet this restriction. That is the the set of even numbers from 2 to 100 inclusive.
So I think the answer is 1
+647 
