suppose we have a finite set X and a set S of subsets of X and we want to determine is there a subset S' of S such that all members of X belong to exactly one set in S' I think the best problem to reduce to this problem is 3-colorable graph and i think X is the set of vertices.But i can't find the best rule for creating set S from G. is there any idea?



how to reduce 3-colorable graph to this?
This problem is indeed NP-complete and was in fact one of [Karp's 21 NP-complete problems](http://en.wikipedia.org/wiki/Karp%27s_21_NP-complete_problems). Googling [exact cover](http://en.wikipedia.org/wiki/Exact_cover) will lead to enlightenment. 


