# On proving NP-completeness by reduction to 3-partition problem

Consider a problem $X$ can be reduced to 3-partition problem. So, when 3-partition has a solution then $X$ has a solution. But if 3-partition does not have a solution, they $X$ may or may not have a solution. In this case, is it legal to say that the problem $X$ is np-complete?

• Problems don't have solutions, problem instances do. You seem to be confused with the fundamentals; our reference questions can help.
– Raphael
Aug 5, 2016 at 7:52
• It is not illegal to make false mathematical statements. Aug 5, 2016 at 9:33
• @TomVanDerZanden Put the statement down. Step away from the statement. Sorry, couldn't resist... :-D
– Juho
Aug 5, 2016 at 13:27

1. The thing you describe isn't a reduction. It must be that the instance of $X$ has a solution if, and only if, the instance of 3-partition has a solution.
2. Reducing $X$ to 3-partition just proves that $X$ is in NP. To prove completeness, you need to reduce an NP-complete problem to $X$.