NP-complete problems are the hardest problems whose solutions can be efficiently checked for correctness. An efficient method of solving any NP-complete problem would translate directly into efficient solutions for all of them.
Many famous and interesting problems are NP-complete, but this is not one of them! This is the problem of how to distribute “Elmo’s World” segments onto a series of video releases.
Nobody knows a good way to solve NP-complete problems. The Elmo’s World people were not able to solve their problem either.