Can an AI have original thought?

This one is for an ex-colleague of mine who wanted to know if it (Auto Coder AI) can do crosswords and an original game. First the crossword. Instead of it inventing it I get it to search for existing game code and retrieve it. Then I ask it to make up its own original game. This question is all about how smart AI is, can it have original thought? If you don't like crosswords then skip to the original game. I don't play games much since the days of Doom II so have little understanding how good it is. I will let you judge.