The tags fifteen and gameoffifteen clearly refer to the same program. Unfortunately, the file is called
fifteen.c while the problem set refers to "The Game of Fifteen" so people will instinctively try to use both of these names, and they don't start with the same letters so people won't always see one when they start typing the other.
Generally speaking, multiple-word tags are hyphenated rather than run together. I think the proper way to deal with this is to replace gameoffifteen with game-of-fifteen (much easier to read, isn't it?) and make fifteen a synonym for the full, hyphenated version of the tag.
This way, we only have to retag 6 questions. The tag synonym would have to be proposed by Kareem or curiouskiwi (1,250 rep privilege).