You either read the earlier version before it was corrected, or you're misunderstanding. The problem is not the N-Queens problem, it's the N-Queens /completion/ problem. The problem is this:

Here's an NxN board with k queens already placed. Is there a way to place another N-k queens so they are all mutually non-attacking?

Most instances will be easy, but current algorithms to solve this are such that for each N, the time taken in the worst case is an exponential function of N.