Ok, I'm afraid that this article has quite a long way to go before it's ready for good article status. The following are the pieces that you need to work on:
The key problem, as noticed by Crisco, is the lack of cited sources. Ideally, we'll see citations for all the information in the article. "The eight queens puzzle as an exercise in algorithm design", for instance, completely lacks references. Statements like "There is currently no known formula for the exact number of solutions." really need citations. An overreliance on general references means that it is unclear what is cited to what- see the guideline. (Further, the "footnote" in "Edsger Dijkstra used this problem in 1972 to illustrate the power of what he called structured programming. He published a highly detailed description of the development of a depth-first backtracking algorithm.2" should really be a real footnote, using <ref>Blah</ref>.)
On the flip side, unless it's particular contentious information, it will not need to be cited in the lead. The lead should exist to summarise everything else that's in the article- right now, it is very short, and fails to do that.
It seems very odd that you start to talk about Python before you've talked about the issue mathematically, or even started to offer explanations/solutions. Surely, they would need to come first. This is an article about a mathematic problem- not software engineering.
The in-text external links in "Related problems" are not desirable. Further, there seem to be a very high number of external links in the external link section- are they really all needed? Only external links which add something that our article does not/cannot should really be there.
I am failing to see what "An animated version of the recursive solution" and "Sample program" are adding to the article. The article should not just be a dumping ground for stuff which helps people solve the problem. (Also, this is a journal article, and should be cited as such.)
The reference formatting is currently inconsistent: Template:Cite journal and Template:Cite book may help. Many of the references are very good- the books and journal articles- but some, like this, are hardly ideal.
As this really needs to be completely rewritten to bring it in line with cited sources and place it in a more logical order, it doesn't really seem worth me going into any prose issues (though the article has clearly been written by several people- it lacks any kind of unity). As such, I'm going to have to fail the article at this point, as it needs significant work. I hope this is something you're willing to do- you may be able to find people willing to help at Wikipedia:WikiProject Mathematics or Wikipedia:WikiProject Chess. Good luck! J Milburn (talk) 15:56, 13 April 2012 (UTC)[reply]