On first pass, this looks quite solid and ripe for promotion. I only have one small issue I've seen so far (below), but note that I've also done some minor copyediting as I went, and in one case, moved an image. If you disagree with any of my tweaks, please feel free to revert.
"The number of codes that can be obtained from 2, 3, 4, 5, 6 ... needles is 2, 6, 12, 20, 30 ...  respectively." -- I'm confused by the external link in this sentence. Is this meant to be a reference? It also appears to be a dead link.
It is a link to the integer sequence, it's not dead, it was just malformed. I've now formatted it as a ref and used the OEIS template. It is part ref and part further information for more terms in the sequence. By the way, it was not me who nominated the article for GA, while I am happy to provide information, I think the nominator should take the lead in dealing with GA issues/comments. SpinningSpark 21:39, 7 March 2013 (UTC)
Thanks--as it happens, that was all I needed, so we're all set. -- Khazar2 (talk) 00:34, 8 March 2013 (UTC)