I asked this question: Guess the 5 letter word.
As I commented, the FAQ says, "if your question generally covers ... a software algorithm ... then you’re in the right place to ask your question!" It also says you should ask, "practical, answerable questions." My question is a practical, answerable algorithms question. In addition, it doesn't violate any of the "should I not" examples.
I don't see any conflict with the FAQ, but it was downvoted multiple times and closed almost immediately. That says to me that either the FAQ no longer matches the site, or something about my question jumped out as a false negative.
A friend of mine asked it to me, and I thought it was a great question, but I'm not so sure there's any Stack Exchange site to post an interesting algorithms problem to, now. That would be a shame because those questions are fun.
Edit I see that the based on actual problems that you face part of the FAQ is important and not really reflected in my question.
My final food for thought is that I love this question as a computer scientist, it's a great interview question, and isn't it kind of a shame that it doesn't belong on a site about programming and algorithms?
I for one wish there was a better balance between, "Think about this interesting algorithms problem" questions and, "How do I do this in jQuery?" questions.