Currently there are 368 unanswered questions, and 352 that have zero answers.

This means that there are 16 that have at least one answer, but for which the answer has a non-positive vote count. How can I find them?

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Where did you get the number 368 from? I get 3201unanswered questions when I follow your link. – m_goldberg Nov 27 '15 at 1:39
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@m_goldberg This question was asked in January 2013... almost 3 years ago! :) – R. M. Nov 27 '15 at 3:12
    
@R.M. Ah, I failed to notice that. – m_goldberg Nov 27 '15 at 3:31
up vote 3 down vote accepted

The following search query should give you all questions that are categorized as unanswered, but have at least one answer with non-positive vote count:

http://mathematica.stackexchange.com/search?q=isanswered%3Ano+closed%3Ano+hasaccepted%3Ano+answers%3A1

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You can't do that with the tabs on that page or using the search, but you can find them using the API:

unanswered = Last@Reap@Block[{i = 1, more},
      While[{more = "has_more" /. #, Sow["items" /. #]} &@
        Import["http://api.stackexchange.com/2.1/questions/unanswered?pagesize=100&site=mathematica&filter=!BGS1(RNaQDJUqhjM_kktL.ISG39ejq&page=" <> ToString@i++, "JSON"]; 
        more =!= False
       ]
      ]~Flatten~2;

Cases[unanswered, 
 {"answer_count" -> Except[0], "link" -> l_, ___, "title" -> t_} :> Hyperlink[t, l]] // TableForm

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P.S. The filter=... in the URL is an API filter that I created to return only the necessary fields. In essence, this moves the filtering operation from mma to the API service, which makes for cleaner code. The filter is non-expiring and immutable, so this answer will always work. – R. M. Jan 17 '13 at 2:30

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