If I want to search for old questions in need for an answer, I can use a search query like

is:question hasaccepted:no isanswered:no lastactive:6m.. score:1

but since I prefer to answer questions in which someone is actually interested, I would like to refine it to questions where either the OP or one of the users who favourited it has been active in the last $n$ days.

Note: I know that there is a way to search for questions within any given user's favourites, but I don't even know if it is possible to search for questions which have been favourited by at least $k$ persons.

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    $\begingroup$ Cannot be done via the built-in search; you'll need a SEDE query. $\endgroup$ – user147263 Apr 1 '15 at 13:15
  • $\begingroup$ If you have a look at SEDE database schema you have LastAccessDate in the table Users. You also have Posts.FavoriteCount. Maybe you can use this to create your own query tailored for your needs. Or you can use some already existing query. For example, I found this: Old unanswered questions whose asker is still around. $\endgroup$ – Martin Sleziak Apr 1 '15 at 13:19
  • $\begingroup$ If you plan to use SEDE for his, you should also be aware that the data in data explorer are updated only once a week. $\endgroup$ – Martin Sleziak Apr 1 '15 at 13:20
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    $\begingroup$ That said, favorites do not always mean "interested". I sometimes favorite a question when I'm out of delete votes for the day, to come back to it later. Also, it would make sense to answer questions that you are interested in, something you enjoy working on. If a dozen people are dying to know the answer but you personally wouldn't enjoy solving that problem... why should you bother? $\endgroup$ – user147263 Apr 1 '15 at 14:37
  • $\begingroup$ @pizza Of course I will then look through the results for a problem I would enjoy solving. This is meant to reduce the amount of questions I have to sort thorough to those that are in need of an answer someone is still interested in. I know that favourites don't necessarily mean "interested", but I think that's the best metric I have available. Plus, I don't think you keep those "to-be-deleted" stars around for six months or more, do you? $\endgroup$ – A.P. Apr 1 '15 at 14:44

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