I think that a feature that sorts all the unanswered questions randomly would be good, as long as it reordered everything every time the page is refreshed. I often browse the newest page, only to find that I am out of questions that I can answer within five minutes. It would help get attention to old questions that would not be looked at otherwise.
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Here's a SEX-DEX query to do this:
It has a few problems, such as SE's overly aggressive caching allowing
Here's the query parameters I used:
And, the most important part
I could have used
Enjoy the script, and let me know if you have any more requests (besides tag filtering, it turned out to be too complex).