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When I open https://stackoverflow.com, I have the following options for viewing questions:
interesting, featured, hot, week, month
(https://math.stackexchange.com uses “active” instead of “interesting”, and I don’t have any other SE accounts to compare.)

If I click on “Unanswered” at the top, I have the following options:
my tags, newest, votes, no answers

If I click on “Questions” at the top (or a particular tag), I have the following options:
newest, featured, frequent, votes, active, unanswered

With some clicking, I can restrict that to questions that have the desired set of tags (an intersection of the tag groups, if you will). With some careful searching (or a bookmark), I can change that to an arbitrary union or intersection of tag groups (although more than five tags would be cumbersome to type).

In the Android app, I have the following options for displaying questions:
active, newest, hot, votes, unanswered (newest), unanswered (my tags)

The ordering of the results is set by default, and can be the following:
Last Activity Date, Votes, (Incoming?) Links, Asked Date

Featured, Hot, Week, and Month order the results according to some weighting of the votes, views, and answers (where the weighting decreases with time for Hot?). I’ll call this (decaying) hotness.

Looking at this, featured, interesting, unanswered, no answers, and “my tags” are categories of questions. On the other hand, active, frequent, hotness, newest, and votes are ways to order the questions. We should better distinguish these.

I would like to be able to toggle “featured”, “unanswered/no answers”, and “my tags” independently of each other (or choose “interesting”), optionally restrict the results to a time period, and then decide how I want the resulting questions ordered.

I’m aware of similar questions where the answer turns out to be a few clicks or more informed searching (and other unanswered questions that this generalizes). But since this site’s entire existence is to create good questions and answers, I feel like we should be able to search through them more intuitively.

To implement this, I would say that https://stackoverflow.com/questions should be the same as https://stackoverflow.com/, and we remove the top link to https://stackoverflow.com/unanswered. Have “Top Questions” pull up “interesting” questions, and then have checkboxes (going horizontally) for “Featured”, “Unanswered”, and “My Tags”. At the end of the row (where “month” currently sits), give a dropdown menu with sorting options: Last Activity, Frequency (aka links), Date Asked, Votes, and Hotness. Or we go ask https://ux.stackexchange.com/ how to implement it. Restricting dates could be left to the search page.

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