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Hey Simon.
Interesting idea but, in my opinion, given the vast array of topics, for something like this to be engaging you will need to provide a tag selector at the least.
Maintaining a local index of tags, updated daily perhaps, to feed a work-alike tag selector as available on SE sites would be my next step.
I suggest giving a list of 10/15/20 questions instead of redirecting.
Now I click "Go", wait until the question is loaded and if its not satisfactory I need to go back, click "Go", ... Quite a lengthy process (about 5-6 s). If submitting just gave me a list of 10/15/20 question, I could