Question Banks - draw 1 question randomly at a time

I'm pretty certain this can't be done but worth asking.

I want to create an assessment where I have a menu with say 20 buttons on a page for each question - but I want it so these buttons can shuffle the questions that appear when the user selects them.

Each time the user clicks a button, I want it to draw 1 question randomly from a question bank.

Once they make their choice, I would like it to go back to the menu so they can choose another button (but not get the same question they have just answered). 

Come the end, they can press a submit button to get the results slide.

Is this possible? The only solution I can think of is create 20 question banks (or graded question slides) with 1 question each - this way I can shuffle the answers of the question at least, however it won't randomize the questions.

Thanks