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only half a tip now. the answer will come later on...

Question: given that you can use Shift to Add to a selection, and Alt Subtracts from a selection; given also that Shift restraints the ellipse marquee to a circle, and that Alt makes you start drawing from the centre: how will you, using only these keys, the grid an snap to on, and your mouse/pen to drag, draw a square selection and add a circle exactly to the centre of one of its corners?

It's simply a question of dragging, pressing, letting go, pressing again etc.