Missing dollar puzzles like these have had a damaging effect on me for the past 40 years! Damn them! This same puzzle messed with my mind at an younger age. And so to this day, I can't produce a math or logic solution without second and triple-guessing myself! Doesn't matter if I arrive at the correct solution in the first couple of seconds, nor if the answer is staring me right in the face, I still re-examine my answer with an air of self-doubt... all because of this stupid puzzle that shattered my confidence all those years ago!
Another way of tackling the problem requires challenging the wording of the puzzle. Nothing in the wording specifies the formation of the circle. I.e., are the circles DISCS or RINGS? Answers provided thus far assume the circles are to be shaped as discs. But if they can be rings, then only one sheet of paper is needed.
If the "circles" can be rings, here's how it can be done with one sheet of paper. Rather obvious but I like to spell things out anyway:
I guess I/we are missing something obvious, then. Because from strictly an area calculation, at least three sheets of paper are needed.
The combined area of 10 circles with a 2.5" radius is 196.25 sq in. The combined area of TWO 8.5 x 11 sheets of paper is 187 sq in. So no matter how many arcs you divide each circle in order to maximize the coverage of a piece of paper, you'll need AT LEAST three sheets of paper to meet the area requirements alone. As I mentioned In my earlier post, the project can be completed with three sheets of paper.