I think the math professor needs to check his math. While I agree with his assertion that the odds of picking the perfect bracket are about 1 in 100 million trillion, the paper required to have one of each possibility would in no way fill the universe.
A cubic meter of paper contains somewhere on the order of 150,000 sheets - using standard office paper, that would be a stack of 500-sheet reams that is 5 wide, 3 deep and 20 tall. Filling out one sheet for each bracket possibility would take 670 quadrillion of these cubic meters containing 150,000 sheets each. That sounds like a lot, and it is - it would take a cube about 87,000 meters (or about 54 miles) on a side to contain it all. And while that volume of paper would fill the Grand Canyon many times over, it comes nowhere near to filling the universe.
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Jeff Martin of MN 5:23PM March 14, 2012