2013 UMO Problems/Problem 2
Alice and Carl play the following game using a square sheet of paper. On each turn, the player makes a straight cut through the sheet (not necessarily parallel to the sides of the page), creating two new sheets. The sheet with smaller area is discarded (either one if the two are equal), and the player gives the larger sheet to the other player. The first player to receive a sheet of area less than square centimeter from the opposing player loses. If Alice goes first, describe (with proof) the sizes of paper for which she has a winning strategy.
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