2013 UMO Problems/Problem 2
Problem
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.
Solution
See Also
| 2013 UMO (Problems • Answer Key • Resources) | ||
| Preceded by Problem 1 |
Followed by Problem 3 | |
| 1 • 2 • 3 • 4 • 5 • 6 | ||
| All UMO Problems and Solutions | ||
