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MathematicsSingapore International Mathematical Olympiad (SIMO) Home Page2Color in Room ProblemConsider a 10 foot by 10 foot square room. Let every point on the floor of the room be colored either red or blue. Then there exists somewhere on the floor two points of the same color that are exactly one foot apart. Hint: Use Pigeonhole Principle. Can an irrational number raised to an irrational power yield a rational result?Yes. √2^{√2} is either rational or irrational.
