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2-Color in Room Problem

Consider 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.

Solution

Can an irrational number raised to an irrational power yield a rational result?

Yes. √2√2 is either rational or irrational.

  • If it’s rational then we are done.
  • If it’s irrational, then (√2√2)√2 = (√2)√2√2 = (√2)2 = 2 proves the statement.
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Page last modified on February 14, 2017, at 02:27 PM