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Logic problems. The solution to these problems does not usually require a lot of math, but will take some thinking until you find the right approach.
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Difficulty: 3 of 5 Latest: Red, White, and Blue Rating: 4.00

  
A bag contains 3 red, 4 white, and 5 blue balls. Two balls of different
color are removed from the bag and replaced with two balls of the third color.

Prove that no matter how many times this procedure is repeated, it is impossible for all twelve balls in the bag to be the same color.
  
(Solution Posted, 4 Comments) Submitted on 2015-07-29 by Bractals   
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