Great piece by Matt Parker explaining P vs. NP in layman terms:
http://tinyurl.com/2d83t7v
In fact, his introductory lines are the simplist statement of P vs. NP I've ever come across:
"Can you solve a problem as fast as someone can check your answer? Can you show that this is possible for any problem at all? Then $1m (£600,000) is all yours."
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