The Clairvoyant Penny

http://commons.wikimedia.org/wiki/File:United_States_penny,_obverse,_2002.jpg

Mathematician Thomas Storer offers a foolproof way to foretell the future: Flip a penny and ask it a yes-or-no question. Heads means yes, tails means no.

How can you be sure the answer is accurate? Simple: Flip it again and ask, “Will your present answer have the same truth value as your previous answer?”

  • Suppose the answer is yes. This is either true or false. If it’s true, then the original response was true. If it’s false, then the truth value of the original response is not false, i.e., it’s true.
  • If the answer to the second question is no, this too is either true or false. If it’s true, then the original response was true. If it’s false, then the original response was not false, i.e., true.

Since all the outcomes agree, the penny’s original response is guaranteed to be correct.