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Odd Escape
You are being held prisoner in a small room. Only you and a gaurd are inside the room. There are three identical doors that lead out of the room. The gaurd offers a choice: you may exit through one of the three doors. Two lead to your execution, one leads to escape. You have no knowledge of the doors and so you choose randomly, door #1. You indicate your choice to the gaurd and he says, "I cannot tell you how to escape, but I can tell you that door #2 will NOT lead to escape." Assuming that the gaurd is impartial and is telling the truth, what should you do?
-Stick with your original choice, door #1.
-Change to door #3.
-It doesn't matter, it's 50/50.
This is not an easy one, but it is also not a trick question by any means. Please justify (mathematically, if possible) any answer.
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