Smullyan Logic Puzzle: Either Tiger behind Door 1 or Gold behind Door 2 "The prisoner is presented with two doors. In a room behind each door is either gold or a tiger. The sign on the doors are either both true or both are false.
Door 1: Either there is a tiger behind this door or gold behind the second door.
Door 2: There is gold behind this door.
Which door should the prisoner open?"
I have been trying to figure out the answer to this question. If I interpret Sign 1 as an inclusive or, then I end up getting 3 "no contradiction" cases, but it doesn't tell me which Door is the best choice (unless we actually care about probability such as 2/3 chance of getting Gold). To mitigate this, the best I could come up with is to interpret Sign 1 as an exclusive or.
Solution attempt
EDIT: Here are other places on the internet where the same problem appears.
http://pi.math.cornell.edu/~araymer/Puzzle/PuzzleNights.html
(Page 4) http://www2.gcc.edu/dept/math/faculty/BancroftED/teaching/handouts/MATH213_rules_of_inference.pdf
https://www.ibtimes.co.uk/mathematician-puzzle-maker-raymond-smullyan-dead-97-1605912
 A: Smullyan, like all of math, uses the inclusive or as the default.  
If door 1 is false, there is gold behind door 1 and a tiger behind 2.  Then 2 is also false, and there is a tiger behind 2.  This is consistent.
If door 1 is true so is 2 and there is gold behind 2.  We do not know what is behind 1 because the gold behind door 2 is enough to make it true.
As stated there is no solution to the problem.  I don't have this book (is it The Lady or the Tiger?) but the ones I have of his are very carefully proofread.  Do you have the problem right?
A: Did Smullyen say there was a solution?
If the "or" is inclusive then, if they are both true there is Gold behind door 2 and we don't know about Door 1; it could have either.  And if they are both false then there is a tiger behind Door 2, and gold behind door 1.
So are we to assume that the likelihood truth or false is 50-50?  What about Gold or tiger given any flexibility?  
Id say go with Door 1-- it definitely has gold in one case but doesn't definitely have a tiger in the other... but keep your fingers crossed.
....
If its an exclusive or, which I doubt as Ross Millikan points out why I think that, then
If they are both true then there is gold behind both.
If they both are false then there is gold behind door one and a tiger behind the door two.
......
But just because a problem can be stated, doesn't mean it can be solved.  If it's an inclusive "or" it can't be resolved, but who ever said it could?
