An evil warden holds you prisoner, but offers you a chance to escape. There are 3 doors A, B, and C. Two of the doors lead to freedom and the third door leads to lifetime imprisonment, but you do not which door is what type. You are allowed to point to a door and ask a single yes-no question to the warden. If you point to a door that leads to freedom, the warden does answer your question truthfully. But if you point to the door that leads to imprisonment, the warden answers your question randomly, either saying “yes” or “no” by chance. Can you think of a question and figure out a way to escape for sure?
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This puzzle is a variation of the ace and jacks problem, a preliminary problem in the paper about “the hardest logic puzzle ever.” Boolos, George (1996). “The hardest logic puzzle ever”. The Harvard Review of Philosophy. 6: 62–65. http://www.hcs.harvard.edu/~hrp/issues/1996/Boolos.pdf
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Hey, this is Presh Talwalkar.An evil warden holds you prisoner,but offers you a chance
to escape.There are three doors A, B, and C.Two of the doors lead to freedomand the third door
leads to lifetime imprisonment,but you do not know
which door is what type.You are allowed to point
to a doorand ask a single yes/no question
to the warden.If you point to a door
that leads to freedom,the warden does answer
your question truthfully,but if you point to the door
that leads to imprisonment,the warden answers
your question randomly,either saying yes or no
by chance.Can you think of a questionand figure out a way to escape for sure?Give this problem a try,
and when you're ready,keep watching the video
for the solution.So here's a way that you
can escape for sure.Point to door A
and ask the question,"Does Door B lead to freedom?"If the warden answers "Yes,"
then pick door B.If the warden answers "No,"
then pick door C.This strategy is guaranteed to workregardless of the door type
of A.So why does it work?Let's work through the logic.Door A can either have
two different types.It can either lead to freedom,in which case the
warden is truthful,or it can lead to imprisonment,in which case the warden
answers randomly.Let's consider the first case,
that the door leads to freedom.In this case, if the warden
answers "Yes" to your question,then that means the warden is
answering truthfully,and Door B does lead
to freedom.Similarly, if the warden says Door B
does not lead to freedom,the warden is answering truthfully,which means door B
leads to imprisonment.That means the other door,
door C, leads to freedom.So you can see that
if the warden answers "Yes,"you should pick door B,and if the warden answers "No,"
then you should pick door C.But what about the case
where door A leads to imprisonment,and the warden answers randomly?Well, in this case, if door A
leads to imprisonment,that means the other two doors,
B and C, lead to freedom.So you can always pick doors
B and C in these casesno matter what the warden answers.So if you pick door B
when the warden answers "Yes,"that will lead to freedom,and you pick door C when the
warden answers "No,"that once again
will lead to freedom.So this shows that logically,if you pick door B when the
warden answers "Yes,"and if you pick door C
when the warden answers "No,"you are guaranteed tofind a door that leads you to freedom.Did you figure it out?Thanks for watching this video.
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