Press "Enter" to skip to content

The HARDEST Logic Puzzle Ever (Simpler Version): Two Doors To Freedom Riddle

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?

My blog post for this video: https://wp.me/p6aMk-55e

Source
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

If you like my videos, you can support me at Patreon:
https://www.patreon.com/mindyourdecisions

Connect on social media. I update each site when I have a new video or blog post, so you can follow me on whichever method is most convenient for you.

My Blog: https://mindyourdecisions.com/blog/
Twitter: https://twitter.com/preshtalwalkar
Facebook: https://www.facebook.com/pages/Mind-Your-Decisions/168446714965
Google+: https://plus.google.com/108336608566588374147/posts
Pinterest: https://www.pinterest.com/preshtalwalkar/
Tumblr: https://preshtalwalkar.tumblr.com/
Instagram: https://instagram.com/preshtalwalkar/
Patreon: https://www.patreon.com/mindyourdecisions

Newsletter (sent only for big news, like a new book release): http://eepurl.com/KvS0r

If you buy from the links below I may receive a commission for sales. This has no effect on the price for you.

My Books
“The Joy of Game Theory” shows how you can use math to out-think your competition. (rated 3.8/5 stars on 31 reviews)
http://amzn.to/1uQvA20

“The Irrationality Illusion: How To Make Smart Decisions And Overcome Bias” is a handbook that explains the many ways we are biased about decision-making and offers techniques to make smart decisions. (rated 4.6/5 stars on 3 reviews)
http://amzn.to/1o3FaAg

“Math Puzzles Volume 1” features classic brain teasers and riddles with complete solutions for problems in counting, geometry, probability, and game theory. Volume 1 is rated 4.4/5 stars on 13 reviews.
http://amzn.to/1GhUUSH

“Math Puzzles Volume 2” is a sequel book with more great problems. (rated 4.3/5 stars on 4 reviews)
http://amzn.to/1NKbyCs

“Math Puzzles Volume 3” is the third in the series. (rated 3.8/5 stars on 5 reviews)
http://amzn.to/1NKbGlp

“40 Paradoxes in Logic, Probability, and Game Theory” contains thought-provoking and counter-intuitive results. (rated 4.3/5 stars on 12 reviews)
http://amzn.to/1LOCI4U

“The Best Mental Math Tricks” teaches how you can look like a math genius by solving problems in your head (rated 4.7/5 stars on 4 reviews)
http://amzn.to/18maAdo

“Multiply Numbers By Drawing Lines” This book is a reference guide for my video that has over 1 million views on a geometric method to multiply numbers. (rated 5/5 stars on 3 reviews)
http://amzn.to/XRm7M4

Video transcription:

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.
Please subscribe to my channel.I make videos on math and game theory.You can catch me on my blog,
"Mind Your Decisions,"which you can follow on
Facebook, Google+ and Patreon.You can catch me on social media:
@preshtalwakarIf you like this video,
please check out my books.There are links
in the video description.

Tags:

mathematics,math,maths,riddle,brain teaser,puzzle,math puzzle,logic puzzle

Be First to Comment

    Leave a Reply

    Your email address will not be published. Required fields are marked *