Can you solve the Prisoner’s Hat Puzzle | 90% People Fail to Solve | Puzzle

Can you solve the Prisoner’s Hat Puzzle | 90% People Fail to Solve | Puzzle


One fine morning you wake up to find yourself
not at your home but at some strange place. You and 9 other individuals have been captured
by super intelligent Alien Over Lords. The Aliens think that we humans look quite
tasty but their custom forbids them from eating highly co-operative and logical beings. Now since they don�t know if you qualify,
they decide to give you a test. So aliens tell you that you will all be placed
in a single file line, facing forward in size order so that each of you can see everyone
lined up ahead you. However, you can�t look behind you or step
out of the line. Doing so will convince aliens that you are
not co-operative and they will eat you instantly. Now, each of you will have either white or
a black hat on your head assigned randomly and they won�t tell you how many of each
colour they are. When they say begin, each of you will start
guessing the colour of their own hat, one at a time, starting from the back and moving
up the line. Don’t even try saying any other word other
than Black or White, or signalling others by whistling or making any other sound. Doing so will convince the Aliens that you
are all not so logical or co-operative and you all will be eaten immediately. If at least 9 of you guess correctly, you�ll
all be spared. They give you 5 minutes to discuss and come
up with a plan. After that, you will all be made to stand
in a line and wear your respective hats. Can you think of some plan which can guarantee
to save everyone? Pause the video here if you want to solve
this on your own as I will be explaining the answer in the later part of this video. The key here is that the person standing at
the back of the line can see everyone�s hat and he can say black or white to pass
some coded information down the line. So what meaning can be assigned to those two
words that will allow everyone else to deduce their own hat colours. It can�t be the total number of black or
white colour hats as there can be more than two possible values but what does have the
two possible values is that number�s parody which means whether the number is odd or even. So the solution is that the person going first
will say, Black, if he sees an odd number of black hats and will say, White, if he sees
an even number of black hats. Let’s see how it solves the problem if the
hats are placed like this. The tallest person sees 3 black hats and he
says black which conveys to everyone that he sees an odd number of black hats. He gets his own hat colour wrong but that’s
okay as you are collectively allowed to have one wrong answer. Prisoner 2 also sees an odd number of black
hats, hence, deducing that her hat must be white and answers correctly. Prisoner 3 sees even black hats, so he deduces
that his hat must be black and answers correctly. Now, prisoner 4 is looking for an even number
of black hats since 1 was behind her but she finds an odd number of black hats, deducing
that hers must be black and answers correctly. Now Prisoner 5 to 9 are all looking for an
odd number of black hats and they see 1 black hat which in turn is an odd number, hence
deducing that their hat must be white. So, finally, it all comes down to you. Now, since all the 9 prisoners behind you
can see an odd number of black hats, so, it can only mean one thing and that is your hat
is Black!! Now you will find that this strategy works
for any possible arrangement of the hats. The first person has a 50% chance of giving
the wrong answer but the parody information he conveys allows all 9 people in front of
him to guess their hat colour correctly. So each person begins with expecting to see
an odd or even number of hats of the specified colours. If what they count doesn�t match then it
means their own hat is that colour and every time this happens, the person standing next
in line switches the parody they see. So, that�s it. You saved the day. You are all free to go. Looks like aliens will have to find someone
less logical to fill their tummy. If you liked solving this puzzle, make sure
you give a big thumbs up to this video. Share it with your friends to see if they
can solve it and tell me in comments if you were able to solve it on your own. Subscribe to my channel by clicking the Red
Subscribe button which you can see below this video as I will keep bringing such puzzles
which will give you some food for thought. See you all soon, stay blessed.

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About the Author: Sam Caldwell

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