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.

Did you steal this from Ted-ed?

You cop rioted