Hat Puzzle

The hat is always on top of the brain and hat puzzle is the best brain teaser.
Hat Puzzle is an induction puzzle that involves knowing the thinking of other people and reasoning from the third person point of view. There are many variations.


The Puzzle of Black and White Hats.

The puzzle of the black and white hats

Cannibals ambush a safari in the jungle and capture three men. The cannibals give the men a single chance to escape uneaten.

The captives are lined up in order of height, and are tied to stakes. The man in the rear can see the backs of his two friends, the man in the middle can see the back the man in front, and the man in front cannot see anyone.

The cannibals show the men five hats. Three of the hats are black and two of the hats are white.
Blindfolds are then placed over each man's eyes and a hat is placed on each man's head. The two hats left over are hidden. The blindfolds are then removed and it is said to the men that if one of them can guess what color hat he is wearing they can all leave unharmed.

The man in the rear who can see both of his friends' hats but not his own says, "I don't know". The middle man who can see the hat of the man in front, but not his own says, "I don't know". The front man who cannot see ANYBODY'S hat says "I know!"

How did he know the color of his hat and what color was it?


     


The puzzle of four hats.

The puzzle of four hats

Four men are lined up on some steps. They are all facing in the same direction. A wall seperates the fourth man from the other three.

So to summarize: Man 1 can see men 2 and 3. Man 2 can see man 3. Man 3 can see none of the others. Man 4 can see none of the others.

The men are wearing hats. They are told that there are two white hats and two black hats.

The men initially don't know what colour hat they are wearing. They are told to shout out the colour of the hat that they are wearing as soon as they know for certain what colour it is.
They are not allowed to turn round. They are not allowed to talk to each other.

So the question is -Who is the first person to shout out and why?


     

Man2 is the first person to shout out that he is wearing a white hat.
Man3 and man4 can't see anyone and therefore no way that they can tell their own hat color.
Man 1 can see man2 wearing a white hat and man3 wearing a black hat and therefore can't tell his own hat color. He will remain silent.
Since man1 is silent, man2 will knows that he is wearing a white hat.
Man2 knows that man1 can see his and man3’s hats. If he is wearing a black hat, then man1 will see two black hats and will immediately know his own hat color sice they are told that there are two white hats and two black hats.
Because man1 has kept quiet, man2 knows that he must be wearing a white hat.



 


 

Difficult puzzle

The King's Wise Men (In search of wistom).

The puzzle of five hats

The King called the three wisest men in the country to his court to decide who would become his new advisor.

He showed the men five hats. Three of the hats were black and two of the hats were white.

He placed a hat on each of their heads, such that each wise man could see all of the other hats, but none of them could see their own. The two hats left over were hidden.

The wise men were forbidden to speak to each other. The king declared that whichever man stood up first and announced correctly the color of his own hat would become his new advisor.

The wise men sat for a long time before one stood up and correctly announced the answer.

What did he say, and how did he work it out?


  

All three wise men were wearing black hats.

1) Suppose that you are one of the wise men. Looking at the other wise men, you see they are both wearing white hats. Since there were only two white hats, you would immediately know that your own hat must be black.

2) Now suppose that you see the other wise men, and one is wearing a white hat and the other is wearing a black hat. If your own hat was white, then the man you can see wearing the black hat would be himself seeing two white hats and would - by the logic above - have immediately declared his hat color. If he doesn't do this, it can only be because your hat isn't white, therefore it must be black.

3) In this particular puzzle, you see the other wise men and both are wearing black hats. You can't work anything out from this. However, if your own hat was white, then two other wise men would be seeing a black and a white hat, and the wiser one would have declared his hat color by the rule above. Thus, if none of them has done so, they must also be seeing two black hats and thus your hat must be black.

"This is also the reason why a lot of intellectuals wear black hats".


Difficult puzzle

Bipartisan immigration reform bill.

By the end of days, the illegals/undocumenteds who are arrested at the border will be ordered to stand in a single line, facing to the same direction. It can be a short or a long line depending on the number of persons being arrested that day and the location.
A black or a white hat, in random order, will be put on every undocumented's head in a way that they can't see the color of their own hats.
The line is formed in such that each undocumented can see the hats of all undocumenteds in front of him, but can't see the hats of the undocumenteds behind him.
Now, one by one and starting from the last person in the line, every undocumented has to shout one word, either "black" or "white", that matches the color of his hat.
If he guesses right, he will be given a green document that allows him to stay in USA, become a citizen in 5 years and vote for Democrats.
Those who guess wrong will be shot in the head instantly and later buried in a mass grave presided over by a Catholic priest.
All other undocumenteds can hear what he shouts and whether he is shot or not.
There can't be no communication between the undocumenteds, but they are allowed to plot a strategy before the lineup.

What is the best strategy for the highest number of undocumenteds to get their green documents?

Acorn, a community organizing group with close tie to Obama, is lobbying congress for a "bilingual plan" that allows the undocumenteds to shout in English or in Spanish. Republicans insist on "English only". Why the "bilingual plan" is better than "English only" for the undocumenteds?