Hats Puzzles

Four wise men with hats puzzle

June 5, 2017 by Ionel Rata 1 Comment

Four wise men are wearing Black and White hats so that each of them can only see the others’ hats.

They are told that at least one of their hats is white and at least one is black.

Asked, in turn, if they can tell the color of their own hat?

The first wise man says no, then the second wise man says no, but then the third wise man could give the right answer.

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Three blue and two red hats puzzle

November 3, 2015 by puzzler 1 Comment

At a party, four people played a game. Three of them sat one behind the other, so that Abe saw Bill and Cal, and Bill only saw Cal, who sat in front and saw nobody else.

Dave had 5 hats which he showed to his three friends. Three of the hats were blue and two were red.

Now Dave placed a hat on the head of each of his three friends, putting aside the remaining two hats.

Then he asked Abe what color his hat was.

Abe said he couldn’t tell.

Bill was asked the color of his own hat, but he didn’t know for certain either.

Cal, though he couldn’t see any hat at all, gave the right answer when asked what color his hat was.

Do you know what color Cal’s hat was and how he reasoned to find out the correct answer?
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Who will shout first ?

May 10, 2015 by puzzler 9 Comments

Four criminals are caught in a minor offence, they pleaded judge to release them without any punishment. As it was a minor offence, judge told them that they will be freed without punishment, but only if they can solve a puzzle

All four of them are lined up on some steps(as shown in the picture above). A wall separates the 4th person from other three.
So to summarize:-
Criminal 1 can see 2 and 3
Criminal 2 can see 3
Criminal 3 and 4 can’t see any one else

Criminals are wearing hats, they are told that there are two white hats and two black hats. They can’t see their own hat color and are told to shout their hat color as soon as they get to know for certain what color it is.

They are not allowed to turn around or move.
They are not allowed to talk to each other.
They are not allowed to take their hat off.

Who will shout first ?

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10 prisoners and hats puzzle

April 20, 2013 by puzzler 12 Comments

Their are 10 prisoners in a jail for a minor crime, they all request the jail officer to set them free, jail officer agrees to release them tomorrow, saying i will

Make you all stand in a queue in ascending order of your heights(smallest first).
You will not be allowed to turn your head(they have to look straight)
I will put one hat on your head, either BLACK or WHITE in color.
Everyone of you has to tell the color of his hat starting from the tallest prisoner, you can only say BLACK or WHITE.
You all will be released, if and only if at least 9 of you guess your hat’s color correctly.

Can you suggest a strategy to the prisoners to maximize the chances of their release?

10 prisoners and hats puzzle

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Hats and IIT students

December 7, 2007 by Ankur 5 Comments

Nine IITians were sitting in a classroom. Their prof wanted to test them. One day he told all of his 9 students that he has 9 hats, colored either in red or black. He also added that he has at least one hat with red color and the no. of black hats is greater than the no. of red hats. He keeps those hats on their heads and ask them tell me how many red and black hats I have? Obviously students can not talk to each other or no written communication, or looking into each other eyes; no such stupid options.
Prof goes out and comes back after 20 minutes but nobody was able to answer the question. So he gave them 10 more minuets but the result was the same. So he decides to give them final 5 minutes. When he comes everybody was able to answer him correctly.

So what is the answer? and why?

See Solution : Hats and IIT students

After first interval of 20 minutes :

Lets assume that their is 1 hat of red color and 8 hats of black color. The student with red hat on his head can see all 8 black hats, so he knows that he must be wearing a red hat.

Now we know that after first interval nobody was able to answer the prof that means our assumption is wrong.

So there can not be 1 red and 8 black hats.

After second interval of 10 minutes :

Assume that their are 2 hats of red color and 7 hats of black color. The students with red hat on their head can see all 7 black hats and 1 red hat, so they know that they must be wearing a red hat.

Now we know that after second interval nobody was able to answer the prof that means our assumption is again wrong.

So there can not be 2 red and 7 black hats.

After third interval of final 5 minutes :

Now assume that their is 3 hats of red color and 6 hats of black color. The students with red hat on their head can see all 6 black hats and 2 red hats, so they know that they must be wearing a red hat.

Now we know that this time everybody was able to answer the prof that means our assumption is right.

So there are 3 red hats and 6 black hats.

Now as everybody gave the answer so there can be a doubt that only those 3 students know about it how everybody came to know ?

Then here is what i think, the professor gave them FINAL 5 minutes to answer, so other guys will think that the professor expects the answer after 3rd interval (according to prof it must be solved after 3 intervals), so this is the clue for others.

Hats Puzzles

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