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: Guess the color of the hat!  ( 12682 )
« : August 28, 2007, 11:20:20 AM From Poonam»

Guess the color of the hat!

Mrs. Harrison has 6 lovely hats, 3 blue, 2 yellow and one pink. Alice, Betty, Cindy and Debbie are lined up as shown in the figure. Mrs. Harrison help them put the hats on them so they will not see what color hat they have on.

Alice can see what color of hats Betty, Cindy and Debbie are wearing.
Betty can see what color of hats Cindy and Debbie are wearing.
Cindy can see what color hat Debbie is wearing.
Debbie can not see any of the hat colors.

Mrs. Harrison ask them what color of the hat they are wearing. Alice said she can not tell. Betty said she can not tell either. Cindy also can not tell. However, Debbie was able to tell what color she was wearing after knowing that everyone else could not tell.

How did Debbie figure out what color she was wearing?

If you find it tough then solve this before working on the above puzzle

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« #1 : August 28, 2007, 11:55:16 PM From spazinvader»

Is the two left out hats can be seen by any of them?
« #2 : August 29, 2007, 09:47:38 AM From Poonam»

« #3 : September 01, 2007, 04:09:38 PM From bunnyonnet»

« #4 : September 04, 2007, 12:22:15 AM From spazinvader»

I got it.

The answer is blue.
The analysis will be a long essay.
Guru do u wants me to post that essay? ;D
« #5 : September 05, 2007, 09:27:13 AM From Poonam»

Hey post the explanation Spazinvader!
« #6 : September 05, 2007, 10:32:01 AM From kvk»

let their names be  A ,B, C ,D
 A can only tell his hat color if he sees 2Y AND 1P colored hats on B,C, &D
But A dint tell the answeR.
the possible combinations for the colors of hats on D,C,B are respectively:
Among the 16 cominations, B is certain to tell the answer in the last three combinations i.e[PYB, YPB, YYB]....But couldn't tell the answer
so the three combinations are eliminated.

NOW, In the remaining combinations , consider the colors of hats of C&D:
NOW, The combinations are:
In above combinations, C is certain in last 2 cases  and uncertain in the first three cases.
so, last two combinations are eliminated....now the remaining combinations are:
Now D is able to tell his hat's color...which is blue...

« #7 : September 05, 2007, 01:15:39 PM From Poonam»

Nice deduction, kvk!
« #8 : September 05, 2007, 05:57:11 PM From kvk»

is there any shortcut?
« #9 : September 05, 2007, 09:18:48 PM From spazinvader»

There is a shortcut.
Since there is only one pink hat and two yellow hats,we can reduce the combinations which has two yellow hats.Only the combination other than pink will survive as there is only one.
So the last one will not be pink.
Also if it is yellow, others could have guessed their in their turn.
So yellow is also ruled out.
Hence the only color is blue
« #10 : October 26, 2007, 05:11:23 PM From jaiswal»

the answer is blue and the logic is straight.
Lets call the girls A,B,C,D

now if D have had seen 2 yellows and 1 pink on the heads of A, B or C then she would have told that her hat is blue. But she couldn't  => at least one blue on A, B or C.

now as C also couldn't guess => at least one blue on A or B. because if there is no blue on A & B then C could have easily guessed her hat color as blue.

now as B also couldn't guess => A is wearing a blue hat. because if A is not wearing blue then B could easily guess her hat color as blue.

thus A is wearing the blue hat and she is intelligent enough to guess that.
« #11 : November 21, 2007, 02:30:34 PM From iammilind»

I am bit confused here. Currently condition is,A can see B,C,D; B can see C,D; C can see D; D can see none.

we have 3 blue, 2 yellow and 1 pink hats.
Suppose the situation is like this:
A(blue), B(blue), C(yellow), D(yellow).

In the above case also, A,B,C will not be able to answer their hat color, then how D will be deriving to blue(or any other color), even though she is wearing yellow ??

I think number of hats are too many to judge.
« #12 : November 21, 2007, 10:41:29 PM From spazinvader»

I guess u r wrong iammilind.
In ur case say
A(blue), B(blue), C(yellow), D(yellow).
In this A surely cannot answer.
After then,B will see 2 yellow hats.
Since A cannot answer,B can be sure that he is not having pink hat.This is because,if he had pink hat,this makes that 2 yellow and 1 pink are already there and so A wont have any problem that he would be surely having blue hat.
So his hat colour is not pink and 2 yellow are already out.
So B will guess that his hat colour is blue.

I guess u understood.I am not sure how i have explained.
« #13 : November 22, 2007, 10:49:48 AM From iammilind»

Sorry for the wrong example.
Yes, it was my mistake for those particular colors. But consider the following situation:

A(blue), B(blue), C(blue), D(yellow)

A can't answer because     he can wear yellow/blue/pink
B can't answer because                    ''              (with confused A)
C can't answer because                    ''              (with confused A,B)
so now how D will answer ?    (while A,B,C are confused)

This is one of the combination, there are other combinations also in which D can't answer.
This example looks fine, but I can't gaurantee whether I have given the exact  one, there could be a right answer for this also as spazinvader explained. :-X
« #14 : November 22, 2007, 10:39:17 PM From spazinvader»

u have given a very good case.But however,it is wrong.
A(blue), B(blue), C(blue), D(yellow)
In this,
A can't answer(because he may have blue,yellow,pink)
B can't answer(because he may have blue,yellow,pink)
but C can answer now(Get ready for a long explanation)

This is because,he can see a yellow hat before him.So if he wear a yellow hat, then B could have answered.That is,B can see 2 yellow hats and since A cannot answer,his hat is blue as A could have easily told his hat colour if he see 2 yellow and 1 pink in front of him.
So the chance of C's hat colour being yellow is washed out.
Now C's hat colour be pink.If it is,then also B could have guessed it.
This is because,the combination will be like this

A(any colour),B(any colour),C(pink),D(yellow)
Since A cannot guess and B can see a pink and yellow,he could tell that his hat colour should be blue.If his colour is yellow,A would have guessed it.

So the chance of C having pink colour after the failures of A and B is also washed out.So the only possibility is that he can wear blue.
So C would have guessed like this.

I guess,i am not very simple in my explanation.I know that.But i am very poor in explaining things.So reply at the place where u get doubt and i will try my level best at that point.
« #15 : November 23, 2007, 10:43:40 AM From iammilind»

Yes, you are right. Explanation is correct.
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