| Username |
Post |
| Karuna |
Posted
on 09-Nov-01 03:10 PM
HOW?
There were 3 inmates in a prison. One was totally blind. The other was half blind; meaning he could see with only one of his eyes. And the third could see with both his eyes. They were serving life term.
One day, the prison guard came up to them and said, ‘I am giving you guys a chance to be a free man. Here is what you have to do’.
The guard goes on, ‘ I have 3 white hats and 2 red hats. I am going to mix them up and put one on each of you. It could be either white or red. Then you have to tell me what color hat you are wearing. You cannot look at your hat or ask others, but you can look at others’ hat. If you can tell me the right answer, you will be a free man, BUT if you guess wrong, then you will be sentenced to death!’
The guard then goes back to his office, asks the men to close their eyes and puts the hats on them. He asks the first inmate who has normal vision. He says, ‘I don’t know’. The guard then asks the half-blind person what hat he’s wearing. He also says, ‘I don’t know’. Then he walks up to the blind guy and tells him that there is no point asking him since he was blind.
‘But I know what color hat I am wearing!’ shouts the blind man.
‘What color?’ asks the prison guard. And the blind person gives the right answer. The blind inmate knew what hat he was wearing. HOW DID HE KNOW?
This was class question in a LOGIC course given by the teacher.
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| Biswo |
Posted
on 09-Nov-01 03:33 PM
Hi Karuna:
Don't write the answer rightnow! I am working on it.
Thanks for a good brainteaser. First I thought must a be a white. But hey, it is not
so easy a question!
For higher level mathematicians, please go to the following site of Clay
Mathematics Institute for a peek at the 7 problems. If you can solve them, you will
win US$1 million each from the Institute.
http://www.claymath.org/prizeproblems/index.htm
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| nobody |
Posted
on 09-Nov-01 04:02 PM
White hat... Two "I don’t know"s because those two are wearing reds and they see a white and red hats on others' heads, which is not enough to deduce the color of their head. Two don't know's tells the third guy, they each can see only one red hat, which then must be on their head...
If I got it right, "Elementary, my dear Watson"... :-)
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| nobody |
Posted
on 09-Nov-01 04:02 PM
read head=hat
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| joie de vivre |
Posted
on 09-Nov-01 04:08 PM
I'm in total agreement with 'nobody'. And no, not just cause I 'think' he's right, he just beat me to it :)
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| Biswo |
Posted
on 09-Nov-01 04:12 PM
nobody ji:
What if both of those saw 'two' white hats on others head? They would
still say 'I don't know'. And the answer is 'white' for the hat of blind man.
In case they see each of other wearing one red,then the blind man is wearing Red
hat. So I am still confused.
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| Shail |
Posted
on 09-Nov-01 04:21 PM
Nobody's answer is correct but I didn't fully understand his/her logic so I'll give it a shot.
OK. The first guy who could see obviously didn't see two red hats. Because if he did, he would know that he himself was wearing white.
So he either saw a combination of one red and one white or a combination of two white hats.
So now the 2nd guy also can see those two options, but he has the advantage of knowing the 1st guys answer. Since there are only 2 red hats, if the 2nd guy sees red hat on the blind guy, he knows that he himself is not wearing red (otherwise the 1st would have known he was wearing white and called it, by process of elimination).
So it's obvious that blind guy is not wearing the 2 red hats. What's left?
White ;-)
Peace out,
Shail
>HOW?
>There were 3 inmates in a prison. One was
>totally blind. The other was half blind;
>meaning he could see with only one of his
>eyes. And the third could see with both his
>eyes. They were serving life term.
>One day, the prison guard came up to them
>and said, ‘I am giving you guys a chance to
>be a free man. Here is what you have to do’.
>The guard goes on, ‘ I have 3 white hats and
>2 red hats. I am going to mix them up and
>put one on each of you. It could be either
>white or red. Then you have to tell me what
>color hat you are wearing. You cannot look
>at your hat or ask others, but you can look
>at others’ hat. If you can tell me the right
>answer, you will be a free man, BUT if you
>guess wrong, then you will be sentenced to
>death!’
>The guard then goes back to his office, asks
>the men to close their eyes and puts the
>hats on them. He asks the first inmate who
>has normal vision. He says, ‘I don’t know’.
>The guard then asks the half-blind person
>what hat he’s wearing. He also says, ‘I don’
>t know’. Then he walks up to the blind guy
>and tells him that there is no point asking
>him since he was blind.
>‘But I know what color hat I am wearing!’
>shouts the blind man.
>‘What color?’ asks the prison guard. And the
>blind person gives the right answer. The
>blind inmate knew what hat he was wearing.
>HOW DID HE KNOW?
>
>This was class question in a LOGIC course
>given by the teacher.
|
| Biswo |
Posted
on 09-Nov-01 04:25 PM
Shailji:
Will you please come to chat if you have free time? The chatter are discussing
this same problem!
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| Shail |
Posted
on 09-Nov-01 04:28 PM
Sorry bud,
I'm working so can't be chatting. But if you'll send any questions to this forum, I'll be checking and would be happy to answer it.
Shail
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| Biswo |
Posted
on 09-Nov-01 04:32 PM
I still see your answer is incorrect.
That is why..
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| Shail |
Posted
on 09-Nov-01 04:36 PM
Would you be a little more specific, please?
And the reason I can't come is because my network security doesn't allow me to download the java applet for GBNC chat.
|
| Smart Nepali |
Posted
on 09-Nov-01 04:42 PM
I think I finally found the answer.
1) Reason One
The answer is RED hat. The blind guy was wearing red hat.
There are 7 combinations by which the hat can be placed on the prisoners head.
Of the 7 combinations, 4 of them are that the BLIND was wearing WHITE hat and 3 of them are the BLIND was wearing RED hat. So there is the higher probabilty that the Blind Guy is wearing WHITE 4:3
2) Reason 2 my friend's anwer
Usually the prison is dark and White hat can be easily seen because white is usually brighter so the blind man could tell it was white. I don't know. Am I right?
Who got the answer so far?
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| nobody |
Posted
on 09-Nov-01 04:55 PM
option 2 1 0 (eyes)
1 W W W
2 W W R
3 W R W
4 W R R
5 R W W
6 R W R
7 R R W
After first person responded:
can't be option 4 because then the only hat left is white. So, new options:
option 2 1 0 (eyes)
1 W W W
2 W W R
3 W R W
5 R W W
6 R W R
7 R R W
After second person responds: can't be option 6 by same argument.
Option 2 can't be possible, because second guy kpows its (W,W) or (W,R) between him and blind, there can be only one red between the two and if blind has it, he has the answer.
This leaves us with:
option 2 1 0 (eyes)
1 W W W
3 W R W
5 R W W
7 R R W
... white for blind. Hope that helps, Biswo.
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| visitor |
Posted
on 09-Nov-01 05:01 PM
Let's assume, A=Two-eyed, B=one-eyed and C=blind.
Obviously we can eliminate the chance of having red hats on both B and C. So the possible combination after first round of elmination in the order of A, B and C :
R/W W R
R/W W W
R/W R W
Again it is obvious both A and C should not have red hat each. So we can eliminate one more combination. we are left with following 5 combinations:
W W R
R/W W W
R/W R W
Which means it is possible C can have either Red or White hat. Any contradictions to this conclusion?
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| Shail |
Posted
on 09-Nov-01 05:04 PM
Hmmmm nice illustration Biswo/nobody but I thought I said the same thing. Where did you find the fault in my logic?
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| nobody |
Posted
on 09-Nov-01 05:05 PM
if C has the red hat, B would know he has white because, between B and C, there can be only one red hat or else A would have answered...
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| Biswo |
Posted
on 09-Nov-01 05:06 PM
I am still with visitor.
I think nobody has answer. But I didn't understand how he ruled out option 2.
Please put it more clearly,ok?
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| nobody |
Posted
on 09-Nov-01 05:06 PM
yep, same logic... more graphical. That's what Microsoft has done to us... :-)
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| n |
Posted
on 09-Nov-01 05:09 PM
Or is it Barron's GRE technique?
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| nobody |
Posted
on 09-Nov-01 05:10 PM
n=nobody...
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| visitor |
Posted
on 09-Nov-01 05:13 PM
I am still at loss to grasp Nobody logic behind eliminating #2 in his list of possible combinations. Am I missing something or is he?
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| joie de vivre |
Posted
on 09-Nov-01 05:15 PM
Biswo - I guess I no longer need to explain why the answer is white. I’d say Shail’s done a pretty good job of mapping it out for you. (Sorry nobody, I didn’t have time to read yours - lenghty responses are too distracting at work!).
|
| nobody |
Posted
on 09-Nov-01 05:18 PM
OK...
Since A couldn't decide, we know B and C have 1 white and 1 red or 2 whites between them, but not two reds.
If B had seen red on C's head (irrespective of what's on A's head even though B can see it) he would have known he has white hat on... And he would be having PinaColada in some Carribean Island right now. But he see's a white on blind, which means he can be wearing a white or a red.
unless A was planning to screw all in the first place.
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| Math Professor, MIT |
Posted
on 09-Nov-01 05:20 PM
Hello Everyone,
I think all you guys are using the right logic except Smart Nepali. He seems to be totally lost. Help him if you can. NOBODY almost got it but he was not able to give a "CLEAR" explanation for OPTION 2 which has left VISITOR boggled. NOBODY you can give a better explanation if you are a true lover of mathematics or LOGIC.
Regards
Daniel Stoichkov
Professor, MIT
|
| le chef du nuit |
Posted
on 09-Nov-01 05:21 PM
basic assumption: all 3 are smart mfs who can work out logic problems
call them guy1, guy2, guy3
proof that guy3 has white on, using refutation
assume that guy3 has a red hat on
guy2 can now have either red or white
if guy2 has red, guy1 knows that he has white, so guy2 cant have red. Therefore, when guy1 says "dunno", guy2 will realize that he must have a white hat on. so, he cant say 'dunno'
but, he does say dunno, which leads us to conclude that our assumption that guy3 was wearing red always leads to a contradictions, hence is false
hence, guy3 has a white hat on
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| Biswo |
Posted
on 09-Nov-01 05:23 PM
Nobodyji
I got the point. Thank you very much. Have a good weekend.
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| SP |
Posted
on 09-Nov-01 05:28 PM
What if all three had white hats?
The first one seeing 2 white hats would say "I don't know" because his could be white or red
The second one seeing 2 white hats would feel the same way.
Now how would the blind guy arrive at the correct conclusion?
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| Gandit Guru |
Posted
on 09-Nov-01 05:32 PM
uhhh......
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| Biswo |
Posted
on 09-Nov-01 05:33 PM
SPji:
Easy. The blind guy still says 'White'.
In the logic given by nobody, (set of W and Rs), you can see seven options.
Two options are automatically removed. WWR is not possible also. So, it leaves
with only four combiation (WWW, WRW, RWW, RRW) where all four option for
blind person are W (White).
I hope you got it. It is a real good question for a nice friday.
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| Shail |
Posted
on 09-Nov-01 05:34 PM
You don't need to prove that blind guy is wearing white. You just have to disprove that blind guy could wear red. Look at the top at my first answer.
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| Gandit Guru |
Posted
on 09-Nov-01 05:36 PM
Uhhh....
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| visitor |
Posted
on 09-Nov-01 05:37 PM
Thanks Nobody. I see the point.
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| Karuna |
Posted
on 09-Nov-01 05:42 PM
Thanks for giving your time and energy for this question.
But this is only the easy part.
Here is the challenging part.
This time it was the situation EXCEPT that the middle person was BLIND and the third person was half blind. The third person was able to answer correctly. What color hat was he wearing and the REASONING?
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| Curious G. |
Posted
on 09-Nov-01 05:48 PM
>The first one seeing 2 white hats would say "
>I don't know" because his could be white
>or red
>
>The second one seeing 2 white hats would
>feel the same way.
>
>Now how would the blind guy arrive at
>the correct conclusion?
Hmmm
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| Biswo |
Posted
on 09-Nov-01 05:50 PM
Hi Karuna:
Wait for the answer. I am off to home now!
It was a nice Friday, and I love this site!
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| Shail |
Posted
on 09-Nov-01 05:53 PM
Karuna,
You have to give a little more information. Assuming that the 2nd person was the blind person, what was his answer when the guard asked him what color his hat was??
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| visitor |
Posted
on 09-Nov-01 05:55 PM
What do you mean by half blind? Is this just to differentiate between 3 ppl?
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| could only see witKaruna |
Posted
on 09-Nov-01 06:02 PM
The SCENARIO is exactly as before. Go to the first Question.
Except that this time.
The middle person was the BLIND guy and the last person to answer was teh half-blind, meaning he could only see with one of his eyes.
And the third half-blind guy was able to tell the right anwer, i.e. the color of the hat he was wearing!
Is it clear now?
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| anepalikt |
Posted
on 09-Nov-01 09:17 PM
give me the bloody answer!
you guys are driving me insane... i hate logic problems. they never make sense to me.
just make sure whoever gives the answer explains it really well for dullards like me! :)
good one Karuna!
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| Makuro |
Posted
on 10-Nov-01 01:06 AM
White is the answer. How do I know? well first I made truth table. Then start eliminatiing using the conditions we were provided. Eventually you end up with
1 2 3
r r w
r w w
w r w
w w w
You see the third person who is blind is left with only white color.
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| thaha bhayo |
Posted
on 10-Nov-01 03:30 AM
karuna babe,
all three are wearing white........
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| Gokul |
Posted
on 10-Nov-01 10:05 AM
First solution:
A (2 eyes)
B (1 eye)
C (0 eye)
Suppose C is red.
When A said I don't know, that means B is NOT red. That is B is WHITE. In that case B should know it is WHITE. Since it does not know, our assumption is wrong.
From Reductio Ad absurdum, C is white.
==========================================================================
2nd solution:
A (2 eyes)
B (0 eye)
C (1 eye)
Suppose A red, B red C white.
Obviously, A can not know its color by looking at (B-red and C-white).
B is blind. It only infers that B and C are both not red.
The only way for C to know its color is if it sees
A red and B red.
Since it said correctly, it MUST HAVE seen A red and B red.
That means its color is WHITE.
The problem does not say that C will always know its color. It just says that C once said correctly and the only scenario in which C would be able to know its color is the above one.
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| Siwalik |
Posted
on 10-Nov-01 12:09 PM
Does logic always hold? Remember the question a teacher asked her pupil: How many birds will be left if there were ten and one was shot?
The pupil answered: none. That to me is better logic, grounded on pragmatism.
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| anepalikt |
Posted
on 10-Nov-01 12:58 PM
maybe it is sour grapes, in that I have never been terribly strong in logic problems. my gres will vouch for that :) but have to say that at times logic is seems just a sort of intellectual mind teasing. I agree siwalik, what is logic without pragmatism and I woudl say, heart/compassion and relevance.
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| Biswo |
Posted
on 10-Nov-01 01:13 PM
I am with Gokul. That half-blindness part is a red herring.
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| Siwalik |
Posted
on 10-Nov-01 01:20 PM
That's right. If we agree there is such a thing as half-blindedness, then we will logically have to accept that if a two-eyed person can see two miles, then a one-eyed person can see one mile. Or a two-legged person can run twice as fast as one-legged.... etc.
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| Vikash |
Posted
on 15-Nov-01 04:04 PM
I think it is white but how can a blind person see?
I think the blind person guessed and he became lucky.
I don't see any logic behind this...
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