1. Three wise men and their reasoning skills:
Problem Statement:
Three wise men were tested for their reasoning skill by being blindfolded and having a finger rubbed on each of their foreheads, after being told that one or more would have
smudges on their foreheads. Actually, all three were given smudges. They were told to tap once if they saw one or more spots on removing the blindfold and to tap twice
if they decided that there was a spot on their own forehead. When the blindfolds were removed, all three tapped once. After a pause, one man tapped twice. What was his reasoning?
Solutions:
1. Prasad
Best Solution (clear logic and best presentation) - Thanks to Prasad
Best Solution (clear logic and best presentation) - Thanks to Prasad
Let us name the wise men as A, B and C with all possible scenarios as shown below:
X indicates the presence of the smudge in the forehead of the wise man on top of the column
Case 1: (Rows 1, 2 and 3)
If only one of them received the smudge, then the one who received the smudge cannot notice any smudge and would not tap. Since all of them tapped once, they all realize that there must be at least two smudges.
Case 2: (Rows 4, 5 and 6)
If only two of them received smudges, those with the smudges would notice no smudge on the third and realize that they themselves must have a smudge. They both would have tapped a second time. This cannot occur if the third also has a smudge.
Case 3: (Row 7)
Since Case 2 did not occur, one of them realizes that it is because all three have received smudges. So he goes ahead and taps twice after a pause.
2. Anthony:
A man taps second only when he knows for sure that he is having a spot on forehead. Lets put him as A. If only one of them were given, then it is easier to find out by the fact that only two people will tap first and the one who didnt tap will tap after a pause. If two of them were given, (Say A not given) all three will tap first. But the persons who were given (B/C) sees that the other person (C / B) also taps in first round and finds out that they themselves are given. A, who quickly strikes out these two scenarios knows that all three were given, since B and C couldn't decide only becuase A himself was given. But why the other two B & C couldnt come to the same conclusion at the same time is a very good question, but thats not part of our concern if we are to explain A's logic only.
3. T. V. Sivakumaran
The most intelligent guy who who tapped twice , let us say A should have thought as follows.
If he didin't have the smudge in his forehead, B would have easily found out that he must have it on his own forehead, since both A and C has tapped once looking at the smudge on his (B's) forehead. He would have immediately tapped twice.
Ditto for C.
4. Rahim
Let A, B and C be the 3 wise men.
Let A be the one who found out: his reasoning : "I must be having the spot because, if not, B would have tapped twice as C also has a spot but tapped only once !" A's argument : If I had no spot, then B, who is wise, would have tapped twice thinking that he was having a spot because C had tapped looking only his spot. Since B was smarter than C, say. Since I also had a spot, B was confused. May be, B thought, C had tapped looking at my, (A's) spot. B would have thought he may or may not have a spot. If A and B both no spot, then C wud not have tapped at all !
The beauty in this puzzle is, any one else, that is B or C, would have given a similar reason. But A was a little smarter than the other 2. A quickly decides that he too must be having the smudge and taps twice.
X indicates the presence of the smudge in the forehead of the wise man on top of the column
A
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B
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C
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Scenario 1
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x
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Scenario 2
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x
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Scenario 3
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x
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Scenario 4
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x
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x
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Scenario 5
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x
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x
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Scenario 6
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x
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x
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Scenario 7
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x
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x
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x
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Case 1: (Rows 1, 2 and 3)
If only one of them received the smudge, then the one who received the smudge cannot notice any smudge and would not tap. Since all of them tapped once, they all realize that there must be at least two smudges.
Case 2: (Rows 4, 5 and 6)
If only two of them received smudges, those with the smudges would notice no smudge on the third and realize that they themselves must have a smudge. They both would have tapped a second time. This cannot occur if the third also has a smudge.
Case 3: (Row 7)
Since Case 2 did not occur, one of them realizes that it is because all three have received smudges. So he goes ahead and taps twice after a pause.
2. Anthony:
A man taps second only when he knows for sure that he is having a spot on forehead. Lets put him as A. If only one of them were given, then it is easier to find out by the fact that only two people will tap first and the one who didnt tap will tap after a pause. If two of them were given, (Say A not given) all three will tap first. But the persons who were given (B/C) sees that the other person (C / B) also taps in first round and finds out that they themselves are given. A, who quickly strikes out these two scenarios knows that all three were given, since B and C couldn't decide only becuase A himself was given. But why the other two B & C couldnt come to the same conclusion at the same time is a very good question, but thats not part of our concern if we are to explain A's logic only.
3. T. V. Sivakumaran
The most intelligent guy who who tapped twice , let us say A should have thought as follows.
If he didin't have the smudge in his forehead, B would have easily found out that he must have it on his own forehead, since both A and C has tapped once looking at the smudge on his (B's) forehead. He would have immediately tapped twice.
Ditto for C.
4. Rahim
Let A, B and C be the 3 wise men.
Let A be the one who found out: his reasoning : "I must be having the spot because, if not, B would have tapped twice as C also has a spot but tapped only once !" A's argument : If I had no spot, then B, who is wise, would have tapped twice thinking that he was having a spot because C had tapped looking only his spot. Since B was smarter than C, say. Since I also had a spot, B was confused. May be, B thought, C had tapped looking at my, (A's) spot. B would have thought he may or may not have a spot. If A and B both no spot, then C wud not have tapped at all !
The beauty in this puzzle is, any one else, that is B or C, would have given a similar reason. But A was a little smarter than the other 2. A quickly decides that he too must be having the smudge and taps twice.
2. Just4Fun 2 - (English) Reasoning Skill: Three ladies and Five Hats
Problem Statement:
Miss
Swank, Miss Social, and miss Highhat descended upon the hatter and
demanded the latest creations in chapeaux. The hatter asked the three
ladies to take three chairs. He had, however, arranged the chairs sin
such a manner that Miss Highhat could see the hats that Miss Swank and
Miss Social tried on, and Miss Swank could see Miss Social's hat, but
Miss Social could not see the other two ladies' hats. The hatter showed
the ladies five hats, three of which were green and two of which were
pink. He mixed the hats and from the rear placed a hat upon each
ladies; head. He asked Miss Highhat the color of her hat. She relied
that she did not know. He asked Miss Swank the color of her hat. She
replied she did not know. When Miss Social was asked the color of her
hat, she could tell the hatter the correct color. What was the color of
Miss Social's hat?
Problem source:
"General College Mathematics", W. L. Ayres, Cleota G. Fry, H. F. S. Jonah, McGraw Hill Book Company, 1952 p.35
Problem source:
"General College Mathematics", W. L. Ayres, Cleota G. Fry, H. F. S. Jonah, McGraw Hill Book Company, 1952 p.35
Good one!:-)
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