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
Solutions:
Sivakumaran Venkataraman:
A
can find out the color of her hat only if the other two, B & C have
pink ones. Even if one of them is green she can't guess. Since she says
'no' B & C guess that one of them at least must be having a green
hat. B can guess that she has a green hat only if the C's hat is pink.
Since B also says no, C easily guesses that hers is Green.
Vasudevan Tirumurti
Green.
Miss.Highhat can guess right only if the two hats she sees are pink. -
there are only two pink hats and if she sees two pink she has to be
wearing green. So at least one hat is green. Both could be Green too.
Given this Miss Swank can guess that her hat is green only if she sees
Miss. Social wearing pink hat. If Miss. Social is wearing green it wont
be clear if Miss.Highhat saw two greens or one. She could not guess.
Ergo Miss.Social is wearing Green.
Rahim (using his own "reformed" spelling)
Social was wearing green and she said so.
When
she heard Hihat telling that she did not no the kolor of the hat she
herself was wearing Soshial konluded that (i) Both myself and Swank r
wearing green (ii) I am having green and Swank pink (iii) vice versa.
But
when Swank also said "I do not no" Social was sure she she was not
wearing pink. Had she been wearing pink, Swank wud have said "I am
having green"
Prasad: 
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