Background:
When I was a student of the Government Arts College, Chennai (then Madras) (former Madras Mohammedan College and now Govt. Arts College for Women), the American Library (then known
as the USIS library) was within walking distance from the college along Mount Road in the direction towards Thousand Lights. I became a member of the library and used to walk over there during breaks and borrow books.
One of the books I remember was titled "General College Mathematics" by Ayres, Fry and Jonah.
One of the books I remember was titled "General College Mathematics" by Ayres, Fry and Jonah.
Several years later I went to Purdue University in West Lafayette, Indiana to pursue my Doctorate. At that time,
I found the same book for sale in an old books store.
When I opened, I found the authors Ayres, Fry and
Jonah were faculties of Purdue University. This added
to my interest and I went ahead and bought that book.
As I have moved to several different parts of the country
in the past 35 years, I got rid of many books at each move
but retained a few. This book, "General College
Mathematics" is one of them.
In this book, every chapter also has a "Problem Just
In this book, every chapter also has a "Problem Just
for Fun". These problems were solvable by simple
mathematics (algebra), reasoning or both. I could
solve some of the problems even as a freshman in college
back then; many were too much for me. The book does
not give answers.
Many of those problems are not solvable by me even today!
Many of those problems are not solvable by me even today!
I want to share these with you all and get the solutions.
Let me start with one of the logic problems from this book:
Let me start with one of the logic problems from this book:
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?
A man taps second only when he knows for sure that he is having a spot on forehead. Lets put him as A.
ReplyDeleteIf 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 couldnt 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.
Anthony,
ReplyDeleteReceived your answer. I agree with your reasoning. I think many would be able to reason it out but their wording will be different. I will post all the answers by Sunday, Sep. 2nd.
So far only 3 have sent their answers - you and 2 of my college class mates.
Visit this link to see more answers: http://advancedwordpuzzles.blogspot.com/2012/09/solutions-to-logic-and-math-puzzles.html
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