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Polya's problem solving process

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sierra white

on 6 November 2013

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Transcript of Polya's problem solving process

Polya's problem solving process

The Birthday Problem


You and your colleagues know that
your boss A’s
birthday is one of the following
10 dates
:

Mar 4, Mar 5, Mar 8
Jun 4, Jun 7
Sep 1, Sep 5
Dec 1, Dec 2, Dec 8

A told you only the month of his birthday, and told your colleague C only the day.
After that,
you first said: “I don’t know A’s birthday; C doesn’t know it either.”

After hearing what you said, C replied: “I didn’t know A’s birthday, but now I know it.”
You smiled and said: “Now I know it, too.”
After looking at the 10 dates and hearing your comments, your administrative assistant wrote down A’s birthday without asking any questions. So what did the assistant write?

Understanding the Problem
We are to find out when Boss A's birthday is using the previous information
There is 10 different possibilities
You know the Month
Your colleague C know the day
Knowing the Problem Solving Process

George Pólya was a Hungarian Jewish mathematician. He was a professor of mathematics from 1914 to 1940 at ETH Zürich and from 1940 to 1953 at Stanford University
George was also the inventor of the problem solving process
How to Solve It (1945) is a book he created about the problem solving process
The Four Problem Solving Steps

Understand the problem
Devise a plan
Carry out the plan
Look back
Background Information
Devise a Plan
We know that the 10 dates we have are our only possibilities

March 4, March 5, March 8,
June 4, June 7,
September 1, September 5,
December 1, December 2, December 8
There are only two days that don't repeat which are the 7th & the 2nd which make them unique. If the month had been June, the day C was told of may have been 2; if the month had been December, the day C was told of may have been 7.) Now C knows that the month must be either March or September. He immediately figures out A’s birthday, which means the day must be unique in the March and September list. It means A’s birthday cannot be Mar 5, or Sep 5.
Process of elimination, the birthday must be Mar 4, Mar 8 or Sep 1.
Among these three possibilities left, Mar 4 and Mar 8 have the same month. So if the month you have is March, you still cannot figure out A’s birthday. Since you can figure out A’s birthday, A’s birthday must be Sep 1.
the birthday is September 1.
Understanding the problem -
READ the problem
What are you expected to find
What information your given
Explain the problem in a way that you understand it BEST
Use pictures or diagrams
Devise a plan-
Look at the unknown
Ask your self questions
Relate
Carry out the plan-
Follow the plan
CHECK EACH STEP
Look Back-
Is It Reasonable?
What did i learn?
How can i use it to solve other problems?
How else could i have solved the problem?



Carry out the plan
March 4,

March 5, March 8,
June 4, June 7,
September 1,
September 5,
December 1, December 2, December 8
Did your plan work? yes the plan worked because we found out when the boss birthday ( http://questionsininterview.com/welcome-to-questionsininterview-com/problem-solving-interview-questions/the-birthday-problem-interview-question/ )
What did you learn from the problem? We must read at least twice before trying to solve the problem, and we must use the problem solving process in order to solve the problem completely .



Look back
Full transcript