Lecture 17

# Sample problem 15 of the people in topeka have

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Sample Problem 15% of the people in Topeka have unlisted numbers. You select 200 names at random from the Topeka phone book. How many of these people will have unlisted numbers? Did you say 30? The correct answer is zero

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Sample Problem A man wanted to enter an exclusive club but did not know the password that was required. He waited by the door and listened. A club member knocked on the door and the doorman said, "twelve." The member replied, "six " and was let in. A second member came to the door and the doorman said, "six." The member replied, "three" and was let in. The man thought he had heard enough and walked up to the door. The doorman said, "ten" and the man replied, "five." But he was not let in. What should have he said? Three. The doorman lets in those who answer with the number of letters in the word the doorman says.
20 Mutilated Checkerboards Kaplan & Simon (1990) A checkerboard consists of 64 squares. These squares can be completely covered by placing 32 dominos on the board so each covers two squares. If we eliminate two opposing corners, can we cover the remaining squares with 31 dominos?

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21 Kaplan & Simon Methods 4 groups, each receive different condition Pink Black Bread Butter Blank squares Colors
22 Goal: Parity Representation Insight: Laying down a domino must cover different squares (black & pink, never black & black) When you remove two corners, you remove two like squares The answer? No, 31 dominos will not cover the board

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23 How most people do this Started with 64 squares, took 2 away. 62 / 2 = 31, so 31 dominos should do it. Then when they try it on paper, it doesn’t work. Try utilizing the words on the paper Notice domino covers bread and butter Also notice two breads were removed Come to the correct conclusion
24 Kaplan & Simon Results Bread & butter group solved the problem twice as fast as blank group Color and pink & black groups: In between blank and bread & butter

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Methods of Representing the Problem Symbols translating words into symbols 6x + 18 = 0, solve for x misunderstanding oversimplification
Methods of Representing the Problem Matrices matrix—chart showing all possible combinations of items most useful for complex, stable, categorical information Demo 11.3 Rm. 101 Rm. 102 Rm. 103 Anderson Mono Green Gall bladder Lopez T.B.

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Problem Representation   Diagrams instructions for assembling objects hierarchical tree diagram Graphs Buddhist monk problem
Buddhist Monk Problem Exactly at sunrise, a Buddhist monk set out to climb a tall mountain. The monk climbed the path at varying rates of speed, stopping many times along the way to rest and eat. He reached the temple just before sunset. At the temple, he fasted and meditated for several days. Then he began his journey back along the same path, starting at sunrise and walking, as before, at variable speeds with many stops along the way. However, his speed going down the hill was greater than his average climbing speed.

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• Spring '08
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• Gick, Analogy Approach

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