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Problem Solving Featuring Polya’s Problem
Solano County Mathematics April 28, 2016
with Michael Serra
© 2016 Michael Serra 2
Classics of Problem Solving The Nine Dot Puzzle. Draw no more than four straight lines (without lifting the pencil from the paper) that will cross through all nine dots.
The Frog and the Well. Freddie the Frog is at the bottom of a 30-‐foot well. Each day he jumps up 3 feet, but then, during the night, he slides back down 2 feet. How many days will it take Freddie to get to the top and out?
The Book Worm Problem. Volumes 1 and 2 of a two-‐volume set of math books sit next to each other on a shelf. They sit in their usual order: Volume 1 on the left and Volume 2 on the right. Each front and back cover is 1/8 inch thick, and the pages portion of each book is 1 inch thick. If a bookworm starts at the first page of Volume 1 and burrows all the way through to the last page of Volume 2, how far will she travel?
© 2016 Michael Serra 3
What are their ages?
Lucy and Ethyl meet after many years. Lucy asks, “How old are your three daughters?” Ethyl: “The product of their ages is 36.” Lucy: “But that’s not enough information.” Ethyl: “Well, the sum of their ages is the same number as the post office box that we shared at college.” Lucy: “But that’s still not enough information.” Ethyl: “The oldest one looks like me.” Lucy: “Oh, now I know their ages.”
The Spider and the Fly Problem
Inside a rectangular room, measuring 30’ in length and 12’ in width and height, a spider is at a point on the middle of one of the end walls, 1 foot from the ceiling, as shown at A; and a fly is on the opposite wall, 1 foot from the floor in the center, as shown at B. What is the shortest distance that the spider must crawl in order to reach the fly, which remains stationary? Of course the spider never drops or uses its web, but crawls fairly.
© 2016 Michael Serra 4
Polya’s Problem Into how many parts do five planes* divide space? *random planes or find the maximum number of parts.
Resources How To Solve It, George Polya Discovering Geometry, Michael Serra
Smart Moves, Michael Serra
Pirate Math, Michael Serra
The Canterbury Puzzles, H.E. Dudeney
Overcoming Math Anxiety, Sheila Tobias
Michael's website: www.michaelserra.net
Business email: [email protected]