w w w. P u z z l e B a s e d L e a r n i n g. e d u. a u Copyright © 2008 Hybrid Publishers 1 Puzzle Power: Problem-Solving Made AWESOME! Adapted from Puzzle-Based Learning: An Introduction to Critical Thinking, Mathematics, and Problem Solving by Zbigniew Michalewicz & Matthew Michalewicz

w w w. P u z z l e B a s e d L e a r n i n g. e d u. a u Copyright © 2008 Hybrid Publishers 2 Puzzle-Based Learning Puzzles represent “unstructured” problems; they teach how to think “out of the box.” Puzzles are not attached to any chapter of any text. Puzzles illustrate many general and powerful problem-solving techniques. Puzzles illustrate importance of science. Puzzles are fun and easy to remember!

w w w. P u z z l e B a s e d L e a r n i n g. e d u. a u Copyright © 2008 Hybrid Publishers 3 Topic #1 The problem: What are you after?

w w w. P u z z l e B a s e d L e a r n i n g. e d u. a u Copyright © 2008 Hybrid Publishers 4 A man has to take a wolf, a goat, and some cabbage across a river. His rowboat has enough room for the man plus either the wolf or the goat or the cabbage. If he takes the cabbage with him, the wolf will eat the goat. If he takes the wolf, the goat will eat the cabbage. Only when the man is present are the goat and the cabbage safe from their enemies. How should the man carry the wolf, goat, and cabbage across the river? A puzzle

w w w. P u z z l e B a s e d L e a r n i n g. e d u. a u Copyright © 2008 Hybrid Publishers 5 Topic 2 Intuition: How good is it?

w w w. P u z z l e B a s e d L e a r n i n g. e d u. a u Copyright © 2008 Hybrid Publishers 6 Puzzle 1.2 You drive a car at a constant speed of 40 km/h from A to B, and on arrival at B you return immediately to A, but at a higher speed of 60 km/h. What was your average speed for the whole trip?

w w w. P u z z l e B a s e d L e a r n i n g. e d u. a u Copyright © 2008 Hybrid Publishers 7 Topic 3 Modeling: Let’s think about the problem a bit more

w w w. P u z z l e B a s e d L e a r n i n g. e d u. a u Copyright © 2008 Hybrid Publishers 8 A good model A good model should be precise enough to allow for a meaningful solution, but on the other hand, it should not be so complex that it is too difficult to use. A good model should satisfy two intuitive requirements: It should be general enough, so that irrelevant details of the problem are hidden. It should be specific enough, so that we can derive a meaningful solution.

w w w. P u z z l e B a s e d L e a r n i n g. e d u. a u Copyright © 2008 Hybrid Publishers 9 Puzzle 1.1 At six o'clock in the morning the wall clock struck 6 times and the time between the first and last strokes was 30 seconds. How long will the clock take to strike 12 times at noon?

w w w. P u z z l e B a s e d L e a r n i n g. e d u. a u Copyright © 2008 Hybrid Publishers 10 Lessons learned Rule #1: Be sure you understand the problem, and all the basic terms and expressions used to define it. Rule #2: Do not rely on your intuition too much; solid calculations are far more reliable. Rule #3: Solid calculations and reasoning are more meaningful when you build a model of the problem by defining its variables, constraints, and objectives

w w w. P u z z l e B a s e d L e a r n i n g. e d u. a u Copyright © 2008 Hybrid Publishers 11 Practice, Practice, Practice!!!