1. Topic 3 Games and Puzzles Unit 1 Topic 1

2. You just used reasoning to determine what happened in the story. In this unit, we are going to do the same. We are going to figure out what happens based on information that we are given.

3. Information Games or puzzles develop your problem solving skills by allowing you to create and analyze strategies. There are many strategies that you can use to solve a puzzle or win a game. Guess and Check 1. Guess an answer that fits one of the facts. 2. Check the answer against the other facts. 3. If necessary, adjust your guess and check again. Look for a Pattern 1. Organize the given information and look for a pattern. 2. Use the pattern to solve the problem. 3. Check that your answer is reasonable. Solve a Simpler Problem 1. Break the original problem into smaller parts or into a simpler problem. 2. Solve the simpler problem. 3. Extend what you have learned to solve the problem. 4. Check that your answer is reasonable.

4. Solve Using a Diagram or Table 1. Represent the situation using a diagram or a table. 2. Use the diagram or table to solve the problem. 3. Check that your answer is reasonable. Work Backward 1. Start with what you know. 2. Work backward to get an answer. 3. Check that your answer is reasonable. Use Logic 1. Starting with what you know, identify possible answers. 2. Use elimination and logical conclusions to identify an answer. 3. Check that your answer is reasonable.

5. Example 1 Solving a Number Puzzle Three puzzles are shown below. A number in a box of a puzzle is the sum of the two numbers in the circles adjacent to the box. Notice that 2 times the bottom left circle gives the right box value.

6. Example 1 Solving a Number Puzzle Solve the three puzzles below. Possible strategies that you may use include guess and test and look for a pattern. a)b) c) Try this on your own first!!!!

7. Example 1: Solution Solving a Number Puzzle Solve the three puzzles below. Possible strategies that you may use include guess and test and look for a pattern. a)b) c) 3 6 9 8 910 14 24 34

8. Example 2 Solving a Handshake Puzzle Eight people in business meet for the first time. Each businessperson shakes the hand of every other businessperson once. In total, how many handshakes were exchanged? Possible strategies that you may use include drawing a diagram, solving a simpler problem, or looking for a pattern. Try this on your own first!!!!

9. Example 2: Solution Drawing a diagram. 1 2 3 4 5 6 7 1 2 3 4 5 6 1 2 3 4 5 876 7 handshakes6 handshakes5 handshakes 1 2 3 4 1 2 31 2 1 5432 4 handshakes 3 handshakes 2handshakes 1 handshakes Solving a Handshake Puzzle

10. Example 3 Solving a Logic Puzzle Using a Table One Saturday, five friends visited the zoo. Each wore a different coloured t-shirt and each rushed to see their favourite animal upon arriving at the zoo. Using the clues provided, can you name each child’s favourite animal and the colour of t-shirt they wore? 1.One of the children wore the t-shirt that was the same colour as their favourite animal. 2.Steven, who was not wearing red, went to the kangaroo pavilion and Ashlee, who did not visit the lions, wore a yellow t-shirt. 3.While visiting the lions, Chase saw the girl with the red shirt at the monkey exhibit. 4.Paul, who did not like elephants, heard the boy in the purple t-shirt saying that the lions were his favourite. 5.On her way to visit the monkeys, Michelle passed Steven who was wearing the black t-shirt. Try this on your own first!!!!

11. Example 3: Solution - Clue 2 X X X X X X X X XX X X X X X XXX The X and the are information given directly in clue 2. The X’s can then be entered based on the given information.

12. Example 3: Solution - Clue 3 X X X X X X X X XX X X X X X XXX X X X X X X

13. Example 3: Solution - Clue 4 X X X X X X X X XX X X X X X XXX X X X X X X X X X X X X

14. Example 3: Solution - Clue 5 X X X X X X X X XX X X X X X XXX X X X X X X X X X X X X X X X X X X X X

15. Example 3: Solution X X X X X X X X XX X X X X X XXX X X X X X X X X X X X X X X X X X X X X Ashlee – Yellow Shirt Chase – Purple Shirt Michelle – Red Shirt Paul – White Shirt Steven – Black Shirt Based on what is left and clue 1 you can complete the puzzle.

16. Example 4 Solving the Amount of Money at the Start A troll said to a fool, “Walk across my bridge and I will double the money you have in your pocket. In fact, each time you walk across the bridge I will double your money. But there is one small thing. Since I am so generous you must give me $24 after each crossing.” The fool agreed. He crossed the bridge, stopped to count his money and his money doubled. He threw $24 to the troll. He crossed the bridge a second time. His money doubled and he paid the troll $24. He crossed a third time and again his money doubled. But now he had only $24 and he had to give it all to the troll. How much money did he start with? Hint: Working backward is a possible strategy to solve this problem. Try this on your own first!!!!

17. Example 4: Solution Solving the Amount of Money at the Start Hint: Working backward is a possible strategy to solve this problem. Must give $24 after each crossing He crossed a third time and again his money doubled. But now he had only $24 and he had to give it all to the troll. 24  24 = 0 His money doubled and he paid the troll $24. Second Crossing If his money doubled he must have had $12 that became $24 for his third crossing. ?  24 = 12 For his second crossing he must have had $36 before paying the $24.

18. Example 4: Solution Solving the Amount of Money at the Start First Crossing If his money doubled he must have had $18 that became $36 for his second crossing. ?  24 = 18 So he must have had $42 before paying the $24. Before the $42 doubled he would have started with $21.

19. Example 5 Solving a Sudoku Puzzle A Sudoku Puzzle is shown on the next slide. The objective in a Sudoku Puzzle is to fill the 9 × 9 grid with digits so that each column, each row, and each of the nine 3 × 3 sub-grids that compose the grid contains all of the digits from 1 to 9. Determine the number missing in the shaded box for the Sudoku Puzzle below. Using logic is a possible strategy to solve this problem. Try this on your own first!!!!

20. Example 5: Solution Solving a Sudoku Puzzle To solve the puzzle the square, the row and the column must have the values Cross out the ones that appear in the square, row and column. Determine which of the left over numbers can only go in the shaded box. So the solution is.

21. Need to Know: There are many strategies that you can use to solve a puzzle or win a game, such as, guess and check look for a pattern solve a simpler problem solve using a diagram or table work backwards use logic You’re ready! Try the homework from this section.