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Apr. 2005Number GamesSlide 1 444444444 444 444444444 444 444444444 5555 5555555 55555555 555 55555 5555555 555555 5555 555 555555555 55555555 55555 Number Games A Lesson in the “Math + Fun!” Series 11111 1111111 111111111 1111 1111 111 111 11111 111 1111 1111111111 11111111 111111 222 2222 22222 222 222222222 2222222222 222 3333 33333 333333333333 333 3333 333 333 333 333 333 33 333 333

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Apr. 2005Number GamesSlide 2 About This Presentation EditionReleasedRevised FirstApr. 2005 This presentation is part of the “Math + Fun!” series devised by Behrooz Parhami, Professor of Computer Engineering at University of California, Santa Barbara. It was first prepared for special lessons in mathematics at Goleta Family School during the 2003-04 and 2004-05 school years. The slides can be used freely in teaching and in other educational settings. Unauthorized uses are strictly prohibited. © Behrooz Parhami

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Apr. 2005Number GamesSlide 3 What Number Did You Choose? 1. Pick a number from this list: 1 2 3 4 5 6 7 8 9 10 2. Multiply the number by 9. If the result has two digits, add the two digits; otherwise leave the number alone. 3. Subtract 5 from the number that you got in step 2. 4. Pick the letter that corresponds to the number you got in step 3. 1 = A, 2 = B, 3 = C, 4 = D, 5 = E, 6 = F, 7 = G, 8 = H, etc. 5. Pick a country in Europe whose name begins with your letter. A = Austria,...B = Belgium,... C = Croatia,...D = Denmark,... E = England,...F = France,... etc. 6. Use the last letter in your country’s name as the first letter of an animal. 7. Use the last letter of your animal’s name as the first letter of a color.

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Apr. 2005Number GamesSlide 4 How Did the Game Work? 1. Pick a number from this list: 1 2 3 4 5 6 7 8 9 10 2. Multiply the number by 9. 9 18 27 36 45 54 63 72 81 90 If the result has two digits, add the two digits You get 9 in all cases! 3. Subtract 5 from the number that you got in step 2. You get 4 4. Pick the letter that corresponds to the number you got in step 3. 1 = A, 2 = B, 3 = C, 4 = D, 5 = E, 6 = F, 7 = G, 8 = H, etc. 5. Pick a country in Europe whose name begins with your letter. A = Austria,...B = Belgium,... C = Croatia,...D = Denmark,... E = England,...F = France,... 6. Use the last letter in your country’s name as the first letter of an animal. Kangaroo 7. Use the last letter of your animal’s name as the first letter of a color. Orange

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Apr. 2005Number GamesSlide 5 More Mind-Reading Games 1.Think of a 2-digit number (10-99). 2.Multiply your number by 5. 3.Add 500 to the result of step 2. 4.Add the number of your siblings. 5.Double the result of step 4. You got a 4-digit number that starts with 1, has your original 2-digit number in the middle, and double the number of your siblings at the end. 1.Think of a number between 1 and 30. 2.Tell me in which of the five lists below the number appears. List A : 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 List B : 2 3 6 7 10 11 14 15 18 19 22 23 26 27 30 List C : 4 5 6 7 12 13 14 15 20 21 22 23 28 29 30 List D : 8 9 10 11 12 13 14 15 24 25 26 27 28 29 30 List E : 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 ACEACE BDEBDE

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Apr. 2005Number GamesSlide 6 Activity 1: Mind-Reading Game 1.Think of a number between 1 and 20. 2.Tell me in which of the five lists below the number appears. List A : 1 4 6 8 9 11 14 16 19 List B : 2 6 7 8 12 17 20 List C : 3 4 6 9 13 14 18 19 20 List D : 5 7 8 9 15 16 17 18 19 20 List E : 10 11 12 13 14 15 16 17 18 19 20 Play the following mind-reading game with your friends and family (First, discover how to tell the number if you know which lists it is in) Challenge: Add a List F to the five lists given above, and complete the lists, so that you can play the game with numbers up to 40.

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Apr. 2005Number GamesSlide 7 Activity 2: More Mind-Reading Games Your final result is 36, isn’t it? Your final result shows the month and day of your birth 1.Pick any number and write it down 2.Add 10 to your number 3.Add 20 to the result 4.Subtract 4 from the result 5.Add 15 to the result 6.Subtract 5 from the result 7.Subtract your original number I know what your number is! 1.Write down your BD month (1-12) 2.Multiply your number by 5 3.Add 6 to the result 4.Multiply the result by 4 5.Add 9 to the result 6.Multiply the result by 5 7.Add the day of your BD (1-31) 8.Subtract 165 from your result The Birthday Number Game Explain how this game works. Change the numbers to make your own game. Explain how this game works.

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Apr. 2005Number GamesSlide 8 Euclid’s Game for Two Players A referee writes two numbers on the board The two players take turns writing the difference of two numbers already on the board, provided the difference is a new number The player who cannot write a new number loses The total number of values written on the board is n = the larger number / greatest common divisor of the two numbers If n is odd, player 1 wins 24 6 Referee 18 Player 1 12 Player 2 80 15 65 50 35 Player 1 loses

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Apr. 2005Number GamesSlide 9 Activity 3: The Game of Nim Write three numbers on three lines The two players take turns reducing one of the numbers The player who makes the last move loses Challenge: 1.Discover a winning strategy with (5, 3, 1), if you are the first player 2.Play the game with other numbers such as (7, 4, 2), (6, 5, 3),... 5 3 1 Start Player 1 2 3 1 Player 2 2 2 1 Player 1 2 2 0 Player 2 2 1 0 Player 1 0 1 0 Loses! Player 2 0 0 0

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Apr. 2005Number GamesSlide 10 The Four 4s Puzzle Use four 4s and any number of math symbols (such as +, , , /, ,...) to form as many different numbers as possible. 3 = (4 + 4 + 4) / 4 4 = (4 + 4) / 4 + 4 5 = (4 4 + 4) / 4 2 = 4 / 4 + 4 / 4 or 4 – (4 + 4) / 4 6 = (4 + 4 + 4) / 4 8 = 4 (4 / 4) + 4 7 = 4 + 4 – 4 / 4 or 44 / 4 – 4 9 = 44 / 4 – 4 or 4 / 4 + 4 4 10 = (4 + 4 / 4) 4 11 = 44 / ( 4 + 4) 12 = 4 (4 – 4 / 4) 13 = 44 / 4 + 4 14 = 4 ( 4 + 4) – 4 15 = 44 / 4 + 4 16 = 4 4 + 4 – 4 or 4 4 4 / 4 17 = 4 4 + 4 / 4 18 = 4 ( 4 + 4) + 4 20 = 4 (4 + 4 / 4) 22 = 4 4 + 4 + 4 25 = (4 + 4 / 4) 4 1 = 4 – 4 + 4 / 4 0 = 4 – 4 + 4 – 4 Examples 24 = 4 ( 4 + 4 + 4) 19 = 4.4 4.4 21 = 4.4 4 + 4 23 = 4 (4 + 4) –.4

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Apr. 2005Number GamesSlide 11 Activity 4: The Five 5s Puzzle Use five 5s and any number of math symbols (such as +, , , /, ,...) to form as many different numbers as possible. 3 = 4 = 5 = 2 = 6 = 8 = 7 = 9 = 10 = 11 = 12 = 13 = 14 = 15 = 16 = 17 = 18 = 20 = 22 = 25 = 1 = 55 / 5 – 5 – 5 0 = 5 (5 / 5 – 5 / 5) Examples 24 = 19 = 21 = 23 =

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Apr. 2005Number GamesSlide 12 Activity 5: Birth Year Puzzle Use the digits in your year of birth, in order, plus any number of math symbols (+, –,...) to form the numbers from 0 to 10. 3 = (1 + 9 – 9) 3 4 = 5 = 2 = –1 + 9 – 9 + 3 6 = (1+ 9 / 9) 3 8 = 7 = 9 = 10 = 1 = 1 + (9 – 9) 3 Examples for 1993 0 = 1 (9 – 9) 3 3 = –1 + 9 – 9 + 4 4 = 1 9 – 9 + 4 5 = 1 + 9 – 9 + 4 6 = 1 + 9 / 9 + 4 8 = (1 + 9 / 9) 4 10 = 1 9 – 9 + 4 1 = 1 + (9 – 9) 4 Examples for 1994 2 = –1 – 9 / 9 + 4 7 = 1 (9 / 9) + 4 9 = 1 + 9 + 9 – 4 0 = 1 (9 – 9) 4 1 = 1 + (9 – 9) 5 2 = 3 = 4 = 5 = 1 – 9 / 9 + 5 6 = 7 = 8 = 9 = 10 = (1 + 9 / 9) 5 Examples for 1995 0 = 1 (9 – 9) 5

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Apr. 2005Number GamesSlide 13 Activity 6: Your Phone Number Write down your phone number, with space between digits Example: 5551253 Now, try to make as many different numbers as you can by Putting , , , signs between the digits. 0 =5 5 5 1 2 5 3 1 =5 5 5 1 2 5 3 2 =5 5 5 1 2 5 3 3 =5 5 5 1 2 5 3 4 =5 5 5 1 2 5 3 5 =5 5 5 1 2 5 3 6 =5 5 5 1 2 5 3 7 =5 5 5 1 2 5 3 8 =5 5 5 1 2 5 3

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Apr. 2005Number GamesSlide 14 Another Game for Two Players Put some playing cards (or numbers) in a row Players take turns removing a card from either end of the row At the end, add up the numbers to see who wins

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Apr. 2005Number GamesSlide 15 Game Tree Player 1 Player 2 Player 1 Player 2 Player 1 0 [1 2 5 4 8 6] 0 6 [1 2 5 4 8] 01 [2 5 4 8 6] 0 1 [2 5 4 8] 61 [5 4 8 6] 2 6 [1 2 5 4] 86 [2 5 4 8] 1 6 [4 8 6] 27 [5 4 8] 23 [5 4 8] 69 [2 5 4] 6 6 [8 6] 6 6 [4 8] 8 7 [4 8] 7 7 [5 4] 10 Player who wins 1 3 [4 8] 11 3 [5 4] 14 9 [5 4] 8 9 [2 5] 10 1212211 Score for Player 1 Score for Player 2 Cards left

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Apr. 2005Number GamesSlide 16 Some Surprising Predictions Answer these questions quickly. If you pause, it won’t work. What is 1 + 1? What is 2 + 2? What is 3 + 3? What is 4 + 4? What is 5 + 5? What is 6 + 6? What is 7 + 7? What is 8 + 8? What is 9 + 9? What is the first vegetable that comes to your mind? What is 2 + 2? What is 4 + 4? What is 8 + 8? What is 16 + 16? Quickly, pick a number between 12 and 5 No one knows why these guesses work for most people.

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Apr. 2005Number GamesSlide 17 Next Lesson Thursday, May 19, 2005 What is special about 40? (Hint: Forty) The only number with letters appearing in alphabetical order What is special about 6? (Hint: Divisible by 1, 2, 3) The smallest perfect number What is special about 38? (Hint: XXXVIII) The last Roman numeral in alphabetical order

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