Download ppt - Math Plus Fun, Number Games

Apr. 2005 Number Games Slide 1

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Number GamesA Lesson in the “Math + Fun!” Series

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About This Presentation

Edition Released Revised Revised

First Apr. 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


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.

http://robinlawrie.tripod.com/strangeanimal/kangaroo.jpg


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

http://robinlawrie.tripod.com/strangeanimal/kangaroo.jpg


More Mind-Reading Games1. 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 29List B: 2 3 6 7 10 11 14 15 18 19 22 23 26 27 30List C: 4 5 6 7 12 13 14 15 20 21 22 23 28 29 30List D: 8 9 10 11 12 13 14 15 24 25 26 27 28 29 30List E: 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

A

C

E

B

DE


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 19List B: 2 6 7 8 12 17 20List C: 3 4 6 9 13 14 18 19 20List D: 5 7 8 9 15 16 17 18 19 20List 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.


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 down2. Add 10 to your number3. Add 20 to the result4. Subtract 4 from the result5. Add 15 to the result6. Subtract 5 from the result7. Subtract your original number

I know what your number is!

1. Write down your BD month (1-12)2. Multiply your number by 53. Add 6 to the result4. Multiply the result by 45. Add 9 to the result6. Multiply the result by 57. 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.


Euclid’s Game for Two Players

A referee writes two numbers on the boardThe two players take turns writing the difference of two numbers already on the board, provided the difference is a new numberThe 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

18Player

112

Player2

80 15

65 50

35Player 1

loses


Activity 3: The Game of NimWrite three numbers on three linesThe 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 player2. Play the game with other numbers such as (7, 4, 2), (6, 5, 3), . . .

531

Start Player 1

231

Player 2

221

Player 1

220

Player 2

210

Player 1

010

Loses!

Player 2

000


The Four 4s PuzzleUse four 4s and any number of math symbols (such as +, , , /, , . . .) to form as many different numbers as possible.

3 = (4 + 4 + 4) / 44 = (4 + 4) / 4 + 45 = (4 4 + 4) / 4

2 = 4 / 4 + 4 / 4 or 4 – (4 + 4) / 4

6 = (4 + 4 + 4) / 4

8 = 4 (4 / 4) + 47 = 4 + 4 – 4 / 4 or 44 / 4 – 4

9 = 44 / 4 – 4 or 4 / 4 + 4 410 = (4 + 4 / 4) 411 = 44 / (4 + 4)12 = 4 (4 – 4 / 4)

13 = 44 / 4 + 414 = 4 (4 + 4) – 415 = 44 / 4 + 4

16 = 4 4 + 4 – 4 or 4 4 4 / 417 = 4 4 + 4 / 418 = 4 (4 + 4) + 4

20 = 4 (4 + 4 / 4)

22 = 4 4 + 4 + 4

25 = (4 + 4 / 4)4

1 = 4 – 4 + 4 / 40 = 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


Activity 4: The Five 5s PuzzleUse 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 =


Activity 5: Birth Year PuzzleUse 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) 34 =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 + 44 = 1 9 – 9 + 45 = 1 + 9 – 9 + 46 = 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) 41 = 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


Activity 6: Your Phone NumberWrite down your phone number, with space between digits

Example: 5 5 5 1 2 5 3

Now, try to make as many different numbers as you can by Putting , , , signs between the digits.

0 = 5 5 5 1 2 5 31 = 5 5 5 1 2 5 32 = 5 5 5 1 2 5 33 = 5 5 5 1 2 5 34 = 5 5 5 1 2 5 35 = 5 5 5 1 2 5 36 = 5 5 5 1 2 5 37 = 5 5 5 1 2 5 38 = 5 5 5 1 2 5 3


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 rowAt the end, add up the numbers to see who wins

http://www.magiclibrary.net/rarities/poker-dci-legend-membership-ace-of-spades.jpg

http://www.acclaimimages.com/_gallery/_SM/0006-0409-0916-2803_SM.jpg





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] 2 7 [5 4 8] 2 3 [5 4 8] 6 9 [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

1 21 2 2 1 1

Score forPlayer 1

Score forPlayer 2Cards left


Some Surprising PredictionsAnswer 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.


Next LessonThursday, 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