f38 Number Games

7/30/2019 f38 Number Games

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Apr. 2005 Number Games Slide 1

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Number GamesA Lesson in the Math + Fun! Series

11111

1111111

111111111

1111 1111

111 111111

111

111 11111

111 11111

111 11111

111 111

1111 11111111111111

11111111

111111

222

2222

2222

22222

222 222222 222

222 222

222 222

222 222

222222222

222222222

2222222222222 222

222 222

222 222

3333 3333

3333 3333

33333 33333

33333 33333

33333 33333333333333333

333333333333

333333333333

333 3333 333

333 3333 333

333 333 333

333 333 333333 33 333

333 33 333

333 333


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About This Presentation

Edition Released Revised Revised

First Apr. 2005

This presentation is part of the Math + Fun! series devisedby 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


3/17


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 countrys name as the first letter of an animal.

7. Use the last letter of your animals name as the first letter of a color.
http://robinlawrie.tripod.com/strangeanimal/kangaroo.jpg


4/17


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 90If 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 countrys name as the first letter of an animal.

Kangaroo

7. Use the last letter of your animals name as the first letter of a color.Orange
http://robinlawrie.tripod.com/strangeanimal/kangaroo.jpg


5/17


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.

ListA: 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29

ListB

: 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 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

A

C

E

B

D

E


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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.

ListA

: 1 4 6 8 9 11 14 16 19List 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.


7/17


Activity 2: More Mind-Reading Games

Your final result is 36, isnt 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 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 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.


8/17


Euclids Game for Two PlayersA referee writes two numbers on the board

The two players take turns writing the difference of two numbersalready 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

Ifn is odd, player 1 wins

24 6

Referee

18Player

1

12Player

2

80 15

65 50

35

Player 1

loses


9/17


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), . . .

53

1

Start Player 1

23

1

Player 2

22

1

Player 1

22

0

Player 2

21

0

Player 1

01

0

Loses!

Player 2

00

0


10/17


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 = 44/44 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 = 44 + 4 4 or 444/417 = 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 + 4/4

0 = 4 4 + 4 4Examples

24 = 4 (4 + 4 + 4)

19 = 4.4 4.4

21 = 4.4 4 + 4

23 = 4 (4 + 4) .4


11/17


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 50 = 5 (5/5 5/5) Examples

24 =

19 =

21 =

23 =


12/17


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) 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 + 4

4 = 1 9 9 + 45 = 1 + 9 9 + 4

6 = 1 + 9/9 + 4

8 = (1 + 9/9) 4

10 = 1 99 + 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) 52 =

3 =

4 =

5 = 1 9/9 + 5

6 =

7 =8 =

9 =

10 = (1 + 9/9) 5

Examples for 1995

0 = 1 (9 9) 5


13/17


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 3

4 = 5 5 5 1 2 5 3

5 = 5 5 5 1 2 5 36 = 5 5 5 1 2 5 3

7 = 5 5 5 1 2 5 3

8 = 5 5 5 1 2 5 3


14/17


Another Game for Two PlayersPut 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
http://www.acclaimimages.com/_gallery/_SM/0006-0409-0916-4708_SM.jpghttp://www.acclaimimages.com/_gallery/_SM/0006-0409-1011-0543_SM.jpghttp://www.acclaimimages.com/_gallery/_SM/0006-0409-1010-5207_SM.jpghttp://www.acclaimimages.com/_gallery/_SM/0006-0409-0916-2803_SM.jpghttp://www.magiclibrary.net/rarities/poker-dci-legend-membership-ace-of-spades.jpghttp://www.acclaimimages.com/_gallery/_SM/0006-0409-0916-4708_SM.jpghttp://www.acclaimimages.com/_gallery/_SM/0006-0409-1011-0543_SM.jpghttp://www.acclaimimages.com/_gallery/_SM/0006-0409-1010-5207_SM.jpghttp://www.acclaimimages.com/_gallery/_SM/0006-0409-0916-2803_SM.jpghttp://www.magiclibrary.net/rarities/poker-dci-legend-membership-ace-of-spades.jpg


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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 for

Player 1

Score for

Player 2Cards left


16/17


Some Surprising PredictionsAnswer these questions quickly.

If you pause, it wont 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 toyour 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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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 smallestperfect number

What is special about 38? (Hint: XXXVIII)The last Roman numeral

in alphabetical order

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f38 Number Games