Math Plus Fun, Number Games

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  • Number Games

    444444444

    444444444

    444444444

    444

    444

    444

    444444444

    444444444

    444444444

    444

    444

    444

    444444444

    444444444

    444444444

    5555

    5555555

    55555555

    555 555

    555

    55555

    5555555

    5555555

    555555

    5555

    555 555

    555 555

    555555555

    55555555

    55555

    A Lesson in the Math + Fun! Series

    11111

    1111111

    111111111

    1111 1111

    111 111

    111

    111

    111 11111

    111 11111

    111 11111

    111 111

    1111 1111

    1111111111

    11111111

    111111

    222

    2222

    2222

    22222

    222 222

    222 222

    222 222

    222 222

    222 222

    222222222

    222222222

    2222222222

    222 222

    222 222

    222 222

    3333 3333

    3333 3333

    33333 33333

    33333 33333

    33333 33333

    333333333333

    333333333333

    333333333333

    333 3333 333

    333 3333 333

    333 333 333

    333 333 333

    333 33 333

    333 33 333

    333 333

    Math has many uses in geography. This lesson focuses on the relationship of math to making and using maps.

  • About This Presentation

    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

    EditionReleasedRevisedRevisedFirstApr. 2005

  • 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.

    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.

    Orange kangaroo from Denmark

  • 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

    Orange kangaroo from Denmark

  • More Mind-Reading Games

    Think of a 2-digit number (10-99).Multiply your number by 5.Add 500 to the result of step 2.Add the number of your siblings.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.

    Think of a number between 1 and 30.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

    A

    C

    E

    B

    D

    E

  • Activity 1: Mind-Reading Game

    Think of a number between 1 and 20.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.

  • Activity 2: More Mind-Reading Games

    Your final result is 36, isnt it?

    Your final result shows the month and day of your birth

    Explain how this game works.

    Change the numbers to make your own game.

    Explain how this game works.

  • Euclids 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

  • 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:

    Discover a winning strategy with (5, 3, 1), if you are the first playerPlay the game with other numbers such as (7, 4, 2), (6, 5, 3), . . .

  • 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

    24 = 4 (4 + 4 + 4)

  • 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 =

  • 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.

    This puzzle becomes more or less difficult, depending on your birth year. It is pretty simple for most years. However, for someone born in 2005, it is hard: 0 = 2x0 + 0x5, 1 = 2^0 + 0x5 = 2.0x0.5, 2 = 2 + 0 + 0x5, 3 = -2 + 0 + 0 + 5, 4 = -2^0 + 0 + 5, 5 = 2x0 + 0 + 5, 6 = 2^0 + 0 + 5, 7 = 2 + 0 + 0 + 5; I got stuck a this point!

  • 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

  • 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

  • Game Tree

    Player 1

    Player 2

    Player 1

    Player 2

    Player 1

  • Some Surprising Predictions

    Answer 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 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 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

    Math has many uses in geography. This lesson focuses on the relationship of math to making and using maps.

    Orange kangaroo from Denmark

    Orange kangaroo from Denmark

    This puzzle becomes more or less difficult, depending on your birth year. It is pretty simple for most years. However, for someone born in 2005, it is hard: 0 = 2x0 + 0x5, 1 = 2^0 + 0x5 = 2.0x0.5, 2 = 2 + 0 + 0x5, 3 = -2 + 0 + 0 + 5, 4 = -2^0 + 0 + 5, 5 = 2x0 + 0 + 5, 6 = 2^0 + 0 + 5, 7 = 2 + 0 + 0 + 5; I got stuck a this point!

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