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Handout #2

Thu= rsday, October 05, 2006

    Problem 1

    How two cavemen could compare who killed more bears if neither of them can cou= nt? (They have kept the score of the killed bears on the walls of their caves = by drawing a new picture of a bear after each successful hunt.)

     

    Those are Egyptian notation of numbers:

    Decimal

    Number

    Egyptian

    Symbol

     Name

    Decimal

    Number

    Egyptian

    Symbol

     Name

    1 =3D

    wa'

     

     

     

    10 =3D

    medj

    10,000 =3D

    djebe'

    100 =3D

    shet

    100,000 =3D

    hefen

    1000 =3D

    kha'

    1,000,000 =3D

    heh

     

    To write down= any other number they would combine as many characters as needed, e.g.:

    3 =3D

     

    30 =3D

    300 =3D

     

    3000 =3D

    12 =3D

     

    721=3D

     

    Problem 2

    Convert to Egyptian the following numbers:

    21

    371

    4 685

    901

    1 010 101

     

    Convert those Egyptian numbers to decimal:

     

     

    What's wrong with those two numbers?

     

     

     

    Problem 3

    Perform addition and subtraction of Egyptian numbers without(!) converting them to decimal:

     

     

    Problem 4

    Convert each of the numbers to Egyptian notation and multiply or divide it by two:=

    Number

    Operation

    Result

     

    Number

    Operation

    Result

    23

    *2

    =3D

     

    36

    /2

    =3D

    17

    *2

    =3D

     

    78

    /2

    =3D

    140

    *2

    =3D

     

    214

    /2

    =3D

    36

    *2

    =3D

     

    502

    /2

    =3D

    Do you think it's easier to perform these operations in decimal or in Egyptian notations?

     

     Problem 5

    How would you multiply by some other number in this system? What about 3, 5, 1= 0 or 12?

    Same question for division

     (optional) = Ask your parents to help you with a research on how did ancient Egyptians do multiplication of big numbers. You may check your local library or use Internet for this.

     

     Problem 6

    To paint a wooden cube all over Tom has spent 2 ounces of red paint. After th= at John sawed the cube into 8 smaller cubes (by the way, how could he do that= ?) and Tom had to paint the new sides of them green. How much of green paint = Tom had to use?

     

     Game of Nim

    This game is for two players. They arrange 12 stones into 3 rows on the table: = row with 3 stones, row with 4 stones and last row with 5 stones. In his/her tu= rn each player can take any number of stones from any of the rows, but only f= rom one row. The player who takes the last stone from the table wins.

 

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