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Handout #7

Thu= rsday, November 09, 2006

    Problem 1

    Imagine that you are the king (or the queen) of a small country where no number sy= stem exists. Ambassadors from Egypt and Greece have arrived to greet you and tr= y to convince to adopt their number systems because it will be much easier to t= rade with your country if you do. Go over all the facts you know about both sys= tems and compare them. Which one would you choose?

    Results of your research put in a table similar to this one:

     

    Egyptian

    Greek

    Is it easy = to learn?

     

     

     

    Are there a= ny limitations?

     

     

     

    Which of th= em is more efficient notation?

     

     

     

    Is it conve= nient to compare numbers ("at a glance")?

     

     

     

    Is it conve= nient to perform addition / subtraction?

     

     

     

    Anything el= se?

     

     

     

     

    Problem 2

    No matter which system you'd choose one of the ambassadors is going to be offended and a war with his country might begin. You've called up the coun= cil of wise men in your government and asked them for advice. After thinking f= or a while one of the men suggested to create a new system by mixing up those t= wo and still keeping most advantages of both of them.

    What might have been the wise man's idea?

     

     Problem 3

    Describe the rules for conversion between this new system and the Greek and Egyptian systems. Demonstrate the rules on at least 5 examples.

     

     Problem 4

    Rabbit knew that Winnie-the-Pooh would visit him today and decided to hide his la= st jar or honey. He took three boxes of different colors, put the honey into = one of them and made the following notes on the lids:

    Red box

    There is no= honey here

    Blue box

    Honey is he= re!

    Green box

    Honey is in= the blue box

    Rabbit was cheating so only one of the notes is true. In which box Winnie-the-Pooh should look for the honey?

     

     

 

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