Xmania Math Asignment?

This is my whole entire assignment: I dont want the answers necessarily, I just would like a boost to get me going. I do know the number system is base 5.

The Story: We are suddenly in a different place and time - in Xmania. The system of counting (sheep, rocks, etc.) has been "A, B, C, D" and anything more than "D" is "many." As Xmanians became more prosperous, there was a need to count higher than D. There was a young mathematician working on expanding the counting system, but unfortunately she was eaten by a bear before she presented her idea to the council. All that was found in her cave were a string of symbols.

The string: E A B C D AE AA AB AC AD BE BA BB BC BD CE CA CB CC CD DE DA DB DC DD AEE AEA AEB AEC AED

1. Can you determine the counting system the mathematician was working on? Prepare a powerpoint presentation of the system for the council. (remember that you are in another place and time You do not have words like "one, two, or tens.")

2. The council wants to be able to calculate with the new system. Can you solve these problems in the new system? (You must stay within Xmanian to solve these problems.)

2a. Mok has BBC sheep and Tok has DEA. Who has more sheep? How many more? Explain.

2b. Suppose Mok buys B sheep every day for AE days and Tok sells C sheep every day for D days. After all transactions are complete, who has more sheep? Explain?

2c. Lok is getting old and wants to leave her sheep to her children. She has DBC sheep and C children. Can she leave an equal number of sheep to each child? Explain.

3. BONUS: The mathematician seemed to have been working on a research paper before she was eaten, but unfortunately all that was found was a scrap of paper that read:

...ume that the sum of the numerals is divisable by D, then the number itself is divisable by D.

Proof: Given any numb...

What was she trying to prove? Can you complete the proof?

2 Answers

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  • 8 years ago
    Best Answer

    hopefully you've worked this out, but basically E=0, A=1, B=2... but as u said you're working with a base 5 number system. and you can't use normal numbers for your explanation for ques. 1

    2a

    Tok has more. since both are the same number of digits, look at the most left digit and D > B

    now to substract:

    CD this is since C>A

    DEA

    - BBC

    = ABB

    so, starting on the right, originally A>C so you carry over one digit from the place next to it (but the E is equivalent to 0 so carry over again from the next place) so the first 2 digits of the top number kind of become CD and then for the right hand most digit u basically want to substract C from AA which gives B. for the other 2 digits just subtract BB from CD (instead of DE since you had to carry over one to the right hand digit) giving you ABB

    2b

    first u need to multiply B and AE

    first multiply B and E and it gives you E (since E is basically 0)

    then B times A and put that number in the digits place second from the right.

    B x A = B

    so B x AE = BE

    then u need to subtract BE from Mok's original BBC

    starting from the right hand most digits

    C - E = C (since E is 0)

    B - B = E

    B - nothing = B

    so BBC - BE = BEC

    i hope you can use these concepts to get you throught the rest. hope it helps

    Source(s): I've done Calculus AP
  • 3 years ago

    Xmania

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