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How to determine the base of a Number given a problem?

  1. Aug 23, 2004 #1
    The problem is a follows

    142 alpha 214 = 331
    and
    431 beta 123 = 303

    where alpha and beta are unknow operators

    I am pretty sure they are +,-,*,/

    I know the radix (base) must be 5 or higher because 4 is present

    By assuming the base to be 5 and converting to decimal, I discover beta = - and the base is indeed five. But if I convert the first part the first part to decimal useing base 5 the answer is wrong.

    It is possible I copied the problem incorrectly

    In general, my question is, how to determine the base to a number system given a problem similiar to the one above.
     
  2. jcsd
  3. Aug 23, 2004 #2

    HallsofIvy

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    The only way I could think of is to TRY various bases, various operations and SEE which one works. Somethime the best way to solve a problem is actually do all the "donkey work".
     
  4. Aug 23, 2004 #3

    Gokul43201

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    If you are restricted to just the +/- operations, you can rewrite the problem in term of two unknowns (if alpha, beta are given to be distinct; else three unknowns). Let the base be 'b' :

    [tex](2+4b+b^2) + (-1)^n (4+b+2b^2) = 1+3b+3b^2[/tex]

    and [tex] (1+3b+4b^2) + (-1)^m (3+2b+b^2) = 3+3b^2~~~n,m ~\epsilon~ {0,1}[/tex]
     
    Last edited: Aug 23, 2004
  5. Aug 23, 2004 #4

    Gokul43201

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    Here's another thing to notice ...and this, in conjuction with the above type of method, gives you a solution.

    <small number> alpha <large number> =<larger number>, all numbers positive

    So alpha must be addition or multiplication. But the number of digits of LHS and RHS are the same (three), so it must be addition. By a similar reasoning, beta is subtraction.

    Thus, you copied the problem down incorrectly.
     
    Last edited: Aug 23, 2004
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