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How to determine the base of a Number given a problem? |
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| Aug23-04, 08:10 PM | #1 |
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How to determine the base of a Number given a problem?
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. |
| Aug23-04, 08:21 PM | #2 |
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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".
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| Aug23-04, 10:32 PM | #3 |
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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] |
| Aug23-04, 10:44 PM | #4 |
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How to determine the base of a Number given a problem?
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. |
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