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Math Help - Find the code

  1. #1
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    Smile Find the code

    hi
    In a library,books are being coded with this method AAA, AAB,...,AAZ, ABA, ABB, ..., ABZ, ACA, ...
    What is the code of the 8273(th) book ?
    i followed some hints,and i found the code  MGE (Euclid's division)
    is it correct ?
    is there any other way to solve this problem ? because i don't understand how the Euclid's division helps find the solution
    thanks a lot.
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  2. #2
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    Hello, Raoh!

    In a library, books are being coded with this method:
    . .  AAA, AAB \hdots AAZ,\;ABA, ABB \hdots  ABZ,\;ACA,ACB \hdots ACZ,\;\hdots ZZZ

    What is the code of the 8273^{rd} book?

    i followed some hints,and i found the code MGE (Euclid's division)
    Is it correct? . . I got {\color{blue}MFE}

    Is there any other way to solve this problem?
    Because i don't understand how the Euclid's division helps find the solution.

    We are working with three-digit "numbers", written in base-26,
    . . using the "digits": . A,B,C, \hdots Z

    With the Euclidean Algorithm, we have: . 8273 \;=\;(12)(6)(5)_{26} \;=\;MFE_{26}

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  3. #3
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    thanks a lot ( 3273^{rd} )
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  4. #4
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    Quote Originally Posted by Soroban View Post
    Hello, Raoh!


    We are working with three-digit "numbers", written in base-26,
    . . using the "digits": . A,B,C, \hdots Z

    With the Euclidean Algorithm, we have: . 8273 \;=\;(12)(6)(5)_{26} \;=\;MFE_{26}
    In base 26 notation it appears that
    A=0, B=1, C=2, D=3, E=4, F=5, G=6, ... ,M=12

    IF AAA identifies the first book:
     A \times 26^2 + A \times 26^1 + A \times 26^0 = 0
    The first book has serial number equivalent to zero.

    The 8273rd book should therefore should have a serial number equivalent to 8272.


     12 \times 26^2 + 6 \times 26^1 + 4 \times 26^0 = 8272

    12 = M
    6 = G
    4 = E

    If I were doing the coding,
    the 8273rd book would have code: MGE
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  5. #5
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    thanks a lot,i was searching for an explanation like that,very well indeed
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