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Math Help - Long division with letters problem

  1. #1
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    Long division with letters problem

    Hi,

    I have found a long division problem and I am getting stuck with the solution, to be honest i dont even know where to start!!

    (The . above the X is not for recurring numbers, it is just there so the top line of the division sits correctly)

    The question is: solve the following long division, each letter represents a unique digit (0-9)

    Code:
    .      B
    XZD)BUMG
        APZK
         ABU
    Thanks for your help
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  2. #2
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    I don't quite get you.
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  3. #3
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    Quote Originally Posted by MysticGenius View Post
    Code:
    .      B
    XZD)BUMG
        APZK
         ABU
    You should notice stuff like B > 1 , B = A + 1, B * XYD > 999, ...

    HINT: XZD = 934
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  4. #4
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    Quote Originally Posted by Wilmer View Post
    You should notice stuff like B > 1 , B = A + 1, B * XYD > 999, ...

    HINT: XZD = 934
    Thanks very much for this but i still do not follow how you got XZD=934..

    please can you elaborate?

    Thanks in advance

    MG
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  5. #5
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    Trial and error, after establishing some reasonable ranges...

    Only 2 equations given:
    B(100X + 10Z + D) = 1000A + 100P + 10Z + K

    1000B + 100U + 10M + G - (1000A + 100P + 10Z + K) = 100A + 10B + U

    With 10 variables, you'd need 10 equations to "solve"; so some guesswork required.

    These are known as "alphametic puzzles". Use google to see examples.
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  6. #6
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    Quote Originally Posted by Wilmer View Post
    Trial and error, after establishing some reasonable ranges...

    Only 2 equations given:
    B(100X + 10Z + D) = 1000A + 100P + 10Z + K

    1000B + 100U + 10M + G - (1000A + 100P + 10Z + K) = 100A + 10B + U

    With 10 variables, you'd need 10 equations to "solve"; so some guesswork required.

    These are known as "alphametic puzzles". Use google to see examples.
    Hi,





    thanks for that, I have looked through google and there is no real explanation on this just a load of solutions to common puzzles.

    based on the assumption you have solved this and have showed what XZD is, please can you show me how you got that?

    thanks
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  7. #7
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    I wrote a looper program.

    Full solution: 7210 / 934 = 7 remainder 672
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  8. #8
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    Quote Originally Posted by Wilmer View Post
    I wrote a looper program.

    Full solution: 7210 / 934 = 7 remainder 672
    sounds interesting, can you share this with me?

    i was actually hoping for the workings, as I actually want to know how to do this - Can someone show me how to do this by hand?

    Thanks
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  9. #9
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    Changed your lettering to a to j:
    Code:
           a
        ====
    bcd)aefg
        hicj
        ====
         hae
    My program (simplified):
    Loop 10 variables a to j from 0 to 9 keeping the variables distinct
    Keep a > 1, h = a-1, b > 0

    u = 100*b + 10*c + d
    v = 1000*a + 100*e + 10*f + g
    w = 1000*h + 100*i + 10*c + j
    x = 100*h + 10*a + e

    If w = a * u and x = v - w then print a,u,v,w,x

    Result: 7, 934, 7210, 6538, 672

    I don't think anybody can show how to do this completely by hand,
    as it's a bit like teaching how to dig a hole
    But you never know: perhaps someone can...but won't be me!
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  10. #10
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    Quote Originally Posted by Wilmer View Post
    Changed your lettering to a to j:
    Code:
           a
        ====
    bcd)aefg
        hicj
        ====
         hae
    My program (simplified):
    Loop 10 variables a to j from 0 to 9 keeping the variables distinct
    Keep a > 1, h = a-1, b > 0

    u = 100*b + 10*c + d
    v = 1000*a + 100*e + 10*f + g
    w = 1000*h + 100*i + 10*c + j
    x = 100*h + 10*a + e

    If w = a * u and x = v - w then print a,u,v,w,x

    Result: 7, 934, 7210, 6538, 672

    I don't think anybody can show how to do this completely by hand,
    as it's a bit like teaching how to dig a hole
    But you never know: perhaps someone can...but won't be me!
    Thanks so much...can i ask what software you used? was it matlab?

    MG
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  11. #11
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    I use UBasic, and do the programming myself; here tizz:

    FOR a = 2 TO 9
    FOR b = 1 TO 9 : IF b = a THEN NEXT b
    FOR c = 0 TO 9 : IF c = a OR c = b THEN NEXT c
    FOR d = 0 TO 9 : IF d = a OR d = b OR d = c THEN NEXT d
    u = b*100 + c*10 + d
    FOR e = 0 TO 9 : IF e=a OR e=b OR e=c OR e=d THEN NEXT e
    FOR f = 0 TO 9 : IF f=a OR f=b OR f=c OR f=d OR f=e THEN NEXT f
    FOR g = 0 TO 9 : IF g=a OR g=b OR g=c OR g=d OR g=e OR g=f THEN NEXT g
    h = a-1 : IF h=b OR h=c OR h=d OR h=e OR h=f OR h=g THEN NEXT g
    v = a*1000 + e*100 + f*10 + g
    x = h*100 + a*10 + e
    FOR i=0 to 9: IF i=a OR i=b OR i=c OR i=d OR i=e OR i=f OR i=g OR i=h THEN NEXT i
    FOR j=1 to 9: IF j=a OR j=b OR j=c OR j=d OR j=e OR j=f OR j=g OR j=h OR j=i THEN NEXT j
    w = h*1000 + i*100 + c*10 + j
    IF w = a*u AND x = v - w THEN PRINT a,u,v,w,x
    ENDLOOPS

    Hope that helps.
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