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Math Help - Quickie #5

  1. #1
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    Quickie #5

    In the following cryptarithm, each letter represents a distinct digit (base 10):

    . . . . . 7(FRYHAM) \:=\:6(HAMFRY)

    Identify the digits.
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  2. #2
    Senior Member OReilly's Avatar
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    Quote Originally Posted by Soroban View Post
    In the following cryptarithm, each letter represents a distinct digit (base 10):

    . . . . . 7(FRYHAM) \:=\:6(HAMFRY)

    Identify the digits.
    7(461538)=6(538461)
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  3. #3
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    Hello, OReilly!

    Your solution is correct.

    You offer no explanation . . . did you use some software?

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  4. #4
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    Hey Soroban:

    I scratched my head on this one for a while.

    One could tackle this in many ways, but if we let FRY=f and HAM=h, then

    we can whittle it down to something easier to solve.

    Then we have:

    7(1000f+h)=6(1000h+f)

    7000f+7h=6000h+6f

    6994f=5993f

    gcd(6994,5993)=13. Divide through by 13.

    538f=461h

    Now, the ol' switcharoo.

    I was amazed this actually worked.

    I didn't see the very last part right away.

    Because we can switch them around and have 538461 and 461538

    7(461538)=6(538461)
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  5. #5
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    Quote Originally Posted by Soroban View Post
    In the following cryptarithm, each letter represents a distinct digit (base 10):

    . . . . . 7(FRYHAM) \:=\:6(HAMFRY)

    Identify the digits.
    Hello Soroban,

    your problem needs "nothing else" but counting. So I wrote a small program (see attachment) and the result popped up rather immediately. There isn't any mathematical thinking or deduction involved so I didn't dare to publish my "solution". so this post is only for the records.

    EB
    Attached Thumbnails Attached Thumbnails Quickie #5-fryham.jpg  
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  6. #6
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    Lovely, Galactus!

    That is exactly the Quickie solution.


    Punchline: .Your final equation was: . 538f = 461h

    Since 638 and 461 are relatively prime (you already divided out the GCD),
    . . the only solution in positive integers is: . f = 461,\:h = 538

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  7. #7
    Eater of Worlds
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    Smile

    Quote Originally Posted by Soroban View Post
    Lovely, Galactus!

    That is exactly the Quickie solution.


    Punchline: .Your final equation was: . 538f = 461h

    Since 638 and 461 are relatively prime (you already divided out the GCD),
    . . the only solution in positive integers is: . f = 461,\:h = 538

    Even a blind hog finds an acorn once in a while.
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