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Thread: 24x21 = 42x12

  1. #1
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    24x21 = 42x12

    24x21 = 42x12

    Can anyone see why the above works and are there any other examples?
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  2. #2
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    Re: 24x21 = 42x12

    $24 \times 21= (12 \times 2) \times 21 = 12 \times (2 \times 21) = 12 \times 42$
    There are infinitely many.
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  3. #3
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    Re: 24x21 = 42x12

    Ah i was more interested in finding different categories of

    abxcd = baxdc
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  4. #4
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    Re: 24x21 = 42x12

    10 > a,b,c,d > 0

    (10*a + b)*(10*c + d) = (10*b + a)*(10*d +c)

    Simplifies to: a*c = b*d
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  5. #5
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    Re: 24x21 = 42x12

    Quote Originally Posted by rodders View Post
    24x21 = 42x12
    Can anyone see why the above works and are there any other examples?
    $ \begin{align*}(24)~\times(21)&=~(42)\times(12)\\(2 ^3\cdot3)\times(3\cdot 7)&=~(2\cdot3\cdot7)\times(2^2\cdot3)\\\\(2^2\cdot 3^2)\times(2\cdot 7)&=~(7)\times(2^3\cdot3^2)\\\\(3^2)\times(2^3 \cdot 7)&=~(2\cdot7)\times(2^2\cdot3^2)\end{align*}$
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  6. #6
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    Re: 24x21 = 42x12

    DenisB was way ahead of me.
    Last edited by Archie; Mar 2nd 2018 at 06:05 AM.
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