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Can you find the smallest positive number such that if you shuffle the digits of the number in a particular order, the shuffled number becomes twice the original number.

Source: http://gpuzzles.com/mind-teasers/very-hard-maths-riddle/

I understand the answer is $125874 => 251748$

$251748$ is twice the $125874$ and have same digits $1,2,4,5,7$ & $8$

but how to solve this non programmatic ?

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    $\begingroup$ One way is to play fool and answer it in base $2$. The answer becomes $01$, which turns $10$. ;) $\endgroup$ – user147444 May 5 '14 at 17:14
  • $\begingroup$ Or in base 8, where $52_8 = 2\cdot 25_8$. $\endgroup$ – MJD May 5 '14 at 17:19
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    $\begingroup$ It's odd that the answer has the same digits as 142857, which is well-known to have the same property. $\endgroup$ – MJD May 5 '14 at 17:23
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    $\begingroup$ Related: Regularities when $n$ and $2n$ contain the same digits $\endgroup$ – MJD May 5 '14 at 18:32
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I have a detailed solution to this problem written up on the math.SE blog.

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