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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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4  
One way is to play fool and answer it in base $2$. The answer becomes $01$, which turns $10$. ;) –  user147444 May 5 at 17:14
    
Or in base 8, where $52_8 = 2\cdot 25_8$. –  MJD May 5 at 17:19
1  
It's odd that the answer has the same digits as 142857, which is well-known to have the same property. –  MJD May 5 at 17:23
2  

1 Answer 1

I have a detailed solution to this problem written up on the math.SE blog.

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