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 ?

  • 5
    One way is to play fool and answer it in base $2$. The answer becomes $01$, which turns $10$. ;) – user147444 May 5 '14 at 17:14
  • Or in base 8, where $52_8 = 2\cdot 25_8$. – MJD May 5 '14 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 '14 at 17:23
  • 2

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

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