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Question

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 ?

One way is to play fool and answer it in base $2$. The answer becomes $01$, which turns $10$. ;) — , May 05 '14 at 17:14
It's odd that the answer has the same digits as 142857, which is well-known to have the same property. — MJD, May 05 '14 at 17:23
Related: Regularities when $n$ and $2n$ contain the same digits — MJD, May 05 '14 at 18:32

score 9 · Answer 1 · answered Jun 12 '14 at 00:49

9

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

answered Jun 12 '14 at 00:49

MJD

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