A meeting of number family

Logic Level 4

Find the smallest 5-digit-integer \(N\) so that \(2N\) is also a 5-digit-integer and all digits \( 0, 1, 2, 3,\ldots,9\) contain in both \(N\) and \(2N\).

Note: Each number, \(N\) and \(2N\) must contain 5 distinct digits and all the digits in \(N\) must different from those in \(2N\).


This problem is a problem in USAMTS (USA Mathematical Talent Search) contest.
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