A meeting of number family

Logic Level 4

Find the smallest 5-digit-integer NN so that 2N2N is also a 5-digit-integer and all digits 0,1,2,3,,9 0, 1, 2, 3,\ldots,9 contain in both NN and 2N2N.

Note: Each number, NN and 2N2N must contain 5 distinct digits and all the digits in NN must different from those in 2N2N.


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