What?! Is that even possible?!

Let \(d(n)\) be the set of digits of \(n\). Find the minimum of \(n\) that satisfies

  • \((1): 10^{5} \leq n \leq 10^{6}\)
  • \((2): |d(n)| = |d(2n)| = |d(3n)| = |d(4n)| = |d(5n)| = |d(6n)| = 6\)

Details:

  • If \(A\) is a set, then \(|A|\) is the number of elements in set \(A\).
  • This problem is from Thailand POSN, which is held today. XD
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