\section*{Problem 6 - 021016}

Determine the smallest natural number \(n\) that has the following properties:

a) its decimal representation ends with the digit 6;

b) if this last digit 6 is removed and written as the first digit before the other unchanged digits, the result is four times the number \(n\).
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We know that the number \(n\) ends in 6. Therefore, the quadruple of \(n\) ends in 4. This is also the second-to-last digit of \(n\).

Since \(n\) ends in 46, the last two digits of \(4n\) are 84. Thus, \(n\) ends in 846. If we continue this method, we get the number 153846 for \(n\).