4. Extreme set (from 6th grade, $\mathbf{1}$ point). From the digits 1 to 9, three single-digit and three two-digit numbers are formed, with no digits repeating. Find the smallest possible arithmetic mean of the resulting set of numbers.
Solution. Let the sum of the first digits of two-digit numbers be $n$, and the sum of the remaining digits be $k$. Then the arithmetic mean is $\frac{10 n+k}{6}$, and this number will be the smallest only if the sum $n$ includes the digits 1, 2, and 3, and the sum $k$ includes the digits from 4 to 9, regardless of the order. Then $\frac{10 n+k}{6}=\frac{60+39}{6}=16.5$.

Answer: $16.5$.