Task 10.2. Given a natural number $n$. Roma wrote down three numbers $n, n+1, n+2$ on the board one after another, without spaces. He obtained a certain sequence of digits, in which there are consecutive digits 6474. Find the smallest possible value of $n$.
Answer: 46.

Solution. It is clear that for $n=46$ the condition is satisfied.

Suppose there exists $n<46$. One of the three numbers that Roma has should contain the digit 6, and for $n<46$, it must be in the units place. By a simple enumeration, one can verify that the corresponding values $n=4,5,6,14,15,16,24,25,26,34,35,36,44,45$ do not work.