2. A natural number, not ending in zero, had one of its digits erased. As a result, the number decreased by 6 times. Find all numbers for which this is possible.
Answer: 108 or $12a$ when $a=1,2,3,4$.

Solution. Let's represent the original number in the form $m+10^{k} a+10^{k+1} n$, where $a$ is a decimal digit, and $k, m, n$ are non-negative integers, with $m>0$, otherwise $m=0$ and $n=a=0$. Then the equation will take the form $m=10^{k-1}(2a+8n)$. By the condition, the number $m$ does not end in 0 and therefore is not divisible by 10. Thus, $k=1$ and $m=2a+8n$, with $m<10$. Therefore, there are two cases.

1) $n=0$. Then $m=2a$, and the original number is $12a$, where $a \in\{1,2,3,4\}$.
2) $n=1$. Then $a=0, m=8$, and the original number is 108.