Task A-1.4. (4 points)

If we delete the units digit of a number, we will get a number that is 2010 less than the original number. What is the original number?
## Solution.

Let $x$ be the number obtained after deleting the last digit, and $n$ the deleted digit. We have

$$
10 x + n = x + 2010
$$

or

$$
9 x = 2010 - n
$$

Since $n \in \{0, 1, 2, \ldots, 9\}$, we can check all possible values for $n$ and by direct substitution, we find that $x$ is a natural number only for $n=3$.

From this, it follows that $x=223$, so the desired number is 2233.

Note. The solution to the equation $9 x = 2010 - n$ can also be obtained by considering the remainders when dividing by 9.