1. How many times will a three-digit number increase if the same number is appended to it?
1. Let's write down a random three-digit number (531) and append the same number to it, resulting in -531531. Let's find their quotient:

$$
531 \times 531: 531=1001
$$

The pattern found is also valid for other three-digit numbers.

Answer: The three-digit number will increase by 1001 times.