A six-digit number can be multiplied by three by reducing its first digit by three and appending a three at the end. Which number is this?

 

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Solution. Let the six-digit number be $x$. By reducing its first digit by 3, it means the number decreases by 300,000. Since we need to add a 3 at the end of the number, the place values shift one position to the left. Thus, we can write the following equality:

$$
3 x=(x-300000) \cdot 10+3 .
$$

From this, $7 x=2999$ 997, so $x=428571$ and $3 x=1285713$.