Problem 1. A six-digit number ends with the digit 5. If this digit is moved to the beginning of the number, i.e., it is deleted from the end and appended to the start of the number, then the newly obtained number will be 4 times larger than the original number. Determine the original number.
Solution. Let's denote the five-digit beginning of the original number with $x$, so the original number is equal to $10 x+5$. The newly obtained number can be written as $500000+x$, and from the condition of the problem, the equation $4(10 x+5)=500000+x$ is written. By solving the equation, we get that $x=128200$. Therefore, the original number is 128205.