4. Dima recorded his digital password in code: P, AR, AK, RU, SS. The key to the code: different digits are represented by different letters, and the same digits by the same letters, two letters together represent a two-digit number, numbers are separated by commas, the difference between any two adjacent numbers is the same (the right number minus the left number). Restore the password.
Answer: $5,12,19,26,33$.

Solution. All these numbers can be determined if we know the first number and the difference $d$ between two consecutive numbers. The first digits of the second and third numbers coincide, meaning they are in the same decade, and their difference, equal to $d$, does not exceed 9. Therefore, by adding $d$ to the first (single-digit) number, we can only get a two-digit number starting with 1, i.e., $\mathrm{A}=1$. Similarly, $\mathrm{P}=2, \mathrm{C}=3$, because in these cases, a number not exceeding 9 is added to a two-digit number, and the first digit increases by 1. We get the sequence: P, 12, 1K, 2V, 33.

Notice that $1 \mathrm{~K}-12=2 \mathrm{~V}-1 \mathrm{~K}=33-2 \mathrm{~V}=\mathrm{d}$. Adding these equations, we get: 33-12=3d, d=7. We have restored the last number and the difference. It is now easy to restore the sequence: 5, 12, 19, 26, 33.

Comment. 1 point for finding each of the digits A, P, C. 3 points for finding the difference $d$, 1 point for the final answer, points are cumulative. If the correct answer is found by trial and the uniqueness is not proven - 5 points. If the sequence: P, 12, 1K, 2V, 33 is justified, but trial is used afterwards - 6 points.