3. Let's call a four-digit number accompanying the year $\overline{20 a b}$ if it also ends in $\overline{a b}$ and, in addition, is divisible by $\overline{a b}$ (a two-digit number), for example, the number 4623 accompanies the year 2023. How many numbers accompany the year $2022?$
Solution. $\overline{m n 22}=\overline{m n} \cdot 100+22 \Rightarrow \overline{m n} \cdot 100: 22 \Rightarrow \overline{m n}: 11: 11,22,33,44,55,66,77$, 88,99 - 9 numbers.

Answer 9.

## Grading Criteria.

Correct answer with valid reasoning - 7 points.

Valid reasoning for divisibility by 11 and description of the set of numbers, but incorrect answer - 5 points.

Valid reasoning for divisibility by 11 - 3 points.

Valid reasoning for divisibility by 22, leading to answers $22,44,66,88$ - 4 numbers - 1 point.

Incorrect solution or only the answer - 0 points.