Task 1. How many three-digit numbers are there that read the same from left to right and from right to left?
Solution. First method. Since the three-digit number must be read the same from left to right and vice versa, the first and third digits must be the same, i.e., the number is of the form $\overline{x y x}$. The first digit in a three-digit number cannot be zero, so $x$ can be one of the numbers $1,2,3,4,5,6,7,8$ or 9, i.e., there are 9 possibilities in total. The middle digit $y$ can be zero, i.e., one of the digits $0,1,2,3,4,5,6,7,8$ or 9, meaning there are 10 possibilities in total. Therefore, there are $9 \cdot 10=90$ such numbers.

Second method. The student can also try to list the numbers. If they list some of them, they get 10 points, and if they list all 90 numbers, they get all 20 points.