Vojta wrote the number 2010 a hundred times in a row without spaces. How many four-digit and how many five-digit palindromic numbers are hidden in this sequence? (A palindromic number is a number that reads the same backward as forward, e.g., 39193.)

(L. Hozová)
Vojta's notation starts like this: 2010201020102010 ... If Vojta wrote 2010 twice in a row, there would be one five-digit symmetrical number 20102 and one five-digit symmetrical number 10201 in the notation. If he wrote 2010 three times in a row, each of the above symmetrical numbers would appear twice. If we continue this reasoning, we find that when Vojta wrote 2010 a hundred times in a row, each of the mentioned symmetrical numbers appeared $99 \text{times}$, i.e., 99 times the number 20102 and 99 times the number 10201.

Thus, the notation contained $2 \cdot 99=198$ five-digit symmetrical numbers. There are no four-digit symmetrical numbers in the notation.