František Všímálek was writing down consecutive numbers from the multiplication tables of three, five, and nine. He did not leave spaces between the numbers and proceeded as follows: first, he wrote down the multiples of three, then immediately after the last of these, he started writing down the multiples of five, and finally the multiples of nine. He noticed that in his sequence, palindromic numbers appeared. (A palindromic number reads the same backward as forward, for example, 272, 3553, 98089.) František wrote down all palindromic numbers with three or more digits and arranged them in ascending order. Which number was in the third position in this sequence, and which was the last?

(L. Hozová)
František wrote the multiplication tables like this:

$$
3691215182124273051015202530354045509182736455463728190 .
$$

Symmetrical numbers in the multiplication table of three are 121, 151, 212, and 242. For the multiplication table of five, these are 101, 51015, 202, 52025, and others. For the multiplication table of nine, we observe the following numbers: 4554, 645546, 36455463, etc. Symmetrical numbers arranged in ascending order form the sequence

$$
\text{101, 121, 151, 202, 212, .., 09182736455463728190.}
$$

The third number in this sequence is 151 and the last one is 09182736455463728190.

Evaluation. 1 point for writing the sequence; 2 points for the number 151 in the third position; 3 points for the last number. If the student does not want to write the zero at the beginning of the number, then the last number will be 918273645546372819, which is also considered a correct solution.