On each kilometer of the highway between the villages of Yolkiino and Palkino, there is a post with a sign. On one side of the sign, it shows how many kilometers are left to Yolkiino, and on the other side, how many kilometers are left to Palkino. Borya noticed that on each post, the sum of all the digits is 13. What is the distance from Yolkiino to Palkino?
Let the distance from Yolkiino to Palkiino be $n$ kilometers. Clearly, $n \geq 10$. Moreover, $n \leq 49$ (otherwise, the sum of the digits on the 49th milestone would be greater than 13).

On the tenth milestone from Yolkiino, one side reads 10, and the other side reads $n-10$, which does not exceed 39. The sum of its digits is 12. Therefore, $n-10=39$ (the sum of the digits of smaller numbers does not exceed 11).