Question 127
Taja and Lili play a game in which there are 10 balls on the table, numbered with the natural numbers from $1$ to $10$. In the first move of the game Taja chooses a natural number $n$, and then the girls alternately take one ball each from the table until there are no balls left. Lili takes the first ball from the table and Taja takes the last one. The girl whose sum of the numbers on all her balls is closer to the number $n$ wins. Which girl has a winning strategy?