Question 148
Initially the equation
$$
\star \frac{1}{x-1} \star \frac{1}{x-2} \star \frac{1}{x-4} \dots \star \frac{1}{x-2^{2023}} = 0
$$
is written on the blackboard. Asli and Zehra alternately make moves, Asli begins. A person making a move replaces one of the stars in the equation with either $+$ or $-$. What is the maximal number of real solutions of the obtained equation that Asli can guarantee, regardless of Zehra's strategy, after all the stars have been replaced?
$$
\star \frac{1}{x-1} \star \frac{1}{x-2} \star \frac{1}{x-4} \dots \star \frac{1}{x-2^{2023}} = 0
$$
is written on the blackboard. Asli and Zehra alternately make moves, Asli begins. A person making a move replaces one of the stars in the equation with either $+$ or $-$. What is the maximal number of real solutions of the obtained equation that Asli can guarantee, regardless of Zehra's strategy, after all the stars have been replaced?