PAMO 2025 Problem 2

Let $x_1,x_2,\ldots,x_{20}$ and $y_1,y_2,\ldots,y_{20}$ be 2 sequences, so that each term of each sequence is either $0$ or $1$ . How many couples $((x_i),(y_i))$ where $i=1,2,\ldots,20$ of such sequences exist such that $$x_1y_1+x_2y_2+\ldots+x_{20}y_{20}$$ is an even number ?