In a book written in 628 AD, there is also such a problem: "An experienced architect built a magnificent palace for the king, which has eight doors. Each time, one door, or two doors, or three doors... are opened. How many different ways are there to open the doors?"
The answer is 255.
$$
\begin{aligned}
C_{8}^{1} & +C_{8}^{2}+C_{8}^{3}+C_{8}^{4}+C_{8}^{5}+C_{8}^{6}+C_{8}^{7}+C_{8}^{8} \\
& =8+28+56+70+56+28+8+1 \\
& =255
\end{aligned}
$$