66. After the tourists have walked 1 km and half of the remaining distance, they still have to walk a third of the entire distance and 1 km. What is the total distance?
66. After the tourists have walked 1 km, half of the remaining distance is one third of the entire distance plus 1 km, which means the entire remaining distance is $\frac{2}{3}$ of the entire distance plus 2 km. Thus, the entire distance is $\frac{2}{3}$ of the entire distance plus $2+1=3$ (km), which means 3 km is $\frac{1}{3}$ of the entire distance $\left(1-\frac{2}{3}=\frac{1}{3}\right)$. Therefore, the entire distance is 9 km $(3 \cdot 3=9)$.