3. (8 points) There is a rope. The first time, fold it in the way shown in the left figure, and mark the fold (1). The second time, fold it in the way shown in the middle figure, and mark the folds (2) and (3) respectively; the third time, fold it in the way shown in the right figure. If the distance between point (2) and point (3) in the right figure is 20 cm, then the total length of the rope is $\qquad$ cm (assuming no gaps between the rope segments, and ignoring the thickness of the rope and any loss at the bends)


【Solution】Solution: From the second figure, we know: the distances from (1) to (2), (1) to (3), (2) to the endpoint, and (3) to the endpoint are all equal;
From the third figure, we know that the rope from (2) to the endpoint is divided into 3 equal parts.
Let each part be $x$, then the distance from (3) to the rope endpoint $=20+x$,
So $3 x=20+x, x=10$ (cm),
Then the distance from (3) to the rope endpoint is 30 cm,
The total length of the rope is $30 \times 4=120$ (cm).
Therefore, the answer is: 120.