How to calculate the resistance of a complicated circuit?
That's simple: in high school they did not tell you the bad part of the story: Y-\$\Delta\$ transform.

The series parallel technique works well... Almost in all cases, but when you need to solve such a bad guy then you need to use all your weapons. You should read the wikipedia article, anyway given a three impedances circuit, either arranged as a star, i.e. a central node common only to the impedances and three external nodes, or as a triangle, i.e. three nodes where only two of the tree impedances connects, it is possible to transform it in the other fashion, that is transform a triangle in a star and vice versa. The formulas are all written on wikipedia, I am not copying them here, the interesting part is that with series, parallel and Y-\$\Delta\$ transforms you can solve almost any network.

In your particular case you'd trasform the ABD triangle in a star with tips in ABD and center c (that's a new node), then compute the series cA->AC and cD->DC and then the series Bc->cC. If you write it down you'll grasp this in seconds.

There also is another transform called star-mesh transform, which is a generalization of the Y-\$\Delta\$ transform. Please note that with more than three impedances, that is our case of interest, the transform is not reversible since it results in an increased number of impedances.