Find the equivalent resistance for the circuit shown above.

Note that the 4 and 5 are NOT in parallel because the 2 and 8 are in between. The 1 and 2 are NOT in series because the 4 is in between. The 1 and 7 are NOT in parallel because the 4 is in between. The only combination you can make (at first) is the 3, 6, and 9 are in series, so:

Now the 5 and 18 are in parallel:

The 2, 3.9, and 8 are in series:

The 4 and 13.9 are in parallel:
Finally, all three are in series

Req = 1 + (4 || {2 + [5 || (3+6+9)] + 8}) + 7

= 11.1 ohms