The answer for this question has a directly connect port being blocked. the connection from sw1 back to the root switch sw3. I thought each path from the root switch that is directly connected to the root is marked as a root port, and the election for the other ports of the non root switch would make a selection to forward or block. what am I missing?
This is a tricky question, you have to realize that each switch will set its own blocking and forwarding state based on it's place in the network. Think about it like this:
SW1-B--------------------SW2 SW3 is the root bridge so all of it's links are in the designated state, including the 100Mb/s link. Remember
B + + B the STP cost numbers, 100Mb/s = 19, Gb/s = 4. If you add up the link from SW1 to SW3 the direct route is
| + + | 19. But the route that toes SW1-SW4-SW3 (4+4 = 8) and is lower then the direct link and will be used. The
| + + | goes for the link between SW1 and SW2, SW1-SW4-SW3-SW4 (4+4+4 = 12) vs the direct link cost of 19. Do
| + | numbers for the last one SW2 to SW4 and you'll see the lower cost is more hops.
| + + |
| + + | Then notice that the lower Router ID between two non-root bridges has the open port.
| + + |
SW3+++++++++++++SW4
----- & | = 100 MB/s
+++++ = 1 Gb/s
B = Blocking state