Host capacity on a /29 LAN — include the router interface in the count A router interface is configured 192.168.192.10/29. Counting all usable IPs on that LAN, including the router interface itself, how many hosts can be addressed on this /29 segment?

Introduction / Context:Small subnets such as /30 and /29 are common on WAN links and access segments. You must know exactly how many usable host addresses each mask provides to avoid over-subscribing a subnet or wasting address space.

Given Data / Assumptions:

• Prefix length /29 means mask 255.255.255.248.
• Usable host count follows 2^h − 2, where h is the number of host bits.
• The question explicitly includes the router interface in the total.

Concept / Approach:For /29, host bits h = 32 − 29 = 3. Therefore, usable hosts = 2^3 − 2 = 8 − 2 = 6. This total includes any router interface addresses and all attached host devices. The network and broadcast consume the two excluded addresses in each /29 block of 8 addresses.

Step-by-Step Solution:Compute host bits: h = 3.Compute usable hosts: 2^3 − 2 = 6.Confirm that 192.168.192.8/29 spans .8–.15 with usable .9–.14, which contains .10.Therefore, total usable addresses on that LAN (including the router) = 6.

Verification / Alternative check:Block size for /29 is 256 − 248 = 8 addresses per subnet. Usable = 8 − 2 = 6 corroborates the formula above.

Why Other Options Are Wrong:

• B/D: 8 or 32 count total addresses in unrelated masks or fail to exclude network/broadcast.
• C: 30 is the /27 usable count.
• E: 4 corresponds to /30 (2 usable hosts).

Common Pitfalls:Confusing “hosts total” with “usable hosts,” and forgetting that the question includes the router interface in the same count.

Final Answer:6