You administer the private network 192.168.10.0 and must subnet it to support up to 12 hosts per subnet while maximizing the number of subnets. Which subnet mask should you choose (standard IPv4 addressing, network and broadcast excluded)?

Introduction / Context:
Subnet design balances two goals: providing enough host addresses in each subnet and creating as many subnets as possible from a given block. Here the base block is 192.168.10.0/24 and each subnet must support up to 12 hosts.

Given Data / Assumptions:

• Base network: 192.168.10.0/24.
• Required: at least 12 usable host addresses per subnet.
• Objective: maximize number of subnets.
• Usable hosts = total addresses per subnet − 2 (network and broadcast).

Concept / Approach:
For a /n mask, total addresses per subnet are 2^(32 − n). Usable hosts are that total minus 2. We must find the smallest subnet that still gives ≥ 12 usable hosts; that choice maximizes the number of subnets within the /24 space.

Step-by-Step Solution:
Check /29 (255.255.255.248): 2^(32−29) = 8 total → 6 usable (too few).Check /28 (255.255.255.240): 2^(32−28) = 16 total → 14 usable (meets ≥ 12).Check /27 (255.255.255.224): 32 total → 30 usable (meets, but larger than needed, so fewer subnets).Therefore choose /28 to maximize subnets while meeting host requirement.

Verification / Alternative check:
In a /24, /28 yields 16 addresses per subnet and 14 usable. The /24 can be divided into 16 such subnets (0, 16, 32, …, 240). A /27 would produce only 8 subnets; a /26 only 4. Thus /28 best satisfies “maximum subnets.”

Why Other Options Are Wrong:
255.255.255.248 (/29): Only 6 usable hosts; fails the ≥ 12 requirement.

255.255.255.224 (/27): Works, but produces fewer subnets than /28.

255.255.255.192 (/26): Far more hosts than needed; fewest subnets among listed valid masks.

255.255.255.252 (/30): Only 2 usable hosts; typical for point-to-point links.

Common Pitfalls:
Forgetting to subtract network and broadcast when counting usable hosts; mixing up total vs usable; choosing a larger subnet than necessary, which reduces how many subnets you can create.

Final Answer:
255.255.255.240 (/28)