You have network 192.168.10.0 and need at least 25 usable host addresses per subnet while maximizing the number of subnets. Which subnet mask should you choose?

Introduction / Context: Subnet design balances host capacity and number of subnets. Given a Class C-like private block 192.168.10.0, we must pick a mask that provides at least 25 usable hosts in each subnet and yields the greatest number of such subnets.

Given Data / Assumptions:

• Network: 192.168.10.0/24 as the starting block.
• Required usable hosts per subnet: ≥ 25.
• Goal: maximize number of subnets.

Concept / Approach: For a /27 mask (255.255.255.224), each subnet has 32 addresses total and 30 usable (subtract network and broadcast). For a /28 (255.255.255.240), there are 16 total, 14 usable—insufficient. A /26 (255.255.255.192) has 62 usable but halves the number of subnets compared to /27.

Step-by-Step Solution: Check /28: 2^(32-28) = 16 total, 14 usable < 25 → invalid.Check /27: 2^(32-27) = 32 total, 30 usable ≥ 25 → valid.Between valid candidates, choose the one that yields more subnets (/27 over /26).

Verification / Alternative check: Subnet counts in a /24: /27 yields 8 subnets (0,32,64,96,128,160,192,224), each with 30 usable; /26 yields 4 subnets with 62 usable—fewer subnets than /27.

Why Other Options Are Wrong: 255.255.255.192 (/26): Meets hosts but fewer subnets than /27.

255.255.255.240 (/28): Only 14 usable, below 25.

255.255.255.248 (/29): Only 6 usable, far below requirement.

255.255.255.255 (/32): Single host route, not a subnet mask for multiple hosts.

Common Pitfalls: Forgetting to subtract 2 addresses per subnet for network and broadcast; mixing up total vs usable host counts.

Final Answer: 255.255.255.224