Find mask to meet a subnetting requirement

Question

I am currently trying to solve this question:

What mask would you use so that 172.27.0.0 can have 10 subnets with 3110 hosts each?

How can one reason about these type of questions?

My attempt: 172.27.0.0 implies 16 bits are already used for the network address?

To have 10 subnets, one would require ceil(log2(10)) = 4 bits.

To have 3110 hosts, one would require ceil(log2(3110)) = 12 bits, since 2**12 = 4096 > 3110 + 2.

Answer 1

1. Find base mask: 172.27.0.0 is a class B address, so the base mask is 16.
2. Find number of bit for subnets: For 10 subnets, one requires ceil(log2(10)) = 4 bits
3. Find number of bits for hosts: For 3110 hosts, one requires ceil(log2(3110)) = 12 bits, and it works since 2**12 = 4096 > 3110 + 2
4. Check feasibility: 12 + 4 bits = 16, so the requirement is feasible.
5. Calculate subnet mask: The subnet mask is the base mask + required bits for the subnets: 16 + 4 = 20

Final answer: 172.27.0.0/20