This is one of the most difficult problems in network designing if you are not very careful. Otherwise, it is just a simple problem. But how a very difficult problem suddenly becomes simple? Because everything you design in networking will work. If your network was slow, one of the reasons could be that you were just a bad designer!
To prevent such issues, choosing the best summarization can help your network perform better.
The main idea of this problem is to combine all of these network IPs in one subnet. My initial guess of solving this problem is to use the subnets \(\displaystyle 0, 8, 16, 24, \cdots\)
What does this mean? It means that I will start with the network address \(\displaystyle 172.1.0.0\) so that the broadcast address will be \(\displaystyle 172.1.7.255\) and in this range I will contain all IPs in that network shown in the OP.
Let me make a table to plant the idea in your head in a nicer visualization.
Address\Subnet | 1 | 2 | Last Subnet |
|---|
Network Address | 172.1.0.0 | 172.1.8.0 | . . . . . |
First Host Address | 172.1.0.1 | 172.1.8.1 | . . . . . |
Last Host Address | 172.7.254 | 172.1.15.254 | . . . . . |
Broadcast Address | 172.7.255 | 172.1.15.255 | . . . . . |
As you can see subnet \(\displaystyle 1\) will contain all the IPs in the network. So my initial guess for the best summarization is a network address \(\displaystyle 172.1.0.0\) with a subnet mask \(\displaystyle 255.255.248.0\) which can be written more precisely as \(\displaystyle 172.1.0.0/21\)
I will talk more about subnet masks and this new precise notation in later posts.
Now after a little break, I have discovered that the network in the OP will not use the IP address \(\displaystyle 172.1.0.44\), for example. Since my new subnet design will include it, I have a flaw in the design which is there are a lot of IP addresses that will not be used. This is a waste of resources.
Therefore, I have to think of a better design (summarization). Now I am thinking of using the subnets:
\(\displaystyle 0,4,8,12, \cdots\)
My new table is:
Address\Subnet | 1 | 2 | Last Subnet |
|---|
Network Address | 172.1.0.0 | 172.1.4.0 | . . . . . |
First Host Address | 172.1.0.1 | 172.1.4.1 | . . . . . |
Last Host Address | 172.1.3.254 | 172.1.7.254 | . . . . . |
Broadcast Address | 172.1.3.255 | 172.1.7.255 | . . . . . |
Now as you can see my new design will use subnet \(\displaystyle 2\) which will contain all the IPs in the OP without wasting a single one. So my best summarization for the network in the OP is the network address \(\displaystyle 172.1.4.0\) with a subnet mask \(\displaystyle 255.255.252\) or just simply \(\displaystyle 172.1.4.0/22\)
