On subnet masks:
Each of those 123 triplets represents a binary byte. Four triplets = 64 bits. That is how long every IPv4 address is.
The subnet mask defines your "subnet" - those bits of the IP address that must be constant for every device on your network. For a "Class C" subnet it is 11111111.11111111.11111111.00000000 - 24 1's followed by 8 0's.
This means that for devices to be on the same network, those first 24 bits of their addresses must all be the same, and the last 8 must be unique to each device.
This is the default mask for most routers, including yours. It means that the third "triplet", whether a 1 or a 2 or anything else (i.e. 001 or 002 but we don't bother to write leading zeroes), must be the same for all hosts.
Yes, you can change the mask to 255.255.0.0 (I think that makes it a "Class B" network), and big companies have to do that sort of thing. But it's probably easier and less confusing to do it the default way.
On printers and IP addressing
My network printer installed itself on the network automatically, I simply plugged in and switched on. In fact, it must reconnect every time it is switched on. My Linux box happily found it in several guises, one via its IP address, another via dnssd://[something.like.a.domain.name]/ which suggests to me that it is under the thumb of my router, which acts as a dhcp service and therefore manages my network settings for me, using dynamic IP addressing.
If I looked on successive days, I'd probably see different IP addresses. So I just installed the printer as dnssd://[something.like.a.domain.name]/ and I've not had a printer access problem since.
Static IP allocation? Why make a yoke for your own neck?
The eternal help vampire