Bdtyktl

Please be patient with me, I am new to networking and trying to understand. So, we have 3 computers with the same subnet mask, 255.255.255.0 and the same default gateway, 192.168.12.1 connected to a switch, and the first two have the same network address and the third one, a different network address, 192.168.12.113, 192.168.12.205, 192.168.112.97. Can these computers communicate with each other? If not, why not?

The third will not be able to communicate with the first ones without the help of a router or additional configuration.

The reason is that the first two won't try to reach the third by broadcast because it is not in their subnet and the reverse applies as well.

Is there a particular reason why you configure different networks if you want them to communicate?

The answer is no. Because current subnet configuration allows only 192.168.12.. If computer 192.168.112.97 have additional network interface with IP in 192.168.12. subnet, then yes.
Or if change mask.

Hosts within same subnet will communicate directly; that's what a subnet means. So I assume your question is about hosts that belong to different subnets, such as 192.168.12.205 and 192.168.112.97.

Technically, being on the same switch all of them are capable of communicating directly at Ethernet layer. If host A sends Ethernet frames with destination = host B, it will succeed. However, the IP layer doesn't know this, because the subnet mask tells it otherwise – so the hosts will not attempt direct communication and will need a router by default.

(In other words: Ethernet link creates the possibility of direct communication, IP configuration informs the host that such possibility exists.)

But it is possible to inform the IP stacks that direct communication is possible even to hosts within a different network address, by adding custom routes to each host's routing table. These would have to be "link" routes, specifying just the interface but not a gateway. (That's actually what the subnet mask does; it creates a link route.)

ip route add 192.168.112.0/24 dev eth0