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Without a router: 1

With a router: 253+....

With the exception that your router(Or network switch) doesn't run out of ports; In which case you just add in another network switch & daisy chain it either via uplink port or any free ethernet port. Make sure that you obtain a network SWITCH & not a network HUB as hubs devide bandwidth for every item you plug into the hub(Affects LAN speed & network latency) & switches always run at the full line speed.

Some routers have multiple LAN ports & some take it even further so that it lets you assign what ports will do what(e.g. WAN, LAN, LAN2, LAN3...) This allows for multiple sub-nets.

So lets say that your external ip is: 0.0.0.0 for visualization purposes....

Your routers main LAN or internal IP is: 192.168.0.1

You can have 253 clients or PC's on the 192.168.0.2-192.168.0.254 address range.

Your routers secondary LAN IP is: 192.168.1.1

You can have 253 clients or PC's on the 192.168.1.2-192.168.1.254 address range.

Your routers tertiary LAN IP is: 192.168.2.1

You can have 253 clients or PC's on the 192.168.2.2-192.168.2.254 address range.

You can theoretically keep going in this fashion to build your own local Intranet(Local version of internet) But does not require registering with RIPE or any other Regional Internet Registries.

The reason you can't have 192.168.x.1 or 192.168.x.255 is because they are already assigned. 192.168.x.1 is the routers internal IP & it is also used by DHCP & other services within the router. 192.168.x.255 is the rebroadcast IP address per subnet.

In fact I believe this also applies to Internet IP address; You won't ever see 255 or 1 at the end of your external IP.

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Q: How many PC on internet through one modem can you use?
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