See this: http://img26.picoodle.com/img/...

Kindly see the pic b4 answering

IBM has two offices; one in India and another one in USA. There are two service providers for those two countries and the
public ip for router 1 and router 2 is also entirely different since two different ISPs and two different NSPs. If the two
routers' ip addresses are not in a particular series, is it possible to have a VPN between those two offices? My friend told
that to have VPN between any two routers, the IPs should be in the same series and if he is right then how these two routers
have VPN to communicate since router 1 gets an IP from its respective ISP which is governed by APNIC and router 2 gets an IP
from its respective ISP governed by ARIN. Or will the APNIC and ARIN mutually agree to give the same series for these two
routers??

Note: Well, moreover, who is the default gateway most of the time, switch or router? or it is just an imaginery point where
datas comes in and goes out?? If so where does that imaginery point lie?

Well, I think you have a slight missunderstanding of VPN.

A VPN creates a tunnel, inside the existing connection. So the ISPs on either end make no difference at all to the system. The USERS routers at either end will create the VPN (not the providers) Once the VPN is established you have a private LAN between the two locations! (Notice, that is a LAN not WAN on either end!)

So forget the provider, the routers that have to have the same series are YOUR ROUTERS LANs which are behind the Providers on either end of the connections. The public IP's make no difference they are only used to establish the initial connection then its the VPN and Local Lan IP's that make the the VPN. The MAIN gateway will be whichever unit is designated as the gateway when setting up the VPN.