Why do we need to configure OSPF in all 3 routers in order for PC-A to ping PC-C?
Why is OSPF needed?
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If there was a connection between R1 and R3 you could use dynamic routing, such as OSPF, however, here on the left side there are only one innside router connected to ISP, and to the right there is one router talking to the ISP. -So OSPF will not help you in this case, unless ISP uses OSPF, witch is rare. Static routes may be best here.
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I don't think you'll be able to configure OSPF on the ISP router. Usually they won't allow you to configure IGP to an ISP. It is common to use EGP like BGP.