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Consider a very large network of 10000 routers.Two host A and B are connected to this network,host A sends data to host B and after some unit of time host A receives ICMP time exceeded message for the same data packet. The maximum number of routers that can be travelled by packets when ICMP message reaches back to HOST A ?
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With 8 bit TTL maximum 255 possible, so answer will be (255+254)= 509.
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Consider the small example:
A--1--2--3--4--5--B

Where A and B are hosts and 1,2,3,4,5 are routers and let's assume TTL value is 3.Let RouterVisit be counter initialized to 0.

So when A will send a packet router 1 will receive and decrement the TTL and RouterVisit will be incremented to 1.

Status: TTL 2 and RouterVisit 1

When router 2 will receive packet

Status: TTL 1 and RouterVisit 2

When router 3 will receive packet

Status: TTL 0 and RouterVisit 3

As TTL becomes 0 ICMP packet will be sent from router 3 to Host A.

So ICMP packet will go from router 3 to router 2(won't count router 3 again as we are currently at that router only.).

Status: TTL 0 and RouterVisit 4

From router 2 to router 1

Status: TTL 0 and RouterVisit 5

From router 1 to host A.

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