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In the diagram shown below, $L1$ is an Ethernet LAN and $L2$ is a Token-Ring LAN. An $IP$ packet originates from sender $S$ and traverses to $R$, as shown. The links within each $\text{ISP}$ and across the two $\text{ISP}$s, are all point-to-point optical links. The initial value of the $\text{TTL}$ field is $32$. The maximum possible value of the $\text{TTL}$ field when $R$ receives the datagram is _______.

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Each time a packet visits network layer it decrements it's TTL field. Source initializes it and others decreaments it. Inside LAN it never goes to network layer, it is forwarded from data link layer itself.. in routers it goes upto network layer to make a routing decision.. and the router decrements it because the packet has visited the network layer.. and at the receiver too, the packet has visited the network layer and network layer will do it's job and decrements the TTL value.

There are $5$ routers, So Network Layer will be visited $5$ times  and $1$ time on the destination

So, TTL $= 26$

PS:) A receiver decrements TTL value and then checks whether it is $0$ (or) not. So, $26$ is the answer (not $27$)

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TTL value only decrement at router and at destination.It is very very important to keep in your mind until exam finish.

So Total router=5

Destination=1

Initial TTL value=32

When Packet reaches the receiver=32-(5+1)=26
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TTL field reduced at each router, there are total 5 routers and finally at receiver.

=32 -(5+1)=26
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