Exercise 3: Why traceroute Needs Increasing TTL Values, Not One Fixed TTL — Possible Solution
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Explanation:

Per the chapter, "it sends packets with increasing TTL (time-to-live)
values, and each router along the path that decrements a packet's TTL
to zero sends back an ICMP 'time exceeded' message, revealing itself
as one hop in the chain." The entire mechanism depends specifically on
GETTING each individual router along the path to reveal itself one at
a time, and a single fixed TTL value could only ever cause exactly one
router -- whichever one happens to be sitting at that specific hop
count -- to trigger a response.

If traceroute sent every packet with the same fixed TTL, say TTL=5, only
the router that is exactly 5 hops away would ever decrement that value
to zero and send back a "time exceeded" message; every router closer
than that (hops 1 through 4) would simply forward the packet onward
without ever reaching zero, and would never reveal themselves at all.
The result would be, at best, information about a single router
somewhere along the path, with no way to build a complete, ordered
picture of the entire route.

By deliberately sending a sequence of packets with TTL=1, then TTL=2,
then TTL=3, and so on, traceroute forces a DIFFERENT router to be the
one that hits zero and responds with each successive packet: the
TTL=1 packet reveals the very first hop (it decrements to zero
immediately, at the first router), the TTL=2 packet passes that first
router unharmed but hits zero at the second router, and so on, one
additional hop revealed with each incrementing TTL value. This is
exactly how the chapter's own description of traceroute's value --
"seeing exactly where along a path traffic stops, or slows
dramatically" -- becomes possible in the first place: without the
full, ordered sequence of hops that only incrementing TTL values can
reveal, there would be no way to see the path as a complete chain, or
to identify precisely where along the chain a failure or slowdown was
actually occurring.

WHY THIS WORKS AS AN ANSWER
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This explains why a single fixed TTL could only ever expose one router
along the path, and why the incrementing sequence is specifically what
forces each successive router to reveal itself in order, directly
using the chapter's own mechanism description rather than restating
that TTL values increase without explaining why that's necessary.