Exercise 2: Why "No Letter Maps to Itself" Is Useful Information — Possible Solution
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Reasoning through it without the daily key:

The reflector's guarantee means that for ANY position in the message,
the ciphertext letter at that position can never be identical to the
plaintext letter at that same position — regardless of what the daily
key actually is. That's a piece of information that holds true across
every possible key setting, not just one.

This matters because a codebreaker who suspects a particular word or
phrase appears somewhere in the plaintext (for example, a guessed
piece of standard military phrasing) can test that guess against the
ciphertext WITHOUT needing to know the key at all: slide the guessed
word along the ciphertext, position by position, and any alignment
where a letter of the guess matches the SAME letter in the ciphertext
at the same position can be immediately thrown out — that alignment
is provably impossible, because Enigma could never have produced it.

This sharply narrows down which positions in the ciphertext a guessed
word could possibly start at, turning an otherwise blind search (try
every key against every possible position) into a much smaller,
targeted one (only test the handful of positions the "never maps to
itself" rule hasn't already eliminated).

WHY THIS WORKS AS AN ANSWER
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This is reasoning toward exactly what Chapter 4 formalizes as "crib
dragging" — the chapter deliberately holds back the full technique,
asking only for the conceptual insight that a structural guarantee
true across ALL possible keys can eliminate candidate alignments
without ever needing to know the specific key in use. That's the same
category of insight as Chapter 1's Kerckhoffs's Principle applied in
reverse: just as the algorithm being public doesn't break the system
by itself, a public, key-independent STRUCTURAL property of the
algorithm can still leak real information to an attacker, even while
the actual secret (the daily key) remains completely unknown.