Which Alice?

ALICE IN PUZZLE-LAND
both possibilities la and 1b and seeing that B could answer no in
either case), but if B answered no, the judge would know that B
must be the spy (because 1b is ruled out, since it would mean that B,
a knight, denied that A [a spy] is a spy). So B must have answered
no, and B was then convicted. This completes our analysis of Case 1.
Case 2 can be analyzed in a similar manner, and we rely on the
reader to fill in details. Suppose Case 2 holds. If A was the one
questioned, then he must have answered no for the judge to have
been enabled to make a conviction, and A was convicted. If B was
the one questioned, he must have answered yes for the judge to
have been enabled to make a conviction, and B was convicted. We
leave the verification of these facts to the reader (which, as I have
said, is not very different from the reasoning of Case 1).
Let us summarize what we know so far:
If Case 1 holds, then either A was asked the third question, answered
yes, and was the spy, or B was asked the third question,
answered no, and was the spy.
If Case 2 holds, then either A was asked the third question,
answered no, and was the spy, or B was asked the third question,
answered yes, and was the spy.
We thus have the following four possibilities:
Step 2: This is as far as we can get without the additional
information about the two friends of Mr. Anthony. We are given
that either both of them solved the case, or that neither of them did;
we will prove that it is impossible that both of them solved the
problem.
Consider the first friend: If Mr. Anthony answered him affirmatively,
then the friend would have known that Case 1a must hold
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