Which Alice?

ALICE IN PUZZLE-LAND
is not a spy; so he knows that A must be either the knight or the spy.
If Case 2 held, the judge couldn't have known whether A was the
knight or the spy; hence he couldn't have known who the spy was.
So Case 1 holds, and the judge knew that A can't be a knave (since
he made a true statement); hence A must be the spy.
AN EQUALLY INTERESTING CASE Since A, B were asked the
same questions as in the last problem, we can use the same table (see
page 161).
Consider that point of the trial right before the judge asked C
whether he was a spy. At that point, the judge did not know of any
of the three that he was definitely not the spy; otherwise he would
have acquitted him. This rules out Cases 1 and 2, because in either
of those cases the judge would have known that C was either a
knight or a knave and would have acquitted him. So either Case 3
or Case 4 must hold.
Now, we consider the judge's reasoning after C answered.
Suppose Case 3 holds. Then the judge knows that C is either the spy
or the knight. If C answered no, the judge would have known no
more than before and couldn't have convicted anyone. If C
answered yes, the judge would have known that C was the spy,
because a knight could not say that he was the spy. So, if Case 3
holds, then it must have been C who was convicted.
Suppose Case 4 holds. Then the judge knows that C is the spy or
the knave. If C answered yes, the judge couldn't have made a
conviction (because either a knave or a spy could say he is a spy). If
C answered no, then the judge would have known that C was the
spy, because a knave could not make the true statement that he isn't
a spy. So in Case 4, it was also C who was convicted.
It might be well to point out that it is impossible for you or me to
know whether Case 3 or Case 4 is the one which actually holds, nor
is it possible for us to know what answer C actually gave. All we do
know is that since the judge did make a conviction, then either Case
3 holds and C answered yes, or Case 4 holds and C answered no,
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