Which Alice?

ALICE IN PUZZLE-LAND
WHO IS MURDOCH? Since A claims to be the spy, then he is
either a knave or the spy. Likewise C claims to be the spy, so he also
is either a knave or the spy. So one of A, C is a knave and the other
a spy. Therefore, B is the knight; hence his statement is true; so A
must be the spy.
THE RETURN OF MURDOCH If A is Murdoch, all three
statements are true, which is impossible since one of them is a
knave. If C is Murdoch, all three statements are false, which is also
impossible since one of the three is a knight. Therefore, B must be
Murdoch.
A MORE INTERESTING CASE If we had not been told that
after C's accusation the judge knew who the spy was, then we could
not solve this problem. But we are given that the judge knew, and
this is the vital clue!
Suppose C had accused A. Then the judge couldn't have known
who was the spy, because it could be that A is the spy, B the knave,
and C the knight, or that B is the spy, A the knight, and C the
knave, or it could also be that C is the spy, A the knave, and B the
knight. So if C had accused A, the judge couldn't have made a
conviction.
Now, let's see what happens if C accused B. This means that A
and C both accused B. Then their accusations are either both true
or both false. If they were both true, then B would really be the spy,
and since the accusations are true, A and C must both be knights
(neither could be a spy, since B is), and it is not possible that there
are two knights. Therefore, their accusations were false, which
means that B is not the spy. Could A be the spy? No, for if he were,
then B and C would have both lied in accusing each other, which
would make both of them knaves, which is not possible. Therefore,
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