Which Alice?

Solutions to the Puzzles
the only possibility is that C is the spy (and B, having accused C, is
the knight, and A, having accused B, is the knave).
In summary, if C accused A, then the judge couldn't have made a
conviction, but if C accused B, the judge would know that C was the
spy. Since the judge did know, then it must have been that C accused
B, and the judge then convicted C.
A STILL MORE INTERESTING CASE We do not know what A
and B answered. There are four possible cases to consider: (1) A, B
both said yes; (2) A said no and B said yes; (3) A said yes and B said
no; (4) both said no.
These cases will come up again in the next two problems, and we
will now analyze them with care.
Case 1—they both said yes: Since A claims he is the spy, then he is
either the knave or the spy (because a knight could never claim to
be a spy). If A is the knave, then he lied; hence B lied when he said
that A told the truth; so B is not a knight, and since A is the knave,
B is the spy. This means that C must be the knight. So if A is the
knave, B is the spy, and C is the knight.
Suppose A is the spy. Then he answered truthfully; so B
answered truthfully in saying that A answered truthfully; so B must
be the knight. This makes C the knave. So if A is the spy, then B is
the knight, and C is the knave. Let us record these two possibilities
(which we'll call la and 1b) of Case 1:
Case 2—A said no and B said yes: Since A denied being the spy, he is
the knight or the spy. (A knave would lie and say he was the spy.) If
A is the knight, he told the truth; hence B also told the truth in
affirming that A told the truth; so B can't be the knave, so he must
be the spy. This makes C the knave.
If A is the spy, then he lied; hence B also lied when he affirmed
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