Which Alice?

Solutions to the Puzzles
false, which makes A a knave (he can't be the spy, because C is).
This leaves B as the knight, but then how could he, a knight, make
the false claim that A is a knight? So it is impossible that C is the spy.
Therefore, C is the knave. Then B's claim is false, which means he is
a knave or the spy, but C is the knave, so B must be the spy. This
leaves A as the knight. So A is the knight, B is the spy, and C is the
knave.
THE CASE OF THE BUNGLING SPY One false statement which
would convict him is "I am a knave." A knight could never lie and
claim to be a knave, and a knave would not tell the truth and say he
is a knave. Only the spy could claim to be a knave.
ANOTHER BUNGLING SPY A true statement which would
convict him is "I am not a knight." Again, neither a knight nor a
knave could say that, because a knight would not lie and say that he
is not a knight, and a knave would not tell the truth and say that he
is not a knight. So only the spy could say that.
THE CASE OF THE FOXY SPY If A had answered yes, he would
have got convicted, because the court would have reasoned as
follows:
"Suppose B were the spy. Then all three are telling the truth,
which is impossible, since one of them is a knave. Therefore, B can't
be the spy. His statement, therefore, was false, so B is the knave. C's
statement was false, and since C is not the knave, he is the spy."
So, if C had answered yes, the court would have known that he is
the spy. Therefore, C cleverly answered no, and the court could not
tell whether or not he was the spy. (As far as the court could know,
either he could be a knight and B the spy, or a knave and A the spy,
or he could be the spy.)
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