Which Alice?

Solutions to the Puzzles
and that C was convicted in either case. So we know that C was
the spy.
THE MOST INTERESTING CASE OF ALL We use the same
table that we used in the solution to the last two problems (the table
is on page 161).
Step 1 : After B answered the judge's question, the judge made an
acquittal. If either Case 3 or Case 4 held, then any of the three
defendants could have been the spy, and the judge could not have
made an acquittal. Therefore, Case 1 or Case 2 must be the one that
holds, and in both cases, C cannot be the spy, but either of the
others could be. So it was C who was acquitted. So we know that C
was acquitted and that either Case 1 or Case 2 holds, and we can
now completely forget about Cases 3 and 4.
After C left the court, the judge asked either A or B (we don't
know which) whether the other was a spy, and he got the answer
Yes or No, but again we don't know which. Thus there are four
possibilities for Case 1 and four possibilities for Case 2, making
eight possibilities altogether. Now we shall eliminate half of them,
using the given fact that the judge, after getting the answer, made a
conviction.
Suppose Case 1 holds. Suppose A were the one who was asked
the question. If he answered yes (thus claiming that B was the spy),
the judge could have eliminated 1a, because if A is a knave and
B the spy, A could not have told the truth that B is the spy. Thus the
judge would have eliminated 1a and known that 1b must hold and
that A is the spy. If A answered no, the judge could not have made
a conviction, because it could be that A is a knave who lied when he
said that B wasn't the spy, or A could be the spy who told the truth
when he said that B wasn't the spy. Therefore, it is not the case that
A answered no. So if A was the one who was asked, then he
answered yes and was convicted. Now, suppose it was B who was
asked whether A was the spy. If B answered yes, then the judge
couldn't have made a conviction (as the reader can see by examining
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