Which Alice?

Solutions to the Puzzles
two possibilities (4A and 4C) in which at most one defendant told
the truth; in Case 6 there are again two possibilities (6B and 6C); in
Case 7 there are the two possibilities 7A and 7C; and in Case 8 there
are the two possibilities 8B and 8C. So, in none of these four cases
could the Jabberwocky have known who was guilty. On the other
hand, in Case 1, possibility 1A is the only one in which there was at
most one true statement; in Case 2, 2B is the only possibility; in
Case 3, 3A is the only one; and in Case 5, 5B is the only one. So we
know that one of the Cases 1, 2, 3, 5 is the one which actually holds.
Now, Tweedledee was told that the Jabberwocky solved the
problem, so Tweedledee also knew that the actual case was either 1,
2, 3, or 5. If he had been told that A claimed to be guilty, then he
would have ruled out Cases 1, 2, and 3 and known that Case 5 must
hold, which means that B is guilty (because 5B is the only possibility
under Case 5 in which at most one true statement was made). This
means that Tweedledee would have solved the problem, but we are
given that Tweedledee didn't solve the problem; therefore, he was
not told that A claimed to be guilty; he was told that A claimed to be
innocent, so he knew that Case 5 didn't hold, but he had no way of
knowing whether Case 1, 2, or 3 held; hence he didn't know
whether A or B was guilty. Anyway, we now know that one of the
Cases 1, 2, or 3 holds.
Now we consider Tweedledum. He was told about the Jabberwocky,
so he also knew that one of the Cases 1, 2, 3, 5 must hold,
but he was not told about Tweedledee; so he did not know that Case
5 was ruled out. Now, he asked either about B or C, but we don't
know which. Suppose he asked about B. If the White Knight told
him that B claimed to be guilty, then Tweedledum would have
ruled out Cases 1, 2, and 5, and would have been left just with Case
3; so he would have solved the problem (concluding that A was
guilty). But he didn't solve the problem; so if he asked what B said,
then he was told that B claimed to be innocent. So we now know
that if Tweedledum asked what B said, then Case 1 or Case 2 holds.
Suppose Tweedledum asked what C said. If he had been told that
C said that A was guilty, he would have eliminated Cases 1, 3, 5 and
solved the problem (concluding that B was guilty). But he didn't
solve the problem, so he must have been told that C claimed that A
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