Which Alice?

Solutions to the Puzzles
he and the Knave both lied, so this is out. Therefore the Knave of
Hearts stole it (and, humorously enough, he told the truth—and so
did the Fish-Footman).
THE SEVENTH TALE It is impossible that the Cheshire Cat
stole it, because the thief would then be telling the truth. Therefore
the Cheshire Cat didn't steal it (and the Cat and the Duchess were
both lying). If the Cook stole it, then all three would be lying, which
is contrary to what was given. Therefore the Duchess stole it (and
hence the Duchess is lying, the Cheshire Cat is lying, and the Cook
is telling the truth).
THE SEVENTH TALE (CONTINUED) Again, the Cheshire Cat
couldn't have stolen it for the same reason as the last problem.
Suppose the Duchess stole it. Then the Cat is lying and the Cook is
telling the truth— which contradicts the given fact that if the
Duchess stole it, the other two are either both lying or both telling
the truth. Therefore the Duchess didn't steal it, so the Cook did.
(And the other two are both lying or both telling the truth — in fact
they are both lying. In fact all three are lying.)
THE EIGHTH TALE To begin with, the Dormouse couldn't
have stolen the butter, because if he had, he would be telling the
truth — which would mean he stole the milk. So the Dormouse
didn't steal the butter. Therefore the March Hare or the Hatter
stole the butter. If the March Hare stole the butter, then his
statement about the Hatter would be true (remember, the one who
stole the butter told the truth), which would mean that the Hatter
stole the butter, but it is not possible that both stole the butter.
Therefore the March Hare didn't steal the butter. This means that
the Hatter stole the butter. Therefore his statement was true, which
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