Which Alice?
Which Alice?
Which Alice?
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ALICE IN PUZZLE-LAND<br />
that A told the truth, which makes B the knave; hence C must be<br />
the knight. So here are the two possibilities—2a and 2b—under<br />
Case 2:<br />
Case 3—A said yes and B said no: Since A claims to be the spy, then (as<br />
in Case 1) A must be the knave or the spy. If he is the knave, then<br />
he lied; so B told the truth; hence either B is the knight (and C the<br />
spy) or B is the spy (and C is the knight). If A is the spy, then he told<br />
the truth; hence B lied, which means B is the knave and C the<br />
knight. Thus we have three possibilities:<br />
Case 4—both said no: Since A denied being the spy, then (like Case<br />
2) he is the knight or the spy. Suppose he is the knight. Then he<br />
told the truth. Then B lied; so either he is the knave (and C the<br />
spy), or he is the spy (and C the knave). Suppose A is the spy. Then<br />
he told the truth; hence B also told the truth, which means B is the<br />
knight (and C is the knave). So we again have three possibilities:<br />
For convenient reference, let us record all four cases in the<br />
following table.<br />
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