Which Alice?
Which Alice?
Which Alice?
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ALICE IN PUZZLE-LAND<br />
since his statement is true, he is not Tweedledum carrying a red<br />
card; so he must be Tweedledee carrying a red card.<br />
ROUND THREE Either-or means at least one (and possibly<br />
both); so if he were carrying a black card, then it would be true that<br />
either he is Tweedledum or he is carrying a black card, which would<br />
mean that a holder of a black card made a true statement. This is<br />
impossible, so his card cannot be black. Since his card is red, his<br />
statement is true, which means that either he is Tweedledum or his<br />
card is black. Since the second alternative doesn't hold, then he<br />
must be Tweedledum. So he is Tweedledum carrying a red card.<br />
ROUND FOUR This time it cannot be determined whether he<br />
is holding a red or a black card, but in either case, he must be<br />
Tweedledee. Suppose his card is red. Then he speaks truly, so he is<br />
either Tweedledum carrying a black card, or Tweedledee carrying a<br />
red card. He can't be the former (since his card is red), hence he<br />
must be the latter, so he is Tweedledee.<br />
On the other hand, suppose his card is black. Then his statement<br />
is false, which means that he is neither Tweedledum with black nor<br />
Tweedledee with red. So he is either Tweedledum with red or<br />
Tweedledee with black. The former is not possible (since his card<br />
is black), so the latter holds—which means again that he is<br />
Tweedledee.<br />
68<br />
ROUND FIVE Suppose the speaker is carrying a red card.<br />
Then his statement is true, which means that Tweedledum is<br />
carrying a black card; so the speaker must be Tweedledee. Suppose<br />
the speaker is carrying a black card. Then his statement is false; so<br />
Tweedledum is not carrying a black card. Yet the speaker is<br />
170
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