Which Alice?
Which Alice?
Which Alice?
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Solutions to the Puzzles<br />
ROUND FIVE (ORANGE AND PURPLE) The first statement of<br />
the first one agrees with the statement of the second one, so they are<br />
either both lying or both telling the truth. Therefore, their cards<br />
are of different colors (same principle again!). This means that it is<br />
true that at least one card is purple; so the first one is telling the<br />
truth. Therefore, his second statement is also true, so he is<br />
Tweedledum. (Also, his card is orange and Tweedledee's is purple.)<br />
ROUND SIX (ORANGE AND PURPLE) The two are contradicting<br />
each other, so one is lying and one is telling the truth. Therefore,<br />
their cards are of the same color (same principle again!). This<br />
means the first one's statement is true.<br />
WHO IS WHO? The figure on the back is either a square or a<br />
circle. Suppose it is a square. Then a square means yes and a circle<br />
means no, so the second brother's answer meant no, which was a lie!<br />
On the other hand, suppose the figure on the back is a circle. Then<br />
a circle means yes, so the second brother's answer meant yes, which<br />
is again a lie, since a square was not on the back! Therefore, the<br />
second brother lied, so he is Tweedledee.<br />
WHAT QUESTION SHOULD ALICE ASK? Many questions can<br />
be devised which will do this; the simplest one I can think of is "Is<br />
your card red?"<br />
Whatever sign is given in answer must mean yes, because one<br />
with a red card would truthfully say it is red, and one with a black<br />
card would lie and claim his card is red. So the second one's<br />
response meant yes. Suppose he responded by drawing a square in<br />
the air. Then he means yes by a square; hence he has the prize. If<br />
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