Dear dtnl42,
Here you go.
Easy Puzzle #1
Question:
A traveler on his way to the Valley of the Kings came upon a fork in
the road where two imps stood. He knew that one of the imps always told
the truth and the other always lied, but there was no way to tell them
apart. The imp standing at the road that branched to the left said,
"One of these roads leads to the Valley of the Kings, and the other
leads to the Valley of Death!" The imp standing at the right said,
"This road leads to the Valley of Death, and the other leads to the
Valley of the Kings!" Which way should the traveler go?
Answer:
Suppose the imp at the right is telling the truth, so it is indeed
the case that the left road leads to the Kings and the right road to
Death. Then the imp at the left would be lying, yet his statement is
accurate: there is indeed one road leading to the Kings and another to
Death. Thus, the imp at right must be lying. The traveler should take
the road to the right.
Easy Puzzle #2
Question:
The Forest of Doubt is inhabited by demons who always lie and by angels
who always tell the truth. A traveler is looking for a way out of the
Valley of Doubt when he comes across two figures, one tall and one short.
The tall one offers to act as a guide. "What kind of creature are
you?" asks the traveler. "Either I am a demon or this short fellow is an
angel," replies the tall one. Can the traveler use one of them as a guide?
Answer:
Suppose the tall figure is an angel. Then his statement is true, and
the short one must also be an angel. Now suppose the tall figure is a
demon. Regardless of the short one's identity, the statement is then
true, for the tall figure is indeed a demon. Yet demons can't tell the
truth. Thus, both figures are angels and make reliable guides.
Medium Puzzle #1
Question:
A traveler on his way to the Valley of the Kings reached a fork in the
road where stood a pair of talking camels. The traveler remembered from a
lecture on the subject of camels and llamas that one species always lied
and the other always told the truth, but he couldn't remember which was
which. The camel standing at the road that branched to the left said, "At
least one of these branches leads to the Valley of the Kings." The camel
at the right said, "The left branch leads to the Valley of Death." Which
way should the traveler go: left, right, or must he turn back?
Answer:
Suppose camels always lie. Then the statement of the camel at left is
false, so neither branch leads to the Valley of the Kings. But then the
camel at right would be making an accurate statement, which contradicts
our supposition. Thus, it must be the case that camels always tell the
truth. Since the camel at right tells us that the left branch leads to
Death, it must be the right branch that leads to the Kings. The traveler
should therefore turn right.
Medium Puzzle #2
Question:
A sailor disembarks on a flinty beach of Antarctica which is populated
by constantly truthful cormorants, invariably lying albatrosses, and
by penguins who sometimes lie and sometimes tell the truth. A bird who
is tanning in the Antarctican sun says to the sailor, "Either I am an
albatross or else one plus one is three." Is this bird a cormorant,
an albatross, or a penguin?
Answer:
Suppose this bird is an albatross. That makes his statement true, yet
albatrosses always lie, which contradicts the supposition. Now suppose
he is a cormorant. Then the statement is true, and if the bird is not an
albatross, it follows that one plus one is three. Yet this is a falsehood
that a cormorant would never utter. The only remaining possibility is
that the bird is a penguin making a false statement.
Hard Puzzle #1
Question:
An adventurer who sought the Golden Pinecone came into a glade where stood
three pine trees. In one of them, he knew, grew the Golden Pinecone, but
he didn't know which one. At the base of each tree sat a bear, and the
adventurer knew that only one of the three bears was capable of telling
the truth; even this bear, however, occasionally lied. Papa Bear said,
"The Golden Pinecone is not in my tree." Mama Bear added, "It's in my
tree." But the Baby Bear rejoined, "No, it's not in her tree," as he
pointed at Mama Bear. Where is the Golden Pinecone?
Answer:
If all three bears are lying, then the Golden Pinecone is not in Mama
Bear's tree, making Baby Bear's statement true, which contradicts the
premise. Thus, exactly one of the bears must be telling the truth. If
it is Papa Bear, we have the same contradiction as before. So Papa Bear
must be lying, which means the Golden Pinecone is in his tree. Mama Bear
is therefore lying, while Baby Bear is telling the truth.
Hard Puzzle #2
Question:
A traveler finds himself in the Forest of Doubt, which is inhabited
exclusively by truth-telling angels and lying demons. Three figures appear
in the dusk. The first one says, "All of us are demons." The second
adds, "Exactly one of us is an angel." The third remains silent. Can
the traveler identify the three figures?
Answer:
If the first figure were an angel, his statement would imply that he is
a demon, which is a contradiction. He must therefore be a demon, so his
statement is false and at least one figure is an angel. Now suppose the
second figure is a demon. Then the third and last figure must be the
angel, which is exactly what the second figure is saying, so he can't
be a demon. The second figure must therefore be an angel, indeed the
only angel according to his statement, so the third figure is a demon.
Hard Puzzle #3
Question:
A traveler reaches a fork in the road. One branch leads to the Valley
of the Kings, the other to the Valley of Death. Nearby is a hut where a
pair of identical twins live, one of them a constant truth-teller and
the other a perennial liar. When the traveler knocks on the door, one
of the twins emerges to answer a single question. What question could
the traveler ask that would ensure he received a correct answer?
Answer:
"When people ask you which road leads to the Valley of the Kings, how do
you answer?" The truth-teller gives his usual honest answer. The liar
cannot faithfully report his usual crooked answer, so he must give the
opposite answer, which is accurate.
Regards,
leapinglizard |
