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Logic Problems
Logic Problem #1:
This problem involves a wolf, a goat, a bag of cabbage, and a ferryman. From an initial position on the left bank of a river, the ferryman is to transport the wolf, goat, and bag of cabbage to the right bank. The difficulty is that the ferryman's boat is only big enough to transport himself and one other object at a time. Yet, for obvious reasons, the wolf cannot be left alone with the goat, and the goat cannot be left alone with the bag of cabbage. How should the ferryman proceed? (Provide all the steps to the solution.)
Level: medium-easy
Click to Expand Answer to Problem #1
Answer: First, you take the goat across the river. Then, you come back and you can choose either of the remaining objects. Let's say you take the wolf. You leave the wolf on the other side of the river and (this is important) take the goat with you. Then, you grab the cabbage, and (important again) leave the goat there. Then when you take the cabbage to the other side, only the wolf is there, and it's safe. Then you go back for the goat. (You can also choose the cabbage instead of the wolf in that step, but then you do the same in a different order is all.)
Logic Problem #2:
In the back of an old cupboard you discover a note signed by a pirate famous for his bizzare sense of humor and love of logical puzzles. In the note he wrote that he had hidden treasure somewhere on the property. He listed 5 statements and challenged the reader to use them to figure out the location of the treasure.
a) if this house is next to a lake, then the treasure is not in the kitchen
b) if the tree in the front yard is an elm, then the treasure is in the kitchen
c) this house is next to a lake
d) the tree in the front yard is an elm or the treasure is buried under the flagpole
e) if the tree in the back yard is an oak, then the treasure is in the garage.
Where is the treasure hiddden?
Level: medium-hard
Click to Expand Answer to Problem #2
Answer: The treasure is under the flagpole (d). Here's why: The first three (a through c) cancel each other out. Since the house is next to a
lake, the treasure is not in the kitchen. Also, (part d) since the treasure is not in the
kitchen, the tree in the front yard is not an elm. Since the tree in the front yard
is not an elm, the treasure is buried under the flagpole. Part (e) is just to throw you off, it has nothing to do with anything, because you don't know if the tree in the back yard is an oak or not; there has
been no information to tell you this one way or another.
Logic Problem #3:
The logicial Raymond Smullyan describes an island containing two types of people: knights who always tell the truth and knaves who always tell a lie.
1) You visit the island and are approached by two natives who speak to you as follows:
A: B is a knight
B: A and I are opposite of type.
What are A and B?
Level: medium-hard
Click to Expand Answer to Problem #3
Long Answer: Let's assume A is telling the truth, so thus is a knight. A says that B is a knight. That would mean both are knights. But B says A and I are oppositite. So that would bring us to a contradiction, since knights don't lie, and thus they can't be opposite and both be knights. So now let's assume B is telling the truth, and thus is a knight. B says A and I are opposite, which means that A is a knave. Well, knaves lie, and A says that B is a knight. So that brings us to another contradiction. A, being a knave, cannot be telling the truth to say that B is a knight. So next, we assume they are both lying, so both are knaves. A is lying, because B is not a knight, and B is lying because they are not both opposite. So they are both knaves.
Short Answer: A and B are both knaves.
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