Thread by @objkshn

The GHOSTS of HERE and NOW: A logic problem for the earthly bound:

There are some ghosts in the kingdom of Here who have been put on the endangered spirits list. Ghosts are of two types: RATIONALS and PREDATORS. 1/

Some ghosts have reasoned that scaring the wits out of the living, while perhaps amusing, is not the proper way for a civilized spirit to behave. These ghosts prefer to live in harmony with the living. They are known as RATIONALS. 2/

Some ghosts, on the other hand, are reluctant to give up their traditional ways of haunting, nor do they mind hurting humans. These ghosts are known as PREDATORS. 3/

The council after careful and thoughtful deliberation has decreed that RATIONAL ghosts shall be protected but that PREDATOR ghosts should be destroyed. The council, after a fair bidding process, hires you and your Ghostbusting company – to identify which ghosts are which. 4/

In addition to being rationals or predators, ghosts in Here are of two different colors related to their veracity (truthfulness). Gray rational ghosts always tell the truth; red rationals always lie. Red predators always tell the truth; gray predators always lie. 5/

After a while, however, blue ghosts from the adjacent land of Now began appearing in the kingdom of Here. Blue ghosts might be RATIONALS or PREDATORS, but they all lie. 6/

To tell if a ghost is protected, it would help to know its color but the colors of a ghost are only visible to other ghosts. To humans, they all appear translucent. Applying logic, however, a skilled Ghostbuster can ask questions to deduce the color and type of each. Ready? 7/

Before we go any further, you might find the following charts helpful or useful in keeping track of things. 8/

PROBLEM ONE: One Ghost

A ghost is approached by a Ghostbuster. The ghost, when asked his color and type, responds as follows:

Ghost: I am either blue or gray.

What type is the ghost?

PROBLEM TWO: Two Ghosts

Two Ghostbusters confront two ghosts, each of whom is asked his color and type. Their answers follow:

Ghost A:I am from Now.
B and I are predators.

Ghost B:A is not from Now, but I am.
I am a rational.

What is the color and type of each ghost?

PROBLEM THREE: Three Ghosts

A Ghostbuster learns the following when he overhears:

Ghost A:C is from Now.
I am not a red predator.
Ghost B:A is from Now
A and C are both rationals.
Ghost C:B is from Now.
B is a predator.

What is the color and type of each ghost?

PROBLEM FOUR: Two from Now

A Ghostbuster confronts 3 ghosts, exactly 2 of whom are known to be blue ghosts from Now, who advise:

Ghost A: B is from Now & I am a rational.
Ghost B: C is from Now & I am a rational.
Ghost C: I am a rational.

What color and type is each ghost?

PROBLEM FIVE: One Ghost from Now

3 ghosts, exactly one of whom is blue, state:

Ghost A: C is a gray rational. I am a gray rational.
Ghost B: A is a predator. A is blue. I am a rational.
Ghost C: A is not gray. B is from Now.

What color and type is each ghost?

PROBLEM SIX: Three Ghosts Again

3 ghosts, at least one of which is from Now, share:

Ghost A: I am either red or gray. C and I are the same color.
Ghost B: A is not red. C is blue.
Ghost C: A’s statements are false. B is not a rational.

What color and type is each ghost?

PROBLEM SEVEN: How Many Are Protected?

Ghost A:I am gray.
We three are protected by the council.
C is red.
Ghost B:I am not protected by the council.
C is gray.
Ghost C:A and I are not the same type.
A is red.
B is rational.

What color and type is each ghost?

PROBLEM EIGHT: Who Speaks for Whom?

Ghost A: If asked, B would claim C is a predator.
I am gray. B is a rational.
Ghost B: If asked, C would claim A is a rational.
C is red.
Ghost C: If asked, A would claim B is red.
A is gray.

What color and type is each ghost?