A group of logic puzzles, wherein you travel to the strange world of there Wherewolves: beings who change between human and wolf form based on where they are. Right now, it's hardly a large collection of riddles, but I may add to it later. The entire text is given below, and the attached filed has the text formatted in a PDF document.

*******

To Go Where Wherewolves Are

You are an interdimensional explorer, and have built a bridge to the mysterious world of the Wherewolves, looking to learn its secrets. These Wherewolves don’t shift between human and wolf-man form based on the phase of the moon, for their world has no moons! Instead, your form is determined by where you are located.
The surface of the world is dotted with a vast multitude of large islands, each populated by many Wherewolf villages. Wherewolves vary as to where they take different forms, but each village is situated so that no one changes form within any one village.

Furthermore, Wherewolves are the inheritors of ancient magical devices forged by their ancestors. Every island has a complex system of portals spread throughout its villages, allowing for very quick travel. Portals only connect villages on the same island, and any given portal is not necessarily two-way. You very much hope to learn the secrets of these portal networks.


******


Part 1: Meetings and Introductions - Riddles

(1)

You meet a very cordial wolfman (for these creatures do not become brutish and feral in their wolf forms) and ask about the world’s portals. He says, “Ah! Well, the network of portals is different from island to island, but each island has its own patterns and regularities. For example, on this island, if someone is a wolf in a village, then there is always some portal there she can take where she will be a wolf on the other end. This is true no matter where she is a wolf and where she is a human.”

“But,” you tell him, “I’m more interested in how the villages themselves are connected.”

“I just told you something about how they are connected! Think about it!”

What can you conclude about the way villages are connected by portals?


(2)

“Here’s another fact,” he continues, “if you’re a wolf in every village connected via portals to some other village, then you must be a wolf in that village.”

What can you conclude from this?


******


Part 1-Solutions

(1)

According to the Wherewolf, his statement is true no matter where one is a human and where one is a wolf. Imagine, then that someone is a wolf in only one village on the whole island. If she is a wolf there, then there must be a portal taking her somewhere else where she is a wolf. Since that village is the one and only place she’s a wolf, then there must be a portal that connects that village to itself (perhaps one that takes you from one part of the village to another).

This example can be applied to all villages in the island, since for every village, we can consider a Wherewolf like the one above. Therefore, every village has a portal to itself.


(2)

We know that if someone is a wolf in every village connected to some single village via portals, then they must be a wolf in that single village. Therefore, if someone is not a wolf in a single village, then they cannot be a wolf in every village connected to it. In other words, if someone is human in a village, they must be human in at least one other village connected to that one.

Using a similar logic to that in the last puzzle, we can say that if someone is a human in exactly one village, then that village must have a portal to itself. If what the Wherewolf said is true no matter where one takes human and wolf form, then every village must be connected to itself.

So the answer to this puzzle is exactly the same as the answer to the last!


******


Part 2: A Trip to the Pub - Riddles

“I see,” you say, now seated with your new acquaintance at a local pub. “If the things you tell me would be true for any Wherewolf, then there must be certain things that are true about the portals on the island.”

“Indeed,” responds your new friend. “If we keep talking, there’s probably some vocabulary I should teach you. If someone is a wolf in a village, then that village is one of their wolf-villages. Similarly, a village where someone is human is one of their human-villages.”

“Seems sensible enough.”

“Here’s some more complex terminology: if a Wherewolf is in a village where every portal leads to one of their wolf-villages, then that village is one of their squared wolf-villages. If someone is in a village where at least one portal leads to one of their wolf-villages, then they are in one of their diamond wolf-villages.”

“I assume that if someone is in a village where every portal leads to one of their human-villages, it is one of their squared human-villages? And if at least one portal leads to one of their human-villages, it is one of their diamond human-villages?”

“Exactly!”


(1)

“Now consider this: there is an island where, if someone is in one of their squared wolf-villages, then every portal in that village leads to another one of their squared wolf-villages.”

What can you say about the island’s portals?


(2)

“There is yet another island where, if someone is in one of their wolf-villages, then every portal in that village leads to one of their diamond wolf-villages.”

What do you know about this island’s portals?


(3)

“One very interesting island has this property: if you are in one of your diamond wolf-villages, then every portal there leads to another one of your diamond wolf-villages.”

What can you conclude from that?


******


Part 2-Solutions

(1)

Imagine a Wherewolf with only one human village. If they are in a village connected to one which is not a squared wolf, then the original village is not squared wolf either. Thus, if they are in a village connecting to another village which in turn connects to that one human village, then the original village also connects to that one human village.

Again, this information is true for any arbitrary Wherewolf, so we can imagine any village on the island as being that singular human-village. Therefore, the general rule is this: if village A is connected to B, and B is connected to C, then A must be directly connected to C.


(2)

Take, again, the example of someone who has only one wolf-village. That Wherewolf’s diamond wolf-villages are all those villages with a portal to the one wolf-village. Thus, every portal out of that one village takes you to a village with a portal back to it.

This must be true of every village on the island. Therefore, we can say that if there is a portal from one village to another, there must be a portal from the latter village taking you back to the former. (Perhaps all portals on this island are two-way.)


(3)

Suppose someone has only one wolf village. A diamond wolf-village for them would thus connect to that one village. According the statement given, any other village that you can get to from that diamond wolf village is has a portal to the wolf village. This property must hold true for any arbitrary werewolf, and thus any arbitrary village. So we can say that if village A has portals to villages B and C, then there must be a portal from village B to C.