Ttdfjt

<sub>Dear PSE users and moderators,

I’m new here in PSE, but I really need your help. There was this person who gave me a black envelope consisting 10+1 pages of puzzles, and also a scribble saying: “Find our favorites and you will be accepted to join our ‘pyramid cult’. Feel free to ask for help from your beloved friends on PSE. They will surely guide you into all the truth.” I’m also a newbie on grid puzzles, so, could you please give me any hint to solve these? It’s getting harder and harder later on..

- athin</sub>

_{Previous page: #1 Numberlink | Next page: #3 Akari}

Rules:

1. Draw a line to make a single loop.


2. Lines pass through the centers of cells, moving in perpendicular direction with one of the cell sides, or turning. The loop never crosses itself, branches off, or goes through the same cell twice.


3. A region, bordered by bold lines, is called a "room". The loop goes through each room only one time. Once the loop leaves a room, it cannot return to enter this room.


4. In each room, the loop goes through all of the moon cells (C) or all of the sun cells (O). The loop cannot pass through both moon cells and sun cells in one room.


5. After the loop goes through the moons in one room it has to go through all the suns in the next room it enters and visa versa.

^{Special thanks to chaotic_iak for testing this puzzle series!}

Breaking in:

Can the loop pass through the moon in the central region?

If it does, both ends of this path will go one of the five colored regions. If the two regions visited are not adjacent to each other, then we will not be able to visit both the region in between them and the top region. So they must be adjacent, and then they must go around the edges in opposite directions to eventually meet up at the top.


The only way this can happen is if one of the two ends goes directly to the yellow region. If this is the left end, it must then go to orange and red -- but it can't do that, since the moon in the orange region blocks the path. And if this is the right end, it must then go to green -- but it can't do that either, since the sun in the yellow region blocks the path. So the moon in the center region is not visited.

Step 2:

The right endpoint cannot go down and right, so it must go up. The left endpoint must then go down and left, and the right endpoint curves around to the left region (because of the moon in the region above the center).

Step 3:

The dark blue region must be accessed from the light blue region (since the other adjacent region has already been visited). Similarly, the dark green region must be accessed from the two light green regions (since the other adjacent region is going to the dark blue instead). From this, we can determine most of the loop's path.



And finally, since the lower endpoint is blocked from going to the bottom right region, the loop can be completed.

The finished loop:

From the letters in the unvisited cells, we can see that the pyramid cult's favorite camera brand is INSTAX.

Here is a simplification of @Deusovi's proof that the middle region must be a sun:

If it is a moon (C), then the 'fishes' to the left and right need to be suns (O). However, we also know that the (C-O) arrangement in the bottom left region forces the red connection:




and the red line must connect to the moon in the bottom left region, as well as to the orange line. This however isolates the bottom middle region (it must have different source and destination regions, and if the right fish joins to it, then it must have both a moon and sun in order to join the bottom right region). Hence the middle region contains a sun.