Black or White
Solution
We are presented with a set of eight mini logic puzzles.
Figuring out the rules of the logic puzzle
There are 48 dashed circles highlighted in green, and the givens instruct us to place a total of 48=22+26 black and white pearls in the circles. These instructions refer specifically to pearls so we know for sure that these are Masyu pearls.
However, the grid also has some suns and moons present, and is also divided into several rooms each with dimensions 2 × 3 — neither of which are normally found in Masyu puzzles. So there is another kind of logic puzzle present! These are characteristics of another Nikoli-style logic puzzle called Moon-or-Sun (the title of the puzzle is also a hint at the genre of the puzzle present).
Both Masyu and Moon-or-Sun have the same end goal, which is to draw a single closed loop throughout some cells in the grid. To be brief:
- In Masyu, the loop needs to pass through every pearl and turn in a certain way defined for each pearl.
- For black pearls, the loop must make a right-angled turn in the pearl and go straight on the adjacent cells.
- For white pearls, the loop must pass straight through the white pearl and make a right-angled turn on at least one of the cells next to the white pearl.
- In Moon-or-Sun, the loop needs to pass through every room exactly once (once it exits a room it can never re-enter). Moreover, the loop must alternate passing between "moon rooms" and "sun rooms", defined as follows:
- A sun room is a room where the loop passes through all the sun cells and only the sun cells.
- A moon room is a room where the loop passes through all the moon cells and only the moon cells.
See the links above for examples and more details on the rules of the logic puzzle.
With both elements present, for each grid we realize there is indeed a unique way to draw the loop such that both the Masyu and Moon-or-Sun conditions are simultaneously satisfied for that single loop. Even though the colors of the pearls are not given, knowing that the pearls must be either black or white (and that the loop must pass through it!) still adds constraints to the logic puzzles to make the solution unique. Moreover, the path of the loop then lets us determine whether the pearl should be black or white.
Strategy
We can then proceed to solve the minis and fill in the pearls. Here are a couple of strategies that can help with solving the minis:
- The rooms are arranged in the same 4 × 3 fashion in every mini, and in fact there are only two different ways for the loop to pass through these.
- In particular, the rooms in the corner only have two neighbors and must connect to both. So for example, we know in the upper-left room, the loop must pass through exactly one of its three eastern walls and one of its two southern walls.
- In particular, in the center row, the eastern walls of the leftmost room can never be used, and the western walls of the rightmost room can never be used.
- Regardless of which of the two overall shapes the loop has, sun rooms and moon rooms must alternate throughout the grid. So as soon as we know whether a single room must be a moon room or sun room, we know for every room whether it's a moon room or sun room.
- The pearls are extremely powerful, because we know the loop must pass through them but also turn in a specific way.
Each mini is solvable independently from the others; the total pearl count is only for checking work.
Example walkthrough for the first mini
Here is a walkthrough for the first mini, reproduced below, as an example.
 🌙 |  ◌ |  ☀️ | ☀️ | ◌ | ☀️ | ||
| ☀️ | 🌙 | 🌙 | 🌙 | ||||
| ☀️ | 🌙 | 🌙 | 🌙 | ||||
| ◌ | 🌙 | ◌ | ☀️ | ||||
| 🌙 | ☀️ | ☀️ | |||||
| 🌙 | ☀️ | ☀️ | 🌙 | ||||
| ☀️ | 🌙 | ||||||
| ◌ | 🌙 | ◌ | ☀️ |
Consider the bottom-right pearl. Notice that regardless of the color of the pearl, it must either pass through the moon to its left, or through the sun on its right (and both if it is a white pearl). Either way, this tells us the positions of the moon and sun rooms. So, in the figure below we highlight all the suns and moons we must pass through in a light blue shade, while we completely black out the suns and moons we must not pass through. Then, remembering our observation that the four corner rooms must connect their orthogonal neighbors, we can already fill in most of the path on the leftmost and rightmost column.
Next we consider the room containing the bottom-left pearl. In order for the path to pass through both that pearl and its sun, the pearl must be black and the path exits the room to the moon in the adjacent room. This forces the bottom-right pearl to be white, so the path must bend at the sun next to it. Hence we have finished the bottom row of rooms. At this point the center two rooms can only be completed in one way, too.
At this point the colors of the remaining pearls are clear and the path can only be finished in one way, as shown below.
Solutions to the logic puzzles
We can then proceed to solve the minis and fill in the pearls. The unique solutions are shown in the table below. (The total count of black and white pearls is not needed to solve any mini; that is, each puzzle is solvable individually without considering any of the others.)
Solution 1
Solution 2
Solution 3
Solution 4
Solution 5
Solution 6
Solution 7
Solution 8
Extraction
Finally, to extract an answer, note that we have conspicuously placed six pearls in each mini, and the pearls are lined up in two columns of three each. Given the whole puzzle is themed around black and white, we use Braille to read a letter from the black pearls in each mini.
Doing so gives us the final answer SOLSTICE.