Black or Whiteor Moon or Sun
Solution
This puzzle is an extension of the earlier puzzle Black or White, in which we needed to place a black or white pearl in every green cell. This version consists of only a single much larger grid.
Figuring out the rules of the logic puzzle
This time, the puzzle is entitled Black or White or Moon or Sun, and the counts include moons and suns. The total number of objects to place is 168, the entire size of the grid, meaning we are asked to fill the entire grid with pearls, moons, or suns, and draw a loop satisfying the Masyu and Moon-or-Sun constraints from before. To repeat the rules in brief from the last puzzle:
- 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.
Like in the previous puzzle, 39 of the cells are already marked as pearls, so we know the black and white pearls should be placed in those cells, and the remaining cells should be filled with moons and suns. Actually filling in the remaining moons and suns, though, isn't important to solving the logic. Because every cell is filled, the logic puzzle can really be thought of as:
- Find a valid loop satisfying all the constraints
- Take every moon room, and fill in moons on the cells passed through (that don't already have a pearl) and suns in the other cells.
- Take every sun room, and fill in suns on the cells passed through (that don't already have a pearl) and moons in the other cells.
Finding the loop
Strategy
So we focus on just finding the loop to start. This is a much tougher logic puzzle than the minis from before, but it can still be solved systematically and is less scary than our initial reaction might be upon opening the puzzle page and seeing a nearly empty grid. Some overall strategies for solving the grid are:
- Like before, the pearls each carry a lot of information, even before knowing whether the pearl should be black or white. In general, black pearls are rarer, because the bending L-shape of a black pearl always causes the loop to exit the room at least once, and this puts a lot of restrictions on the shape of the loop.
- The rooms also similarly carry a lot of information, since we know each room can only be entered once. For example, like before, we know that the upper-left room must be connected to the two rooms next to it.
- There are several different orders of the rooms that the loop can move through this time, unlike the previous minis where there were only two. Despite this, sun rooms and moon rooms must still alternate throughout the grid in a checkerboard fashion, regardless of the shape of the loop! 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.
Breaking in
A good place to break in is the bottom-left corner, which has two pearls and a single moon. A bit of experimentation shows that it actually must be a sun room: there are only two ways the loop could move through the pearls in that room, and the case where it's a moon room causes the room immediately to its east to encounter issues due to the pearl there. Hence, we can immediately deduce the bottom-left room is a sun room, and therefore that
- Every room with a moon in the bottom row is a sun room;
- The two rooms with moons in the top row must be moon rooms;
- The room with the moon in the second row and rightmost column is a sun room.
From here, we can actually move to the upper-right room. We know the loop must pass through its pearl in a Masyu fashion, it must pass through the moon, and it must enter and exit through its western and southern wall. There's in fact only one way to do this that is compatible with the room immediately to the west, and so we know exactly how the loop looks here to start too.
Completed grid
Following through with the logic slowly, we can fill in the entire grid. The completed grid is shown in the image below. (The specially shaded rooms will be explained momentarily for extraction.)
Note the total counts given in the puzzle are not necessary to complete the logic puzzle and are only there to assist with double-checking and help clarify what the rules of the puzzle are.
If we then fill the entire grid with moons and suns, we get the following:
 ☀️ | ☀️ |  🌙 | 🌙 | ☀️ | 🌙 | ☀️ |  ⚫ | 🌙 | 🌙 | 🌙 | ⚫ | 🌙 | 🌙 |
| 🌙 |  ⚪ | ☀️ | ⚫ | ☀️ | ⚪ | 🌙 | ☀️ | 🌙 | ⚪ | 🌙 | ☀️ | 🌙 | 🌙 |
| 🌙 | ☀️ | 🌙 | ⚪ | 🌙 | 🌙 | ☀️ | ☀️ | 🌙 | 🌙 | ☀️ | ⚫ | ⚪ | ☀️ |
| ☀️ | ☀️ | ☀️ | 🌙 | ⚪ | 🌙 | ⚪ | ☀️ | ☀️ | ☀️ | 🌙 | ⚪ | ☀️ | 🌙 |
| 🌙 | ⚪ | ☀️ | ⚪ | ☀️ | ☀️ | ⚪ | ☀️ | 🌙 | ⚪ | 🌙 | 🌙 | 🌙 | 🌙 |
| 🌙 | ⚪ | ☀️ | 🌙 | ⚪ | ☀️ | 🌙 | 🌙 | 🌙 | ☀️ | ☀️ | ⚪ | 🌙 | 🌙 |
| 🌙 | 🌙 | 🌙 | ☀️ | 🌙 | ⚫ | 🌙 | ⚪ | ☀️ | ⚪ | 🌙 | ⚫ | ⚪ | ⚫ |
| 🌙 | ☀️ | 🌙 | ⚪ | ☀️ | 🌙 | 🌙 | ⚫ | 🌙 | ⚫ | 🌙 | 🌙 | ☀️ | 🌙 |
| 🌙 | 🌙 | 🌙 | ⚪ | ☀️ | 🌙 | 🌙 | 🌙 | ☀️ | ☀️ | 🌙 | 🌙 | ☀️ | ⚪ |
| 🌙 | ⚪ | 🌙 | 🌙 | 🌙 | ☀️ | 🌙 | 🌙 | 🌙 | ⚫ | ⚪ | 🌙 | ☀️ | ☀️ |
| 🌙 | ⚪ | 🌙 | 🌙 | ☀️ | ☀️ | 🌙 | 🌙 | 🌙 | ☀️ | 🌙 | 🌙 | ☀️ | 🌙 |
| 🌙 | ☀️ | ⚪ | 🌙 | ☀️ | ⚪ | 🌙 | ⚫ | ⚪ | ☀️ | 🌙 | ⚪ | ☀️ | 🌙 |
Extraction
Finally, we turn to the extraction. Now that every cell is filled with symbols, the puzzle tells us to treat moons and black pearls as black, and suns and white pearls as white. This means that each of the 28 rooms could potentially form a Braille letter. However, only nine of the rooms actually form a Braille letter; they are highlighted below.
| ☀️ | ☀️ | 🌙 | 🌙 | ☀️ | 🌙 | ☀️ | ⚫ | 🌙 | 🌙 | 🌙 | ⚫ | 🌙 | 🌙 |
| 🌙 | ⚪ | ☀️ | ⚫ | ☀️ | ⚪ | 🌙 | ☀️ | 🌙 | ⚪ | 🌙 | ☀️ | 🌙 | 🌙 |
| 🌙 | ☀️ | 🌙 | ⚪ | 🌙 | 🌙 | ☀️ | ☀️ | 🌙 | 🌙 | ☀️ | ⚫ | ⚪ | ☀️ |
| ☀️ | ☀️ | ☀️ | 🌙 | ⚪ | 🌙 | ⚪ | ☀️ | ☀️ | ☀️ | 🌙 | ⚪ | ☀️ | 🌙 |
| 🌙 | ⚪ | ☀️ | ⚪ | ☀️ | ☀️ | ⚪ | ☀️ | 🌙 | ⚪ | 🌙 | 🌙 | 🌙 | 🌙 |
| 🌙 | ⚪ | ☀️ | 🌙 | ⚪ | ☀️ | 🌙 | 🌙 | 🌙 | ☀️ | ☀️ | ⚪ | 🌙 | 🌙 |
| 🌙 | 🌙 | 🌙 | ☀️ | 🌙 | ⚫ | 🌙 | ⚪ | ☀️ | ⚪ | 🌙 | ⚫ | ⚪ | ⚫ |
| 🌙 | ☀️ | 🌙 | ⚪ | ☀️ | 🌙 | 🌙 | ⚫ | 🌙 | ⚫ | 🌙 | 🌙 | ☀️ | 🌙 |
| 🌙 | 🌙 | 🌙 | ⚪ | ☀️ | 🌙 | 🌙 | 🌙 | ☀️ | ☀️ | 🌙 | 🌙 | ☀️ | ⚪ |
| 🌙 | ⚪ | 🌙 | 🌙 | 🌙 | ☀️ | 🌙 | 🌙 | 🌙 | ⚫ | ⚪ | 🌙 | ☀️ | ☀️ |
| 🌙 | ⚪ | 🌙 | 🌙 | ☀️ | ☀️ | 🌙 | 🌙 | 🌙 | ☀️ | 🌙 | 🌙 | ☀️ | 🌙 |
| 🌙 | ☀️ | ⚪ | 🌙 | ☀️ | ⚪ | 🌙 | ⚫ | ⚪ | ☀️ | 🌙 | ⚪ | ☀️ | 🌙 |
But the extraction image shows a loop of 28 rooms with nine of the rooms highlighted in green, matching the number of valid Braille letters. Moreover, if we consider the rooms in the order visited by the loop, we see that the valid Braille letters line up exactly with the green cells. (The cell at 12 o'clock also conveniently lines up with the upper-left cell, and the loops have the same orientation, but this information is not necessary.)
Reading those green cells in Braille yields the following table:
| Loop Order | Cell location | Braille | Letter |
|---|---|---|---|
| 1 | Row 1, Col 2 | ⠝ | N |
| 2 | Row 1, Col 4 | ⠊ | I |
| 3 | Row 1, Col 7 | ⠛ | G |
| 4 | Row 2, Col 6 | ⠓ | H |
| 5 | Row 4, Col 6 | ⠞ | T |
| 6 | Row 4, Col 5 | ⠋ | F |
| 7 | Row 4, Col 3 | ⠁ | A |
| 8 | Row 3, Col 2 | ⠇ | L |
| 9 | Row 4, Col 1 | ⠇ | L |
Hence the final answer NIGHTFALL.
(Strictly speaking, if we were convinced the extraction must be Braille, then the image of the loop at the bottom with green highlights is unneeded for extracting the answer. We can just read the valid letters in loop order and get the answer! However, the loop was added anyway to assure solvers that they were doing the right thing, even when only some of the rooms gave valid Braille letters.)