here is the next set of our puzzle series for beginners. To be fair, Galaxies (sometimes the longer name “Spiral Galaxies” is used) is not the most classic puzzle style I could think of. On the other hand, Dissection Puzzle types are somewhat rare in the community, and those with variable size and shape of the resulting regions are even rarer, so I think for the sake of diversity it is a decent addition. Here is today’s PDF file: Galaxies
Rules: Divide the grid along the grid lines into regions so that each region contains exactly one dot. Each region must have rotational symmetry, and the dot must be located in the center of rotation.
Example and solution:
I will keep the part about solving techniques shorter this time, mainly because there aren’t many. The most important thing in Galaxies puzzles is to have a notation that works for you. As with most Dissection Puzzles you can either draw borders or skeletons, and when in doubt I recommend both – it is rather slow but helps you keep track of all the things that matter.
Solving steps basically break down into two types: keeping different regions separated, and making sure that each cell belongs to a region at all. (We have seen this in other puzzles before, like Shikaku.) The two lie at different ends of the spectrum, in a manner of speaking, and the puzzles are most enjoyable when there is a nice balance between them.
Drawing borders along the grid lines helps you… well, establish the boundaries of a region. For example, the cells R1C4 and R1C5 in Galaxies 1 (from the PDF file) cannot belong to the same region because the latter contains half a dot, but the former already has a dot. Likewise, R1C2 and R2C2 must lie in different regions, so you can draw border segments between those cells. Note that not even a piece of a dot can belong to another region, so whenever parts of dots are given in adjacent cells, they can be separated.
This typically does not get you very far, but here is the cute part: If you have located a border piece for a region, you can draw another piece in the exact opposite position (relative to the dot in question). For example, the border between R1C4 and R1C5 translates to a border between R1C3 and R1C4, based on the B dot. Similarly, the border separating R1C2 and R2C2 implies another border segment between R3C2 and R4C2.
Cells near the edge of the grid – or even a corner – are a good place to start with this. For example, the “I” dot in the same grid is already boxed in from the right and from below, hence two more borders can be drawn on the other sides. In short, a dot in a corner cell always becomes a region of size 1. Something similar works for dots on an edge, like with the “H” region in Galaxies 1, or even with a dot on a vertex next to a corner (the situation is present in the example).
Steps of this kind also occur in abundance in grid parts where many dots are clustered together. Sometimes they just give you the same information from different directions (as with the border segments between R4C1 and R4C2 and between R5C2 and R5C3 in Galaxies 2), but most of the time it is worth exploiting such constellations.
It is noteworthy that the term “clustered” can be stretched. For instance, there are quite a few dots on edges in Galaxies 2, and the top-right corner area does not seem particularly stuffed. Yet there are a lot of border segments to be located, since dots on edges or vertices generally cover more ground.
Extending borders like this can be a slow and tedious process. At the same time, there will be situations when it is hard to connect a given cell to a dot at all. Or, I should say, when there is only one option – not necessarily hard, but informative because there is no alternative. A very simple case can be seen with the bottom-left corner in Galaxies 2. The cell R5C1 should be separated by R4C1 from the other technique, so it has to belong to the “G” region.
This step does not only occur when an empty cell is surrounded by a lot of border segments, but also when it is far away from most dots at all. For example, there is not a lot going on near the cells R4C5 and R5C5 at this point, but no region except the one with the “F” dot can include these particular cells. And the borders those two cells already have can be transferred to the other side as before.
That second kind of solving technique is especially tricky when the cell to look at is unremarkable. Just as areas with lots of dots invite the first technique, areas with very few dots are susceptible to the second. But what if the relevant cells lies at some intermediate distance, with a moderate number of dots nearby? They can easily be overlooked, and that is mostly where the difficulty in this puzzle style comes from.
The point is, there are no really difficult steps, but it may difficult to spot the simple ones. That is why Galaxies puzzles in smaller grids are generally easier: They are easy to survey, and it is almost impossible to hide anything in them.
What you should keep in mind is that the regions can be really enormous. To demonstrate what I mean, I have designed the last few puzzles of either size in today’s set so that they include surprisingly large galaxies. Transferring border segments from one side to another requires more care in case of large regions, but then, discovering the extent of giant galaxies is where (in my opinion) the beauty of this puzzle type lies. Have fun!