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An entry in Fortnightly Topic Challenge #35: Restricted Title 1. Inspired by the title of this xkcd comic, but in no way related or affiliated beyond the shared name.


This is the stingray nebula:

Stingray Nebula

Spectacular, isn't it?


This is a nebula map of another part of the sky:

Unfinished nebula map

Unfortunately, it only contains data from a limited spectrum of light, so whilst you can see the stars, you can't see the nebulae themselves. I need your help restoring it...

Luckily, as with all nebula maps, it follow the standard rules, which - as I'm sure you'll recall - consist of:

  1. Every square of the map belongs to exactly one nebula
  2. Each nebula consists of a single set of contiguous squares connected by edges
  3. All nebulae have at least one axis of reflective symmetry
  4. The letter in each star is a relative magnitude indicating the number of squares in the containing nebula:
    • $A$ is strictly less than $B$, which is strictly less than $C$, and so on...
    • In this map, $A = 1$ and $L = 20$
  5. Stars are considered to be part of a nebula, thus cannot be shared and must be taken into account when applying rule 3

Complete the nebula map by indicating which squares of the grid are contained within each nebula.

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  • 1
    $\begingroup$ Is a nebula necessarily connected? $\endgroup$ – Riley May 29 '18 at 2:29
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    $\begingroup$ @Riley - yes, all squares within a given nebula are contiguous (on edges, so no diagonals). $\endgroup$ – Alconja May 29 '18 at 2:42
  • $\begingroup$ Must the shown letters be symmetric within the nebulae? For example, is a straight horizontal line with five squares connecting the Es in the top left corner allowed? $\endgroup$ – Austin Weaver May 29 '18 at 3:12
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    $\begingroup$ @AustinWeaver - that would still be symmetrical anyway (vertically mirrored), but yes, stars are part of the nebula, so rule 3 still applies. $\endgroup$ – Alconja May 29 '18 at 3:27
  • $\begingroup$ Lovely puzzle. Saw Alconja, was not disappointed. $\endgroup$ – BmyGuest Jun 8 '18 at 8:24
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Resident Grid Detective checking in to drop off the answer to this lovely puzzle. Step by step pics coming soon.

enter image description here

Step by step ish:

enter image description here This happens because G is at least area 7. Test the I just above G, which is now at least area 8; it doesn’t work in a nebula by itself, so it needs to join with the I above it, and with the area restriction of at least 8 you can make some progress on its shape. enter image description here Now note that little cranny above the Is - This can only be accessed by the J, which tells us the axis of symmetry for the J is vertical. Also, the Es which are at least 5 get forced to join up and go down. This forces the J to expand around the A. enter image description here The cell to the upper right of the J has to be taken by one of the Hs, and this only works if they join up like so.enter image description here When this happens, the F gets forced down, and a lot of stuff also happened with the L - I’ll try to explain that! Essentially in the top right 4x5 area, there are 20 cells. At most 1 is taken by the F, exactly 3 by the C, at most 12 by the Ds and the rest would have to be taken by the L. This means the L has to go up into that area. L can’t have a vertical axis of symmetry (you can’t fit 20 cells like that) so a horizontal axis of symmetry forces the L to extend upwards like so. And then the Ds to the right, which we know have area 4, get forced. enter image description here The cell to the lower right of the lower right A can only be taken by L, so we get more stuff. Also noticing that L can’t quite get big enough at the right side without crushing the D/Cs at the top, L has to extend left. Now the D to the upper left of L gets forced to join with the D above, and L gets forced to expand a bit more in the top left like so: enter image description here enter image description here Also the F in the corner got forced to join with another F by virtue of being at least 6 squares. Minor bifurcation incoming: the B above the Fs either extends left of up. If you assume it goes to the left, there’s a magic cell that needs to be taken up by K, which traps an F at the bottom like so: enter image description here I forgot to mention the D extended left and up because it’s the only letter that could take those cells. Anyway that blue stuff is all bad, so the B has to actually go up instead. enter image description here That forces the D to be a square. Now the blue circled area can only be taken by K or F, and it can’t all be taken by F, so K has to extend there and it can only do so in this way: enter image description here This forces the E above the K down as it’s the only letter which can take that cell. This causes a chain reaction of things - the E can only be completed to 5 cells by making a T shape, Fs turn out to be size 7, and the Fs down at the bottom right almost get completed. If the currently uncompleted F takes the cells adjacent to the star, then neither K nor F can take the cell to the upper right of that F area. So the F gets completed as a sort of tilted W: enter image description here and the rest is pretty easy to finish up.

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