An entry in Fortnightly Topic Challenge #32: Grid Deduction Hybrids

Introducing: Jormungand

A combination of Ouroboros (Slitherlink) and Numbersnake (Numbrix) to create the greatest snake-themed grid-logic puzzle the world has ever seen![Citation Needed]

  • Each Numbered clue is a clue to the Ouroborus, as you may have guessed
  • Each Numbered clue is also a portion of a clue to the Numbersnake: i.e. a 1 could represent a 1, or it could represent a 12, or a 31. Any number that contains that digit.
  • All other rules of Ouroborus and Numbersnake apply.

Triangles, Triangles Everywhere!

  • $\begingroup$ Diagonals allowed? $\endgroup$ Jun 21 '17 at 16:48
  • 6
    $\begingroup$ Am I missing something? The top-right two ones seem to indicate that a slitherlink is impossible. $\endgroup$ Jun 21 '17 at 17:03
  • $\begingroup$ So, is this on an icosahedron or something? (Also, how could it be a 31 if there are only 20 triangles?) And are the two puzzles entirely separate? $\endgroup$
    – Deusovi
    Jun 21 '17 at 17:17
  • 2
    $\begingroup$ @greenturtle3141 yes, you are missing something. Deusovi he's just giving an example, but yes he should've chosen 11 or something instead. $\endgroup$
    – dcfyj
    Jun 21 '17 at 17:27
  • 1
    $\begingroup$ @Deusovi 31 as an example doesn't apply to a puzzle of this size (but may apply to a potential future puzzle using similar rulesets), and the two puzzle solutions are separate save for their layout and clues. $\endgroup$
    – Sconibulus
    Jun 21 '17 at 17:30

Jormungand is (a variant of) the name for the snake in Norse mythology that wrapped around the earth. This is apparently (According to OP) a hint that

This is a 3D puzzle!

Most people realised this when they discovered the image given is impossible to solve.

So the first step is realising the image given is a

net of an icosahedron - a 3d shape with 20 faces.

I cut it out, folded it and stuck it together to get:

enter image description here ta da!

I also created (a pretty rubbish) 3d model - viewable here (I believe the link may expire after a while, if it does and you want to see, ping me and I can update.)

Note: I solved the slitherink the day before greenturtle answered, but my mum made me go to bed because it was late so I didn't have time to write up an answer myself.

I solved the slitherink the same way as greenturtle did, so go upvote his answer too and see it for the explanation. I will borrow his picture of the completed net because it is neater:

enter image description here

Now the solution to the numbrix.

The first thing I thought of was that the two 0s must be 10 and 20. Both 0s are connected to a chain of empty triangles that lead up to a 2. These empty triangles must be the numbers 3-9.

enter image description here enter image description here

So the question is which 0 is the 10? Well there are 7 numbers 3-9 and for only one of the 0s allows 7 spaces to the 2 (the one furthest left in the picture) and the other requires an extra 2 numbers. so we can fill out numbers 2-10 + 20:

enter image description here

Now from 10 there is only one direction 11 12 can go so we can fill those in:

enter image description here

From there 13-19 are pretty straightforward

enter image description here (the 0 here should be a 20)

And we get the final number:

enter image description here

Here is the final net:

enter image description here

How it works:

enter image description here

Great puzzle! Very enjoyable



Like Deusovi pointed out, it appears that this is puzzle is probably the net of an icosahedron, and so this puzzle is actually in 3D.

Clearly the 3D is scary, and trying to solve it as-is will make both the solver and the reader bored. So...




X'ing out the edges of the 0 triangle reveals some basic deductions:




We must X out this edge. If it was part of the Slitherlink, then the line will get trapped.

Also noteworthy:


This edge must be part of the Slitherlink. If it was not, then the other two edges of the 2 triangle must be part of the Slitherlink. You can see why this would be absurd.

Now look:


The line must go down, by process of elimination. It can't go left because one of the 1 triangles will have 2 filled edges, and it can't go up-right because the other 1 triangle will not be able to have any filled edges.



Going backward a bit, we see that we must connect these two parts together!

Finally, the rest of the Slitherlink is forced and does not warrant further discussion:



Completed net:


The Slitherlink is done! I don't know about the other part.

  • 3
    $\begingroup$ Someone actually went ahead and took the time to do it. Good job. $\endgroup$ Jun 22 '17 at 4:41
  • 1
    $\begingroup$ I just posted the solution for the Numbrix. Should we make a community wiki to join answers for a full solution? $\endgroup$ Jun 22 '17 at 7:07
  • $\begingroup$ Nicely solved, that's a far prettier folding job than I'd have managed $\endgroup$
    – Sconibulus
    Jun 22 '17 at 13:10

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