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This is follow-up problem for Another four 3D masyu

Your little dog has been abducted by aliens, and they will do unthinkable things to it. That is unless you provide solutions for problems C and D, precisely following the 3D masyu rules. In the previous problem it was proven impossible. It seems all is lost but you must do your best to try and save your dog.

This is a three-dimensional masyu puzzle. The five squares depict the layers of a $5\times5\times5$ cube. The goal is to make a single loop in 3D space which fulfills the following properties:

  • The line passes through centres of cells and makes 90-degree turns only.
  • The line cannot cross itself or branch off in multiple directions.
  • The line passes through every circle.
  • When passing through a white circle, - in this particular puzzle those not present
  • When passing through a black circle, the line must make a turn in the circled cell and continue straight for at least one cell on both sides.

enter image description here

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    $\begingroup$ Does this answer your question? Another four 3D masyu $\endgroup$
    – fljx
    Commented Apr 22 at 12:12
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    $\begingroup$ @fljx I think I got it the point here is to rot13(svaq n fbyhgvba rkcybvgvat n ybbcubyr va gur ehyrf, rira gubhtu vg jbhyq abg or npprcgrq va gur fcvevg bs znflh). OP really needs to clarify the question, maybe adding lateral-thinking tag, or some hint that this differs from the previous problem $\endgroup$
    – Fluorine
    Commented Apr 22 at 13:16
  • $\begingroup$ @fljx: Answered question you pointed, is also posted by me, moreover, I assure you, it was intended originally to add this follow-up. I add tag lateral-thinking. $\endgroup$
    – Alexey Birukov
    Commented Apr 22 at 13:31
  • $\begingroup$ @Fluorine: thank you very much for question improvement! $\endgroup$
    – Alexey Birukov
    Commented Apr 22 at 14:14

2 Answers 2

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The way to find the answer to this impossible problem is:

By using the rule "The line passes through centres of cells and makes 90-degree turns only." This rule actually allows for diagonal crossing, as long as you do 90-degree turns and all the cells you cross are crossed by their centers.

Version C:

Variant C

I fiddled around with the diagonal in the central layer, sending one extremity up and one down, the rest worked out by it itself

Version D:

Variant D

Well this one ended up being a mess, and I'm really not convinced my solution has any elegance but I started by the diagonal at the top, as it worked nicely in the previous one, that's basically the only logical move i made, the rest was heuristic, trying to free as much "columns" in the cube to allow for movement between layers. Maybe someone will come up with a better put answer, easily obtainable and a bit more logical.

Anyone feel free to double check the correctness of these, my head hurts with this 3D stuff so I'm not 100% confident in particular for version D.

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  • $\begingroup$ Very good, I hope you enjoyed it as much as I did! $\endgroup$
    – Alexey Birukov
    Commented Apr 23 at 8:53
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I think I found a more symmetric solution for both variants.

I reuse the notation from my answer to the previous puzzle. Green X marks a line going through the layer orthogonally at that cell. In addition, the half-lines in D indicate a line going through the layer at 45 degrees.

Variant C

Finding this was pretty much a brute-force by hand.

Variant D

This one went very smoothly from the first (leftmost) layer to the third, and to the fifth. The idea of using the center dot as a bridge for the fifth layer also came out naturally, which I especially like about this solution.

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  • $\begingroup$ Indeed, great addition! $\endgroup$
    – Alexey Birukov
    Commented Apr 23 at 8:51

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