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I have applied all of the techniques that I know of, and can't figure out the next logical step. I even turned on the visual clues, but it didn't help.

What would be the next move without resorting to guessing? slitherlink_honeycomb_hard

Update: this puzzle is from a free android app called Slitherlink by Ejelta

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    $\begingroup$ There's a triangle of three fours near the top right, the line always must pass through the centre of such a triangle. The vertical path leading to said centre cannot be empty, else the line between the 5 and one of the fours has nowhere to go. (Posted as a comment, since this gets only one more mark on the grid, and doesn't count as a proper answer) $\endgroup$
    – Bass
    Jan 29 at 0:22
  • $\begingroup$ @Bass that feels like one of those patterns I might have stumbled upon before, but never quite employed it outright... thanks! $\endgroup$
    – slinack
    Jan 29 at 16:59

2 Answers 2

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Building on fijx's excellent answer, here is how it can be continued.

The yellow lines are given by fijx.

Using the same line of reasoning, we must have one of the A's, one of the B's, one of the C's and one of the D's. This forces line E. Line E forces the 2 other green lines around the 4.

enter image description here

After that all of the blue lines can be deduced easily.
The rest of the puzzle is left as an exercise since the OP only asked for the "next logical step".

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There are a couple more lines you can add:

One of A and B must be a line to complete the 3.
So one of C and D must be a line to continue the loop.
So one of E and F must be a line to complete the 4.
So G must be a line to continue the loop.

And, one of H and I must be a line to complete the 5.
So one of C and E must be a line to continue the loop.
So one of D and F must be a line to complete the 4.
So J must be a line to continue the loop.
enter image description here

but I can't see an obvious continuation from there.

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  • $\begingroup$ This is not an answer. It is barely more than Bass's comment. $\endgroup$
    – Daniel Mathias
    Jan 29 at 14:36
  • $\begingroup$ @DanielMathias The poster asked for a "next step", not a complete solution. And I couldn't think of a way to explain this without the picture, so posted as an answer. $\endgroup$
    – fljx
    Jan 29 at 15:03
  • $\begingroup$ Read Bass's comment above. The explanation there is quite clear, though it only indicates one of the lines. Others apparently disagree with by opinion, so I'll leave it at that. $\endgroup$
    – Daniel Mathias
    Jan 29 at 15:28
  • $\begingroup$ This definitely gave me another insight I might be using from now on... Thanks for the very clear explanation! I only accepted Florian's answer because from there I could definitely carry on $\endgroup$
    – slinack
    Jan 29 at 17:05

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