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Based on user477343's Find the Path puzzle I have produced a slightly larger puzzle based on a similar mechanic. Goal is as follows:

  • Draw a continuous path between the two red dots.
  • The path must follow the edges of the marked grid (including the blue outside edges).
  • The path cannot trace any edge more than once and must not cross itself, but it may intersect with itself at any corner.
  • The numbers in each square in the grid show the number of edges of each square that must be followed by the path.

enter image description here

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I solve it in two stages.

First stage is

to solve which edges to include. This is relatively straightforward, starting at the zeroes and fours, and keeping in mind that every intersection other than the start and end point must have an even number of edges that meet there. There is only one solution.
enter image description here

The second stage is

to determine how to split each intersection where four edges meet. A simple way to do this is to make all intersections look like \ \, i.e. connecting bottom and left together, and right and top together. Then find any loop that is unconnected to the rest, and switch one of the intersections on its boundary from \ \ to / / (connecting bottom to right, left to top). This connects that loop to some other part. Repeat this until there are no separated loops left, and you will end up with one long line, as required. There are many valid ways to choose the intersections.
enter image description here

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    $\begingroup$ Did you find it interesting-ish? I am still looking at a way to force a single solution for the 'no-crossong' rule. $\endgroup$ – Penguino Oct 1 '18 at 19:48
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    $\begingroup$ @Penguino I play a lot of slitherlink, so it felt a little odd to have intersections with 4 edges meeting. Once I got used to that it wasn't very difficult, as I don't think I needed to use much look-ahead or make use of any tricky technique. This may have to do with the fact that every cel contained a number. I'm sure many of the clues could be removed to make it harder. I think that forcing a single solution for the crossings will be tricky, because it will drastically limit the shape of the path. $\endgroup$ – Jaap Scherphuis Oct 1 '18 at 20:52
  • $\begingroup$ Scherphius good suggestion - another option I have considered is having two or more paths (that cant trace over each other but can intersect), perhaps with different coloured numbers to tell how many edges of all/some colours surround all/some squares $\endgroup$ – Penguino Oct 1 '18 at 23:49

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