10
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Here is a regular Gokigen Naname a.k.a Slalom a.k.a Slant puzzle.
An online (mobile-friendly) version is available here.

enter image description here

Rules:

  • Put a slash (diagonal line) on each cell.
  • Each number in a circle denotes the number of slashes touching it.
  • The slashes should not form a loop.
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6
  • $\begingroup$ This is a fun puzzle type, I love this! To clarify because I've never solved this type before: When you say the slashes should not form a loop, do you mean that the slashes shouldn't connect in a way that they form an enclosed loop anywhere in the puzzle? $\endgroup$
    – Sciborg
    Commented Sep 17, 2020 at 1:38
  • 1
    $\begingroup$ Wow - I saw this and thought "Hashi!" which I love, but this is an awesome puzzle type of its own... Thanks for the link. $\endgroup$
    – Graylocke
    Commented Sep 17, 2020 at 2:06
  • $\begingroup$ @Sciborg yep, that's correct :) $\endgroup$
    – athin
    Commented Sep 17, 2020 at 3:09
  • $\begingroup$ @athin Awesome! Great puzzle :) $\endgroup$
    – Sciborg
    Commented Sep 17, 2020 at 3:11
  • $\begingroup$ If a corner does NOT have a number on it, does that mean that no lines are touching it? $\endgroup$
    – Vilx-
    Commented Sep 17, 2020 at 10:25

1 Answer 1

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You can get this far with relatively simple arguments based on a single clue at a time:

enter image description here

Then, there's a useful pattern to notice:

If two 1s in the middle of the grid are diagonally adjacent, they cannot be directly connected. That would create a loop around both of them.

This gives us a bit more:
enter image description here

That deduction can actually be extended:

You can't have any "1-2-2-2-2-2-2-1" chains that don't touch the edge, with any number of 2s in the middle, because then you would draw a loop around all of them!

This lets you draw a slash on any 2 that has three 1s diagonally adjacent to it: the fourth edge must be used, because if it wasn't, you'd have a 1-2-1 chain and a loop.

enter image description here

And now it's time for a big deduction:

enter image description here The lines marked in red must connect to the edge of the grid somehow, because they cannot form a loop.

The yellow-highlighted 1 clues block them off -- they cannot traverse those clues on their path to the edge of the grid. This determines their escape routes:
enter image description here

And now we can finish off the puzzle, with just single-vertex deductions. The solution is below:

enter image description here

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5
  • 1
    $\begingroup$ At least one of your deductions is not based on rules given by OP. It is said nowhere that lines have to end at the edge. I searched for the rules and for this puzzle it is absolutely ok for a line just to stop anywhere in the grid. So I think your solution -though obeying all given rules- used wrong additional rules to be created... don't know if it matters though $\endgroup$
    – Tode
    Commented Sep 17, 2020 at 13:20
  • $\begingroup$ Very nicely done! :) $\endgroup$
    – athin
    Commented Sep 17, 2020 at 22:33
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    $\begingroup$ @TorstenLink Apparently Deusovi noted above "The lines marked in red must connect to the edge of the grid somehow, because they cannot form a loop." This is actually not an added rule: lines have to end at the edge can be deducted by not forming a loop. Some sources "added" that rule just to help solver skip that deduction I think. $\endgroup$
    – athin
    Commented Sep 17, 2020 at 22:47
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    $\begingroup$ @TorstenLink If a line doesn't connect to the edge, the lines immediately around it form a loop. This works just like the 'chains' mentioned earlier, but on a bigger scale. $\endgroup$
    – Deusovi
    Commented Sep 18, 2020 at 3:00
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    $\begingroup$ Love the solve.. I got stopped staring at exactly your screen 4 and 5 for ages! $\endgroup$
    – Graylocke
    Commented Sep 18, 2020 at 4:00

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