# Gokigen Naname - 1 and 2

Here is a regular Gokigen Naname a.k.a Slalom a.k.a Slant puzzle.
An online (mobile-friendly) version is available 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.
• 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? Commented Sep 17, 2020 at 1:38
• Wow - I saw this and thought "Hashi!" which I love, but this is an awesome puzzle type of its own... Thanks for the link. Commented Sep 17, 2020 at 2:06
• @Sciborg yep, that's correct :) Commented Sep 17, 2020 at 3:09
• @athin Awesome! Great puzzle :) Commented Sep 17, 2020 at 3:11
• If a corner does NOT have a number on it, does that mean that no lines are touching it? Commented Sep 17, 2020 at 10:25

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

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:

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.

And now it's time for a big deduction:

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:

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

• 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
– Tode
Commented Sep 17, 2020 at 13:20
• Very nicely done! :) Commented Sep 17, 2020 at 22:33
• @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. Commented Sep 17, 2020 at 22:47
• @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.
– Deusovi
Commented Sep 18, 2020 at 3:00
• Love the solve.. I got stopped staring at exactly your screen 4 and 5 for ages! Commented Sep 18, 2020 at 4:00