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Lately, I've been interested in Gokigen Naname a.k.a Slalom a.k.a Slant. Luckily, Simon Tatham has a generator for Slant. Usually, the generated puzzle is so-so, but this particular generated puzzle amused me as it has a nice solving path (without guessing of course.) Then I decide to share the puzzle to you.


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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.

An online (mobile-friendly) version is available here.

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  • $\begingroup$ Do you have a game ID that we can use for Simon Tatham's Slant? You can find it in the "Game" menu under "Specific..." $\endgroup$ – Magma May 6 at 22:03
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    $\begingroup$ Transcribed it myself: 12x10:a11f1d1a3b23c3b22a2b1a1a1c23b2a1131b221a13113a2c22b1g22a21a31b111a13b322b1b1c23a1d1a11c321a2c1a1e1a1 $\endgroup$ – Magma May 6 at 22:06
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    $\begingroup$ Thanks, @Magma! Apparently I forgot to include that.. $\endgroup$ – athin May 6 at 22:09
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Solution:

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Step by step:

(This is the first time I've tried to solve one of these, so sorry if my explanations and/or logic are confusing or in a weird order and if my terminology is weird :) )

1:

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Adjacent threes must have lines away from each other as so, which complated a one. The one bottom right must have a line into it as so.

2:

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Two ones, diagonally adjacent and not on the edge, cannot go into each other without forcing a closed loop around the two ones, so all diagonally adjacent ones have a line between as so.

3:

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Completed dots can now have the cells around filled in as it is known the slashes don't go into the dots. This completes some more dots.

4:

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Closing off the completed three, completes a one, which when closed off means a slash goes into the one on the left. When this gets closed off, it completes some of the surrounding twos.

5:

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Closing off some more twos creates some more completed dots which can then also be closed off.

6:

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The three cannot go into the 1 without forcing two lines into a one to close off a completed two further down. So the slant must be the other way, which completes a 3 which causes other completions when being closed off.

7:

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Closing off the completed two, completes a one, and by closing that one off the bottom right can be completed.

8:

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The almost completed three top right cannot go into the one as closing off will cause a fourth line to go into the three. Therefore it must go into the two, causing a chain of completions via closing off.

9:

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Some simple deductions regarding avoidance of loops can be made bottom left, and further up to the left a completed two can be closed off to complete the lower left side.

10:

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The only solution to the bottom left now is as so.

11:

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The only solution to the bottom right (the key here is to avoid loops as there are a lot of potential ones) is as so.

12 (final):

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The ones top left cannot go into each other without causing three lines into a two, so must be separated. This causes some closing off which completes some twos and from here, we can complete the rest!

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  • $\begingroup$ From step 3 to 4: How do you fill the 1 in row 5/col 4? I am stuck at a similar situation and cannot think of a way to solve that spot. $\endgroup$ – daw May 7 at 15:50
  • $\begingroup$ @daw I'll be honest, I can't remember. I probably played around a lil and found that was the only scenario that worked, but it took a while to solve and I only saved the pictures, and didn't save my notes this time. Sorry :) $\endgroup$ – Beastly Gerbil May 7 at 16:24
  • $\begingroup$ thanks anyway :) $\endgroup$ – daw May 7 at 18:06
  • $\begingroup$ Well done, checkmark awarded! For step 3 to 4, actually there are some deductions which can be made on the left middle-bottom part, e.g. the three and the collection of ones. After that I recall you can start deducing from bottom to top on the left side then have the similar result. (I'm on mobile so I couldn't give the specific path, but that's the idea). $\endgroup$ – athin May 7 at 21:51

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