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This puzzle is part of the Monthly Topic Challenge #13: Variety Slitherlinks.

Adding a bit of colour to enhance the loopy goodness of a traditional Slitherlink.

  • Draw a single, non-intersecting loop that only consists of horizontal and vertical segments between the dots.
  • Numbers inside a cell indicate how many of the edges of that cell are part of the loop.
  • Shade the interior of the loop so that every cell is part of an L, I, T, or S tetromino.
  • No 2×2 group of cells can be entirely shaded.
  • When two tetrominoes share an edge, they must not be of the same type (L, I, T, or S), regardless of rotations or reflections.
    enter image description here

Should be solvable by hand with no guessing/backtracking.

Penpa link (If you want the Penpa automated checker to work, Use Green for the loop, and (DG, GR, LG, BK) for shading.)

fljx
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1 Answers1

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What a wonderful puzzle!

I started with typical sli-li deductions but had to use all the rules to disambiguate.

e.g.,:

Hint1 The adjacency restriction helps disambiguate L and S.

Solution:

Solution

How I started out:

Starting out Got this far with standard slitherlink (I think?)

These squares must be part of an L with long tail up or down due to T adjacency. The x in the upper left is needed to avoid a region with area 1 or 3. tetromino deduction

n1000
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  • Nicely done. Can you add some more detail on your solve path. I'm curious to see how close it was to the intended route, or if there are shortcuts I missed when testing/tweaking. – fljx Aug 03 '23 at 16:01
  • @fljx Is it fine if I add an answer with more detail and explanation? – new Q Open Wid Aug 03 '23 at 16:45
  • Sure. I'll try and retrace my steps and update later. – n1000 Aug 03 '23 at 17:08
  • @fljx, I'm sorry. I deleted most of my solving path while trying to highlight one step in Penpa...still getting the hang of it. I added some of my initial steps, at least. – n1000 Aug 03 '23 at 17:52
  • @newQOpenWid I'd be interested to see it, but I will be accepting n1000's answer as it is complete and was the first one posted. – fljx Aug 03 '23 at 19:10
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    @n1000 When using Penpa, I make heavy use of the "clone" button. It does what it says, and gives you a clone of your current position in a new tab, complete with undo/redo history. I find it very useful for creating an instant backup if I'm about to make a potentially destructive change. – fljx Aug 03 '23 at 19:14
  • Your "started out" image is incorrect - the 3 at (1, 5) is not going to work. – Spitemaster Aug 03 '23 at 22:16
  • It's a good puzzle. I think the disambiguation n1000 mentions at the start is the only place I had to use the "no adjacency" rule. I used the "no 2x2 inside the loop" rule quite a bit. – ralphmerridew Aug 03 '23 at 23:52
  • @Spitemaster good catch. I corrected that later but lost the penpa history while retracing my steps. – n1000 Aug 04 '23 at 00:34