Puzzle 300 (Loop of Death) [Unique]

This is a Loop of Death puzzle, a unique type. Almost all of your favorite (and unfavorite) loop puzzles have been combined into a single type. Detailed rules, along with an example, follow below the image and comments.

Puzzle 300

Puzzle 300

(Click for larger size)
3/20/2011 5:22 AM ET – Fixed a goof in the far bottom right corner that resulted in no solutions by a minor change to the regions. You probably found this contradiction if you made any progress at all in that area. My apologies.

As far as my marathons/unique puzzles go, my guess is this is probably tied for the easiest – size has something to do with that – but I could be completely off in either direction. Of course, this still means it is going to be really hard.

Grid size is 29 by 29 squares. This means 30 by 30 for the vertex clues, although I never used any of the edges. From that, I’m sure some of you are going to figure out what puzzle I paid homage to in constructing this one, but I’ll leave to you all to guess.

Draw a single closed loop passing through adjacent cells that satisfies all of the constraints given below.

Castle Wall
Some grid squares have a thick black border with white dashed lines, and may have a number and arrow. These are standard Castle Wall clues, so the loop cannot pass through them. If the clue is shaded black, it must be outside of the loop, and similarly all of the white clues must be inside of the loop. Furthermore, if the clue has a left or right arrow, the number in that clue tells the total length of horizontal segments in the arrow’s direction. Likewise, if there is an up or down arrow, the number tells the total length of vertical segments. Equivalently, the number tells how many boundaries in the arrow’s direction are crossed by the path.

Some grid squares have a circle that is either white or black. These are standard Masyu clues. At a white circle, the loop must go straight through. Additionally, it must turn on the square visited right before or right after the white circle (it may turn on both, but not neither). At a black circle, the loop must turn, and then go straight through both of the two adjacent squares.

Some vertices (intersections of two grid lines that touch four grid squares) have a white number inside a small gray square. These are standard Slitherlink clues. The numbers indicate how many of the four potential segments surrounding that vertex are a part of the loop.

Some vertices (intersections of two grid lines that touch four grid squares) have a black number inside a small white square. These are standard Corral clues, so they should all be contained inside of the loop. Furthermore, if we treat the loop as a wall, the number tells how many vertices inside the loop can be seen from the number’s square when looking vertically or horizontally, where the number’s own vertex is counted. Note that only the loop can block the “sight” of a Corral clue; anything else (like Castle Wall ones) may as well be invisible to it.

Double Back / Country Road
The grid is divided into a number of regions by thick lines. Each region in the grid must be visited exactly twice. Furthermore, two adjacent unused squares cannot straddle a region boundary – equivalently, if two adjacent squares are unused, they must be in the same region. The shading of the regions is not relevant to solving.

Below is an example puzzle and its only solution. It is designed more to be a reference for what clues mean what while you’re solving.

Example problem Example solution


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20 Responses to “Puzzle 300 (Loop of Death) [Unique]”

  1. Zotmeister Says:

    Why do I feel as though a gauntlet has been thrown in my direction? Seriously, though, I’m honored, and although I already was inspired to update The One Ring, I’m doubly inspired now. Something tells me I’ll be making another birthday present to myself, fifth-anniversary style… – ZM

  2. Scott Handelman Says:

    When you say the corral clue tells how many vertices can be seen, does that mean until it sees the loop, or until it sees anything blocking its path (like, for example, a castle wall clue)?

  3. Me Me Says:

    this is nice.

  4. Me Me Says:

    Do the intersections that are part of/inside a castle wall clue count for the corral clue?

  5. rob Says:

    Success, yay!

    Thanks for a wonderful puzzle. Looking back, I ran into a contradiction due to that mistake you corrected early on my first try, but second time I didn’t notice I put three lines through the bottom second-from-right area, only running into a contradiction very late. Third try, I took a different order, but again ran into a contradiction near the end. I was quite surprised when I compared partial solutions and noticed the puzzle had changed. It turns out that both times I had made a wrong deduction how the white Masyu clue and the Slitherlink 2 in that same area fit together.


  6. Me Me Says:

    So are the “intersections” in the eyes count? (without dotted lines)

  7. Jonah Says:

    Wow. This was just a joy to solve. You’ve really outdone yourself.

  8. Blaine Says:

    Doh! I’ve trapped myself into numerous contradictions in the lower right corner again and I can’t seem to undo them. Need to start over. I hope the 3rd time is a charm. 🙂

    • Blaine Says:

      Well, I started over and then got to the exact same situation. Then it finally dawned on me on how I was supposed to resolve the situation in the gray region between the bottom of the skull and the corner region. Can’t believe I was almost there and abandoned my progress thinking I’d made some major logic mistake earlier. An assumption about down-up vs. left-right blinded me to another route.

      Another very enjoyable puzzle and a nice construction with the sparse clues. I really like the double-back logic and how the number of known crossings of the region border (usually 3) would then drive information on the final crossing.

  9. Andy Says:

    Woohoo! Finally finished, after working on it sporadically this weekend and last.. My longest sticking point came with 3 of the 4 skull-region boundary crossings located, it drove me crazy needing to find the last one, knowing it would settle so many things.

    Extremely enjoyable to solve – really liked the separate mini-discoveries in each corner, and the center was rewarding to finish up with. I was also repeatedly surprised at how important each of the Corral clues ended up being – the key to the puzzle in my opinion.

    Thanks! Definitely worth the wait, and another puzzle I’m already looking forward to solving again someday.. (Which reminds me, enough time has passed that I should revisit #200)

    • MellowMelon Says:

      The importance of Corral stems from the fact that I was trying to keep the givens pretty sparse, and Corral gives the most information per clue.

      I take it you eventually noticed you can independently reach each of the skull boundary crossings by starting at any corner of the puzzle. The bottom left is probably the hardest one; is that the one that stumped you?

      • Andy Says:

        Haha, the lower left it was. I narrowed down the exits from that 6×6 to somewhere in the NE 3×3 pretty early, but eventually felt silly that I missed the interaction between the down-6 Castle Wall and white Masyu clue for so long. Then again with that CW clue, I found I had ignored the color for a while – after that the rest was smooth sailing.

        I did notice the nice boundary-crossing-per-quadrant property, will try to at least remember that in a year’s time for the resolve.. I particularly liked how the SE quadrant’s crossing’s existence was forced by the 13 Corral clue, but its exact location couldn’t be nailed down until near the end..

      • MellowMelon Says:

        Yep, I knew it.

        Regarding the bit about the inexact position of the lower right entrance, my own solution path had it for the lower left entrance too. You trap the loop on the left side between the two black Castle Wall clues, and there isn’t enough room for both ends to get out without going into the skull room. But maybe there’s a direct way to find the crossing that I missed.

        An even more ridiculous version is to find the other three entrances (like you did), then realize that the lower left part of the skull’s boundary is between a black Castle Wall clue and a white one, so there’s a crossing somewhere. But I don’t think you actually skip any of the logic by seeing this as it’s not precise enough; you’d just get some things earlier than usual.

  10. Hans Says:

    Isn´t there an error in the slitherlink clue of the example puzzle ?
    It says that 1 surrounding segment is contained in the loop
    but actually 3 of the 4 segments are used.

    • MellowMelon Says:

      The problem stems from the fact that I am talking about segments being contained in the loop, as in they are a part of the loop. Squares/borders being in the interior in the loop was not supposed to have anything to do with it. I have clarified the wording in the post; hopefully this will clear up your confusion.

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