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Here is a grid-deduction puzzle, whose mechanics I have seen under several names such as 'Castle Wall', which is the one I'll use here.
The goal of Castle Wall is to draw a loop enclosing all the numbers in the grid, such that the number represents how many cells it can 'see' orthogonally, including itself. Below is an example puzzle and its solution to clarify how this works.

enter image description here

Below, is your actual challenge. The answer is a four letter word which is quite thematic with the entire solving process of this puzzle.

enter image description here

PSA to anyone who has already made progress, row 3 column 2 has been edited to clear up an ambiguity. Sorry for the error!

FINAL PSA: Row 3 column 2 has been edited yet again... Yours truly was a bit of a doofus, and cleared up the ambiguity in the wrong way! It's definitely correct, now! Super super sorry for this silly mistake.

PSA again?!? Sorry folks, another edit (I know, how careless can I be?) thankfully, this edit doesn't affect anything you've done so far. A red symbol has been changed in row 2 column 2.

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  • $\begingroup$ Just to be perfectly clear, the 7 in the original puzzle can "see" the 4, but that doesnt count, correct? $\endgroup$ – Tom K. Jan 19 '17 at 12:37
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    $\begingroup$ The 7 can see the 4, yes. The 7 can see exactly 7 cells including itself, and whether or not any of those cells have numbers in them or not is irrelevant to the count. $\endgroup$ – TheGreatEscaper Jan 19 '17 at 12:41
  • $\begingroup$ whoops......... $\endgroup$ – Neil W Jan 19 '17 at 12:43
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    $\begingroup$ Oh yeah... I did count the 7 twice. Thanks for the clarification! $\endgroup$ – Tom K. Jan 19 '17 at 12:45
  • $\begingroup$ @MikeQ start with what you know :) other things will start falling into place later. $\endgroup$ – TheGreatEscaper Jan 19 '17 at 13:33
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Final solution

Continuing where Levieux left off...

we can look at the shapes the red letters spell.
enter image description here
Reading off the left "column" of the three stacked squares, then the right "column", gives us PATH I TO P.

So that instruction tells us to:

make a path using the letters from I to P!
enter image description here
There are four numbers along the path: 5, 4, 7, and 5. Converting those to letters spells out EDGE!

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  • $\begingroup$ I think that path I-P idea was Mike Q's. $\endgroup$ – EKons Jan 20 '17 at 10:34
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The castle walls are:

updated image

David gets credit for (row 2, col 2) and (row 3, col 1) because he correctly answered them first.

With these 6 shapes, you can:

map them to the sides of a cube, and connect sides where the borders of the castle walls completely touch. Then, the red symbols in the 8 corners of the cube seem to be symbols. I was able to get these images. cubes edited The letters AHIOPPTT are an anagram for PATH I TO P or PATH P TO I. But which I and P to use?

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  • $\begingroup$ My general rule of thumb/puzzle design ideal is that you will understand the meaning of all information in a puzzle when it is solved. If there is still unused information in a puzzle of mine, you've either skipped some steps (like a recent case... Oops) or you haven't yet arrived at the end destination :) So, 'cube' is a very astute observation, but not the answer. $\endgroup$ – TheGreatEscaper Jan 19 '17 at 14:41
  • $\begingroup$ Your castle walls are all looking good, and indeed their solutions are the key to constructing the cube. Maybe you're not interpreting the way THESE should be joined in the correct way. $\endgroup$ – TheGreatEscaper Jan 19 '17 at 15:03
  • $\begingroup$ @MikeQ, sorry about downvote. It was accidental. I fixed it now. :) $\endgroup$ – Maria Deleva Jan 19 '17 at 18:30
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Row 2 col 2

2-2

Row 3 col 1

3-1 solution

Using Mike Q's solutions for the other grids, I think the next step might be:

enter image description here

But I can't actually visualize it.

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Elaborating on the work all others have done here before me,

I'm guessing the cube will have to be built up like this:
Cube

I don't know where to go from there yet, though..

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  • $\begingroup$ At this point, having a physical copy would certainly be very helpful :) it's hard to see the next step without a 3D cube. $\endgroup$ – TheGreatEscaper Jan 19 '17 at 16:03
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Stage 1, drawing ths castle walls:

enter image description here
That bottom right square in the 6th puzzle could be inside or outside the wall.

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    $\begingroup$ Oops! That ambiguity was a careless oversight by me. I'll edit the post now. $\endgroup$ – TheGreatEscaper Jan 19 '17 at 15:12
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Row1 Col2

enter image description here

Row3 Col2

enter image description here

Not sure what red paths do yet. But I do notice something:

The loops in total include 99 Tiles. A 5x5x5 Eraser Cube can only have 98 in total among its 6 pieces. (9 for centers of each face, 8 for corners, 3 per edge. 9*6+3*12+8=98) Either this is not an Eraser Cube at all or some numbers are wrong.

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  • $\begingroup$ The numbers are all right, in fact I had to make an edit which removes an ambiguity and causes the loops to include 100 tiles! Everyone seems to be on the rig track of making a cube with these, but perhaps the joins don't work in quite the same way as an eraser cube... $\endgroup$ – TheGreatEscaper Jan 19 '17 at 15:16
  • $\begingroup$ Oops, silly me. The edit was wrong, and the 99 tile solution set is the intended one! It's been fixed now :) sorry for the confusion $\endgroup$ – TheGreatEscaper Jan 19 '17 at 15:41

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