An entry in Fortnightly Topic Challenge #32: Grid Deduction Hybrids


My dear friend researches and designs canal irrigation systems in a remote desert. He's been missing for two weeks. Members of his research team have reported erratic changes in his behavior prior to his disappearance, and that he's been adding random letters and numbers on the edges of his maps. Here are scans of all the maps I could find in his office.

Map 1

Map 2

Map 3

Map 4

Map 5

This last one had no text or north arrow, so I'm not sure if it's oriented correctly.

There were some other strange drawings in his office as well. This was pinned on the wall.

Triptych

This was found in a secret drawer in his desk.

enter image description here

And this was on a piece of vellum on his drafting board.

Vellum

Where could he have gone?

At long last, a hint:

as4s4hetic's observation about the number of sides of the shapes corresponding to the number of Yellow/Red cells is a complete (and quite unlikely) coincidence that unfortunately I didn't catch, forming a red herring I think many are understandably chasing. The shapes have a different meaning. Other than that, as4s4hetic is very much on the right track and excruciatingly close to discovering a critical part of how this hybrid is structured.

  • 5
    +1 Beautiful artwork! Did you draw these yourself? – Wen1now Jun 25 '17 at 0:18
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    @Wen1now sure did. Pencil, watercolor, and micron on watercolor paper, except the vellum. – paramesis Jun 25 '17 at 0:57
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    OK; it looks like each of these is a Yin-Yang puzzle, with red squares indicating cells of one colour. jacoblance.wordpress.com/category/rules/yin-yang-rules I also note that the letters in the first puzzle anagram to SECRET, though I don't know how relevant this is as I can't find an anagram for the letters in the second set. Also, the second puzzle seems to have two solutions, so there's some new rule introduced there that differentiates between them. – edderiofer Jun 25 '17 at 10:30
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    @edderiofer, WIND CANALS as an anagram for the second set? – Peter Taylor Jun 27 '17 at 19:13
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    @PeterTaylor CANAL WINDS seems more likely – as4s4hetic Jan 25 at 12:06
up vote 15 down vote
+100

I have noticed that in the first image,

The number of edges of the shapes in the red squares correspond to the number of orange (and red) squares within the 3x3 grid surrounding the square.

Solving picture 2 using the rules of the game yin-yang (suggested by @edderiofer) gives the unique solution

enter image description here]

Now, adding shapes to the second image using the rule discovered in the first gives the new image

enter image description here]

I actually think it is the number of sides of the shapes rather than the shapes themselves that matter - we can write the sides and coordinates of the shapes as

3, N, I
5, A, N
4, L, W
3, C, A
3, D, S

I believe the solution to the third image could be

enter image description here However, this solution is not unique as the squares highlighted in yellow could be coloured either orange or blue. Also, if we consider the 4x4 square at the left corner as well as the one directly above, neither contain an orange square. I do not know if this is allowed.

The last puzzle looks like a

Corral puzzle https://mellowmelon.wordpress.com/corral/

If you

overlay the last image onto 5th image and rotate it 180 degrees, you get this: enter image description here The numbers seem to correspond to the number of blue squares adjacent to it, except the leftmost 4 would have to be changed to a 3. Coincidence?

  • Oh, cool. And now add the shapes into the red squares! I'm sure the shapes of the red squares will have relevance when we reach the letter map. – TheGreatEscaper Jun 29 '17 at 15:02
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    @TheGreatEscaper Done! :) will be updating with more progress soon! Who needs to sleep anyway – as4s4hetic Jun 29 '17 at 15:15
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    I tried solving that last one as a Corral and didn't really get anywhere. :/ – Deusovi Jun 30 '17 at 0:28
  • @Deusovi oh no :( do you think the type of puzzle could be related to the middle image in picture 6? (next to the yin-yang symbol) – as4s4hetic Jun 30 '17 at 0:38
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    @Deusovi me too! my initial thought was to actually overlay it onto the blank yin yang picture since they're both 8x8 grids. Revisiting the idea now and I just posted an image of something that kinda works. – as4s4hetic Jun 30 '17 at 1:09

Let me try a different approach.

There is one red square in each row and column (fact). That provides us with a free pairwise collocation on rows and columns, or: on the letters written one the up and on the left. This collocations for the first three images (yes, that is a lot of examples!) give you:

1) RC-ET-SE
2) DS-LW-NI-CA-AN
3) ME-AV-NE-AB-DA-OH-SE

Drawing a line through letters is convenient, if we turn around at every collocation (woosh! - left, woosh! - up, woosh! - left again, diving in and out). Now for the first two anagrams are already found, they were just not as explained.

1) SE-[CR]-ET
2) CA-[NA]-LW-[IN]-DS

The third one was harder but still doable (I didn't find any more clues to this one). It's more informative:

3) NE-[VA]-DA-[HO]-ME-[BA]-SE

So, we're talking locations. The hardest part is still to come. The next picture is missing the squares, and anagramising it as is is close to impossible. Yet, we have numbers and experience of as4s4hetic.

THE RULES:
1) There is water and sand. Red is sand (yellow as well). Neither can fold into 2x2 squares. Either is connected.
2) There are trees. Trees are green and square. They are neither sand, nor water. Also, they (probably) don't touch sides of each other.
3) Red sand is in every column and row once (since we already have letters in every row and column)
4) Most important: numbers. Numbers in "water-layer" tell us, how much water in this row/column. Numbers in "tree-layer" tell us, how much wood in this row/column.
5) This '6' in the corner isn't there for fun. It means that we have 6 trees.

That is more than enough to solve the Ncarozple scheme. I'll try to take it slow, because you may not know where to start.

Start with trees. Zero crosses out a column, thus 6 is hard to fit. There is no 4x4 tree in there - it would overload the 3. This 6 is also not 2+1+2+1 because then 3-row needs more trees, 2-row needs more trees, both 1-rows need a 1x1-tree -- we'd be out of (6) trees!
Stay calm and count once more. 3+2+1 = 3 trees. Also 2+1+1 trees in lower rows needed.enter image description here

Step 2:

Let's wrongfully assume the 3x3 tree (read as: treetreetree) is on the right of the treeless line. First, water-5 on the down wants to fill the column (there is place, even one left for the red sand). Then we can locate two 1x1 trees (on the right). But then the down-3 can't be a 3: it's either 2 or 4 (check yourself)! Reductio to absurdum, we get the 3x3 tree to the left.enter image description here

Step 3 (I just don't know how to divide spoilers actually):

The 1 and 3 on the down are odd numbers so they require the 1x1 trees to be near. The rest is easy, up to a point that we don't know if 2x2 is up or down and this 1x1 ships are in one of two ways. But now we can start placing water to find out. enter image description here

Now comes, what I called "Edge theorem" (I never tried an Yin-Ang before).

If you go along the border in Ying-Yang puzzle, the color changes maximum (and usually, exactly) twice. The reasons for it are connectiviness. What's more important: if we put trees like this, the border creates two points that require to change color (2x2 squares). That results in all the up-part being one color, that counteracts with 1-row. enter image description here

The last unusual thing.

We have the trees made, the only other non-Ying-Yang idea I want to use - since every row and every column is supposed to have a red sand, therefore, sand-border goes along all 4 sides, and water-border: 2 maximum. That gives us a take at the borders. The rest is pretty clear.enter image description here

Now, you would ask:

That's all very pretty, but where are the red squares and the order to read them and location of my dear friend?

Patience here. This data is not enough to find the squares. Probably, I missed something important on the rules or the idea of the shapes. But I can compensate with a mind-game.

QUESTION: What starts with Z next to O (or E, or I) and can be connected to locations of dear friends? It's a Zo-ne. And here it might also be a Dear-friend-zone (yeah I'm good at puns). Though only a hypothesis, marking Z-O and reverse N-E as red squares gives us all the others. Well, not all the other positions, but letters for sure. enter image description here

Allright, let's see, it's...

EN-OZ-ER-TO-SP-NE-EC-TA-IL

I spent a lot of time on this one (I still wasn't sure about a 'zone' assumption, btw) and somehow I ended up getting it. The next location hint is

TO-[PS]-EC-[RE]-TA-[LI]-EN-[ZO]-NE !!!

Now it all comes together.

Nevada homebase top secret alien zone is definitely the Area 51. Or not? Unfortunately, I can't finish the decoding. I raise this theme from year ago to let you try once again.

Now, the assumption is:

Shapes are somehow derived from the (filled?) grid. Then, the shapes create order or pattern. This order was supposed to help order the pairs of letters (which I handled myself, so you can reverse-engineer the order I got). The pattern should probably be used on the secret drawer table, to get another message. I don't know if the vellum is needed anywhere.

  • Area 51 is correct! There is only one missing aspect that makes the unscrambling of Nevada Homebase and Top Secret Alien Zone more logically coherent. There is a lot of other redundant information as well that was intended to hint at the rules of the puzzle which may not have been necessary and only added more confusion. Incidentally, Nevada Homebase was removed as a synonym from the Wikipedia page for Area 51 shortly after I posted this puzzle, which quite conveniently obscured the solution a little further. – paramesis Jun 16 at 23:38
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    @paramesis Though I am deeply astounded with your puzzle-quality, your policies on anwers seem quite ridiculous. Here a lot of material is unused (and does the shape-sheet contain one more message), yet you accept the answer. In the 'stars' and 'island' ones everything (or almost everything) is done right, yet the answer is not accepted. Are you checking and waiting solely for the exact answer to the questions? – Thomas Blue Jun 17 at 0:00
  • If you think that guessing further is no real fun you could post your own answers clearing out what was left unguessed in your puzzle. – Thomas Blue Jun 17 at 0:02
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    I certainly see and appreciate your point. Perhaps I was caught up in the excitement of finally seeing this puzzle solved. To be consistent with how I've handled other puzzles in which the correct answer was found ahead of the full logical explanation (art accident at airport), I will go ahead and un-accept this answer until all the pieces are adequately understood. The other puzzles in this series are very close to extracting the final location, which for the purposes of how they relate to the metapuzzle is most important. – paramesis Jun 17 at 0:18
  • Well done! Now I can finally see this puzzle solved (and I think @Alconja 's bounty has found its true recipient - I'll put up the 100 as soon as op awards you the current one :)) – as4s4hetic Jun 17 at 21:33

Relatively trivial progress, but nonetheless:

We can interpret the panel as traversing a path to spell out various logic puzzle genre names: YIN YANG, CANAL VIEW, and FOUR WINDS.
enter image description here
Notably, YIN-YANG is the mechanic used to separate water from ground with respect to all tree-less squares. CANAL VIEW is the genre similar to Corral, but instead of viewing squares of the cave, you view squares of the river instead. We see this in the last puzzle on the vellum. However, I haven't seen any part of this puzzle use FOUR WINDS mechanics.
At any rate, however, this could help us interpret the phrase "CANAL WINDS".

Furthermore, I would like to contest as4s4hetic's assertion that

The first one resolves uniquely using only Yin-Yang rules.

Namely:

enter image description here
There are 2 solutions. Arguably the first one might even be better, with all red squares adjacent to the river.

In the path that phenomist found through the image with the shapes and letters, we can observe that there is a link between the shapes and the number of times that the path traverses the shape. More specific: the squares are traversed once, the triangle twice, the hexagons trice and the pentagon four times. This gives us a way to link these shapes to numbers from 1 to 4.

Applying this to the first picture,

we get the following numbers on the red squares:
enter image description here These numbers correspond to the order in which the solution "SECRET" can be found, but also with the numbers of orange squares reachable (in a straight line) from each of the red squares.

Now we can try to do the same to the solution of the second puzzle found by as4s4hetic:

Numbering the red squares in the order used to find the solution "CANAL WINDS" gives: enter image description here For 1, 2, 4 and 5, we see that again the number equals the number of orange squares reachable from the red square, however for 3 this does not work. It does however hold that there are exactly 3 blue squares reachable from this square. This seems to be the general logic: in each red square we put either the number of reachable orange squares, or the number of reachable blue squares. This should be done in such a way that these numbers are exactly 1, 2, 3,...

We can also apply this logic to the third puzzle, solved by as4s4hetic:

enter image description here

And to the final puzzle, solved by Thomas Blue:

enter image description here

The final mystery left is what to do with the drawing pinned on the wall...

  • I might notice that three drawings are probably a way of saying "Yin Yang", "Canal view" and "Four winds" in that order, same as in shape table. These might be codenames of patterns used in the puzzle. The third one is probably telling about the fact that trees can't be connected (why is it called "four winds" remains a mystery, though). The second is some kind of reference to what you described in here (and it's clear, why it would be called 'canal view'). What remains is how 3-5-7-9 numbers can be tied into it. – Thomas Blue Jun 18 at 11:19
  • @Thomas Blue: Four winds: (worldpuzzle.org/championships/types-of-puzzles/wpc) (I guess it's most similar to the orange square mechanic, but that's actually corral/bag/cave.) Canal View is also a recognized logic puzzle type (gmpuzzles.com/blog/2018/03/…), and so is Yin-Yang (janko.at/Raetsel/Yin-Yang/index.htm) – phenomist Jun 18 at 19:17

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