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Your father was a great, patriotic, American chemist. He won the Nobel Prize 12 times, invented eternal life, and proved that inside each atom is another universe. You inherited the best of his genes. As a renowned mathematician, puzzlemaster, logician, and physicist, you generally make a groundbreaking discovery every day.

Then one day, a lab explosion occurred, and your father... um... "died". See, they never actually found the body, so the police and all his coworkers were very confused. The detective reported that his body must have been thrust into an alternate dimension, for lack of a better explanation.

Obviously, you have tons of doubts. The day after the funeral (where they buried lots of air), you decide to search your father's room, for clues to his "disappearance". Surely an attempt wouldn't hurt.

Alas, the room was indeed stranger than ever. His grand periodic table was covered in... lines?

Periodic Table?

"Such blasphemy!", announces your mother, whose presence you have yet to notice. "I DO NOT REMEMBER PUTTING UP THIS DUMB PAINTING?!!?", she screams. Such discontent was not very normal of her. She's the most sane philosopher in the entire world, enlightening everyone to the ideas of self improvement and living longer spiritually. That is, until your father invented eternal life. Your parents did disagree a bit on that matter.

Your mother dashes out of the room, waving her arms around like a lunatic. Just perfect.

You observe the new painting that disconcerted her so.

Elephant?

"What is this... an elephant? A rhino? What kind of abomination does my father believe this to be? Is this an abstraction of confusion?"

You begin to really sympathize for your mother. This is seriously weird.

"Your Greatness... Your father's will... this is for you..."

Ah, the butler. No, you did not force him to call you "Your Greatness", but the butler sees you as a grand king for your great accomplishments.

"No, Your Greatness, please don't look at me like that... the butler is not always the evil murderer..."

You raise your left eyebrow in slight confusion as you take the will. You open it up, and it reads... um... well then...

i am alive lol

language is vigenere key

so where am i now

...Did your father just mock you from beyond the grave with the most poorly written will ever, in the form of a flippin haiku? Jeez. You figure that "language" is a key, so you crazily go around using the vignere cipher on every object in the room, trying to find meaning. You forget to eat dinner and go to sleep.

Do yourself a favor, will you? Where has your father gone?

(P.S. Just to make sure everyone sees, although it's not 100% critical to the puzzle, zooming in on the elephant rhino might make things a tad bit easier in the somewhat near future.)

Slight hint 1:

Elephant Rhino:

The following changes to the puzzle will not affect the answer:
- Changing the red, orange, and yellow regions to any color of your choice, or removing them altogether.
- Removing the gaps will make the puzzle harder, but are not actually critical.

Periodic Table:

I don't know about this one. I guess just try things until it makes sense?

Slight hint 2:

Elephant Rhino: Count?

Periodic Table: A pencil, paper, and some other object could help.

Slight hint 3:

Both pictures: Really just count things until you get nice numbers that you really like. Maybe you might find a really special number that represents a number of a familiar something. Maybe you might find a really nice sequence that means something to so many, and yet so little. I think this is the last slight hint I can give before things get really spoilery.

Possibly spoilery hint 4:

Something isn't oriented correctly.

Possibly spoilery hint 5:

The ciphertext can be partitioned into 9 not necessarily distinct element symbols.

Probably spoilery hint 6:

12 = 4 + 8, but everyone else is normal.

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    $\begingroup$ "Did your father just mock you from beyond the grave with the most poorly written will ever, in the form of a flippin haiku?" I laughed :-D $\endgroup$ – Rand al'Thor Oct 23 '16 at 20:34
  • $\begingroup$ Why is there a downvote that makes me so sad $\endgroup$ – greenturtle3141 Oct 24 '16 at 2:22
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    $\begingroup$ Some men just want to watch the world burn. $\endgroup$ – Rubio Oct 24 '16 at 18:32
  • $\begingroup$ Aww. I was feeling smug about having noticed the details of the rhino picture, and now everyone will see them. (I haven't figured out what to do with them, though.) $\endgroup$ – Gareth McCaughan Oct 25 '16 at 0:07
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    $\begingroup$ When I see "lol" I mentally say it with one syllable, so yes. $\endgroup$ – greenturtle3141 Oct 30 '16 at 22:55
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Alright, I'm not 100% convinced that I've got this right, but I'll give it a shot. I'll post this as a separate answer, otherwise it becomes a bit messy I think.

The first thing you need is the elephant-rhino painting. Solving this will give you the key to with which to decrypt the ciphertext later. The painting consists of 48 tiles. Rotating this picture 180 degrees makes clear that we're actually looking at a, slightly distorted, map of the USA. Only the not connected states Alaska and Hawaii are missing out. Next, it's important to look at the coloring: only the gray states matter. Using the map Carl Löndahl created, one can see that all the states in between each pair of gray states are all colored the same. Starting in Massachusetts, going through North Dakota and Arkansas to Indiana, all states between Massachusetts and North Dakota are colored red, all states between North Dakota and Arkansas orange and both states between Arkansas and Indiana yellow, whichever route is taken. This also means there's only two possible ways of travelling through all of the gray states. Using the state abbreviations we find:

MA (Massachusetts), ND (North Dakota), AR (Arkansas), IN (Indiana), MA-ND-AR-IN, which is the language, the vigenere key.

Now, to find the ciphertext to decrypt with it. Building on the work Gareth McCaughan had already done, it was easy to find that the circles, as created by the lines on the periodic table, moved through the highlighted elements. Simply counting these circle crossings per element we got: (3, 5, 12, 7, 1, 2, 9, 6) for the elements (C, K, V, Mn, Sr, Rh, Ds, U). Splitting the number 12 in two parts, 4 and 8, gives us exactly the set of numbers 1-9. Now ordering the corresponding elements in the same way, we get: Sr-Rh-C-V-K-U-Mn-V-Ds. Using a Vigenère decryption on the ciphertext

SRRHCVKUMNVDS with key MANDARIN yields GREECECHANIAS, which refers to the city of Chania, on the island of Crete, Greece.

P.S.: Looking back at my earlier answer, I can see now how I close I was. I just never linked the 1-9 sequence to the no. of crossings, just tried randomly ordering these elements.

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I only have a partial answer as well.

The elephant/rhino is a 180 degrees rotated, slightly distorted map of the USA, with all the correct state borders. I don't know what to do with that yet, though. No idea why some midwest states are colored differently. There must also be something special going on with Kentucky/Tennessee...

I'm guessing the solution to the first part will be a set of directions which will somehow lead you to the correct state, through the little gaps in the borders.

What I found for the first part: adding the numbers of the elements each circle passes through yields (from top to bottom, left to right): 135, 133, 48, 139, 141, 117, 129, 133, 115, 295, 134, 115, 241, 117, 42, 152, 48. All of these (except for 295 unfortunately) can be split up into two letters, e.g. 13-5, 13-3, 4-8 --> ME, MC, DH, etc.. Can't figure out what to do with that, though. Tried decrypting the results with several keys. Not sure if "THELANGUAGE" should be the key, or maybe "JAPANESE" (since it's a haiku), or "VIGNERE" (was this intentionally misspelled btw??). Also tried going left to right, top to bottom, but no results there either. Or writing out all the elements, like Gareth McCaughan did: Ds, Mn; Ds, V; Mn, V; C, Ds, V; Mn, C, Ds; U, K, C; K, Ds; Ds, V; V, U; V, Mn, Rh, Ds, U; K, V, U; U, V; Sr, V, Mn, Rh, Ds; U, Mn; K, V; Ds, K, V; V, Mn.

Really love this puzzle! Gonna keep cracking my brain over it and hopefully I can find the answer!

Update: I now know which color is the important one and found the key! Now I gotta figure out what message to decrypt with it...

Update 2: Since OP suggests to count: total number of circles in the periodic table is 17, which also happens to be the number of syllables in a haiku (5-7-5), maybe this tells us something about the ordering of the found elements? Further, number of elements each circle passes through is 2-2-2-3-3-3-2-2-2-5-3-2-5-2-2-3-2. All of these are in the Fibonacci sequence, which might be the "really nice sequence that means something to so many"? Summing all the numbers yields 45, which also happens to be the sum of 1,2,3,4,5,6,7,8,9; another sequence...

Update 3: So close, and yet so far away... I'm still having a hard time finding that ciphertext, even after the latest hint.

I believe that the 17 circles are somehow related to a haiku, but I can't think of an arrangement of the 45 found elements that makes sense, let alone one that reduces the no. of elements to 9.. (9 = 17 (#circles) - 8 (#highlighted elements)??)

Randomly plugging in some elements suggests that the answer may have something to do with Greece, although this might just as well be a coincidence.

I've let go of the Fibonacci hunch, I can't make anything of it and I believe the sequence hint (means so much to so many and yet so little) could also be referencing to the key.. Some other ideas I'm working on:

  • Converting each circle into a single letter, either by summing elements (or rather element numbers) per circle, or subtracting them (orientation of the radius within the circles could be important for this), although subtracting is not straightforward for the circles that cross more than 2 elements. FWIW: a good few of these 2 element-subtractions lead to numbers within the ascii character range.. Other options include summing the number of valence electrons per element and summing the digits for the element sums, but both of these seem a little too far-fetched. All of these options also bring forth the additional problem of how to order the circles, although top-to-bottom, left-to-right seems to be the most logical way.

  • Counting the circle crossings for each of the highlighted elements. For (C, K, V, Mn, Sr, Rh, Ds, U) this yields (3, 5, 12, 7, 1, 2, 9, 6). This way we never get to nine elements, though. Maybe one of them needs to be used twice??

  • Calculating the grand sum of all crossed elements: 2234. No idea how this could be helpful..

  • Something to do with the size of the circles..

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  • $\begingroup$ Ah, I spelled vigenere wrong, it appears. For the colors you describe, only one color is actually critical to the puzzle (the other colors were a result of the paint bucket abuse). As for the elements, you actually got all of them. $\endgroup$ – greenturtle3141 Nov 3 '16 at 0:28
  • $\begingroup$ You are really close on one of your observations. $\endgroup$ – greenturtle3141 Nov 4 '16 at 16:13
  • $\begingroup$ I had to edit the haiku because vigenere had one more syllable than I thought, so the fact that it's a haiku is not relevant. $\endgroup$ – greenturtle3141 Nov 7 '16 at 19:28
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This is not an answer, but some observations...

The map contains some missing parts in their borders (as hinted in the OP), which may indicate that you are able to travel between them (or that they actually are adjacent).

I created the image below, which indicates the...

...connections (or non-connections between the countries) enter image description here I tried to find a set of countries which satisfy the graph, but I haven't found any yet.

The ciphertext...

...might be the highlighted elements in the periodic table. If so, this is $C, K, V, Mn, Sr, Rh, Ds, U$ in some order. Since 'the language is vignere key', I created this code to run through all permutations of the ciphertext and run through a (hopefully) complete list with languages as key and see if the decrypted text is a country (checking with a list of countries). However, it yields no positive result.

One could...

...try to overlay the lines in the map, maybe. I haven't figured out how it would make sense, though. Maybe the element names map to country names or something.

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  • $\begingroup$ I think you added an extra connection to the map, I don't think any 'orange' connects to a 'red' above. $\endgroup$ – Angzuril Oct 25 '16 at 16:54
  • $\begingroup$ @Angzuril You are right, I updated the image. Thanks :-) $\endgroup$ – Carl Löndahl Oct 25 '16 at 17:04
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    $\begingroup$ The thing I find curious is that the graph is almost a tree. It has just that one cycle, of length 3, among the oranges. That seems like it should be significant, but I don't know how. $\endgroup$ – Gareth McCaughan Oct 25 '16 at 23:15
  • $\begingroup$ Eh, try not to focus too much on those gaps. $\endgroup$ – greenturtle3141 Oct 26 '16 at 16:17
  • $\begingroup$ I would try to overlay the lines on the table to the painting $\endgroup$ – bleh Oct 30 '16 at 1:35
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Extremely partial answer, whose only value at present is to maybe save others some redundant work:

Following the second hint,

if we draw a circle (the "other object" is a pair of compasses) centred at each of the ringed dots on the periodic table with radius given by the length of the line from that dot, we find that each of these circles goes through (and reasonably near the middle of) one or more of the elements highlighted in the table.

However,

it's not at all clear what to do next. Here are the elements corresponding to each ringed dot, reading left to right and (where the x-coordinates are very close) top to bottom.

V,U; K,V,U; K,V; K,V,Ds; V,Mn,Rh,Sr,Ds; V,Mn; K,Ds; V,Mn,Rh,Ds,U; V,Ds; C,K,U; C,V,Ds; V,Ds; Mn,U; Mn,Ds; V,U.

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  • $\begingroup$ I think you missed some intersections. I'll redouble-check the picture when I can. $\endgroup$ – greenturtle3141 Oct 30 '16 at 1:54
  • $\begingroup$ I may well have done. It's surprisingly easy to do :-). $\endgroup$ – Gareth McCaughan Oct 30 '16 at 1:55
  • $\begingroup$ ... though looking it over again by eye I don't see any missing. $\endgroup$ – Gareth McCaughan Oct 30 '16 at 1:57
  • $\begingroup$ imgur.com/a/dizrV $\endgroup$ – greenturtle3141 Oct 30 '16 at 4:15
  • $\begingroup$ oh, you mean not "you have missed intersections where circles go through highlighted elements" but "you have missed intersections not corresponding to elements at all"? yeah, certainly have -- I wasn't looking for those. $\endgroup$ – Gareth McCaughan Oct 30 '16 at 11:39

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