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See if you can fill in all the blank letter tiles in this graph

graph

using the clues sets below.


Each set of clues yields a name or word. The name or word is guaranteed to follow some connected path through the letter tiles. The arrows indicate the permissible directions that the path may travel.

Unless otherwise stated in the clues, every word or name starts at the tile in the 12 o'clock position (marked with an asterisk).

Paths are permitted to revisit the same tile multiple times.

It is also permitted to have more than one tile in the graph bearing the same letter.



Clue set #1:

Image_001_a

Image_001_b


Clue set #2:

Image_002_a


Clue set #3:

Image_003_a


Clue set #4:

He is generally associated with a sacred or mystical "cube", which is often depicted as the five Platonic solids nested within each other.

Image_004_a


Clue set #5:

Image_005_a

Image_005_b


Clue set #6:

Image_006_a

Image_006_b


Clue set #7: (This one starts at the tile in the 4 o'clock position.)

Image_007_a

Image_007_b


Clue set #8:

Image_008_a

Image_008_b


Clue set #9:

Image_009_a

Image_009_b


Clue set #10:

Image_010_a

Image_010_b


Clue set #11:

Image_011_a

Image_011_b

Image_011_c


Clue set #12:

Image_012_a


Clue set #13:

Image_013_a


Clue set #14: (This one starts at the tile in the 4 o'clock position.)

Image_014_a

Image_014_b


BONUS:

While her name cannot be found along any connected path, you can find it by dancing (;-) all over the graph.

Image_015_a

Image_015_b



Side notes for topology nerds:

Notice that none of the arrows in the graph cross each other. This makes the drawing a good planar embedding of the graph. As a result, the graph as drawn breaks the plane into discrete, distinct regions, each of which could be uniformly colored with its own color, as you would a coloring book. Like a stained-glass window.

Now, you could just throw the 26 letters of the alphabet onto a page and trace out the entirety of "Hamlet" in one long, continuous path without ever lifting your pen. But you would get thousands of self-crossings in the process and it would be a nasty, tangled mess.

The challenge is to draw the smallest graph possible without any self-crossings. This may sometimes require the same letter to appear on multiple tiles in multiple places. Seeing repeat tiles can feel inefficient or suboptimal, but it is necessary to make the planar embedding work.

If you solve this puzzle and stare at the graph for a while, you might notice that there are places where it could be condensed even further and still maintain a planar embedding. As an example, with a word like REMEMBER, you really only need one "E" tile which be revisited multiple times as it bounces between the "E" and the "R", the "M", the "B", etc. However, all those little back-and-forth loops can get confusing. There is a point at which a drawing is so densely packed with convoluted pathways that it is cruel to the puzzle solvers. So I didn't condense everything as far as I could have. I tried to maintain a general clockwise flow for aesthetics and readability and enjoyment.

But if you think you can condense it to the max, go for it!


Image credits:

1. Wikipedia; Hasbro
2. Wikipedia
3. Wikipedia
4. Wikipedia
5. Wikipedia; Heritage Auctions
6. Wikipedia; Wiki Commons
7. Wikipedia; Wikipedia
8. Wikipedia; Wikipedia
9. Wikipedia; L'Oreal Paris
10. Wikipedia; Wikipedia
11. Wikipedia; Wikipedia; original creation
12. Wikipedia
13. original creation
14. IMDb; IMDb
15. Wikipedia; IMDb

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  • $\begingroup$ (For future reference, [cryptic-clues] is specifically for "cryptic crossword" style clues, which this puzzle doesn't seem to have.) $\endgroup$
    – Deusovi ♦
    Jan 6, 2020 at 17:51

2 Answers 2

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9
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The diagram should be something like this:

enter image description here

and the words being clued are

megatron, megaton, magnetron, Metatron, megalodon, megatherium, theremin, megalith, melanin, melamine, melatonin, metronome, metonym, Theron.

(Note: while I was typing in the list at the end another answer appeared. I haven't looked at it yet.)

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7
  • $\begingroup$ Well done... :) $\endgroup$
    – gustavovelascoh
    Jan 6, 2020 at 16:35
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    $\begingroup$ @gustavovelascoh Sorry to have charged in ahead of you :-). $\endgroup$
    – Gareth McCaughan ♦
    Jan 6, 2020 at 16:38
  • $\begingroup$ Gareth, is it spooky that not only did you get all the letters at the unambiguous "junction" points, but even at the places where there could be ambiguity (e.g., the two tiles floating outside of the 2 o'clock position, or the two tiles floating inside of the 10 o'clock position) your solution still exactly agrees with mine? What are the chances?! Well, I guess 1/4... $\endgroup$
    – SlowMagic
    Jan 6, 2020 at 17:15
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    $\begingroup$ Maybe more than 1/4. It's natural to fill in things left-to-right as one figures them out, and probably the ones you fixed on earlier are also the ones I found earlier. $\endgroup$
    – Gareth McCaughan ♦
    Jan 6, 2020 at 17:19
  • $\begingroup$ Oooh, nice catch with theremin :) $\endgroup$
    – Avi
    Jan 7, 2020 at 0:57
4
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At this moment I have 10/14 words, but one does not fit yet:

The clues are: Megatron, (Megaton?), ?, Metatron, Megalodon, Megatherium, Theremin, (Monolith, monument ?), Melanin, Melamine, Melatonin, Metronome, (Monarchy ?), Theron.

I still have no idea on clue #3

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3
  • $\begingroup$ After checking @Gareth answer I realized that I missed a connection when copying the graph to paper :(, my bad. In addition, There was a clue word that I have never heard before (English is not my first language), Good puzzle, though. $\endgroup$
    – gustavovelascoh
    Jan 6, 2020 at 16:39
  • $\begingroup$ I think the answer to clue 8 is a slightly different word; it should start with the same first four letters as for clue 6 (and others). $\endgroup$
    – user3294068
    Jan 6, 2020 at 17:02
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    $\begingroup$ Nice work, Gustav! As a non-native English speaker, you should take tremendous pride in recognizing all the words but one. I am a native English speaker and, before I started researching for this puzzle, I was unfamiliar with 3-4 of them! (I think even many educated, native English speakers never learned #13, for example.) And, if it makes you feel any better, I misspelled #7 for a long time before I finally looked it up. Good thing, too, because the correct spelling makes the topology work out much more simply. $\endgroup$
    – SlowMagic
    Jan 6, 2020 at 17:13

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