# Troubling Triples

The points appear to be connected, but in the end, we should have worked under aqueous conditions.

$$\begin{array}{|l|c|c|} \hline \textbf{Substance} & \textbf{Temperature (K)} & \textbf{Pressure (kPa)} \\ \hline \text{Acetylene} & 173.1 & 26.6 \\ \hline \text{Ammonia} & 109.5 & 21.9 \\ \hline \text{Argon} & 115.8 & 74.1 \\ \hline \text{Arsenic} & 293.0 & 3,000,000 \\ \hline \text{Butane} & 1941 & 0.0053 \\ \hline \text{Carbon} & 1090 & 3628 \\ \hline \text{Carbon monoxide} & 90.68 & 11.7 \\ \hline \text{Carbon monoxide} & 18.63 & 17.1 \\ \hline \text{Deuterium} & 24.57 & 43.2 \\ \hline \text{Deuterium} & 273.0 & 100 \\ \hline \text{Ethane} & 2,045 & 0.0002 \\ \hline \text{Ethylene} & 113.55 & 0.000019481 \\ \hline \text{Formic acid} & 104 & 0.12 \\ \hline \text{Hexafluoroethane} & 337.2 & 151.7 \\ \hline \text{Hydrogen} & 18.63 & 17.1 \\ \hline \text{Hydrogen chloride*} & 145.0 & 810,000 \\ \hline \text{Iodine} & 195.4 & 6.1 \\ \hline \text{Isobutane} & 1825 & 0.0035 \\ \hline \text{Krypton} & 161.3 & 81.5 \\ \hline \text{Krypton} & 158.96 & 13.9 \\ \hline \text{Methane} & 68.1 & 15.37 \\ \hline \text{Neon} & 68.1 & 15.37 \\ \hline \text{Nitric oxide} & 182.3 & 87.9 \\ \hline \text{Nitrogen} & 192.4 & 120 \\ \hline \text{Nitrous oxide} & 386.7 & 12.1 \\ \hline \text{Nitrous oxide} & 250.0 & 500,000 \\ \hline \text{Oxygen} & 88.48 & 0.019644 \\ \hline \text{Palladium} & 198.0 & 300,000 \\ \hline \text{Platinum} & 273.0 & 3,000,000 \\ \hline \text{Radon} & 54.36 & 0.152 \\ \hline \text{Silane} & 273.13 & 0.611657 \\ \hline \text{Silane} & 134.6 & 0.0007 \\ \hline \text{Sulfur dioxide} & 89.89 & 0.0008 \\ \hline \text{Titanium} & 250.0 & 300,000 \\ \hline \text{Uranium hexafluoride} & 270.0 & 1,100,000 \\ \hline \text{Water} & 88.48 & 0.019644 \\ \hline \text{Xenon} & 115.8 & 74.1 \\ \hline \text{Zinc} & 197.69 & 1.67 \\ \hline \end{array} \\ \tiny\text{*Heated at 0.4 K/min} \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad \\\,\\ \log_{10}(P)\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\\ \begin{array}{|c} \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\\ \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\\ \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\\ \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\\ \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\\ \hline\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\\ \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\\ \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\\ \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\\ \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\\ \end{array} \log_{10}(T)$$

Answer is a thematic word. For copy-paste purposes, here is a Pastebin link to the data.

Hint 1

What kinds of points are these?

Hint 2 (updated)

Once you have the actual data, you can start making the connections. Almost every point can be connected to another one. If there are two points for a substance, treat them separately.

Hint 3 (updated)

What substance do the non-connected points actually represent? Figuring this out will help you rearrange your findings.

• It's been about a week; can we have another hint, please? – Skylar Dec 2 '19 at 15:19
• @Skylar You are 90% of the way to figuring out the main mechanism. I've updated hints 2 and 3 to clarify what needs to be done, but I'd encourage you to take a second look at what you've done already :) – HTM Dec 3 '19 at 5:39

## Intro

The second and third columns represent triple points. The data in the table is from this table on wikipedia (or something based on it), except the substances' names are messed up: some are missing, some are duplicated, and all of them have incorrect triple points listed. Many of the triple points are valid, but listed with the wrong substance. I used Excel to plot the data from the puzzle on a logarithmic scale, as suggested by the axes shown below the table (It's shown next to the table on the Stack Exchange app; don't bother asking why).

## Attempt 1

Once the puzzle's data had been plotted, I drew a line segment between each point from the puzzle's chart to the actual triple point for the listed substance using the table from Wikipedia. If the actual point wasn't already on the graph, I simply moved on to the next one without drawing a line segment. Once I went through all of the items, each point had at least one line segment touching it.

Here's a picture of the results:
(the red lines are just to show detail in the crowded area.)

(click for larger image)

When Hint 3 came out, I realized that this method was incorrect since every point in my picture was connected, so I stopped work on Attempt 1.

## Attempt 2

Instead of connecting each point, I decided to see which substances from the puzzle's chart had their actual triple point somewhere on the chart. If it didn't, I hid the point associated with its "fake" triple point.

These points remained:

(click for larger image)

## Attempt 3

Using the information in the OP's comment below, I started with the picture in Attempt 1 and removed all of the line segments that were connected to the points found in Attempt 2.

• Your Attempt 2 is getting close! To nudge you in the right direction, consider rot13(cybggvat naq pbaarpgvat gur cbvagf gung qb unir na nffbpvngvba.) As for "aqueous," rot13(jr'er jbexvat jvgu gung fhofgnapr ng gur raq.) – HTM Nov 24 '19 at 20:07
• Hmm, it looks like you're missing something, but your ideas are still definitely on the right track. I'll let you ponder a bit more before releasing another hint. – HTM Nov 25 '19 at 5:42

I'm assuming these are supposed to be (at least related to) triple points, based on the name of the puzzle. However, the T/P shown for water is nowhere near its only triple point (273.16 K/0.61173 kPa). I notice that this particular T/P pair is shown in the table, but for Monosilane, which i) is one of 5 compounds listed twice in the table, and ii) doesn't actually exist, according to teh Internetz.

Another observation:

Carbon monoxide, also listed twice in the table, has three triple points, none of them anywhere near the two T/P pairs listed for it in the table. The table appears to be a badly edited, reordered version of one viewable at https://www.engineeringtoolbox.com/triple-point-d_1926.html. The version of the table that appears in this question replaces some of the entries in the ET.com version and seems to randomly reorder the T/P entries, albeit keeping each T/P pair intact.

Conclusion thus far:

If somebody has the wherewithal to match up the entries in the table above by their P/V values to entries in the table on ET.com, it would provide "connections" between elements, possibly leading to some kind of graph. I'm not sure how this will lead to a single thematic word, however, unless the word is freakin' wrong, which in fairness is two words. Personally, I'm'a wait for another hint.

• This seems more like a comment than an answer - it's an observation, but not one that leads forward any significant amount. – Deusovi Nov 21 '19 at 0:27
• rot13(V guvax gur gnoyr vf rvgure onfrq ba uggcf://ra.jvxvcrqvn.bet/jvxv/Gevcyr_cbvag#Gnoyr_bs_gevcyr_cbvagf be fbzrguvat gung vf vgfrys onfrq ba gur Jvxvcrqvn gnoyr. Nppbeqvat gb gur gnoyr, Zbabfvynar vf nyfb whfg pnyyrq fvynar.) – Skylar Nov 21 '19 at 0:28
• @Deusovi rot13(Guvf nafjre abgrf gung gur gnoyr yvfgf gevcyr cbvagf jvgu gur fhofgnapr anzrf bhg bs beqre naq fhttrfgf n cbffvovyvgl sbe ubj gb fbyir vg. V'q fnl gung'f fvtavsvpnag; jbhyqa'g lbh?) – Skylar Nov 21 '19 at 0:32
• Yes, this is on the right track! Apologies if you’re finding this puzzle annoying - maybe the mechanism wasn’t the best way to encode the word I want. And as Skylar said, monosilane is just silane, which I’ll edit in in a bit – HTM Nov 21 '19 at 0:53
• @COTO I tried your suggestion; not sure what it might be: i.stack.imgur.com/LDacy.png (spoiler warning) – Skylar Nov 21 '19 at 3:36