# What is a Dotted Word™?

This is based on the What is a Word/Phrase™ series of Phrase™ and Word™ puzzles, started by JLee.

If a word follows a certain rule, then I call it a Dotted Word™.

Use the example word lists below to find the rule. Each word can be tested for whether it is a Dotted Word™ without depending on other words in these lists.

Dotted Word™, Not Dotted Word™
ONLINE, DIGITAL
HOWDY, HEY
URGES, INSTINCTS
NASAL, BARITONE
POLAND, UKRAINE
WATER, LUBRICATE
FOLIO, DOCUMENT
COBRAS, PYTHONS
REBIND, UNSEAL
PRATTLER, BABBLER
LUAU, FIESTA
RECEPT, RECEIVING
KNIFE, SPOON
FRAMES, BOXES


Hint:

The number of possible Dotted Words™ is relatively small.

Hint 2:

This is a very elementary puzzle. You don't need more than one hint.

• Perhaps the fact that "recept" is included in the list indicates that Dotted Words are relatively hard to find and/or that they were found using a very wide net. – GoldenGremlin Jan 6 '17 at 3:31
• @tilper, the fact that the word is very uncommon may suggest that Mike Q had trouble finding words with this property, and so needed to resort to an uncommon one to fill out his list. This suggests to me that the words might have been found with CPU aid, using a large lexicon. – GoldenGremlin Jan 6 '17 at 16:12
• @MikeQ, it's not a criticism at all! I'm trying to help others by reverse engineering your path to finding these buggers! – GoldenGremlin Jan 6 '17 at 16:39
• I liked the old format. T'was a tradition :/. – Karan Atree Jan 6 '17 at 16:50
• @Joe Sometimes when I'm stuck on a puzzle, I find that taking a break and stretching may help. – MikeQ Jan 12 '17 at 13:39

The last hint and also Gareth's answer make it clear that ...

... all Dotted Words can be split into symbols for chemical elements. But this is not a sufficient condition, because some of the non-dotted words, but not all, can also be "elementarily split".

The distinguishing trait is ...

... that all elements used in the dotted words must be of the same period, i.e. they must occur on the same row in the periodic table:

O·N·Li·Ne: Oxygen (8), Nitrogen (7), Lithium (3), Neon (10): period 2
Ho·W·Dy: Holmium (67), Tungsten (74), Dysprosium (66): period 6
U·Rg·Es: Uranium (92), Roentgenium (111), Einsteinium (99): period 7
Na·S·Al: Sodium (11), Sulfur (16), Aluminium (13): period 3
Fr·Og: Francium (87), Oganesson (118): period 7
Po·La·Nd: Polonium (84), Lanthanum (57), Neodymium (60): period 6
W·At·Er: Tungsten (74), Astatine (85), Erbium (68): period 6
F·O·Li·O: Fluorine (9), Oxygen (8), Lithium (3), Oxygen (8): period 2
Co·Br·As: Cobalt (27), Bromine (35), Arsenic (33): period 4
Re·Bi·Nd: Rhenium (75), Bismuth (83), Neodymium (60): period 6
Pr·At·Tl·Er: Praseodymium (59), Astatine (85), Thallium (81), Erbium (68): period 6
Lu·Au: Lutetium (71), Gold (79): period 6
Re·Ce·Pt: Rhenium (75), Cerium (58), Platinum (78): period 6
K·Ni·Fe: Potassium (19), Nickel (28), Iron (26): period 4
Fr·Am·Es: Francium (87), Americium (95), Einsteinium (99): period 7
La·Nd·La·Dy: Lanthanum (57), Neodymium (60), Lanthanum (57), Dysprosium (66): period 6

(There are several possible divisions for some words, but only one that makes it count as a Dotted Word.)

Why are they called Dotted Words?

No, it has nothing to do with Lewis dots, which would describe the electron configuration in an atom and therefore would refer to the columns in the periodic table.

They are called Dotted words, because some people call a dot a period.

• I think you missed the link to the Lewis Dot. – Sid Jan 12 '17 at 18:10
• There is no link to Lewis ... oh, I see. Fixed, thanks! – M Oehm Jan 12 '17 at 18:14
• Ohhh! Well done. – Gareth McCaughan Jan 12 '17 at 18:18

I thought, after looking at just a few of the words, that a Dotted Word might be one

made out of chemical element abbreviations.

Thus, e.g.,

ONLINE = O/N/Li/Ne and FRAMES = Fr/Am/Es.

Hence the hint saying that the puzzle

is "elementary".

However, this is demonstrably wrong; see below.

ONLINE = O/N/Li/Ne; DIGITAL fails because neither D nor Di exists.
HOWDY = H/O/W/Dy; HEY =He/Y.
URGES = U/Re/Ge/S; INSTINCTS fails because none of {Ct,T,Ts} exists.
NASAL = Na/S/Al; BARITONE fails because none of {It,T,To} exists.
FROG = Fr/Og; TOAD fails because neither T nor To exists.
POLAND = Po/La/Nd; UKRAINE = U/K/Ra/I/Ne.
WATER = W/At/Er; LUBRICATE = Lu/Br/I/Ca/Te.
FOLIO = F/O/Li/O; DOCUMENT fails because neither D nor Do exists.
COBRAS = C/O/Br/As; PYTHONS =P/Y/Th/O/N/S.
REBIND = Re/B/I/Nd; UNSEAL = U/N/Se/Al.
PRATTLER = Pr/At/Tl/Er, BABBLER fails because none of {Bl,L,Le} exists.
LUAU = Lu/Au; FIESTA =F/I/Es/Ta.
RECEPT = Re/Ce/Pt; RECEIVING fails because neither Ng nor G exists.
KNIFE = K/N/I/Fe; SPOON =S/Po/O/N.
FRAMES = Fr/Am/Es; BOXES =B/O/Xe/S.
LANDLADY = La/Nd/La/Dy; DUCHESS fails because neither D nor Du exists.

There are several counterexamples. But this seems to be close to working, and it's hard to believe it's coincidence. I suspect the intended answer is a variation on this theme and perhaps the variation explains why "Dotted Word" is the name.

It's very noticeable that

all the counterexamples are non-DWs that have decompositions, suggesting a rule of the form "a Dotted Word is one that has an 'elementary' decomposition such that ...". (This would also explain how it's possible that relatively few Dotted Words exist, even though a substantial fraction of all words have 'elementary' decompositions.)

A substantial fraction of the counterexamples

are non-DWs whose only decompositions involve noble gases, which (approximately) never form actual chemical compounds. But not all, and O/N/Li/Ne depends on Ne, so this is probably coincidence and in any case can be at most part of the answer.

A related conjecture would be

something along the lines of "a DW is a word with an 'elementary' decomposition that would be a possible chemical compound" or "... where each consecutive pair of elements can actually combine together somehow", but (1) that seems rather complicated and (2) S/Po/O/N seems like it fits any criterion of that sort at least as well as, say, O/N/Li/Ne does.

I notice that

all the Dotted Words have decompositions into at most four elements, and some of the Non-DWs with decompositions require more. (But note e.g. that Fr/Og uses only two elements; and that B/O/Xe/S requires only four but isn't a DW.) This is kinda suggestive of IP addresses, which is particularly interesting given Mike Q's comment to Glorfindel.

An obvious guess if it had worked in every case would be that "Dotted Word"

is just meant to hint at abbreviations, which are often indicated by trailing dots.

Or, more specifically,

conventionally one puts a dot at the end of an abbreviation exactly when its last letter is not the last letter of the thing abbreviated, so perhaps we could allow "Ra" but forbid "Rn" since it comes from Radon and wouldn't be dotted if we followed that convention for element abbreviations.

But clearly we need something smarter...

• What about BOXeS, HeY, and LuBrICaTe? You should check all of the words first. – MikeQ Jan 12 '17 at 16:03
• I already put a comment on the original post - FIESTA can be comprised of chemical element symbols – Joe Jan 12 '17 at 16:04
• Yup, I found some counterexamples once testing. But it's ... surprising ... how large a fraction of words seem to be classified correctly by this criterion. Perhaps it's a deliberate red herring, though. – Gareth McCaughan Jan 12 '17 at 16:05
• (I hadn't seen Joe's comment, but now I have. Sorry, Joe!) – Gareth McCaughan Jan 12 '17 at 16:05
• @Silenus Coincidence. "Dotted" is intentionally vague, but designing a rule that involves solving chemistry problems seems too complicated for this type of puzzle. You should expand your mind, otherwise you'll miss the big picture. – MikeQ Jan 12 '17 at 16:18