# Spectrum Analysis

This is a direct rip-off of Stiv's most recent puzzle. I did ask Stiv for permission in chat, so please take imitation as the sincerest form of flattery.

Below are 15 words and 14 patterns of colored spots. Each of the listed words can be matched to one of the spot patterns via a systematic rule - but two of the listed words match to the same spot pattern.

For the checkmark, (i) identify which words match to which spot pattern (and which two words match to the same spot pattern), (ii) clearly explain the rule behind the matching, and (iii) describe the spot pattern (not depicted here) that would match to the word 'CHATTIER'.

Word list: ATLANTIS, BURGERS, FISHWIVES, HALLIARDS, HASTE, HYPERGAMOUS, LAUREATES, LICK SYRAH, TETCHY, THAMES, URALITE, VASSALS, VOLITION, WATERER. Spot patterns: Red-Orange-Yellow-Green-Blue-Indigo-Violet, Red-Orange-Yellow-Violet, Red-Yellow-Green-Blue-Indigo-Violet, Red-Yellow-Blue-Violet, Red-Green-Blue, Red-Blue, Orange-Yellow-Green-Indigo, Orange-Yellow-Indigo-Violet, Orange-Green, Orange-Blue-Violet, Yellow-Green, Indigo, Indigo-Violet, Violet.

The pattern for 'CHATTIER' would be:

Red-Orange-Green-Indigo

Because in this puzzle, on inspection it becomes apparent that all of the listed words...

...can be spelled out (uniquely) using a concatenated string of chemical symbols of elements in the Periodic Table. For example, the first in the list - ATLANTIS - is comprised of Astatine (At), Lanthanum (La), Nitrogen (N), Titanium (Ti), and Sulfur (S).

Repeating this for the full list gives us:

ATLANTIS = At + La + N + Ti + S
BURGERS = B + U + Rg + Er + S
FISHWIVES = F + I + S + H + W + I + V + Es
HALLIARDS = H + Al + Li + Ar + Ds
HASTE = H + As + Te
HYPERGAMOUS = H + Y + P + Er + Ga + Mo + U + S
LAUREATES = La + U + Re + At + Es
LICK = Li + C + K
SYRAH = S + Y + Ra + H
TETCHY = Te + Tc + H + Y
THAMES = Th + Am + Es
URALITE = U + Ra + Li + Te
VASSALS = V + As + S + Al + S
VOLITION = V + O + Li + Ti + O + N
WATERER = W + At + Er + Er

That's great, but how does that relate to colours? Well, very conveniently here...

...the Periodic Table has 7 rows (or 'periods'), just as a rainbow has 7 different colours! (Recall that the lanthanides-and-actinides 'pop-out' usually displayed at the bottom of the chart is actually just an extension of rows 6 and 7.)

Let's colour it thus, with row 1 being red, down to row 7 being violet:

The rule behind the coloured spot patterns now becomes clear upon comparing the word list and the colour frequencies in the patterns displayed - namely:

The colours relate to the rows of the elemental symbols that make up the word's spelling. e.g. ATLANTIS - At+La+N+Ti+S - uses elements from rows 2 (N), 3 (S), 4 (Ti) and 6 (At and La). Thus it maps to the colours Orange-Yellow-Green-Indigo (the seventh pattern down). Note that a row is only represented once in a spot pattern no matter how many elements feature from within it. Spots are arranged in rainbow order.

(A key step in deducing the pattern's rule for me was noting that all the elements in the spelling of W+At+Er+Er lay in the same row (row 6), as did all of those in Th+Am+Es (row 7), with Indigo-only and Violet-only being two of our target patterns...)

The full word-pattern map is as follows:

This helps us to see that the pattern that occurs twice is Orange-Green, for both LICK and VOLITION. We can also calculate that the spot pattern for CHATTIER must be Red-Orange-Green-Indigo.

• 100% correct! Only thing that may be worth mentioning is rot13(gur qrpbzcbfvgvba vagb ngbzvp flzobyf bs rnpu tvira jbeq vf havdhr). Thanks for letting me borrow your idea! Commented May 28 at 0:35
• @JeremyDover That's true - and I did notice that whilst working my way through! (No 'NO' in sight...!) And you're welcome - it was a really nice alternative spin on the original (and has given me further ideas in turn...).
– Stiv
Commented May 28 at 0:37