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### Solutions for Act III Scene 4 - Deus Ex Machina

The image at the top of the puzzle should be recognisable as a crude code ring - a device where turning any disc cycles through the alphabet in order. Note that this one also has a blank space after the Z, implying that shifting one position past Z shouldn't give the letter A, but a blank.

The rest of the puzzle shows a list of words and synonyms, so it seems reasonable to expect we want to use the code ring on these words to create new ones. The question then is what encoding to apply - for example a simple Caesar shift doesn't reveal anything useful.

The trick here is to realise turning ZEUS into his Roman counterpart JUPITER in the code ring provides a (Vigenere) key that can be used on some other words. That is, ZEUS->JUPITER implies an encoding of +11 to the first character (mod 27, keeping in mind the blank), +16 to the second, -5 to the third, -10 to the fourth, and then +20, +5, and +18 to the next three positions. This ZEUS->JUPITER translation was hinted at by the title "Deus Ex Machina" implying a god should be coming "from/out of" the machine, and being in Latin, implying we want to look to the Roman pantheon. The fact there's a well-defined Roman counterpart for many Greek gods supports this, and the choice of fonts in the left/right column intending to reflect Greek/Roman script was also meant to work as a subtle confirming hint.

Now trying to convert the first word DAGGER using this encoding elicits nonsense, which is not particularly promising. At this point solvers may have already identified the answers to some of the right column's clues, many of which were written to have one clear or at least most obvious answer. For example, the first clue most likely gives the word CALF, which we can't get from DAGGER just yet. But the second clue almost certainly clues KICKER, which with some shrewd observation, matches some properties of the ZEUS->JUPITER conversion. In particular, K as a first letter is what you get if you add 11 to an initial blank space, while the trailing ER of course matches that of JUPITER. What remains is to explain the remaining "ICK" part, and this should hopefully be generated by the left column's THUG. The leap here is to note that we can afford to have blanks between letters in the words we're converting. Indeed if we begin with a blank space followed by the word THUG, denoted _THUG here, and apply the ZEUS->JUPITER translation, we get KICK_ER (_+11=K, T+16=I, H-5=C, U-10=K, G+20=_, _+5=E, _+18=R). Testing the other cases in this way, we can also find the word BLEA_T can become MA_RTYR in this fashion (which is a bit easier to spot naively if you're willing to look that far down the list).

It's nonetheless clear that most words will never convert to a nice new word under the ZEUS->JUPITER encoding, so the other intuitive leap to make is that other Greek gods can also define new encodings that can be applied to these other words. Some early candidates for checking might be Aphrodite, Ares, Athena, or Poseidon, and checking any of these against certain words will confirm they're the right idea. In fact, every god listed as an Olympian other than Apollo (whose Greek name is identical) is represented in at least one encoding in this puzzle. The Olympians were chosen since they include the best-known Greek/Roman gods, and is a common set of gods that is easy to discover/research (despite there being no general consensus on exactly which twelve constituted the ruling party). The fact Zeus, founder and leader of the Olympians, is featured in the top image was also supposed to put solvers in this mindset.

So, putting this all together, we can find a god-encoding for each word in the left column, which in turn helps confirm the words hinted at in the right column. These are:

WordGod conversionResultant word
DAGGERDEMETER->CERESCALF
THUGZEUS->JUPITERKICKER
DELAYSATHENA->MINERVAPUREST
DEFTARES->MARSPOST
PETRELARTEMIS->DIANASWATCH
ABETHERA->JUNOCRAG
AMMOHESTIA->VESTAOMEN
FLUFFATHENA->MINERVARAJA
CITRONSARTEMIS->DIANAFACE
HANDBAGHERMES->MERCURYMANURE
BORGESDIONYSUS->BACCHUSSODAIC
PEERLESSHEPHAESTUS->VULCANNEATLY
KITHERA->JUNOBEG
BLEATZEUS->JUPITERMARTYR
COWPATHERMES->MERCURYHOMER
BOORSPOSEIDON->NEPTUNEEXCLAIM
CANTERDEMETER->CERESBASS