Solutions for Act II Scene 4 - Phases

This puzzle presents us with seventy clues and not much else. The obvious first step is to work out what words these clues refer to, and there should be enough unambiguous clues to give a good list of certain words. Some properties should soon become clear in this process: All the words are four letters long, and many of the words differ by only one or two letters (e.g. NASA and NASH, or AERY, AERO, and MERO).

It should soon become clear that we can in fact make chains of these words such that any adjacent pair differs by exactly one letter - this puzzle is a disguised list of word ladders. This helps to work out any remaining clues, since a single break in any chain can only be occupied by a unique word. The clues end up working out to be:

'Knife' is to 'blade' as 'fork' is to thisTINE
A 'capa' or 'muleta' manoeuvrePASE
A term that can follow 'tabula'RASA
A windy or grating tone of voiceRASP
Absurd poet OgdenNASH
An address in German meaning 'mister'HERR
An annoying or impolite childBRAT
An ensemble of actorsCAST
As 'see' is to 'eyes', this is to 'ears'HEAR
Ashen; fadePALE
Band of Norse troops and court guardsHIRD
Banned item (with "do's") (contraction)DON'T
Blow so as to dent; forceDINT
Bubbly chocolate barAERO
Cavities on either side of the headEARS
Chest; circumstanceCASE
Clear fluids from plants or animalsSERA
Declines (as contraction); accustomedWONT
Department of US space research (abbreviated)NASA
Does wrongly or mistakenlyERRS
Dry earth; gossipDIRT
Edge-sharpening toolHONE
Edibles, or to snack on theseNOSH
Enrobes; wearsDONS
Erodes; chewsEATS
Evoke a goose or carHONK
Feeling; atmosphereMOOD
Funeral serviceWAKE
Got up; flowerROSE
Has 'soft' and 'easy' as antonymsHARD
Hold or ownHAVE
Home for striped insectsHIVE
Hoof; imperial measurementFOOT
Inferior amount; tiny arachnidMITE
Intelligence; babysitMIND
Juno's Greek equivalentHERA
Kind of fungus (US spelling)MOLD
Long for; needWANT
Longest measurements of time after eonsERAS
Metal strap fastened by a pinHASP
Non-SI unit of loudnessSONE
Of a benign or moderate mannerMILD
Of little or no more value thanMERE
Of no practical worth; debatableMOOT
Of one's complexion, pinkROSY
Of the moon, to become smallerWANE
Of words, an action or state of beingVERB
Olfactory organNOSE
One born in BelgradeSERB
Provide by measure; doleMETE
Pulse; hitBEAT
Revulsion; dislikeHATE
Second person archaic form of 'have'HAST
Sign on as an employeeHIRE
Slow down; exhaustTIRE
Sound wave lacking harmonicsSINE
Speed; scoreRATE
Spelling variant of 'eyrie' or 'airy'AERY
The set of cards dealt to a playerHAND
They betray people, or eat cheeseRATS
They sting and produce honeyBEES
Toothpaste flavourMINT
Tricks; prisonersCONS
Urgent; disastrousDIRE
Ursine mammal; carryBEAR
Whack to the head (slang)CONK
What E stands for in QEDERAT
Widespread term for the Epinephelus genusMERO
Word 'red', 'silver', or 'sugar' can precedeBEET

In conjunction we would have been structuring the associated word ladders, and it soon becomes clear there are five ladders of length 14 each. There is one unfortunate split here - BEAR could link to HEAR or BEAT, but since the other three word ladders are uniquely determined, it should be clear at this point that all ladders are the same length, and thus BEAR must link with HEAR (else we get one ladder of length 13, and at best another of length 13 and one of length 2). Another strong hint in favour of this construction is that each ladder was deliberately constructed so that its start and end words are related in some way - mostly by antonymy, as per the usual trick with word ladders, which ask the solver to morph ("phase") a word into its opposite. The word ladders extracted are (note they may have been derived in reverse order):


This is all well and good, but what can we do with these word ladders? There isn't much to go on here, so perhaps we should look at the clues again. There are two hints here: First, the clues themselves are for the most part quite strange-sounding, sometimes with unnecessary words or odd turns of phrase. Second, the clues are presented in a monospace font. Both these hint towards the position of letters being somehow important to the puzzle.

If we reorder the clues by matching them to the order determined by their word ladders, the WAKE-TIRE ladder is hopefully a giveaway: Depending on which order you wrote the ladder in, the first letters of each clue spell the phrase FOLD BETWEEN S'S either down or up the page (i.e. from "Funeral service", "Of the moon, to become smaller", "Long for; need", etc.). This tells us a few things: That the apostrophe is considered a character, that there is a preferred ordering to the word ladder, and that we apparently need to fold something.

First though, we should check the other ladders' clues. With a bit more work, it can be discovered that the second letters of every ROSY-PALE clue, the thirds of every MITE-BEAR clue, the fourths of every FOOT-HAND clue, and the fifths of every HIVE-BEES clue give similar messages (at this point we also discover spaces, unlike apostrophes, are not considered characters). Respectively along with the WAKE-TIRE message again, these are:


It seems as well as being told to fold something, the word SHADE is being clued. For now, let's focus on the more transparent folding clue. Usually in puzzles, the order to fold something is given by a dotted line in a picture. Here we have no pictured or indeed dotted lines at all, so we must construct our own foldable item. The theme so far has been word ladders, so the most logical approach is to draw up our five ladders as rectangular grids and cut these out.

As for the folding itself, in the case of the first WAKE-TIRE ladder, we apparently want to fold between S's. This seems to make some sort of sense, since exactly two pairs of adjacent S's appear in this word ladder, and so "between" must describe the horizontal line (or "ladder rung") between each pair. Folding along these lines must be the next step then, but we still need to know in what direction and how far to take each fold. Looking at the other ladders helps here - some have so many closely-packed folds that it wouldn't be plausible to form a three-dimensional shape my making, for example, ninety-degree folds, and similarly there would not be room for certain parts of some ladders if only one type of fold (valley, say) was used at each juncture. The most logical folding pattern to try then, is alternating full valley and mountain folds at each fold-line, making a typical concertina-like shape. As it will turn out, it doesn't matter what types of folds we make at each line, as long as the folds are always full, 180-degree folds, and the pieces never intersect. This gives us:

Note in the above picture the folded ladders should be flat, but their natural springiness is on display to make it clearer where the folds were made. Also the pieces have been orientated so that the first word of each ladder is visible, which is important (otherwise, our results after the next step would be inverted - it's assumed this is the natural way to arrange each ladder since presumably the first fold made will be at the highest fold line). Again we seem to have nothing left to do in so far as folding, so we can turn to the final unused piece of information: The word SHADE clued by the hidden clues. Taken as an order, we seem to want to shade something. The intuitive leap here is that we want to shade the square in each row of each word ladder that holds the "new" letter per rung. That is, following the word WAKE, we want to shade the cell containing the N in WANE because that's where the new letter/phase has appeared. This step is hopefully not too much of a stretch, since we haven't really used the word ladders' defining property yet, and should have noted by now that many steps of the word ladders are in fact redundant or positioninally repetitive (e.g. in the ROSY-PALE ladder, all but three of the rows change only the first or last letter).

Shading each of these cells doesn't immediately show anything, since much of each ladder is by this point obscured by the folding. The final step here is to realise that we still haven't put the folding step to any use, and that it is in fact a means of overlapping different sections of each ladder. So what we really want to do is obesrve the composition of all shaded cells after folding, which can be done by e.g. imagining (or even actually) drawing the word ladders on a transparency sheet and looking at the resultant overlapping shape after folding (using our theme, one should be able to see between the rungs of a ladder). This effect can also be achieved by holding the shaded, folded ladders in front of a strong light, which is supported by the alternative meaning of SHADE. Doing so gives:

(For want of a stronger light, the overlapped shaded cells have been emphasised in thinner pen.) These resultant shapes hopefully clearly spell the word RUNGS in order, which is the word for the steps of a ladder (and is by loose association connected to the title PHASES <=> STEPS <=> RUNGS).

Design Notes: This puzzle was inspired by the fact I'm always tempted to shade the changed letters in a word ladder to see if they make any sort of pattern. In general the answer is of course no, and it's clearly a very limited canvas on which to work on since each row can only contain one shaded cell/pixel. This led me to looking for some sort of transformation that could be applied to word ladders that allowed rows to have more than one cell shaded, and I soon realised folding would be a neat step since it's fairly easy to clue and thematically links to the idea of a collapsible/folding ladder.

I considered providing the five blank word ladders for cutting-out purposes, but decided the puzzle looked neater without them and hoped the realisation solvers had to make their own ladders would be an exciting one, since construction puzzles very rarely refuse to present the solver with their components as pictures.

The title was originally Steps, but was changed to Phases to prevent teams guessing after only discovering the word ladder link. Hopefully this didn't lead too many teams astray, as the guesslog picked up a lot of guesses related to moons, and I took an embarrassingly long time to realise the connection.

The solve rate of this puzzle was especially surprising to me, as usually when a puzzle's solve rate is worse than expected, we can work out what about the puzzle has made it harder than planned. While this puzzle was a 4-star, it was placed on Day 2 because we assumed the steps were not especially difficult to deduce, since the only steps that aren't explicitly stated are which letters/cells must be shaded, and how to read off the final answer. Furthermore in testing, the only things changed were some of the more obtuse clues. I'm guessing there was some unforeseen alternative avenue of approach to the puzzle that seemed just as if not more enticing than the intended one, and apologise for not spotting it (then and now!). This section will likely be updated once some feedback has come through!

Update: It's since been pointed out that there are a couple more possible splits in the ladders than expected. Remarkably, two testers and the writer somehow only managed to spot the one described above. Luckily none of these splits give ladders of length thirteen, so if one was working with the (admittedly arbitrary) assumption that all ladders would have equal length, this would be resolvable. However it has to be conceded that the split at HIRE (to HIVE or TIRE) is especially unfortunate, since it was hoped the endpoints of the ladders were easily determinable.

The answer is: rungs