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### Solutions for Act V Scene 3 - Cubes

The centrepiece of this puzzle appears to be the strangely-patterned cube, which can be viewed as having its faces split into 2x2 grids. The lines of letters on each face use normal Rubik's cube algorithm nomenclature, which implies we are dealing with a 2x2x2 Rubik's cube. The lines also tell us from what orientation to view each face, which in turn orientates the pattern on each face. The cube can handily fold out to look like:

It now becomes more apparent that each face's pattern is a representation of a binary number, running 1 through 6 in order as given. White squares are read as zeroes, black squares as ones, and the digits are read from left-right, top-bottom. This gives an ordering to the faces.

Now we should probably use the clues on either side of the cube. Once a few words have been found, a clear pattern emerges: each word is six letters long, and contains letters only between A and O inclusive. This seems promising since in binary, the biggest number we can fit on a face is 15 (all black squares), which corresponds with the 15th letter O - and of course there are six faces on the cube. So a natural thing to do is to map each word to the cube by converting each letter to its binary form and mapping these to the six numbered faces of a cube in order.

Now we can guess at the use for the algorithms: applying one to each word's cube will produce a new cube, from which a new word can be extracted. We can probably expect that each algorithm turns one of the words on the left into one of the words on the right. For example, the first word ALBINO transforms into MAMMAL when the very first algorithm F'U'BR'BL is applied to its corresponding cube:

The conversions as ordered by the left column are:

Left wordAlgorithmRight wordAlg face
albinoF'U'BR'BLmammal1
bookedD'B'R'B'Lcoffin3
cajoleU'FR'D2cinema5
dodgedLF'LF'R'Fanimal3
edibleFU2banana6
fiddleU2acidic5
hijackU'F2afghan6
jingleD'RFUenigma4
jokingUF'LFD2minion4
maniacURB'U2cackle2
mockedUF2gaming1

(The right column in the puzzle gives the "right word" column in the above table, but alphabetised.) Note above we have also included the numbered face that each algorithm was taken from, since this is the only piece of information we have yet to use. Indeed we probably want to treat these numbers as indexing factors of some kind, since they're all less than 7. The first guess might be to try indexing into the left or right word, but this doesn't give anything useful - and shouldn't be expected to, since only the letters up to O can be used in this case. The only other obvious thing to index into are the clues themselves. If we do this to the left column, taking the first letter from the clue for ALBINO, the third from the clue for BOOKED, etc., we get WHO COMPOSED. To complete this message then let's index into the right column's clues. This time we also want to order the column so that it lines up with its originating words in the left column. So we want the first letter of the clue for MAMMAL, then the third from the clue for COFFIN, etc. This gives LITTLE BOXES. Combining these we apparently want the composer of the folky song Little Boxes, Malvina Reynolds.

Puzzle Notes: The face orientation was chosen so that it was easiest to read off both a physical cube and a net. The bottom face may have made more sense to some people rotated 180 degrees, but this set up yielded less interesting word pairs.

One of the algorithms included FF, which is more traditionally written F2. This was an unfortunate oversight, but was not corrected as it didn't change any aspect of the puzzle. Thanks to those solvers who pointed this out and apologies for not confirming your hunches with a potentially revelatory reply.

This puzzle was originally a lot more complex. There were 26 words to convert, and the final step involved piecing them together to form a giant 3x3x3 (technically 6x6x6) Rubik's cube. The indexing step then gave a new algorithm to apply to this cube, which resulted in pixellated images appearing on the six faces. Unfortunately these weren't particularly recognisable, and some of the word pairs used were rather obscure. The final version of the puzzle got rid of the crazier steps and allowed for some nicer word pairs as a result.

Update: We were just informed that the initials of the right column all corresponded to the usual cube face letterings, plus A and S which could be respectively interpreted as "anticlockwise" and "squared". While this might be a bit of a stretch, we're sorry for the unintended red herring and probably should have at least noticed the coincidentally high number of [FURBDL] initials in testing.