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Solutions for Act V Scene 2 - Psychosomatic

This puzzle's title and component images imply it might be inspired by the Soma cube, an especially popular 3D construction puzzle. Its goal is to construct a 3x3x3 cube using seven smaller pieces representing the only polycubes formable from three and four cubes that are not themselves cuboid. This solution will refer to the seven component shapes as "pieces", and the smaller component cubes forming each piece as "blocks".

From the images provided several observations can be made. In terms of numbers, there are 7 of each type of Soma cube piece, 14 total block faces with words/phrases written on them, and 8 blocks coloured each of the 7 colours of the rainbow. It can also be seen that each piece has at least one coloured block, and exactly seven pieces have exactly two coloured blocks. In the case of these particular pieces, the two colours can be the same or different.

Identifying what the words/phrases are cluing also helps. From a few clearer examples it can be determined that each clue indicates a two-letter word or abbreviation, and furthermore for each bigram that appears, its reverse is also clued somewhere:

  • stomach muscle = AB
  • barium = BA
  • compare = CF
  • soccer team = FC
  • Д = DE
  • journo = ED
  • whatever = EH
  • this guy = HE
  • lieutenant = LT
  • teralitre = TL
  • saint = ST
  • poet Eliot = TS
  • Paraguay = PY
  • yellow pages = YP

It's reasonable to expect therefore that each pair of clues represents faces that touch each other in a completed cube, and that each of the final seven cubes contains one such pair of clues. A bigger logical leap to make is to notice that each of these bigrams could be interpreted as adjacent letters in a cube. The AB, DE, and ST pairs hint at this (being already alphabetically adjacent), while the CF and EH pairs can each be observed as adjacent letters when the start of the alphabet is written in order on a 3x3 grid:

ABC
DEF
GHI

This somewhat naturally implies a letter assignment to the 26 cubes on the outside of a 3x3x3 cube: label blocks starting from the top-left of the top face from A to I, then adopt a similar labelling rule for the middle face (except skipping the centre block) from J to Q, and repeat again for the bottom face from R to Z:

This ignoring of the centre block helps resolve another mismatch in the original block count: that there are 8 of each coloured block instead of 7. If one of each of these colours is in fact the centre block of each completed Soma cube, there will be exactly 7 of each colour visible on the surfaces of these cubes, which is more symmetrically fitting.

The next logical leap to make then is to decide that the 7 colours on the surface of each cube might spell out a word, since they are naturally assigned letters and ordered by colour.

Using all of the above assumptions gives just enough information to construct the required seven cubes uniquely. For example, one can easily assign the two L-shaped pieces whose faces lack written clues to their appropriate cube goups, since the colours involved in the LT/TL group force green to be one of the already accounted for exposed blocks, and therefore the blue L-shape is forced to join them (as opposed to the green L-shape, which joins the DE/ED group). Each cube's surface blocks spell out a common seven-letter word when read in rainbow order, and one of each colour features as the centre of a cube. The pieces have been grouped per cube below - you can try combining them with this extra information to achieve the required words:

The words we end up getting, ordered by centre colour, are TANGLER, THIRDLY, PREDICT, GAMBITS, PURLOIN, OUTSIDE, and LAMPREY. The centre colour also matches the letter we would like to take from each word: the first letter of the red-centred cube, the second letter of the orange-centred cube, etc. Doing so gives the body, a literal translation of "soma" from Ancient Greek, as well as the name of the resident demonstrative expert in a UK psychological-challenge game show called "The Cube".


Design notes:
A lot of time was spent wondering if this puzzle was pitched at the right difficulty level. Versions existed with more and fewer visual hints, different arrangements of pieces, and different colour assignment rules. Ultimately even though testing implied this puzzle was certainly on the hard end of the spectrum, we decided to use the hardest version that was still provably solvable, mainly because some of the logic steps required to complete it were so enjoyable, and because in general it can often be difficult to produce satisfyingly complex logic puzzles. It's a little unfortunate that some key steps in construction required enough foresight to see the word-construction step coming, but hopefully there were enough hints in the construction of the puzzle itself to imply all that was needed.

The answer is: thebody