# Meta³

#### Solution: FACECENTREDCUBIC

##### Credits: The whole team

Opening the meta pdf, we see a set of cubic equations, each of which can be solved to give:

α = 13, β = 15, γ = 14 (I.S)
δ = 4, ε = 7 (II.S)
ζ = 4, η = 1, θ = 7 (III.S)
ι = 9, κ = 4 (IV.S)
λ = 2, µ = 7, ν = 5 (V.S)
ξ = 12, o = 17, π = 5 (VI.S)

Indexing these numbers into the respective S puzzle answers gives:

α = E, β = D, γ = N (WORDSWITHFRIENDS)
δ = H, ε = G (THEHUNGERGAMES)
ζ = I, η = H, θ = D (HOMICIDE)
ι = T, κ = O (SUMOWRESTLER)
λ = E, µ = I, ν = T (WELLTRIS)
ξ = R, o = S, π = I (LEANINGTOWEROFPISA)

Rearranging these Greek letters as provided reveals the phrase EIGHT HIDDEN TRIOS.

Congrats, meta solved! The meta pdf does directly state that this is the puzzle answer, so it would be safe to type it into the answer submission checker. Upon doing this, we are informed that we're actually not there yet, and instead "it is left up to you to right what's been put down". If we return to the home page, we notice that all the edge cubelets on the Rubik’s cube (at least on the faces corresponding to the days where the central S puzzle have been solved) have been lit up. Previously, none of the edge cubelets were lit.

The most obvious we have to go on at the moment is the phrase EIGHT HIDDEN TRIOS. So far only the central S puzzle answers have already been used, leaving twenty-four other puzzle answers, which might nicely be sorted into eight trios. Looking closely at the answers reveals that there are hidden phrases contained within them, which can be grouped into (ordered) trios. These trios represent common or idiomatic phrases, such as the GOOD, the BAD and the UGLY. Arranged in alphabetical order of the trios:

• ORDINARY (GOOD)S (III.4)
SCU(BA D)IVING (VI.3)
TH(UG LY)FE (I.1)

• OP S(HOP) (VI.1)
(SKI P)OLES (II.4)
HIGH (JUMP)ER (IV.4)

• TURKISH DE(LIGHTS) (VI.4)
TRI(CAMERA)LISM (III.3)
IMPROPER FR(ACTION) (I.2)

LCH(AIM) (I.3)
ISLAND O(F IRE)LAND (IV.2)

• GOB(STOP)PERS (V.3)
HY(DROP)UMP (IV.1)
INTERNET T(ROLL) (II.3)

• GENE(TIC)ALLY MODIFIED ORGANISM (I.4)
REN(T AC)T II (III.1)
EYE (TO E)YE (II.1)

• R(UN O)UT (V.2)
MUSICAL KALEI(DOS)COPE (III.2)
NANOME(TRES) (V.1)

• INTER(VENI)R (V.4)
STREPTA(VIDI)N (II.2)
A(VICI)I (VI.2)

It's not immediately apparent what we can do next, so we consider any other sources of information. We may recall the 3x3 squares that appeared in each central S puzzle on each day but have been ignored up to now. It turns out that this part of the puzzle wasn't entirely necessary to solve the meta, but for the sake of completeness we'll mention it here anyway.

In Act I, the centre 3x3 tiles are outlined with a white box, and the contents in the solved state of the puzzle are:

In Act II, the centre 3x3 squares are outlined with a red box, and the contents in the solved state of the puzzle are:

In Act III, a 3x3 section of the sudoku is outlined with a white box, and the solved state of the puzzle is:

If we colour the rooms by the name of the occupant, and replace each ?? with its letter representation, the resultant 3x3 square will be:

In Act IV, the bottom left corner had a 3x3 of cranes indicating the colours and letters, in the same manner as described by the rest of the puzzle, in that the number of strokes is equal to the equivalent letter.

This results in the equivalent 3x3 square of:

In Act V, parts of the tetrominoes had thick black outlines, and solving the puzzle results in the following 3x3 square:

In Act VI, when all towers are stacked one on top of the other, and red and green pieces removed, if you looked down on the tower, you would see the following 3x3 square, where the letters are made up of the unused symbols:

Looking at the unsolved-but-now-lit-up Rubik's Cube on the home page, we notice that these 3x3 squares map onto the faces of their respective S puzzles because the corner colours (in some orientation) match those on the Cube. Thus we should place the letters in the 3x3s on their appropriate cube faces. If we solve the Cube, the following is what we see:

Reading the faces in rainbow order (red, orange, yellow, green, blue, white), we can find the phrase FIRS / TLET/ TERC / ORNE / RANS / WERS, or FIRST LETTER CORNER ANSWERS.

If we look at the solved Cube again, we notice that each face still has four corners numbered 1, 2, 3 and 4; the difference is that for a given face, the four corners may not correspond to the same acts. We may actually have noticed this bit first, in which case the step outlined above was unnecessary.

On the solved cube, reading in order of the acts then scenes gives us the following ordering of answers. We take the first letters from each of these answers to give us the phrase EIGHT ALGORITHMS IN STORIES.

Face Scene 1 Scene 2 Scene 3 Scene 4
I (red) II.1 EYE TO EYE IV.2 ISLAND OF IRELAND V.3 GOBSTOPPERS IV.4 HIGH JUMPER
II (white) I.1 THUG LYFE VI.2 AVICII I.3 LCHAIM I.4 GENETICALLY MODIFIED ORGANISM
III (orange) VI.1 OP SHOP V.2 RUN OUT II.3 INTERNET TROLL VI.4 TURKISH DELIGHTS
IV (yellow) IV.1 HYDROPUMP III.2 MUSICAL KALEIDOSCOPE VI.3 SCUBA DIVING V.4 INTERVENIR
V (green) V.1 NANOMETRES II.2 STREPTAVIDIN III.3 TRICAMERALISM III.4 ORDINARY GOODS
VI (blue) III.1 ROLY POLY I.2 IMPROPER FRACTION IV.3 EVEREADY II.4 SKI POLES

Given there are eight ‘hidden trios’ and eight ‘algorithms in stories’, it makes sense to match these up; that is, each trio of answers corresponds to one algorithm that we can find in the stories. Reading through the stories, we find a high frequency of the words LEFT, RIGHT, UP, DOWN, FRONT and BACK, the standard moves to solve a Rubik’s cube. To disambiguate, each of these words indicate one turn clockwise of the respective face. If we extract all the moves from the stories given by the trios, we end up with the following eight algorithms:

ORDINARY (GOOD)S / SCU(BA D)IVING / TH(UG LY)FE III.4 / VI.3 / I.1 LDDFFBBLLLUUFF / RUFFDDFFFUUUBB / RRRBDDDLLLDDD
OP S(HOP) / (SKI P)OLES / HIGH (JUMP)ER VI.1 / II.4 / IV.4 RBBRRRBBUULUU / RRUUFFFLLBUBB / DDBLLLBBBUUD
TURKISH DE(LIGHTS) / TRI(CAMERA)LISM / IMPROPER FR(ACTION) VI.4 / III.3 / I.2 UURRRFFUUFF / RRRFFDDLLRRD / FFRFFLDDLLLFU
EVE(READY) / L’CH(AIM) / ISLAND O(F IRE)LAND IV.3 / I.3 / IV.2 BBLDDBBDDRRR / DDBBRULDDF / DDDLUUULBDF
GOB(STOP)PERS / HY(DRO P)UMP / INTERNET T(ROLL) V.3 / IV.1 / II.3 LLUULBBLDDB / DDUUUBFDDUUU / FFFUUUFFDUUUL
GENE(TIC)ALLY MODIFIED ORGANISM / REN(T AC)T II / EYE (TO E)YE I.4 / III.1 / II.1 LLUUBBRRLLLBB / RRRLLDDDRRFFLUU / BBBUUFFFRFFDDR
R(UN O)UT / MAGIC KALEI(DOS)COPE / NANOME(TRES) V.2 / II.2 / V.1 FFRRUURRRBBRRBB / RRUURRRUUUFFLL / DDDRRRBBRRRUFF
INTER(VENI)R / STREPTA(VIDI)N / A(VICI)I V.4 / II.2 / VI.2 RRLFFLLLDDFFDDRRR / DDBBBUUUFFLLLBB / RRDDDRRRLLLBBBUUU

If we apply each of the eight algorithms separately to a solved Rubik’s cube, we are left with eight different cubes. The key is to notice that cubes share faces with adjacent cubes when the trios are in alphabetic order. This forms the following set of cubes which could be ‘glued’ together (on their shared faces) to form a 3x3x24 block:

The final step of this puzzle is to notice that the end faces of this 3x3x24 block is very regular. The entire face is white except for the edge cubelets (red, blue, yellow and green squares), each adjacent to a 3x24 face. Let's look at the 3x24 face that is adjacent to the red cubelet; we should ignore all colours that are not red. Do the same for the other three 3x24 faces, reading only the squares that are the right colour. If we do so, the following message can be found.

(Note: If we haven't noticed that the cubes are glued in alphabetical order of the trios, we may be tempted to form a cube doughnut, since the end faces of the 3x3x24 blocks alre also 'gluable'. We should, however, notice that these faces are much more regular then rest, and so should refrain from gluing as such.)

The message reads NACL LATTICE, which refers to the FACE CENTRED CUBIC crystal lattice structure of crystalline sodium chloride.

#### Authors' notes

Well, we've reached the end. This is it. No more puzzles. Just the meta now. So let's talk about it!

Naturally, as with any other complicated and multi-layered puzzle, there are quite a few issues that we would like to address.

• We accidentally released the meta pdf an hour early, but this was quickly spotted and resolved within two minutes. Since some puzzles were backsolvable from this meta, the early release resulted in the deflation of average solve times for a number of teams. Thankfully, this didn't impact the overall meta solvability or competitive rankings of any teams, since the first team to solve the meta only did so a whole 28 hours after meta release. Furthermore, by Day 6, most of the top rankings were already locked in place, given that teams went into Day 6 on unequal scores. There is not much more that we could add to this point apart from saying that it was one of a handful of technical glitches that we experienced, and we sincerely apologise to any teams that feel particularly wronged by the accidental early release.
• Another concern for us was the backsolving of puzzles on Day 6. During the construction of our meta, we were aware of the potential for backsolving, especially with teams nearing the perfect set, as all they needed to do was identify the missing element of the hidden trio and choose the appropriate first letter, if even. In order to combat this, a majority of our puzzles had answers that were not present in word dictionaries — answers such as OP SHOP, AVICII, and TURKISH DELIGHTS on Day 6, for example. Unfortunately for us, the Day 6 puzzles and their answers turned out to be too well-themed (OP SHOP is Australian slang, AVICII is a Swedish musician, and TURKISH DELIGHTS are a type of sweet). We were understandably disappointed by this outcome, and we implore teams that did not forward-solve these puzzles to at least take a look at them and appreciate the effort that was invested in constructing them. In future, we realise that if the puzzle answers are indeed backsolvable from the meta, then it would perhaps be a better idea for us to release the meta a day later (on Day 7 in the case of this Hunt).
• We also regret to inform our diligent solvers that a number of mistakes were made with the 3x3's outlined in three of the special (S) puzzles. These included:
• a 'cage' addition error in Killer Cluedoku (III.S) resulting in one incorrect edge piece (the 'T' was erroneously represented as a 'Q')
• the incorrect version of Senbazuru (IV.S) being uploaded with four incorrect edge pieces (the four letters should read "FEAE" as opposed to the copy with"ONNJ" that was erroneously distributed to solvers)
• a typo in Infallible (VI.S), which resulted in another incorrect edge piece (the 'W' was misread upside down and was given as an 'M')
While we could say that this did not impact the overall solvability of the meta (a handful of teams circumvented this 'optional' step of the meta), it certainly made things extremely and unnecessarily difficult for a lot of our teams and posed quite the barrier to entry. This is compounded by the fact that these issues were not identified until the final day of the Hunt, and would have, undoubtedly, from a time perspective, impacted a team's ability to solve the meta and to 'complete' the Hunt. For this, we apologise profusely. Sorry.
• There was also a minor issue with one of the moves in the story (the story associated with A Noteworthy Puzzle was missing an "up" move). This was rapidly rectified, and an erratum was issued that may have unduly impacted our teams' comprehension of the puzzle itself. We go apologise for this, but we hope that you can all come to realise why the erratum had to be phrased in such a manner.

As final cursory points, there were also a number of additional issues that were raised by participating teams immediately after the Hunt.

• Some teams did not submit "EIGHT HIDDEN TRIOS" into the answer checker and, therefore, did not progress much further. We felt, however, that we had communicated this instruction clearly enough by placing the word "ANSWER:" directly in front of the blanks.
• Some teams failed to notice that the edge cubelets had been revealed upon submitting "EIGHT HIDDEN TRIOS" as an answer. Yet again, we felt that this had been communicated via a number of media, including but not limited to: the correct answer message, the Rubik's Cube with the greyed-out pieces on the home page of the Hunt, and the fact that the 3x3's explicitly reference the edge cubelets of the Cube.

Well. Looks like that just about does it. Hopefully we've covered several of your concerns in these solutions. If you still have some additional feedback that you would like to provide, the feedback survey is probably your best bet.