mezzacotta Puzzle Competition 2016

Solution: M. 時間の無駄

The title of the metapuzzle turns out to be Japanese for "waste of time", which seems to be telling us to ignore it. Of course, one would hope that there was a reason for this, beyond simply wasting the time of anyone who bothered to translate it, but — at least for now — we shall take the hint and move on to the rest of the metapuzzle.

The table contains entries for each puzzle, complete with space in which we are presumably to insert the puzzle's answer. The third column contains five alphanumeric values, and it seems reasonable to infer that the numbers are to be taken as indices into the puzzle's answer. Doing so would give us five letters, and we would hope that we could get sensible words out of the result, which we could then put into the fourth column.

We immediately strike a small snag, in that the answer to the first puzzle, Pule, has only six letters. However, this process works well for the second puzzle, giving the word THESE. Several other answers where the indices are all within range also yield words, so this must be the right thing to do. The insight required here is that we should wrap around back to the start of the word when the index is too large. Doing so produces sensible words in every case.

(The reason for these large indices was to make it harder to reverse engineer answers to main round puzzles from the metapuzzle. It also allowed for the same letter to be used more than once.)

One caveat here is that we must use the canonical answer for each puzzle. Some puzzles accepted multiple answers, but for the metapuzzle one specific one must be used. Fortunately, the answer server cleared this up for us: When a correct answer to a puzzle was submitted, the solution message returned included the information about whether the answer was the canonical one, and provided that canonnical form if necessary.

Using the canonical answers, and wrapping around the indexing when necessary, we end up with the following completed table:

Puzzle	Canonical Answer	Index	Word
Pule	REDDER	6, A, K, 2, 7	RAKER
Picture Carnival	THE SEEKERS	1, 2, 3, 4, 5	THESE
Free Image Market	ADAM SMITH	10, 5, 14, 3, Y	ASSAY
Destinations	ALHAMBRA	1, 6, 2, E, S	ABLES
Five Squares Plus Another Five Squares	MOUTHWASHES	1, 10, 11, 8, Y	MESSY
Learn Your ABCs	ALPHABET TIME	3, 2, 5, S, 11	PLASM
Bonza	GPW MEREDITH	A, 9, 4, 5, 8	AIMED
Some Faces	ZENO OF ELEA	1, 2, 10, 8, S	ZEALS
I Met a Man	THE SPHINX	A, M, 3, 8, 4	AMENS
Hollow	VOLUME	12, 7, 2, K, 6	EVOKE
Interesting Bunch of People	THE LEAGUE OF EXTRAORDINARY GENTLEMEN	4, 10, 1, 14, 17	LOTTO
Building Blocks	HEMIUNU	7, 3, A, 10, 4	UMAMI
Time and Space	SEMIBREVE	5, A, L, 11, 6	BALER
Swatches	GOJI BERRY	S, 2, 8, 7, 9	SORRY
Animal Quarters	DOVE	1, I, 7, 2, T	DIVOT
All Astir	WIDDERSHINS	7, 5, E, 3, S	SEEDS
Art Elsewhere	LANDSCAPE WITH OBELISK	14, 20, R, 2, 5	OKRAS
Crossover Word	UNCROSSED	10, 2, B, I, 9	UNBID
Signs of Change	NEON	A, 9, I, 7, 1	ANION
Tangram Mix-up	GRAM	8, A, 5, M, 11	MAGMA
Shaggy Cat Story	PANTHERA	I, 11, U, 7, 6	INURE
Protecting the Elderly	SIX MILLION DOLLARS	1, 15, 16, 5, 18	SARIS
Lines	THE INFERNAL TRAIN	11, 10, P, S, 7	LAPSE
Befuddled	QUESTING	A, S, 12, E, 5	ASSET
Cleaving Hearts	SURTOUTS	10, L, 4, R, A	ULTRA

Now we turn our attention to the rest of the metapuzzle. The grids have space for twenty-five words, but five of them are already filled in. That does not leave enough room for all twenty-five of our answers, and in any case there would be the question of what to put where. However, we have another alternative available: We could write the answers in the grids vertically instead of horizontally; there's precisely the right number of spaces for that, and the question of placement is resolved by the spaces already filled in. We can further intuit that we will end up forming words when we read across the grids, at least in the pink shaded sections (but it would be more elegant if every across entry was a word).

With all the answers available this is not an especially difficult task. It is also achievable with fewer than the full set, allowing any missing words to be deduced. The completed grids are:

U S U A L    B I O T A    P L A Z A    U S E R S    M A D A M
L A M I A    A N K H S    L O B E S    N O V A E    A N I M E
T R A M P    L U R E S    A T L A S    B R O K E    G I V E S
R I M E S    E R A S E    S T E L A    I R K E D    M O O N S
A S I D E    R E S E T    M O S S Y    D Y E R S    A N T S Y

This gives us the message ASIDE ANKHS PLAZA BROKE MOONS. A little searching, or familiarity with the Discworld series, reveals that this is a reference to the Plaza of Broken Moons in the city of Ankh-Morpork. We can also now see that the puzzle title was hinting at this series; its romanisation is Jikan no Muda, a sudoku-like puzzle that appears in the Ankh-Morpork Times. The competition grand prize for being the first team to solve the metapuzzle also links into this theme, being a board game based on the Discworld stories.

The two main city features near the Plaza of Broken Moons are the Palace and Sator Square. Given the presentation so far, featuring prominent squares of five words, we can guess that the latter is intended. This guess can be helped along by looking up the other Sator Square (which the Discworld location was named after): It is a five-by-five grid of letters forming words across and down.

The answer to the metapuzzle is SATOR SQUARE.

Puzzle design notes

This puzzle had its genesis in the planning for the ultimately cancelled 2014 CiSRA Puzzle Competition. In that competition, we developed a tradition of awarding virtual medals to teams who fully solved all of the puzzles in each daily group. The medal graphics were based on five different types of puzzles:

A Rubik's Cube.
A Tower of Hanoi.
A labyrinth.
A chess knight, representing chess puzzles.
A tangram construction.

In the past, we had constructed puzzles based around all of these different themes. We collectively had the idea for a new metapuzzle, which would involve constructing a set of five puzzles to appear in the regular puzzle groups, one per day, with one puzzle themed around a Rubik's Cube, another around the Tower of Hanoi, another around a maze, another with a chess theme, and another involving tangrams. The first step of the metapuzzle would involve spotting this set of themes, and then using that to guide extraction of words for each puzzle. This was not the entirety of the idea - there were other aspects to it involving all of the other group puzzles, which I won't divulge now, because we may be able to re-use them for a future metapuzzle.

We would end up with 25 five-letter words, which would then be used essentially as you see in the solution above.

However, when the CiSRA competition folded and we moved to our own private competition, we didn't bring across the graphic design of the CiSRA competition. So the puzzle medals vanished, and the metapuzzle idea partly collapsed.

We didn't start thinking about a metapuzzle again until we had already created several puzzles for the new competition. I realised that with a bit of massaging, the metapuzzle idea we had could still be made to work. We'd need a new way of extracting five-letter words from the group stage puzzles, but that could be done.

After thinking through a few ideas and discarding them as unworkable, we fell back to the most basic idea: indexing letters in the solutions to produce the five-letter words. We knew that if done sloppily this could present a risk of reverse engineering: teams solving the metapuzzle first with partial information, and then using that information to back-solve the solution words to the group puzzles, without actually solving the puzzles.

We did our best to prevent this being viable for any puzzle, but from the guess log it's clear that some teams thought that using many guesses to try out selections from sets of 200 or more possible words might be fruitful. In hindsight, we simply didn't construct this metapuzzle in the most fun way we could, and we have taken that as a valuable lesson learnt for next time.