Meta-eval Times

Written by Catherine Wu and Patrick Xia

Answer: QUIET

In Act II, some puzzles are entangled with one in the opposite dimension. The two puzzles each have their own theme, core mechanic, answer, and solution, but each requires some information or action from the other in order to solve. This puzzle is entangled with Pin the Tail.

In the puzzle, we are asked to suggest “phrases” that satisfy the constraints of 16 teammates. If they satisfy a strict majority of the teammates, those who are satisfied “write their meta” and report back whether the phrase satisfies a second, exact constraint that’s a subset of the first constraint. For example, the first teammate initially wants the Scrabble score of all the letters to sum to under 30, but in reality they want the value to be exactly 18. The initial rejection messages should help us hone in on a constraint, while the second failure messages help us search within the restricted space.

Here are each of the teammates, their initial constraint, the exact requirement, and how it can be deduced. An appendix for determining the exact constraint is in the Appendix. A good start is the word RELAXATION, which satisfies a majority immediately and can be tweaked to tradeoff constraints.

teammateInitial constraintFinal constraintExplanation
1Its scrabble score is less than 30.Its score is exactly 18.A common way to assign points to words is to use Scrabble scores.
2Its Morse code representation has more dashes than dots.It contains exactly 15 more dashes than dots.“Dashing” and 50% clue that dashes in the Morse representation are important.
3Its final letters form a word.The longest word formable has length 8 (using SOWPODS).The rejection messages state that we’re interested in the longest word that can be formed.
4Its length is 1 more than a square number.Its length is 17.The initial clue hints that the length needs to be n^2 + 1.
5It contains, as a substring, a United airport hub.It contains “ORD”.There are 8 United hubs, we can try all of them.
6It starts with one of ROYGBIV.It starts with O.“Palette” hints at color, and the input satisfies this one frequently, which should help narrow down to ROYGBIV.
7It contains the letters of a film directed by Alfred Hitchcock.It contains the letters REARWINDOW.Hitchcock was the “Master of Suspense” who directed many films. If the second constraint is hit (e.g. by Rope, Mary, or Marnie), there is another hint about a release date, which can also narrow down to films.
8It contains, as a substring, exactly one US state abbreviation appears.It contains “OR”.The initial rejection message mentions “abbreviations” while the secondary message more strongly hints things that have been “admitted,” which typically describes US states.
9Following the cardinal direction letters (NSEW) in the string would end directly east of the starting point.There are 13 cardinal directions.“Cardinal” hints directions, and the secondary rejection message is clear that we need to count the number of them.
10It contains, as a substring, a Super Smash Bros. Ultimate character with an extra letter.That character is NESS.“Ultimately” and “bros” clue the franchise, and the rejection message suggests looking at characters in a layout, which clues us towards the character select screen.
11It contains, as a substring, the name of a Finding Nemo character with one letter changes.That character is SQUIRT.The “animated reef movie” is Finding Nemo, and can be confirmed by trying “NIMO.” The secondary rejection message describes a “canonical ordering,” which refers to the character list in the credits.
12The first two letters are ROT13 apart.The word starts with AN.This intentionally vague clue only states that the first two letters have a certain relation. With enough queries, one can find that some words will occasionally satisfy the initial constraint. The secondary constraint suggests that the first letter is flexible, which suggests we care about relative distance.
13It contains, as a substring, a spelled out number (ONE...TEN).It contains ONE.An “index” refers to needing a number up to length 10 (since “EXTRACTION” has length 10), but we can only submit strings. Searching all 10 numbers gets us ONE.
14When typed, top-row keys (of a qwerty keyboard) are the plurality.It contains exactly 12 top-row keys.“Top-row” hints to look at a keyboard.
15It contains as a substring, an anagram of a Greek letter.The Greek letter is MU.The rejection messages of using a different language, “mixed up”, and “alphabet,” suggest looking at other alphabets, e.g. Greek letters. The exact letter can be found by binary search.
16It contains all the vowels (AEIOU) except one.The missing vowel is E.The first message hints that there are five things, which is referring to vowels.

After finding even some of these, we notice that it is impossible to satisfy them all. teammate 16 wants to exclude E while teammate 13 expects the number ONE.

In Pin the Tail, we killed people. Specifically, we killed teammates in this puzzle. By killing teammates, the requirement to hit a majority drops, which relaxes the constraints and helps us discover everyone’s constraints. We can ignore the dead teammates for extraction (in fact, they are negative constraints although observing that is not necessary for solving this puzzle). After killing everyone, the remaining (alive) teammates are the following:

teammateFinal constraint
3The longest word formable has length 8.
4Its length is 17.
5It contains “ORD”.
7It contains the letters REARWINDOW.
8It contains “OR” and no other US state abbreviations.
11That character is SQUIRT.
12The word starts with AN.
14It contains exactly 12 top-row keys.

We know that the answer must have 17 characters. See the Appendix for an example of reaching a solution. Note that if we satisfy all the constraints and don’t get the answer phrase, we get told that the phrase starts with ANSWER, applying yet another constraint. With this constraint, we can find that the phrase we are searching for is ANSWERWORDISQUIET, and entering this confirms that this is indeed the correct answer. Reading this again, we find that the ANSWER WORD IS QUIET.

Author's Notes

Sora isn't in the game yet.

Appendix - All Text Strings and Conditions

Here, we list all the text in the puzzle and how they get triggered. If a strict majority is satisfied, we are told that: “That's a good start! The satisfied teammates leap back to their rooms to type up some prototypes... Here's their report:”. Otherwise, we are told: “Your teammates mill around impatiently, waiting for a better phrase”.

teammate 1
  • Unsatisfied (): That's way too many points -- we won't be able to get them to spell the right word.
  • OK (🆗): If the Scrabble score is...
    • ... under 18 (): Try aiming a bit higher.
    • ... over 18 (): Can you make a less point-heavy phrase?
teammate 2
  • Unsatisfied (): We need to be at least 50% more dashing about this.
  • OK (🆗): If there are...
    • ...under 15 dashes (): You need more.
    • ...more than 15 dashes (): Whoa there, you must have a lot of Ms and Os in your phrase.
teammate 3
  • Unsatisfied (): Mine needs the last letters to form a word.
  • OK (🆗): If the length of the longest formable word is...
    • ...less than 8 (): Sorry, it needs to be longer.
    • ...greater han 8 (): The length of your word is too long (solvers will take the longest possible word), try again.
teammate 4
  • Unsatisfied (): I want to make a square and use the leftover letter for extraction.
  • OK (🆗): If the length is...
    • ... 5 or 10 (): Your square is too small.
    • ... 26 (): Your square is too big.

Note that length 1 would form a length 0 square (not a square), and length 2 would form 2 squares and the hypothetical meta would be ambiguous.

teammate 5
  • Unsatisfied (): Remember that each of the 8 phrases needs to contain a unique code for their "United" metapuzzle.
  • OK (🆗): If the United hub is not...
    • ... ORD (): This one didn't work.
teammate 6
  • Unsatisfied (): I like to start with a splash of color.
  • OK (🆗): If word does not...
    • ...start with "O" (for Orange) (): The color you picked doesn't fit my palette.
teammate 7
  • Unsatisfied (): I couldn't find all the letters I need to identify exactly one entry for my masterful "Meta of Suspense", so you'll have to direct me to a better phrase.
  • OK (🆗): If the release date of the Hitchcock film is...
    • ... is earlier than Rear Window (Sep 1, 1954) (): I need one that comes later.
    • ... later than Rear Window (Sep 1, 1954) (): Can you pick one released earlier?
teammate 8
  • Unsatisfied (): The constraint for this metapuzzle is tricky -- your phrase needs exactly one such abbreviation.
  • OK (🆗): If the US state was admitted...
    • ... 32nd or earlier (): Can you pick something admitted a bit more recently?
    • ... 34th or later (): Can you pick something admitted a bit earlier?
teammate 9
  • Unsatisfied (): We want to end directly due east.
  • OK (🆗): If the number of steps taken (number of NSWE letters)...
    • ... more than 13 (): Your phrase takes too many steps.
    • ... fewer than 13 (): Your phrase doesn't walk far enough.
teammate 10
  • Unsatisfied (): Ultimately, the extra letter has to be inside the name of one of those 'bro's for extraction to work
  • OK (🆗): If the location of the character on the Super Smash Bros. Ultimate character select screen is...
    • ... not in the top row (): It needed to be in the top row.
    • ... in the top row but to the left of Ness (): It needed to be to the right a bit.
    • ... in the top row but to the right of Ness (): It needed to be to the left a bit.
teammate 11
  • Unsatisfied (): It needs a single character from that animated reef movie -- don't forget to change a letter for extraction.
  • OK (🆗): If the location of the Finding Nemo character in the movie end credits appears...
    • ... earlier than Squirt (): Yours is too early. We're relying on the canonical ordering you get at the end.
    • ... later than Squirt (): That character is too far down the list to be usable.
teammate 12
  • Unsatisfied (): I'm not approving because I don't like the relation between the first two characters.
  • OK (🆗): If the first letter...
    • ... is not A (): Can you make the first one start earlier?
teammate 13
  • Unsatisfied (): We need an index for EXTRACTION!
  • OK (🆗): If the number (spelled out)...
    • ... is not ONE (): I don't think that would give us the right extraction.
teammate 14
  • Unsatisfied (): I don't think you prioritized the top row enough.
  • OK (🆗): If the number of letters from the top row of the keyboard is...
    • ... fewer than 12 (): You actually have too many from the top.
    • ... greater than 12 (): Right idea, but you need to add a couple more.
teammate 15
  • Unsatisfied (): Arghh! You're not speaking my language - remember you can mix the letter up a little!
  • OK (🆗): If the letter (in the Greek alphabet) comes...
    • ... in the first half of the alphabet and isn't MU (i.e. before MU) (): It needs to be later in the alphabet
    • ... in the second half of the alphabet (i.e. after MU) (): Unfortunately, we can't use anything from this half of the alphabet!
teammate 16
  • Unsatisfied (): Your clue phrase should have all but one of those five.
  • OK (🆗): If the phrase contains all vowels (AEIOU) except...
    • ... A (): You have to pick a different one to exclude.
    • ... I (): You have to pick a different one to exclude.
    • ... O (): You have to pick a different one to exclude.
    • ... U (): You have to pick a different one to exclude.

Appendix - Solving the Search

Here, we follow one path that gets close to a valid solution. Once we get a valid solution (and if it isn't the intended one), we get told it starts with ANSWER, which heavily constrains the search space. In this solve path, we do not make the assumption of parseable English words. In some cases, we link to Nutrimatic, although there are other websites that should eliminate cases in a similar way. The parentheses means that at most one of those letters can change (for SQUIRT's constraint), [#] marks a number of letters, * marks any number of letters, and < > mark anagramming.

Current phrase options

Explanation

AN*ORD*

Starts with AN, contains ORD

AN*(QUIR)*ORD*

AN*ORD*(QUIRT)*

SQUIRT needs to go somewhere either before or after ORD, although one of the letters could overlap with AN or ORD

AN*(QUIR)*ORD*

AN*ORD*(QUIRT)*


4-5 top-row keys [QWERTYUIOP]

AN, D, and S are not top-row keys (ORQUIRT or). Assuming we change the S from SQUIRT to a top-row key, we still need 4 more. From the REARWINDOW constraint, 3 of those 4-5 need to be EWW. From here, we need to do casework.

Case 1: ORD comes after SQUIRT.

Case 1a: ORD is not fully in the 8 letter word, so we get ANQUIRTORD[7] or ANSQUIRORD[7] and the 8-letter word still needs 5 top-row keys. We can try to find 8-letter words starting with D, RD (none)

We don't find words for this query.

Case 1b: The 8 letter word contains ORD, ANQUIRT[2]<”ORD”[5]> containing 3,4, or 5 top-row keys (and at least 1 W or E)

Querying again, this also does not yield results. A couple possible words end up containing DE or CO (both states).

Case 2a: ORD comes before SQUIRT. Then:


AN*ORD*SQUIRT*, with one letter changed and it would be missing. Possible options are 

i) ANORDQUIR T<ewwTTVV>

ii) ANORD(SQUI RT)<ewwTTV>

iii) <ANORD?>(SQU IRT)<[ew]wTTV>

iv) <ANORD??>(SQ UIRT)[4]

v) <ANORD???>(S QUIRT)[3]

i) Nothing here


ii) Can’t change T, can’t change R


iii) Can’t change I. N can get INTERWAR which has WA as a state, T has no solution; e.g. see this query


iv) Must change a letter (U), and if we do, we need to either stay top-row (no solution) or remove the V wildcard into T again (no solution).


v) Can’t change U, but we can change I, R, or T, or Q. These are all top-row characters and so even if ??? are free, we still need 2-3 top-row characters at the end. Can’t change I to A because of AR. Can’t change R (no solution; IN, IL), can change T to get ANORDWWESQUIRKIER as one solution. 

More cases...

<ANORD????>(SQUIRT)[2]

<ANORD?????>(SQUIRT)[1]



At this point, we can continue trying to changing letters and possibly end in SQUIRREL, which might get a solution. But we are already told it begins with ANSWER. Now (or if we guessed this earlier), we can skip any further casework.

ANSWER*ORD*(SQUIRT)[0,1,2]

The only 8-letter word that could use SQUIRT is DISQUIET. 

ANSWER?ORDISQUIET

ANSWERORDDISQUIET

It must be the first choice, and with REARWINDOW, we know the answer must be ANSWERWORDISQUIET.