Meta: Extraction

This is a metapuzzle, so first we collect answers:

• The Jig is Up: X IS WORD Y IS LETTER
• The Chess Fairy: COMBINE PERMUTATIONS
• The (x, y) Conundrum: FLY A COMPLEX PLANE
• Word Scramble: PERMUTATORIAL EXPLOSION

Then, we notice that the dictionary entry for “extraction” matches the online Merriam-Webster dictionary (as of April 2021, at least). Each of the 14 items says a word or phrase to look up, followed by text about what to do next. How to interpret the text depends on the extraction method of the corresponding puzzle.

• The Jig is Up: Solve cryptic clues to get index.
  • Look up “x”. Cryptic clue answer is four. Extract R.
  • Look up “x”. Cryptic clue answer is ten. Extract E.
  • Look up “letter”. Cryptic clue answer is fourteen. Extract N.
• The Chess Fairy: Extract words that are names of fairy chess pieces, then solve chess puzzles and extract as in “The Chess Fairy”. The letter grid is the same.
  • Look up “combine”. Extract “frog” and solve the appropriate chess puzzle. Extract X.
  • Look up “combine”. Extract “moo” and solve the appropriate chess puzzle. Extract T.
  • Look up “permutation”. Extract “princess” and solve the appropriate chess puzzle. Extract C.
  • Look up “combine”. Extract “gnu” and solve the appropriate chess puzzle. Extract T.
• The (x, y) Conundrum: Index into the definition using the coordinates as in “The (x, y) Conundrum”
  • Look up “complex plane”. 2nd word, 5th letter. Extract E.
  • Look up “complex plane”. 8th word, 1st letter. Extract M.
  • Look up “complex plane”. 4th word, 2nd letter. Extract O.
  • Look up “complex plane”. 6th word, 4th letter. Extract N.
• Word Scramble: Extract 4-letter strings, compute permuation, and extract as in “Word Scramble”
  • Look up “permutator”. From ROTA to ROTA, permutation 1234. Extract A.
  • Look up “explode”. From PRES to SREP, permutation 4231. Extract V.
  • Look up “permutator”. From MAGN to MAGN, permutation 1234. Extract A.

Chess puzzle solutions:

Moo (Knight that can't jump over pieces). Fd6#.

Frog ((1,1)-leaper + (0,3)-leaper). Fe1#.

Gnu ((1,2)-leaper + (1,3)-leaper). Fe2#.

Princess (Bishop + Knight). g6.

We put the letters we extracted in the order specified by the enumeration to get VANEMON EXTRACT.