MATE's META

by Brian Shimanuki and Herman Chau

Answer:
CRASHING AND BURNING OUT

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This is a metameta puzzle that uses all the metapuzzle and regular puzzle answers from the Museum of Interesting Things. Regular puzzle answers that have been solved appear on the puzzle page, possibly with some glitches that erase part of the answer. In addition, each puzzle answer has an icon next to it that is associated with a round in the museum. The icons and their corresponding rounds are as follows:

  • πŸ–ΌοΈ
    is the Art round with meta answer SEEING DOUBLE RAINBOW.
  • 🎟️
    is the Atrium round with meta answer COUNTRY FRIED MISTAKE.
  • πŸ¦–
    is the Natural History round with meta answer WINGED IT.
  • βš›οΈ
    is the Science round with meta answer PUN NOT ELEMENTENDED.
  • 🌏
    is the World History round with meta answer THEY LEFT BIG INNER CIRCLES.

The first step of this puzzle is to extract a bigram from each regular puzzle answer, after erasing the glitched letters. There are 5 methods of extracting bigrams, corresponding to the 5 meta answers. They are as follows:

  • Take the unique repeated bigram, as clued by SEEING DOUBLE RAINBOW. For example, VOLUNTEER FIRE DEPARTMENT extracts to NT.
  • Find the associated country and take its 2-letter country code, as clued by COUNTRY FRIED MISTAKE. For example, SHAMROCK is associated with IRELAND and extracts to IE.
  • Take the first and last letters of the answer, as clued by WINGED IT. For example, N SINK extracts to NK.
  • Find the chemical element that starts with the last 3 letters of the answer, as clued by PUN NOT ELEMENTENDED. For example, OFFICE OF NAVAL INTEL yields TELLURIUM, which extracts to TE.
  • Take the 2 letters immediately left of the 2 O's in the answer, as clued by THEY LEFT BIG INNER CIRCLES. For example, RANDOM DECISION extracts to DI.

Upon extracting the bigrams, we can read across each row in the puzzle to get 8 letter words. Each word can be split into two 4 letter words that appear as subsequences with all their letters occurring in order. Below are the 8 letter words and their splits. Note that while these are not the only valid splits into two 4 letter words, they are the only words that also fit the constraint in the next step.

  • NAMETAGS: NAGS + META
  • MEDITATE: MATE + EDIT
  • GRADIENT: DIET + GRAN
  • RANKINGS: RANG + KINS
  • STINKIER: SINK + TIER
  • PEARLITE: RITE + PEAL
  • PLEIADES: PLEA + IDES
  • DIABETES: DIES + ABET
  • BANTERED: BATE + NERD
  • PORTENDS: REND + POTS

Observe that pairs of consecutive 8 letter words have 4 letter words that are anagrams of each other as clued by the title MATE's META. Each such anagram corresponds to a permutation of the numbers 1234. There are various conventions for permutations and the one used here is one-line notation. The 9 permutations and their inverses are as follows:

  • π₁ = META β†’ MATE = 1432; π₁⁻¹ = MATE β†’ META = 1432
  • Ο€β‚‚ = EDIT β†’ DIET = 2314; π₂⁻¹ = DIET β†’ EDIT = 3124
  • π₃ = GRAN β†’ RANG = 2341; π₃⁻¹ = RANG β†’ GRAN = 4123
  • Ο€β‚„ = KINS β†’ SINK = 4231; π₄⁻¹ = SINK β†’ KINS = 4231
  • Ο€β‚… = TIER β†’ RITE = 4213; π₅⁻¹ = RITE β†’ TIER = 3241
  • π₆ = PEAL β†’ PLEA = 1423; π₆⁻¹ = PLEA β†’ PEAL = 1342
  • π₇ = IDES β†’ DIES = 2134; π₇⁻¹ = DIES β†’ IDES = 2134
  • Ο€β‚ˆ = ABET β†’ BATE = 2143; Ο€β‚ˆβ»ΒΉ = BATE β†’ ABET = 2143
  • π₉ = NERD β†’ REND = 3214; π₉⁻¹ = REND β†’ NERD = 3214

To extract, we use the wheel diagram at the bottom to associate each permutation with a letter from A to X. The wheel diagram tells us that 1234 corresponds to the letter P and we need to fill out the rest of the diagram. The completed diagram is as follows:

Finally, we decode the sequence of permutations at the bottom of the page to obtain the answer CRASHING AND BURNING OUT.