Disorder of Operations (solution)

by Kai Huang

This puzzle consists of 11 instructions for either removing or rearranging letters in strings. Each instruction is also used as a target string for processing. Specifically:

  1. Each instruction is written in all caps without spaces
  2. Then the instruction is applied to itself
  3. Then another instruction is applied

The clue strings given in the puzzle are the results of these transformations.

Here are how the 11 clue strings came about, in the order given in the puzzle.

ALPHABETIZE
    ⇒ apply “Alphabetize” ⇒ AABEEHILPTZ
    ⇒ apply “Omit every fourth symbol” ⇒ AABEHIPTZ

REMOVETHEALPHABETSTWENTIETHLETTER
    ⇒ apply “Remove the alphabet’s twentieth letter” ⇒ REMOVEHEALPHABESWENIEHLEER
    ⇒ apply “Swap each pair of letters” ⇒ EROMEVEHLAHPBASEEWINHEELRE

EXPUNGECHARACTERSATPRIMEINDICES
    ⇒ apply “Expunge characters at prime indices” ⇒ EUGCHAATERAPRIEINDIE
    ⇒ apply “Collapse double letters” ⇒ EUGCHATERAPRIEINDIE

REVERSETHESTRING
    ⇒ apply “Reverse the string” ⇒ GNIRTSEHTESREVER
    ⇒ apply “Expunge characters at prime indices” ⇒ GRSHTERVER

DISCARDSYMBOLSWITHCURVEDANDSTRAIGHTSEGMENTS
    ⇒ apply “Discard symbols with curved and straight segments” ⇒ ISCASYMOLSWITHCVEANSTAIHTSEMENTS
    ⇒ apply “Remove the alphabet’s twentieth letter” ⇒ ISCASYMOLSWIHCVEANSAIHSEMENS

REMOVEVOWELS
    ⇒ apply “Remove vowels” ⇒ RMVVWLS
    ⇒ apply “Alphabetize” ⇒ LMRSVVW

KEEPJUSTTHEFIRSTOCCURRENCE
    ⇒ apply “Keep just the first occurrence” ⇒ KEPJUSTHFIROCN
    ⇒ apply “Reverse the string” ⇒ NCORIFHTSUJPEK

COLLAPSEDOUBLELETTERS
    ⇒ apply “Collapse double letters” ⇒ COLAPSEDOUBLELETERS
    ⇒ apply “Remove characters that rhyme with the word key” ⇒ OLASOULLRS

OMITEVERYFOURTHSYMBOL
    ⇒ apply “Omit every fourth symbol” ⇒ OMIEVEYFORTHYMBL
    ⇒ apply “Discard symbols with curved and straight segments” ⇒ OMIEVEYFOTHYML

REMOVECHARACTERSTHATRHYMEWITHTHEWORDKEY
    ⇒ apply “Remove characters that rhyme with the word key” ⇒ RMOHARARSHARHYMWIHHWORKY
    ⇒ apply “Remove vowels” ⇒ RMHRRSHRHYMWHHWRKY

SWAPEACHPAIROFLETTERS
    ⇒ apply “Swap each pair of letters” ⇒ WSPAAEHCAPRIFOELTTRES
    ⇒ apply “Keep just the first occurrence” ⇒ WSPAEHCRIFOLT

Next, notice that since each instruction string is processed by one other instruction, the strings can be put into a ring. The ring is (with arbitrary starting point and direction):

ALPHABETIZE
OMITEVERYFOURTHSYMBOL
DISCARDSYMBOLSWITHCURVEDANDSTRAIGHTSEGMENTS
REMOVETHEALPHABETSTWENTIETHLETTER
SWAPEACHPAIROFLETTERS
KEEPJUSTTHEFIRSTOCCURRENCE
REVERSETHESTRING
EXPUNGECHARACTERSATPRIMEINDICES
COLLAPSEDOUBLELETTERS
REMOVECHARACTERSTHATRHYMEWITHTHEWORDKEY
REMOVEVOWELS
ALPHABETIZE

Finally, the numbers given at the bottom of the puzzle are used to index into these instruction strings.

Observe that there’s only one way to map the indices in the order given onto the ring such that every index number is valid (not out-of-bounds) for the corresponding string. Specifically, notice that adjacent strings ALPHABETIZE and REMOVEVOWELS are length 11 and 12, respectively, and there’s only one adjacent pair of indices that can fit them (7 and 11). Furthermore, the index 34 adjacent to the index 7 must go with one of the other neighbors of ALPHABETIZE and REMOVEVOWELS, and out of those it only fits with REMOVECHARACTERSTHATRHYMEWITHTHEWORDKEY. This locks down the mapping of indices to strings. The extraction is shown in the table below.

Instruction string Index Letter
REMOVECHARACTERSTHATRHYMEWITHTHEWORDKEY 34 O
REMOVEVOWELS 7 V
ALPHABETIZE 11 E
OMITEVERYFOURTHSYMBOL 13 R
DISCARDSYMBOLSWITHCURVEDANDSTRAIGHTSEGMENTS 15 W
REMOVETHEALPHABETSTWENTIETHLETTER 33 R
SWAPEACHPAIROFLETTERS 13 O
KEEPJUSTTHEFIRSTOCCURRENCE 6 U
REVERSETHESTRING 16 G
EXPUNGECHARACTERSATPRIMEINDICES 9 H
COLLAPSEDOUBLELETTERS 18 T

The answer to the puzzle is OVERWROUGHT.

Sheila Sunshine
Sheila Sunshine