by Dan Katz
Solution: SCIENCE COURT
Each function represented by a Greek letter is an operation on words; to solve the puzzle you need to figure out what each operation does. This can be done by observing the given outputs for each input, and knowing some math helps, since most of the operations are inspired by mathematical operations which use the same letter.
- αi: Shifts the i-th letter of the word forward one position in the alphabet
- χi (character of degree 2): Shifts the i-th letter thirteen positions (rot13)
- τij (transposition): Switches the i-th and j-th letter
- σ (translation): Cycles the entire word, so that the first letter ends up in the second position, the second in the third position, and so on until the last letter, which moves to the first position
- πi (projection): Replaces the word with its i-th letter
- &iotai(j) (inclusion): Creates a new word in which the j-th letter is the input, and all the rest of the letters are A's.
Exponents simply mean to apply the function multiple times; an inverse (-1 exponent) means to "undo" the operation, so α-1 means to Caesar shift backwards, and σ-1 means to cycle backwards.
Finally, a parenthesized superscript j means that rather than viewing letters individually, you should divide the word into j equal-length blocks, and use those blocks as "letters." For instance, τ24 of JUMPSUIT would be JPMUSUIT; &tau24(4) would be JUITSUMP. Note that the superscript works slightly differently on inclusion (the number of blocks refers to the output rather than the input, to match up with projection).
So once you've figured out the syntax, all that remains is to actually carry out the calculation at the end, in which the output is not given. It turns out to be SCIENCE COURT.