Letter and String Extraction

Letter and string extractions are types of puzzle extraction that involve taking portions of strings (substrings or individual letters) for use in constructing a new string, whether it's a final answer or just another step in the puzzle.

The portions that are chosen are based on various criteria that changes depending on the exact extraction method, but can include relationships to other strings, positions of characters within the string, or outside markings and values that indicate specific pieces to use.

Elements

 * Indexing - Extracting particular letters from strings based on a series of provided numbers. Given the number N next to string X, take the Nth letter from string X. For example, an index of 4 into the string THEANSWER would result in the letter A.
 * Index Adjustment - After indexing, the process needs to be repeated on the same set of strings but with new indexes. This can be done by providing new numbers, or by adjusting the original numbers somehow.
 * Marked Elements - When a string is placed in a particular space, some sections or elements are marked, allowing for the extraction of particular characters. These markings may also provide a way to reorder the extracted characters.
 * Positional Extraction - Any kind of consistent way to extract characters based on their position within their strings. These are often reused indexes (such as 'always take the second letters'), but can also be dependent on the lengths of the strings.
 * Centralization - Taking the middle letter or letters from a series of strings. For example, THEANSWER would extract an N.
 * Diagonalization - Assuming one has an ordered set of strings, taking the first letter of the first, the second letter of the second, and so on. For example, the set of AT, ON, HAS, KNOWS, HORSE, and LOITER would extract to ANSWER.
 * Initialization - Taking the first letters from a series of strings. For example, THEANSWER would extract a T.
 * Terminalization - Taking the last letters from a series of strings. For example, THEANSWER would extract an R.
 * Special Letters - Any kind of extraction based on the qualities of particular letters within strings.
 * Eigenletters - When two strings (usually of the same length) share a particular letter in the same position. For example, THEANSWER and OUTGROWTH share a W in the 7th position, which would be extracted.
 * Extraneous Letters - When a string would result in a valid word or phrase if not for an extra letter placed within. For example, THEAZNSWER is almost the phrase 'THE ANSWER', with an extra Z, which would be extracted.
 * Missing Letters - When a string would result in a valid word or phrase if not for a letter conspicuously absent. For example, THEANWER is almost the phrase 'THE ANSWER' but missing the S, which would be extracted.