2,795-Word Puzzle

Your mission impossible is to find the single word that does not belong in these checklists.One list to be checked off (or not) consists of 1,022 (1,021 plus one) words; another of 2,796 (2,795 plus one) similar entries; and the third of 2,979 (2,978 plus one) like items.Each of the three checklists corresponds to a different puzzle: a 1,021-word puzzle, a 2,795-word puzzle, or a 2,978-word puzzle.Each of the 1,021 words, among those on the 1,022-word checklist, is used once (and only once!) in the solution to the 1,021-word puzzle.The odd word out, the remaining 1,022th word, is the needle (word) for which you are searching.Similarly, each of the 2,795 words, among those on the 2,796-word checklist, is used once in the solution to the 2,795-word puzzle.The remaining 2,796th word is your needle.Again, each of the 2,978 words, among those on the 2,979-word checklist, is used once in the solution to the 2,978-word puzzle.The 2,979th word is your word.The three, primary, multiple-word puzzles are each not only composite but also disjointed: the same word might be on two or even all three checklists.The 1,021-word, primary puzzle is made up of 215 distinct, secondary, word puzzles.Each secondary puzzle is termed an "enigma."Similarly, the 2,795-word, primary puzzle is made up of 596 enigmas.Again, the 2,978-word, primary puzzle is made up of 619 enigmas.The game play is a process of elimination involving pattern-recognition.A word in a checklist is eliminated from further consideration as soon as it is used in one of the secondary puzzles associated with the said checklist.Check off the words one at a time in any order and until you finally see which three words (total) remain unchecked.A pronounced whoosh phenomenon can be discerned as you approach the end of each checklist.Each enigma starts off with an odd lot of twelve different letters.In the case of the constituent enigmas of the 1,021-word primary puzzle, the twelve letters are divvied up into two groups of six letters.Similarly, in the case of the constituent enigmas of the 2,795-word primary puzzle, the twelve letters are divvied up into three groups of four letters.Again, in the case of the constituent enigmas of the 2,978-word primary puzzle, the twelve letters are divvied up into four groups of three letters.Each enigma is a chain (ring) of up to eleven different, heretofore unchecked, words from the associated checklist.Most enigmas are four or five words in lengthThe "head" of a word is its first two letters, while the "tail" of a word is its last two letters.Rule 1: the respective heads of the 2nd, 3rd, 4th, and so on, word must match the respective tails of the 1st, 2nd, 3rd, and so on, word.Rule 2: the tail of the final word must match the head of the first word.Rule 3: while letters can be used again and again within a word and throughout the chain, consecutive letters within each word must be from different groups.Rule 4: each consecutive word must use at least one new letter.Rule 5: the chain is kosher when and only when every letter has been used.The theoretical longest chain has eleven words, not twelve, because the first word uses at least two different letters.Each enigma provides a numeric template for each word on its chain.The sequence of prescriptive digits particularize the respective groups from which are drawn the respective letters spelling out the word intended for the slot on the chain.Besides the templates, which as byproducts obviously also have to reveal the respective lengths of the words on the chains, each enigma also provides twelve hints, one for each letter of the twelve-letter working set.Pursuant to Rule 4, the hints reveal the first usage of each such letter.If the first word on a chain uses each letter in the word only once then the word is spelled out and preemptively checked off for you.