Welcome to Paul's Riddle Page

WORDLE is a game in which you have 6 attempts to guess the 5-letter mystery word.
After each guess, you will be told, for each letter of your guess, whether or not letter appears in the mystery word (and if so, if it is in the correct spot).
Here are a few challenges I came up with that were inspired by the WORLDE game (though are unrelated to the actual gameplay of that game).
There are two Rules concerning valid guesses in WORDLE:

I. Every guess must be a valid word in the English language (according to some pre-defined dictionary);
II. (Optional) Every guess must be logically possible based on previous guesses.

For example, Rule II means that if in one guess you learn a letter does not appear in the answer, then that letter must not appear in future guesses; and similarly, if you learn a letter does appear in the answer, then you must guess that letter (and also put it in a location that is consistent with what you know about it) in future guesses.
Meanwhile, Rule I will of course depend on which version of English dictionary you use.

The spirit of the riddle below is as follows (see also the bonus challenge below):

Can you come up with a sequence of guesses that uses all 26 letters in the alphabet?

Motivation:  After your first five guesses in Wordle, you're left with just one more guess, and you haven't gotten a single letter correct (and you've guessed 21 incorrect letters).
Thus, there are 5 remaining unguessed letters, and the mystery word uses all 5 of them.


More precisely, consider the following properties that a sequence of guesses could satisfy:

A. Uses all 26 letters
B. Only common* English words
     * = This property is akin to Rule I above, but here "common" is stricter than just appearing in some version of an English dictionary; namely, that it is a word recognizable/used by the majority of English speakers.
C. Consistent with previous guesses (this is Rule II above)
D. No letters from the first five guesses appear in the mystery word
E. The mystery word contains only "unguessed" letters; i.e. it does not use any letters that appear in the first five guesses
F. They mystery word uses five distinct unguessed letters

While satisfying all six properties A-F above simultaneously may be possible, I do not have a solution -- and I am highly skeptical that such a solution exists.
For example, Properties (C + E) alone imply that no letters are ever repeated between any two words (or, in mathematical terms, the guesses must be pairwise disjoint).
Also, Properties (B + C) alone mean that all six words must each contain a distinct vowel: {A, E, I, O, U, Y}.
[According to some dictionaries, there do exist valid 5-letter words with no vowels; but none of these would satisfy "common" as per Property B: {CRWTH, CWTCH, GRRRL, GRRLS, PHPHT}.]
Meanwhile, Property A -- together with the fact that there are six total guesses, of five letters each -- means (by a simple Counting argument) that there will be exactly four duplicate letters (across all six guesses).

Thus, putting together Properties B, C, and E:
A solution that satisfies all six properties means that there would be a sequence of 6 5-letter words, with two of those words containing 5 distinct letters, and the other 4 words containing exactly one self-duplicated letter (here, "self-duplicated" means that the duplication appears in the word itself, as opposed to being duplicated with another word on the list). While this is technically possible (see e.g. the answer to Variant 4 below), it is certainly very restrictive, and I would be surprised if such a solution exists.

However, solutions to Variants 3 and 4 below come close (and arguably, the solution to Variant 4 does satisfy all 6, although my opinion is that it fails to satisfy Property (B), despite being an accepted sequence of guesses per NYT's WORDLE as of 2025).

Here are some challenges that satsify some (but not all) of the above six properties:

BONUS CHALLENGE: Can you come up with a strategy that is guaranteed to find the mystery word by the sixth guess?

 Discussion (WARNING: Contains spoilers/answers to the Challenge Variant(s) above)

Notice that while the above answers all use all 26 letters (out of the 30 total letters used), they don't necessarily imply anything about exhaustively identifying all possible words.

For example, suppose instead of being limited to just 6 total guesses, suppose WORDLE allowed 7 guesses. Then consider a strategy of guessing as per any of the above answers, e.g.:

VEXED, JAZZY, BROWN, QUICK, FIGHT, LIMPS

Thus, after these six guesses, we would know exactly which letters were (and were NOT) in the answer, but we wouldn't necessarilly know their position, and we also might not know how many times duplicate letters appear (and which letters are duplicated).

In addition to those limitiations, there's also the bigger issue that WORDLE only allows six total guesses, so we couldn't use the above sequence of six guesses to narrow things down and still have one guess remaining.

Now, consider any potential strategy that solves the Bonus Challenge. Then based on the respone(s) given to the guess(es) so far, this strategy must specify what to do next. In particular, consider what happens if a given strategy has the first five guesses all not contain a single match.
To simplify the argument, let's ignore for the moment that a valid guess must be an English word, and just consider all possible permutations of 26 symbols (there are 26^5 such possibilities).
[Aside: without the requirement that guesses must be an English word, WORDLE reduces to the game of Mastermind.]

In this case, consider a strategy in which the first five guesses are disjoint sequences of five distinct letters each, e.g.:

ABCDE, FGHIJ, KLMNO, PQRST, UVWXY

Note that this strategy must represent an example of an optimal strategy/solution, since any solution must specify what happens if the first four guesses have no matches, and one can't do better than having guessed 20 distinct letters up to that point. So we might as well consider what happens in this scenario. But now there's not nearly enough information to guess the word with the final guess; namely, there are three places where we don't have enough information:

i) We never guessed "Z"
ii) While we may know exactly which letters appear, we don't know how many times those letters appear;
iii) We don't know the position those letters appear in.

For example, with the above example strategy in mind, suppose that the first four guesses produced 0 matches. And for the sake of example, suppose that the fifth guess of "UVWXY" indicated that the answer contained only Y (and supposed it is in the incorrect position). Then there would still be 16 possibilities for the mystery word:

0 Z's: YYYYY,
1 Z: YYYZY, YYZYY, YZYYY, ZYYYY,
2 Z's: YYZZY, YZYZY, YZZYY, ZYYZY, ZYZYY, ZZYYY,
3 Z's: YZZZY, ZYZZY, ZZYZY, ZZZYY,
4 Z's: ZZZZY

As another example, suppose that after the same sequence of 5 guesses, and in particular based on the response of the 5th guess, we know that "Z" doesn't appear, and we also know that no letter appears more than once; i.e. we know the 5 distinct letters that appear. Then even in this case, there are 5! = 120 ways to arrange those letters. (We will be able to reduce this space somewhat, based on knowing one position that each letter does NOT go, but this makes the number of possibilities ~ 4!= 24).

Thus, (information theoretically), there is no way to know which of those 24 possibilities is the correct answer. Thus, there does not (cannot) exist a strategy if the dictionary contains all possible arrangements of the 26 letters. So if there *is* a working strategy, it must take into account the reduced size of the dictionary (~20k words in the English language, only a fraction of which have 5 letters; vs. 26^5 possible arrangements of letters). Therefore, coming up with the strategy is going to require knowledge/facts about the English dictionary, e.g. "(almost) all words have at least one vowel", and the fact that some letters are rare, and even rarer in combination with each other.

For example, if we ignore Rule I from above (that all guesses must be English words), then maybe we could do something like a strategy of first guessing "AEIOU", and then, depending on how many hits we get, slowly guessing that same vowel in different places with new letters. For example, if just "A" hits, then we start guessing: "BACDF", "GHAJK", "LMNAP", "QRSTA". (Possibly guessing a second 'A' in the first guess, e.g. "BAACD" instead, just to make sure there aren't two (or more) A's.) Or if both "A" and "E" hit in the first guess, then do the same strategy but this time guessing A and E. Or maybe, if "A" is the only hit, consider guessing next: "BAAAA" so that we know exactly where (and how many) A's there are. Similarly, if "A" and "E" both hit, try doing next: "BAAAA" to figure out where and how many A's, and then use the next guess for E, e.g.: "ECEEE" (assuming 'A' was in the 2nd spot only, so we put 'C' there to get extra info).