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This question assumes a knowledge of Wordle's innards including a review of its source code. This blog is useful background reading.

Is it possible to fail (six unsuccessful guesses) at original Wordle without making mistakes? In other words, is there a Wordle word (from the solutions list) for which there is a valid (from the guesses list) and efficient (always using every clue perfectly) sequence of six guesses that fail? Consider easy and hard mode to be two versions of the challenge.

jay613
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    Looks like a valid question to me. Basically asking "in the solution tree for Wordle using optimal strategy, is there a word located at distance more than 6 from the root?" – justhalf Jan 16 '22 at 18:46
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    @justhalf exactly. Thank you for transporting me back 35 years to 3rd year information theory class. – jay613 Jan 16 '22 at 19:53
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    Btw for completeness, can you put in the question as well what is the difference between easy and hard mode? I don't play Wordle, so not familiar with those. – justhalf Jan 17 '22 at 08:26
  • @justhalf This question assumes an exhaustive understanding of the game and its implementation, so I don't think adding basic descriptions of how to play it would enhance the question. Easy mode allows you to ignore prior clues to some extent. This allows certain strategies including guessing (which I think is why it's called easy) and strategies that sacrifice occasional very high scores in favor of a better average score. Hard mode requires each guess to be consistent with prior clues. – jay613 Jan 17 '22 at 12:20
  • To the person who suggested I add a link to the Wordle Wikipedia article .... I included a link to the actual original game, which includes instructions and complete source code (it's 100% browser) and I also included a link to a thorough analysis of the game. I do not think a link to Wikipedia would enhance the question, partly because every question in every Stack could include links to Wikipedia articles about everything but readers know how to find those, partly because most of the info on Wikipedia is irrelevant to my question. I'm commenting here in case moderators disagree with me. – jay613 Jan 17 '22 at 12:26
  • (for the record I didn't suggest adding Wikipedia article) Thanks for your response! I would usually try to add all the relevant information in the question itself, for example in this case I think the only relevant data is the 2000 word list (+10k words accepted as guess), right? Just with that we can make the search tree and hence answer the question. But seeing Wordle as a unique recent trend that is being talked about everywhere (multiple times in this site as well), I think it's fine. – justhalf Jan 17 '22 at 13:33
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    What is the play optimizing for? Lowest score, or just getting the word? They may have different strategies, leading to different results (and hence, different answers to your question). – Abigail Jan 17 '22 at 16:54
  • @Abigail optimizing here for minimizing "losses", ie failure to guess within 6 guesses. Good point that there would be other approaches for other goals such as best average score. Although, there is no defined score for a loss so most other optimizations would require whimsical new rules. – jay613 Apr 08 '22 at 14:58

2 Answers2

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For 'easy' mode:

No, it is not possible to fail with optimal play. Using some of the strategies outlined in answers to What's the optimal strategy for Wordle?, I found several decision trees that will successfully identify any given solution word in five or fewer guesses.

For 'hard' mode:

There might be a few. For example, if the solution word is one of {bound, found, hound, mound, pound, round, sound, wound}, you might run out of luck. You would need to guess something like PRISM or SHARP early in order narrow down that list.

After modifying my code, I have found a few decision trees that miss only two words. The search was nowhere near exhaustive, so these are not necessarily optimal. I have not ruled out the possibility of a 100% successful decision tree.

Daniel Mathias
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  • I feel like the hard decision tree would have to look at the cases where you have a lot of words off by 1 letter and try to take as many out as possible right away, then hope to keep everything to 6 guesses – Joel Rondeau Jan 16 '22 at 21:42
  • I don't understand "trees that miss only two words" when your example provides a list of 8 words that might be ambiguous at step 5. – jay613 Jan 17 '22 at 12:37
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    @jay613 then in his decision tree it must be the case that the earlier guesses can split them apart on different branches, except for two. – justhalf Jan 17 '22 at 13:43
  • @Daniel, do you have the decision tree that you mentioned for easy mode somewhere? I would like to see it. – justhalf Jan 18 '22 at 09:35
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    My code has only shown that such trees exist. I have again modified my code to search multiple branches at each guess in order to find more optimal trees. An overnight run, checking each possible solution word as first guess, has identified over 900 that have 100% successful trees in hard mode. Next, I'll work on saving some of those trees so that I can share. – Daniel Mathias Jan 18 '22 at 10:17
  • @DanielMathias any update on the optimal tree(s)? =D – justhalf Feb 02 '22 at 18:17
  • Have a look at the answers to the linked question on optimal strategy. Tom Sirgedas's answer include a link to a complete tree for PLATE using only words from the solutions list. – Daniel Mathias Feb 02 '22 at 20:47
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If the requirement is merely that the guesses be valid, and that they be consistent with all clues given thus far, it's possible to not only fail, but get 30 gray squares and still have multiple possible words remaining. If one guesses the words shown below, but the word was (among other possibilities) "newer"/"renew", "green", or "creek", one would get 30 gray squares and still not be able to distinguish among multiple words containing the vowel "e".

"phpht", "xylyl", "mamma", "vivid", "boffo", and "jujus"

supercat
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    A bit of a subversive answer but a good one I think. If you go only by my question and ignore @justhalf's clarification ("optimal strategy"), it is true that you can contrive to lose by making low-value guesses while still remaining faithful to the clues. But any mortal who has lost a game probably knows that instinctively. – jay613 Jul 12 '23 at 20:38
  • Also xyxyl is not (?any longer?) a valid word but your point remains valid. – jay613 Jul 12 '23 at 20:39
  • @jay613: Thanks for the heads-up that I'd misspelled xylyl (which I just confirmed is a valid word when correctly spelled) – supercat Jul 12 '23 at 21:13
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    @jay613: I think finding a six-dud sequence is probably a good puzzle; I did it without using a computer search except for finding a list of the 37 five-letter words without a, e, i, o, or u that are valid in the Scrabble(R) brand crossword game. – supercat Jul 12 '23 at 21:21