Wordler and I Fail on Puzzle 1497 - Cleve Moler on Mathematics and Computing

[poster]

Like millions of other folks, I play Wordle from the New York Times almost every day. The Times reports that Wordle puzzle number 1497 on Friday, July 25, was especially difficult. The average puzzler required 5.7 attempts and many failed to get the answer in the six moves allowed. I have a MATLAB assistant that I call Wordler and, even with her help, I failed on number 1497. Here's why.

(In 2022, Wordle was the most-searched term on Google worldwide. For more interesting facts about Wordle, see the Wikipedia article.)

Contents

• Wordler
• Wordler's Vocabulary
• Word One
• Word Two
• Word Three
• Word Four
• Word Five
• Word Six
• Final Word
• Software

Wordler

Making a move in Wordle involves two tasks. First, thinking of the words that can be played, and second, deciding which of them to play. I like to make all the key decisions myself, so my assistant does not actually play Wordle. When I ask Wordler for help, she just lists all the words that could be played. It is up to me to choose one.

Wordler's Vocabulary

Wordler's vocabulary is a hidden list of 2315 five-letter English words that are the possible solutions. The letter frequencies in this list are not the same as in English itself. For example, English has many five-letter words ending in S, but most of them are plural nouns and third-person singular verbs. The vocabulary does not have any of these. Wordle words end in S less than 2% of the time, compared to 31% of the time with the full set of five-letter words.

Here is a portion of the vocabulary.

dbtypevocabulary1:9dbtypevocabulary291:2951 function vocab = vocabulary(~)2 % vocabulary is 2315 words that are targets.3 4 vocab = [ ... 5 "ABACK" "ABASE" "ABATE" "ABBEY" "ABBOT" "ABHOR" "ABIDE" "ABLED" ...6 "ABODE" "ABORT" "ABOUT" "ABOVE" "ABUSE" "ABYSS" "ACORN" "ACRID" ...7 "ACTOR" "ACUTE" "ADAGE" "ADAPT" "ADEPT" "ADMIN" "ADMIT" "ADOBE" ...8 "ADOPT" "ADORE" "ADORN" "ADULT" "AFFIX" "AFIRE" "AFOOT" "AFOUL" ...9 "AFTER" "AGAIN" "AGAPE" "AGATE" "AGENT" "AGILE" "AGING" "AGLOW" ...291 "WORSE" "WORST" "WORTH" "WOULD" "WOUND" "WOVEN" "WRACK" "WRATH" ...292 "WREAK" "WRECK" "WREST" "WRING" "WRIST" "WRITE" "WRONG" "WROTE" ...293 "WRUNG" "WRYLY" "YACHT" "YEARN" "YEAST" "YIELD" "YOUNG" "YOUTH" ...294 "ZEBRA" "ZESTY" "ZONAL" ];295 endWord One

I always start with the word LEAST. It contains two popular vowels, and I like to use mathematical and other technical words. On July 25, a gold E from the Times tells me that the answer has an E somewhere, but not in slot number 2. The remaining letters are black, so today's answer does not have any L, A, S or T.

(If I were to ask Wordler for assistance with the first word, she would just reply with all 2315 words she knows.)



Word Two

For the second word, I chose PHONE. It has the required E, as well as another popular vowel. It gets a gold O to go with the gold E.

(Wordler's suggestion in this situation would have been the 268 words containing an E in any slot except the second. That's not much help.)



Word Three

I know now that I am seeking a word with an E in any slot except 2 or 5, an O in any slot except 3, and no L, A, S, T, P, H or N. I decided to try COVER and am rewarded with three green letters.

(Wordler knows 23 words meeting the requirements.)



Word Four

Here, for the first time, I decided to ask Wordler. I press the Words button and get some bad news. She tells me she knows seven possible words.

• BOXER
• FOYER
• JOKER
• MOWER
• ROGER
• ROWER
• WOOER

I have only three guesses remaining. My odds of winning are less than 50-50. I chose MOWER because, if it is not correct, the three words containing W would be eliminated.



Word Five

Getting worried, I chose ROGER because it has two Rs. Again, not much luck.



Word Six

This is my last chance and there are still three words remaining.

• BOXER
• FOYER
• JOKER

Which would you choose?

I chose JOKER and strike out.



Final Word

If you happen to have played puzzle number 1497, you realize that Wordler is missing at least one word from her vocabulary. The word that tripped up so many last week is GOFER, which neither I nor my assistant thought of.

(Ever-helpful Google informs us that a GOFER is "a person who runs errands, especially on a movie set or in an office.")

Software

The current version of Wordler isn't ready for public consumption. As we have just seen, her vocabulary is incomplete. I also know of bugs when there are repeated letters. If you would like a copy anyway, send me an email.

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Published with MATLAB® R2024b