Unexpectedly Intriguing!
30 September 2022

The solution to the New York Times Wordle puzzle on 16 September 2022 left a bad taste in the mouths of the online word game's enthusiasts. Many of these players lost their streaks because the solution, PARER, proved to be the hardest puzzle the game has yet presented.

We'll let Cracking the Cryptic's Mark Goodliffe demonstrate how hard it was by going through his thought process in tackling it:

Goodliffe's method is similar to that of many players. He starts with a test word, one that includes some of the more frequently occurring letters in the English language. He then takes the clues he gets from the game to choose the word he uses on the next line, and the process repeats until the sixth and final line is completed, if needed. Most players can solve the daily puzzle within four lines/guesses.

But a word like parer doesn't make it easy to use that process. There were too many viable options that could legitimately work, without even getting to the duplicate letter option.

So what would be a better approach?

If you recognize that the right way to measure your success at Wordle is not how many lines or guesses it takes you to reach the solution, but rather the amount of time you take to reach it, you can take advantage of a process of elimination. By using a series of test words that include the most frequently used letters in English words that are five letters long, you can extract a lot of information about the correct solution.

Recovering Physicist tapped a Scrabble-legal database of five-letter words to identify the letters most frequently used in them. Here's the list, from most common to least:

SEAOR ILTNU DCPYM HGBKF WVZXJ Q

Using this information, we identified some 277 sets of three five-letter words using the first 15 characters without repeating any characters. We then scored the words in each group according to the rank of their letters, where words using the most frequently used letters would get the lowest scores. For example, the score for a word like Goodliffe's test word of GRIME would be found by adding the ranks of its letters: G(17) + R(5) + I(6) + M(15) + E(2) = 45. Surely there must be a better first choice!

If you just went by the first five most frequently used letters, that word will be AROSE (15), but you won't have any test words to follow it if that guess doesn't provide you with enough clues. To have that option, from our 277 sets of words, the set with the lowest first word score is AISLE (19), MOUND (49), and CRYPT (52).

At that point, it occurred to us that it might be better to stack as many frequently used letters as possible into the first two words, ranking them by their combined score. For AISLE and MOUND for example, the combined score is 67.

Going through our list, we found the lowest combined scores, then filtered for the lowest first word score. Following that process, we think the optimal test words for Wordle are....

ARSON, CITED, and LUMPY

ARSON (or SONAR if you prefer) has a score of 22. CITED (or EDICT) would score 39, with a combined score of 61.

Between ARSON and CITED, you should be able to identify enough clues to solve most easier puzzles. If you need to use all three of these test words to get traction for your solution, you will at least be able to confirm what vowels are being used.

In the case of PARER, you could have used all three of these test words and with a bit of luck, have solved the puzzle in the fourth line. You would have identified A, R, E, and P as used letters, and knowing the location of E, you could set up PARE_ as the solution. You could reasonably identify D, R, or S as the last letter, but because the three test words eliminated D and S, you would select R and be rewarded.

But if you set up PA_ER, which would also be reasonable, you would have to consider the letters C, G, L, P, R, V, and Y as creating valid words, before eliminating C, L, and Y because you've already found they're not used. From here, your optimal choice would be to enter a new test word using letters you haven't previously used (G and V). If you used the word GLOVE, you would be down to just two possible options, P and R, with one line to go.

Your odds of winning at that final line then would have been 1 in 2, coming down to your selection of which letter between P and R to drop into that third space. If a 50% chance of winning seems too low, remember that if you're one of the majority of people who lost their Wordle streak on 16 September 2022, your chance of winning that day's game were never that high. The method we've described would have given you a fighting chance, while also helping you work out the solution faster.

P.S.: According to Recovering Physicist, the most frequently used letters found by those who extracted all the words from Wordle's database are:

EAROL TSINU CYDHP GMBFK WVXZQ J

We'll leave it as an exerise to you to identify your optimal test words based on this information!

Update 9 October 2022 P.P.S.: Matt Parker has identified the five Wordle-legal words you need to know if you're willing to burn five guesses just to identify which letters are used in the solution:

FJORD GUCKS NYMPH VIBEX WALTZ

If you use these words, you're really betting on being able to find the answer in one guess. Considering how many anagrams or words with duplicate letters there are, you'll probably find it's not an optimal way to successfully solve a Wordle game.

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