The suggested words in this article are based on algorithmic analysis of the original word lists used by WORDLE. This might be regarded as cheating, although similar results could probably be obtained by using an independent selection of five-letter words. The modified word lists, as used by the New York Times version of WORDLE, have not been accessed.

## WORDLE

The popular game WORDLE can be played here in your browser. The explanation of tile colours on the help page needs some clarification about the grey colour.

When a grey tile has the same letter as a green tile, it means that the letter is not in the word in any spot apart from the green tile:-
When a grey tile has the same letter as a yellow tile, it means that the letter is not in the word in this spot:-

The brain work in solving WORDLE consists in evaluating the constraints that the tile colours have placed on the target word. One solving strategy is to enter only words which satisfy the constraints imposed by the colours of previous words. This does not, however, ensure that a solution will be found in six tries. In this counterexample, the target is ABASE:-

Re-entry of green letters in the same spots provides no additional feedback. A better strategy is to enter three words with no letters in common before trying to guess the target. The WORDLE word lists can be obtained from this web page. Bertrand Fan has pointed out that there are two word lists: the first a list of solutions (La), the second a list of additional valid words which won't be used as solutions (Ta).

Coding in Python, it is not too hard to reproduce algorithms which find the colours for a given word and target, and evaluate the constraints imposed by the colours of the entered words. A set of constraints can be applied to the solutions word list to select the remaining possible words.

A candidate for the three words can be rated by counting the remaining words when the candidate is used against each possible target from the solutions word list and summing these counts. The lowest total is best. Candidates are chosen which include 15 different letters but without restriction to the 15 commonest letters. Random combinations of three words from both word lists were rated: the best combination at first was TILED, PORNY, CAMUS, with a score of 3927. Dividing by 2,315, the size of the solutions word list, gives 1.7, the average count of remaining words for this combination.

Here's an example of these three words in use:-

The remaining brain work is to guess the target from the colours of the three words. It's not too hard to see that the target word might be CRIMP. In this case, no other target word satisfies the constraints.

Another example:-

After three words, the target could be NICHE, NIECE, or WINCE. After choosing the wrong one, only WINCE remains.

## Best three words

There are 8,322 words in both word lists which have 5 different letters. Of the 96,023,008,640 combinations of three of these words, 138,953,994 have 15 different letters. In an exhaustive search of these combinations with 15 different letters, scoring each of them, these three words had the best score of 3,281: 1.42 words on average:-

## Best two words

The same approach can be used to find the best two words to start with. Then there is some chance of guessing the third word and, if that is wrong, a better chance of guessing the fourth word.

There are 8,322 words in both word lists which have 5 different letters. Of the 34,623,681 combinations of pairs of these words, 5,020,842 have 10 different letters. After exhaustively scoring all of these combinations, the following two words had the best score of 9,945: 4.3 words on average. In case the best score didn't need 10 different letters, as was plausible but unproven, the exhaustive search was repeated with all 84,129,906 combinations of pairs of words from both word lists: it gave the same result.

If you share your solution, anyone who knows your starting words obtains the same feedback as if they had entered these two words themselves, effectively giving them two free tries.
You can thwart such exploitation by choosing a random pair of words each day from the following table of pairs of words with scores less than 10200. Randomly swap their order, entering DOILT, CARSE instead of CARSE, DOILT, for example.
 9945 CARSE DOILT 9987 RIANT SOCLE 10057 RIANT CLOSE 10101 TRICE SALON 10115 SOARE CLINT 10119 ROAST CLINE 10131 SARIN CLOTE 10149 LOAST CRINE 10149 LANCE ROIST 10155 TRAIN SOCLE 10159 TRAIL SONCE 10171 TOILE CARNS 10181 STOLE CAIRN

## Best single word

The same approach can be used to find the best single words to start with. In this case, however, it is feasible to score every word in both word lists.

After scoring all 12,972 words in both word lists, this word had the best score of 139,883: 60.4 words on average:-

Christopher B. Jones 2022-03-12