[svat]

Thanks for sharing your code. I had seen other people also mention that these 5 guesses (AESIR, ARISE, RAISE, REAIS, SERAI) all narrow down the list to 168 (in the worst case), but I was curious why the code I wrote to play with this was giving different answers.

After reading your code, I see an error in it. In fact, only RAISE is optimal; the others are worse, and leave bigger lists (according to my code):

    RAISE: 168
    …
    REAIS: 203
    …
    AESIR: 220
    ARISE: 220
    …
    SERAI: 241

The error in your code is that your "evaluateGuess" function (right at the top, in the first 10 or so lines of https://github.com/christiangenco/wordlesolver/blob/9c3bd94a...):

    function evaluateGuess({ solution, guess }) {
      return [...guess].map((letter, index) => {
        return {
          letter,
          included: solution.includes(letter),
          position: letter === solution[index],
        };
      });
    }

is too simplistic, and not actually what the real game does. In the game, for each letter position, there are three possible responses:

• Correct (Green), what you call "position"

• Present (Yellow), what you call "included"

• Absent (Grey)

Here are three test cases, that you could try out on the real Wordle in recent days:

• When the solution is "FAVOR" and our guess is "ERROR", Wordle's response is [Grey, Grey, Grey, Green, Green] — note that for the first two Rs in "ERROR", the correct response is Grey (Absent), because the last R has already "used up" the "Green" response.

• When the solution is "FAVOR" and our guess is "ROARS", Wordle's response is [Yellow, Yellow, Yellow, Grey, Grey] — note that only the first R in "ROARS" gets a Yellow response and the second one gets Grey, because there's only one R in the solution.

• (As pointed out by @pedrosorio in a sibling comment) When the solution is "ABBEY" and our guess is "APNEA", Wordle's response is [Green, Grey, Grey, Green, Grey], but your solver thinks that the second "A" would get a "Yellow" response too.

You mentioned Donald Knuth's Mastermind paper; in fact in the paper (http://www.cs.uni.edu/~wallingf/teaching/cs3530/resources/kn...) Knuth points this out on the very first page:

> Rule 2 is somewhat difficult to state precisely and unambiguously, and the manufacturers have in fact not succeeded in doing so on the directions they furnish with the game […]

and gives an exact rule that you may want to study carefully.

In my code, the `response` function I use (it's not the most efficient, but we can just memoize it) is:

    def response(h, g):
        '''
        - The hidden word is h.
        - The guess is g.
        For each position in the word g, some color:
        - 'green' if in the same position
        - 'yellow' if present (after subtracting 'green's)
        - 'grey' if absent (after subtracting "green"s and "yellow"s)
        '''
        assert len(h) == len(g)
        L = len(h)
        green = [i for i in range(L) if h[i] == g[i]]
        yellow = []
        for i in range(L):
            # We want to check whether g[i] is "present" in h
            if i in green: continue
            for j in range(L):
                if j in green: continue
                if j in yellow: continue
                if h[j] == g[i]:
                    yellow.append(i)
                    break
        return (green, yellow)

Note the three "continue" statements — they are crucial, to match the behaviour of the real Wordle (or Master Mind) on the three test cases I mentioned above.

[svat]

The testcases notwithstanding, I found a bug in my code as well. Fixed my `response` function to:

    def response(h, g):
        assert len(h) == len(g)
        L = len(h)
        correct = [i for i in range(L) if h[i] == g[i]]
        present_h = []
        present_g = []
        for i in range(L):
            # We want to check whether g[i] is "present" in h
            if i in correct: continue
            for j in range(L):
                if j in correct: continue
                if j in present_h: continue
                if h[j] == g[i]:
                    present_g.append(i)
                    present_h.append(j)
                    break
        return (correct, present_g)

and now I too get (AESIR, ARISE, RAISE, REAIS, SERAI) all leaving 168 words. (But the testcases in the above comment still hold, though, make sure your code works for them.)