A Random walk down the Wordle hole…
Have you played Wordle yet? It is a popular word guessing game that has been having a bit of a moment. It is like the old MasterMind game, but for words. You try to guess a word in six tries. After each guess, the game will score your guess, letting you know which letters in your guess are not in the word, or are in the word but at the wrong place, or are at the right place.
I have long suspected that if you simply randomly pick any valid word in Wordle on so-called “hard mode” — where you are required to use any clue previously revealed — you will always complete the puzzle successfully. This is based on the fact that there are only around 2300 answer words, and each guess is going to significantly reduce the # of valid words remaining. So my suspicion is that even if you pick a terrible starting word like “WOOZY”, and pick random words after that, you will always succeed.
Revenge of the Nerds
Well, being a huge nerd, I decided to test this by writing a wordle-solving program. For each of the 2300 possible starting words, we can compute all possible paths to each of the 2300 or so possible answers. This is a bit over 5 million combinations, each with millions of possible paths. It takes some time to compute. But if we do , we find that there are very few paths that are over six steps.
