# Establishing the minimum number of guesses needed to (always) win Wordle

A few weeks ago, I became interested in whether there was a strategy to always “win” Wordle (i.e. to find the secret word in 6 guesses or fewer). This is exactly the problem that Laurent Poirrier examines in his excellent writeup on applying mathematical optimization techniques to Wordle:

Is there a strategy that guarantees to find any one of the 12972 possible words1 within the 6 allowed guesses? Without resorting to luck, that is.

Laurent proved the answer is yes! With careful thought, some clever optimization techniques and over a thousand hours of CPU time, he found a decision tree of depth 5 — yielding a strategy to solve Wordle puzzles in $\leq$ 6 guesses. (Before reading the rest of this article, I’d recommend going through Laurent’s post — it’s quite accessible even if you don’t have a background in optimization).

He observes at the end of his article that an open question remains:

Unfortunately, depth 4 seems to be beyond the reach of my computational resources. It is thus still unknown whether all Wordle puzzles can be solved in 5 guesses.2