Is Wordle always beatable under optimal play on easy mode (where you can guess any valid word)?
To put the question more formally, does there exist a deterministic computer program that can play Wordle successfully, without cheating, for every target word? Wordle is a deterministic game besides the hidden target word, and there is a known, finite list of target words, so this question should be decidable. An examination of Wordle's source code shows that there are 2,315 possible target words and 10,657 additional allowed guess words (12,972 total allowed guess words).
(These are included in case an answer happens to have them; they are not necessary to answer the question.)
Is the answer different for easy mode (where you can guess any valid word) vs hard mode (where your guess has both be a valid word and match the clues you've been given so far)?
If there is such a program, what is the word it uses for it's first guess? (If the program is deterministic, it should always use the same opener)
What is the worst case performance of an optimal program (ignoring the 6 guess limit if there is no optimal program that always wins)?