how many guesses should you expect to make to guess the secret word?

Question

In Guess My Word each day, there is a secret word, and you try to guess it as efficiently as possible by typing in other words. After each guess, you are told whether the secret word is alphabetically before or after your guess. The game stops and congratulates you when you have guessed the secret word.

Each secret word is randomly chosen from a dictionary with exactly 267,751 entries. If you have this dictionary memorized, and play the game as efficiently as possible, how many guesses should you expect to make to guess the secret word?

Answer 1

think powers of 2. you continually divide the alphabet in half being told if you're high or low.

it will depend on the word length as well, because you repeat the process for each letter.

the problem is simplified a little if you limit your available options to actual words.