How you've just played optimal Mastermind
Mastermind is a game all about information. The Code Master selects one of \( 6^4 = 1\,296 \) secret codes. Each incorrect guess gives us information by eliminating some of these; the more codes that are ruled out, the more information that guess has provided. Let's quantify this insight! Suppose a guess gets some response that reduces the number of possible keys from some number \(n\) to a smaller \(n'