@@ -7,10 +7,10 @@ TODO: Introduce game rules and related work.
Let $`N`$ be the number of pegs in the code and $`C`$ be the number of possible peg colors. A *code* is a vector in $`\{0, \ldots, C - 1\}^N`$. The number of possible codes is $`M = C^N`$. The game is played as follows:
1. The codemaker chooses a secret code $`c`$.
2. The codebreaker tries to guess $`c`$ in as few as possible iterations. At each iteration:
* The codebreaker produces a guess code $`g`$.
* The codemaker provides a feedback $`f(c, g) = \langle b(c,g), w(c, g) \rangle`$ where $`b`$ is the number of pegs which are correct in both color and position and $`w`$ is the number of pegs which are correct in color but not in position.
3. The game ends when the codebreaker guesses the secret code (gets feedback $`langle N, 0 \rangle`$) or when a predefined maximum number of iterations $`T`$ is reached.
2. The codebreaker tries to guess $`c`$ in as few as possible iterations. At each iteration $`t`$ :
* The codebreaker produces a guess code $`g_t`$.
* The codemaker provides a feedback $`f(c, g_t) = \langle b(c,g_t), w(c, g_t) \rangle`$ where $`b`$ is the number of pegs which are correct in both color and position and $`w`$ is the number of pegs which are correct in color but not in position.
3. The game ends when the codebreaker guesses the secret code (gets feedback $`\langle N, 0 \rangle`$) or when a predefined maximum number of iterations $`T`$ is reached.
The notion of "correct in color but not in position" is a bit tricky because color repetitions are allowed. To avoid ambiguity, here is a possible feedback implementation:
