论文标题
使用两个和三个钉子的静态黑色PEG AB游戏的最佳策略
Optimal Strategies for Static Black-Peg AB Game With Two and Three Pegs
论文作者
论文摘要
AB〜游戏是类似于流行游戏策划者的游戏。我们研究了该游戏的一个名为static Black-peg Ab〜游戏的版本。它是由两个玩家（Codemaker and the Codebreaker）演奏的。 Codemaker通过在$ p \ le c $ pegs的每种颜色上放置一组$ c $颜色的颜色来创建一个所谓的秘密，这要遵守每种颜色最多一次使用的条件。代码破坏者试图通过提出问题来确定秘密，每一个问题都可能是一个可能的秘密。作为答案，Codemaker揭示了每个问题正确放置的颜色的数量。之后，代码破坏者只有一个尝试确定秘密并因此赢得比赛。 对于给定的$ p $和$ c $，我们的目标是找到最小的$ k $ $ k $的问题，无论秘密秘密如何，都需要获胜，而相应的问题列表，称为$（k+1）$ - 策略。 We present a $\lceil 4c/3 \rceil-1)$-strategy for $p=2$ for all $c \ge 2$, and a $\lfloor (3c-1)/2 \rfloor$-strategy for $p=3$ for all $c \ge 4$ and show the optimality of both strategies, i.e., we prove that no $(k+1)$-strategy for a smaller $k$ exists.
The AB~Game is a game similar to the popular game Mastermind. We study a version of this game called Static Black-Peg AB~Game. It is played by two players, the codemaker and the codebreaker. The codemaker creates a so-called secret by placing a color from a set of $c$ colors on each of $p \le c$ pegs, subject to the condition that every color is used at most once. The codebreaker tries to determine the secret by asking questions, where all questions are given at once and each question is a possible secret. As an answer the codemaker reveals the number of correctly placed colors for each of the questions. After that, the codebreaker only has one more try to determine the secret and thus to win the game. For given $p$ and $c$, our goal is to find the smallest number $k$ of questions the codebreaker needs to win, regardless of the secret, and the corresponding list of questions, called a $(k+1)$-strategy. We present a $\lceil 4c/3 \rceil-1)$-strategy for $p=2$ for all $c \ge 2$, and a $\lfloor (3c-1)/2 \rfloor$-strategy for $p=3$ for all $c \ge 4$ and show the optimality of both strategies, i.e., we prove that no $(k+1)$-strategy for a smaller $k$ exists.
