Mastermind is NP-Complete
نویسندگان
چکیده
In this paper we show that the Mastermind Satisfiability Problem (MSP) is NPcomplete. Mastermind is a popular game which can be turned into a logical puzzle called the Mastermind Satisfiability Problem in a similar spirit to the Minesweeper puzzle [5]. By proving that MSP is NP-complete, we reveal its intrinsic computational property that makes it challenging and interesting. This serves as an addition to our knowledge about a host of other puzzles, such as Minesweeper [5], Mah-Jongg [1], and the 15-puzzle [6].
منابع مشابه
On the Algorithmic Complexity of the Mastermind Game with Black-Peg Results
In this paper, we study the algorithmic complexity of the Mastermind game, where results are single-color black pegs. This differs from the usual dual-color version of the game, but better corresponds to applications in genetics. We show that it is NP-complete to determine if a sequence of single-color Mastermind results have a satisfying vector. We also show how to devise efficient algorithms ...
متن کاملHardness of Mastermind
Mastermind is a popular board game released in 1971, where a codemaker chooses a secret pattern of colored pegs, and a codebreaker has to guess it in several trials. After each attempt, the codebreaker gets a response from the codemaker containing some information on the number of correctly guessed pegs. The search space is thus reduced at each turn, and the game continues until the codebreaker...
متن کاملStatic Mastermind
Static mastermind is like normal mastermind, except that the codebreaker must supply at one go a list of questions (candidate codes), the answers to which must uniquely determine the secret code. We confirm the minimum size list for some small values. Then we solve the game for up to 4 positions. In particular we show that for k sufficiently large the minimium size of a list for 4 positions and...
متن کامل"mastermind by Importance Sampling and Metropolis- Hastings"
Two machine learning algorithms are introduced for playing a one player version of the logical game Mastermind. In the classic game of Mastermind there are two players: the encoder and the decoder. The encoder builds a secret code by selecting a sequence of four pegs, each chosen from six different colors. The decoder then attempts to guess the secret code in as few turns as possible. In this v...
متن کاملFinding an Evolutionary Solution to the Game of Mastermind with Good Scaling Behavior
The main research issue in the game of MasterMind is to find a method that minimizes the number of turns needed to find the solution. But another venue is to find a method that scale well when the size of the search space is increased. In this paper we will present a method that uses evolutionary algorithms to find fast solutions to the game of MasterMind that scale better with problem size tha...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- CoRR
دوره abs/cs/0512049 شماره
صفحات -
تاریخ انتشار 2005