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Contents. Gameplay and rules The game is played using:. a decoding board, with a shield at one end covering a row of four large holes, and twelve (or ten, or eight, or six) additional rows containing four large holes next to a set of four small holes;. code pegs of six (or more; see below) different colors, with round heads, which will be placed in the large holes on the board; and.
key pegs, some colored black, some white, which are flat-headed and smaller than the code pegs; they will be placed in the small holes on the board. The two players decide in advance how many games they will play, which must be an.
One player becomes the codemaker, the other the codebreaker. The codemaker chooses a pattern of four code pegs. Duplicates and blanks are allowed depending on player choice, so the player could even choose four code pegs of the same color or four blanks. In the instance that blanks are not elected to be a part of the game, the codebreaker may not use blanks in order to establish the final code.
The chosen pattern is placed in the four holes covered by the shield, visible to the codemaker but not to the codebreaker. The codebreaker tries to guess the pattern, in both order and color, within twelve (or ten, or eight) turns. Each guess is made by placing a row of code pegs on the decoding board. Once placed, the codemaker provides feedback by placing from zero to four key pegs in the small holes of the row with the guess. A colored or black key peg is placed for each code peg from the guess which is correct in both color and position.
A white key peg indicates the existence of a correct color code peg placed in the wrong position. Screenshot of software implementation (ColorCode) illustrating the example. If there are duplicate colours in the guess, they cannot all be awarded a key peg unless they correspond to the same number of duplicate colours in the hidden code.
For example, if the hidden code is white-white-black-black and the player guesses white-white-white-black, the codemaker will award two colored key pegs for the two correct whites, nothing for the third white as there is not a third white in the code, and a colored key peg for the black. No indication is given of the fact that the code also includes a second black. Once feedback is provided, another guess is made; guesses and feedback continue to alternate until either the codebreaker guesses correctly, or twelve (or ten, or eight) incorrect guesses are made. The codemaker gets one point for each guess a codebreaker makes. An extra point is earned by the codemaker if the codebreaker doesn't guess the pattern exactly in the last guess. (An alternative is to score based on the number of colored key pegs placed.) The winner is the one who has the most points after the agreed-upon number of games are played.
Other rules may be specified. History The game is based on an older, paper based game called. A computer adaptation of which was run on ’s 'Titan' computer system, where it was called 'MOO'. This version was written by Dr. There was also another version for the TSS/8 time sharing system, written by J.S. Felton and finally a version for the ' system at by Jerrold Grochow.
The modern game with pegs was invented in 1970 by, an postmaster and telecommunications expert. Meirowitz presented the idea to many major toy companies but, after showing it at the, it was picked up by a plastics company -, based near,. Invicta purchased all the rights to the game and the founder, Mr. Edward Jones-Fenleigh, refined the game further.
It was released in 1971-2. Since 1971, the rights to Mastermind have been held by of, near,. (Invicta always named the game Master Mind.) They originally manufactured it themselves, though they have since licensed its manufacture to worldwide, with the exception of and who have the manufacturing rights to the United States and Israel, respectively. Starting in 1973, the game box featured a photograph of a well-dressed, distinguished-looking man seated in the foreground, with a woman standing behind him. The two amateur models (Bill Woodward and Cecilia Fung) reunited in June 2003 to pose for another publicity photo. Algorithms With four pegs and six colors, there are 6 4 = 1296 different patterns (allowing duplicate colors).
Five-guess algorithm In 1977, demonstrated that the codebreaker can solve the pattern in five moves or fewer, using an algorithm that progressively reduced the number of possible patterns. The algorithm works as follows:. Create the set S of 1296 possible codes (1111, 1112. 6665, 6666). Start with initial guess 1122 (Knuth gives examples showing that other first guesses such as 1123, 1234 do not win in five tries on every code).
Play the guess to get a response of colored and white pegs. If the response is four colored pegs, the game is won, the algorithm terminates. Otherwise, remove from S any code that would not give the same response if it (the guess) were the code.
Apply technique to find a next guess as follows: For each possible guess, that is, any unused code of the 1296 not just those in S, calculate how many possibilities in S would be eliminated for each possible colored/white peg score. The score of a guess is the minimum number of possibilities it might eliminate from S. A single pass through S for each unused code of the 1296 will provide a hit count for each colored/white peg score found; the colored/white peg score with the highest hit count will eliminate the fewest possibilities; calculate the score of a guess by using 'minimum eliminated' = 'count of elements in S' - (minus) 'highest hit count'. From the set of guesses with the maximum score, select one as the next guess, choosing a member of S whenever possible. (Knuth follows the convention of choosing the guess with the least numeric value e.g. 2345 is lower than 3456.
Knuth also gives an example showing that in some cases no member of S will be among the highest scoring guesses and thus the guess cannot win on the next turn, yet will be necessary to assure a win in five.). Repeat from step 3.
Subsequent mathematicians have been finding various algorithms that reduce the average number of turns needed to solve the pattern: in 1993, Kenji Koyama and found a method that required an average of 5625/1296 = 4.340 turns to solve, with a worst-case scenario of six turns. The value in the sense of is 5600/1296 = 4.321. Genetic algorithm A new algorithm with an embedded algorithm, where a large set of eligible codes is collected throughout the different generations. The quality of each of these codes is determined based on a comparison with a selection of elements of the eligible set. This algorithm is based on a heuristic that assigns a score to each eligible combination based on its probability of actually being the hidden combination. Since this combination is not known, the score is based on characteristics of the set of eligible solutions or the sample of them found by the evolutionary algorithm. ^ Nelson, Toby (9 March 2000).
Retrieved 6 August 2014. Board Game Geek. Retrieved 6 August 2014. Retrieved 2014-07-07. Retrieved 2012-07-09. Retrieved 2012-10-07. Retrieved 2012-07-07.
Archived from (PDF) on 2012-04-25. Retrieved 2017-12-26. Archived from on 2007-08-12.
Retrieved 2017-12-26. Archived from on 2007-08-12. Retrieved 2012-08-07. Retrieved 2006-10-05. Koyama, Kenji; Lai, Tony (1993).
'An Optimal Mastermind Strategy'. Journal of Recreational Mathematics (25): 230–256. Knuth, Donald (2011).
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Selected papers on fun and games. Center for the Study of Language and Information.
(2007–2008). K.U.Leuven (1): 1–15. M.; Cotta, C.; Runarsson, T. 'An experimental study of exhaustive solutions for the Mastermind puzzle'.:. De Bondt, Michiel C. (November 2004). Radboud University Nijmegen.
Retrieved 2010-09-02. Archived from on 2011-07-22. dead link External links.
Books.google.com.ua - The mathematical genius Alan Turing (1912-1954) was one of the greatest scientists and thinkers of the 20th century. Now well known for his crucial wartime role in breaking the ENIGMA code, he was the first to conceive of the fundamental principle of the modern computer-the idea of controlling a computing.
Alan Turing's Automatic Computing Engine: The Master Codebreaker's Struggle to build the Modern Computer. The mathematical genius Alan Turing (1912-1954) was one of the greatest scientists and thinkers of the 20th century. Now well known for his crucial wartime role in breaking the ENIGMA code, he was the first to conceive of the fundamental principle of the modern computer-the idea of controlling a computing machine's operations by means of a program of coded instructions, stored in the machine's 'memory'. In 1945 Turing drew up his revolutionary design for an electronic computing machine-his Automatic Computing Engine ('ACE'). A pilot model of the ACE ran its first program in 1950 and the production version, the 'DEUCE', went on to become a cornerstone of the fledgling British computer industry.
The first 'personal' computer was based on Turing's ACE. Alan Turing's Automatic Computing Engine describes Turing's struggle to build the modern computer.
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The first detailed history of Turing's contributions to computer science, this text is essential reading for anyone interested in the history of the computer and the history of mathematics. It contains first hand accounts by Turing and by the pioneers of computing who worked with him. As well as relating the story of the invention of the computer, the book clearly describes the hardware and software of the ACE-including the very first computer programs. The book is intended to be accessible to everyone with an interest in computing, and contains numerous diagrams and illustrations as well as original photographs. The book contains chapters describing Turing's path-breaking research in the fields of Artificial Intelligence (AI) and Artificial Life (A-Life). The book has an extensive system of hyperlinks to The Turing Archive for the History of Computing, an on-line library of digital facsimiles of typewritten documents by Turing and the other scientists who pioneered the electronic computer.