• Famous for its challenging questions, intimidating setting and pervading air of tense expectation, Mastermind is a legendary tournament quiz show beloved around the world, from the UK to Russia – and soon, Australia, when it returns to our screens after 34 years, weeknights on SBS from April.
• In conclusion, Mastermind is a great game for adult parents that loved Mastermind as a kid themselves, to force on the next generation. Operation, on the other hand, is a game that was spawned by Satan himself.

• Masterminds Tv Show Episodes
• Mastermind Tv Game Show

Famous for its challenging questions, intimidating setting and pervading air of tense expectation, Mastermind is a legendary tournament quiz show beloved around the world, from the UK to Russia – and soon, Australia, when it returns to our screens after 34 years, weeknights on SBS from April.

Mastermind is a long running quiz show that airs on BBC Two.It is hosted by John Humphrys (originally by Magnus Magnusson).The series is run in a knockout format and there are two rounds to each episode. In the first round, the four 'contenders' (as they are invariably called) are asked questions on a specific subject of each contestant's choosing, determined prior to the taping of the episode. John Humphrys hosts the relaunched series of the classic quiz where contenders take the famous black chair under the glare of the spotlight hoping to become Mastermind champion.

With highly respected TV host, journalist and self-confessed quiz junkie Jennifer Byrne (ABC's First Tuesday Book Club, Sunday, 60 Minutes, Foreign Correspondent) at the helm, the program places contenders in the iconic Mastermind chair and gives them two tense minutes to answer as many questions as possible on their chosen specialist subject.

Specialist subjects will include everything from Australian Parrots to The Harry Potter Series; John Cusack to The Whitlam Government Dismissal; Wicked: The Musical to Women in Australia Rallysport – and everything in between.

The contenders will advance to a general knowledge round, and the person with the highest combined score for both rounds is declared the winner. Each Friday the weekly finals will see one person advance to the semi-finals and eventually compete against other winners at the end of the season for the prestigious title of Australia's Mastermind.

Mastermind or Master Mind is a code-breaking game for two players. The modern game with pegs was invented in 1970 by Mordecai Meirowitz, an Israeli postmaster and telecommunications expert.^[1][2] It resembles an earlier pencil and paper game called Bulls and Cows that may date back a century or more.

• 3Algorithms

Gameplay and rules[edit]

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 different colors (or more; see Variations below), 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 even number. 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.^[3]

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.^[4]

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.^[5]

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.

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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.

Masterminds Tv Show Episodes

Other rules may be specified.^[6]

History[edit]

The game is based on an older, paper based game called Bulls and Cows. A computer adaptation of it was run on Cambridge University’s Titan computer system, where it was called 'MOO'. This version was written by Dr. Frank King. There was also another version for the TSS/8 time sharing system, written by J.S. Felton and finally a version for the Multics system at MIT by Jerrold Grochow.^[7]

The modern game with pegs was invented in 1970 by Mordecai Meirowitz, an Israeli postmaster and telecommunications expert. Meirowitz presented the idea to many major toy companies but, after showing it at the Nuremberg International Toy Fair, it was picked up by a plastics company - Invicta Plastics, based near Leicester, UK. 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.^[1][2][8]

Since 1971, the rights to Mastermind have been held by Invicta Plastics. (Invicta always named the game Master Mind.) They originally manufactured it themselves, though they have since licensed its manufacture to Hasbro worldwide, with the exception of Pressman Toys and Orda Industries who have the manufacturing rights to the United States and Israel, respectively.^[9]

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.^[10]

Algorithms[edit]

With four pegs and six colors, there are 6⁴ = 1296 different patterns (allowing duplicate colors).

Five-guess algorithm[edit]

In 1977, Donald Knuth demonstrated that the codebreaker can solve the pattern in five moves or fewer, using an algorithm that progressively reduces the number of possible patterns.^[11]The algorithm works as follows:

1. Create the set S of 1296 possible codes (1111, 1112 .. 6665, 6666)
2. 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)
3. Play the guess to get a response of colored and white pegs.
4. If the response is four colored pegs, the game is won, the algorithm terminates.
5. Otherwise, remove from S any code that would not give the same response if it (the guess) were the code.
6. Apply minimax 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.)
7. 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 Tony W. Lai did an exhaustive depth-first search showing that the optimal method could achieve an average of 5625/1296 = 4.3403 turns to solve, with a worst-case scenario of six turns.^[12]

Genetic algorithm[edit]

A new algorithm with an embedded genetic 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.^[13][14] 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.

The algorithm works as follows:

1. Set i = 1
2. Play fixed initial guess G₁
3. Get the response X₁ and Y₁
4. Repeat while X_i ≠ P:
   1. Increment i
   2. Set E_i = ∅ and h = 1
   3. Initialize population
   4. Repeat while h ≤ maxgen and E_i ≤ maxsize:
      1. Generate new population using crossover, mutation, inversion and permutation
      2. Calculate fitness
      3. Add eligible combinations to E_i
      4. Increment h
   5. Play guess G_i which belongs to E_i
   6. Get response X_i and Y_i

Complexity and the satisfiability problem[edit]

Mastermind Tv Game Show

In November 2004, Michiel de Bondt proved that solving a Mastermind board is an NP-complete problem when played with n pegs per row and two colors, by showing how to represent any one-in-three 3SAT problem in it. He also showed the same for Consistent Mastermind (playing the game so that every guess is a candidate for the secret code that is consistent with the hints in the previous guesses).^[15]

The Mastermind satisfiability problem is a decision problem that asks, 'Given a set of guesses and the number of colored and white pegs scored for each guess, is there at least one secret pattern that generates those exact scores?' (If not, then the codemaker must have incorrectly scored at least one guess.) In December 2005, Jeff Stuckman and Guo-Qiang Zhang showed in an arXiv article that the Mastermind satisfiability problem is NP-complete.^[16]

Variations[edit]

Varying the number of colors and the number of holes results in a spectrum of Mastermind games of different levels of difficulty. Another common variation is to support different numbers of players taking on the roles of codemaker and codebreaker. The following are some examples of Mastermind games produced by Invicta, Parker Brothers, Pressman, Hasbro, and other game manufacturers:

The difficulty level of any of the above can be increased by treating “empty” as an additional color or decreased by requiring only that the code's colors be guessed, independent of position.

Computer and Internet versions of the game have also been made, sometimes with variations in the number and type of pieces involved and often under different names to avoid trademark infringement. Mastermind can also be played with paper and pencil.There is a numeral variety of the Mastermind in which a 4-digit number is guessed.^[18]

See also[edit]

References[edit]

1. ^ ^abNelson, Toby (9 March 2000). 'A Brief History of the Master Mind Board Game'. Retrieved 6 August 2014.
2. ^ ^ab'Mastermind Board Game'. Board Game Geek. Retrieved 6 August 2014.
3. ^'Industrious'. Retrieved 2014-07-07.
4. ^'Wolfram'. Retrieved 2012-07-09.
5. ^'Archimedes'. Retrieved 2012-10-07.
6. ^'Bulls and Cows & co'. Retrieved 2012-07-07.
7. ^'Wayback Machine'(PDF). 2012-04-25. Archived from the original(PDF) on 2012-04-25. Retrieved 2017-12-26.
8. ^'Invicta Toys and Games'. 2007-08-12. Archived from the original on 2007-08-12. Retrieved 2017-12-26.
9. ^'Invicta Toy History page'. Archived from the original on 2007-08-12. Retrieved 2012-08-07.
10. ^'Landmark Reunion for Mastermind Box Models'. Retrieved 2006-10-05.
11. ^Knuth, Donald (1976–77). 'The Computer as Master Mind'(PDF). J. Recr. Math. (9): 1–6.
12. ^Koyama, Kenji; Lai, Tony (1993). 'An Optimal Mastermind Strategy'. Journal of Recreational Mathematics (25): 230–256.
13. ^Berghman, Lotte (2007–2008). 'Efficient solutions for Mastermind using genetic algorithms'(PDF). K.U.Leuven (1): 1–15.
14. ^Merelo, J. J.; Mora, A. M.; Cotta, C.; Runarsson, T. P. (2012). 'An experimental study of exhaustive solutions for the Mastermind puzzle'. arXiv:1207.1315. Bibcode:2012arXiv1207.1315M.Cite journal requires journal= (help)
15. ^De Bondt, Michiel C. (November 2004). 'NP-completeness of Master Mind and Minesweeper'. Radboud University Nijmegen.Cite journal requires journal= (help)
16. ^Mastermind is NP-Complete Retrieved 2010-09-02.
17. ^'BoardGameGeek'. boardgamegeek.com.
18. ^'Bulls and Cows Classic'. Archived from the original on 2011-07-22. [dead link]

External links[edit]