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.
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. Play fixed initial guess G1 3.
Get the response X1 and Y1 4. Increment i 2. Initialize population 4. Generate new population using crossover, mutation, inversion and permutation 2. Calculate fitness 3. Add eligible combinations to Ei 4. Increment h. In November , 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.
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?
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:. Deluxe Mastermind; a.
Number Mastermind 6 digits 4 Uses numbers instead of colors. The codemaker may optionally give, as an extra clue, the sum of the digits. Electronic Mastermind Invicta 10 digits 3, 4, or 5 Uses numbers instead of colors. Handheld electronic version. Solo or multiple players vs. Invicta branded. Travel Mastermind 6 4 Travel-sized version; room for only six guesses Mastermind Challenge 8 5 Both players simultaneously play code maker and code breaker. New Mastermind 8 4 For up to five players Mini Mastermind 6 4 Travel-sized self-contained version; room for only eight guesses Mastermind 6 4 digital version.
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.
Retrieved 6 August Board Game Geek. The codebreaker closes their eyes or leaves the room, and the mastermind creates the secret code by putting 4 colored balls in any order on the top row. You can only use each color once to make your code. The codebreaker returns and starts on the bottom row. They can place any of the colored balls in any order to make their initial guess. Next, the mastermind provides feedback on their guesses by putting 4 black or white balls in the smaller openings at the end of the row.
If the mastermind places a white ball down, it means you placed a correct color in the wrong position. If they place a black ball in one of the slots, you put a correct color in the correct position. This means that if you have 2 of the colored balls in the correct sequence, you will get 2 black balls. If you have 2 colored balls in the right order and 2 of the other colors are correct but misplaced, you will get 2 black and 2 white balls.
After the mastermind provides their feedback, the codebreaker uses the next row to make their next set of guesses based on the feedback from the last row.
Keep repeating this process by laying colored balls down and placing feedback next to each guess. If the codebreaker gets the sequence right before 9 turns are over, they win the round. Once the first round ends, the mastermind and codebreaker switch roles. You can see who can win the most rounds, or play the best out of 3 rounds to complete a game. You can make the game more challenging by allowing the mastermind to repeat colors in their code, or by using more colors to play the game.
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Download Article Explore this Article parts. Tips and Warnings. Related Articles. Article Summary. Part 1. Have the code maker select a code. Mastermind board games have a row of holes set apart at one end of the board, hidden from view under a hinged shield. The person who plays the code maker secretly takes a few colored pegs and places them in that row of holes, in any order. This is the code that the codebreaker will try to guess.
The code maker must put a peg in every hole. He has the option to use more than one peg of the same color. For example, he could put down Green Yellow Yellow Blue. Have the code breaker place her first guess. The other player, or the only player in video game versions, tries to guess what the hidden code is. Sitting on the opposite end of the board, she picks up the large colored pegs and places them in the nearest row of large holes.
For example, she could put down Blue Orange Green Purple. Your Mastermind game might have more holes or different colored pegs. Ask the code maker to give feedback. Next to each "guess row" is a small square with enough holes for four tiny pegs. These pegs only come in two colors: white and red or white and black in some versions.
The code maker uses this to give clues about how good the guess was. The code maker must be honest, and always puts down pegs using these instructions: [3] X Research source Each white peg means that one of the guessed pegs is correct, but is in the wrong hole. Each red or black peg means that one of the guessed pegs is correct, and is in the right hole. The order of the white and black pegs does not matter. Learn through examples.
In our example above, the code maker secretly chose Yellow Yellow Green Blue. The code breaker guessed Blue Orange Green Purple. The code maker looks at this guess to find out which hint pegs to place: Peg 1 is Blue. There is a blue in the code, but it is not in position 1. This earns a white hint peg. Peg 2 is Orange. There is no orange in the code, so no hint peg gets put down. Peg 3 is Green. There is a green in the code, and it is in position 3. This earns a red or black hint peg.
That game is over. Tally the score and change roles. At the end of each game, the Codemaker scores one point for every line of Code pegs placed by the Decoder. If the Decoder does not crack the code in nine attempts, that game is over and the Codemaker scores nine points. Make a note of your score after each game. Players switch roles at the end of each game. When you have completed the agreed number of games, add up your scores - the player with the highest score is the winner. If the Codemaker makes a mistake when giving information to the Decoder, replay the game and award three extra points to the Decoder.
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