Tool to solve Mastermind automatically. Mastermind is a board game based on deduction, created by Mordecai Meirovitz. This board game proposes to the player to find a combination of colours in a minimum of tentatives, receiving at each attempt, a global informatino about correct or incorrect colors and positions.

Mastermind Solver - dCode

Tag(s) : Board Game

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Tool to solve Mastermind automatically. Mastermind is a board game based on deduction, created by Mordecai Meirovitz. This board game proposes to the player to find a combination of colours in a minimum of tentatives, receiving at each attempt, a global informatino about correct or incorrect colors and positions.

The Mastermind solver have to be configured in size (number of pegs in the code) and in size (number of available colours). (A mastermind has generally 4 pegs among 6 colours)

The solver uses text to describe proposals and deduct possible solutions.

Each proposed combination is separated by a carriage return.

The syntax is composed of N letters (where N is the number of pegs and each letter is a colour) and 1 or 2 digits to indicate rightly or wrongly positioned pegs.

Example: Combination RGBY 2 0 correspond to a proposal with in position 1 : R for Red, in position 2 : G for Green, in position 3 : B for Blue and in position 4 : Y for Yellow

Here we use the initial of the color (beware of doubles : Black and Blue for example)

Example: Digits 2 and 0 correspond respectively to 2 pegs in the right position and 0 in wrong position. (Be careful to indicate this with the right number)

It is also possible to indicate jokers (empty cells or unknown indicated by ?,*,- or _) as for the combination, than for right and wrong position.

Example: Black Black Yellow Red (1 in the right position, 2 in the wrong position) is written: BBYR12

Example: Red Green Blue (1 in the right position and ignore the wrongly placed) is written: 'RGB 1?' (? = joker)

According to Donald Knuth, and according to the original rules (combination of 4 colors among 6) it is possible to find the code in 5 steps (or less). The algorithm to use is:

1 - Generate the set E of the 1296 possible codes (from 1111 to 6666).

2 - Propose as first guess 1122

3 - If the answer is correct, the game is over. Otherwise, delete from the set E all the codes that would give the same answer.

4 - For each possible code that has not been attempted, calculate how many possibilities of the set E would be eliminated for each possible answer (combination well placed-misplaced). Give a score to this code equal to the minimum number of possibilities eliminated in E. Propose one of the codes with the best score as guess (preferably a code present in S). Resume in step 3.

This algorithm can find the code in 5 steps (or less).

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Source : https://www.dcode.fr/mastermind-solver

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