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<form id="mastermind_solver" method="post">
  <label for="mastermind_solver_nb_pegs">Number of pegs/slots (Answer code size) C=</label> <input type="text" id="mastermind_solver_nb_pegs" name="nb_pegs" value="4" size="4" spellcheck="false" class=""><br>
  <label for="mastermind_solver_nb_colors">Number of possible colors N=</label> <input type="text" id="mastermind_solver_nb_colors" name="nb_colors" value="6" size="4" spellcheck="false" class=""><br>
  <label for="mastermind_solver_mastermind">Current propositions (minimum 2 - respect the correct syntax)</label><br><textarea name="mastermind" spellcheck="false" id="mastermind_solver_mastermind" class="" data-hasqtip="0">ABCD 20
CDEF 00
BABA 22</textarea><br>
  <label for="mastermind_solver_max_1_letter">Forbidden to use the same color several times <input type="checkbox" id="mastermind_solver_max_1_letter" name="max_1_letter"></label><br>
  <button data-post="mastermind,nb_pegs,nb_colors,max_1_letter" post="mastermind,nb_pegs,nb_colors,max_1_letter" style="margin: 0.1em 140px; cursor: pointer;">Find solution(s)</button>
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Mastermind Solver

Tool/Solver to solve Mastermind automatically by finding a combination of
colours in a minimum of attempts.

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Mastermind Solver - dCode

Tag(s) : Board Games

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Solver' tool for free! Thank you!


MASTERMIND SOLVER

 1. Games and Solvers
 2. Board Games
 3. Mastermind Solver




MASTERMIND GAME SOLVER

Number of pegs/slots (Answer code size) C=
Number of possible colors N=
Current propositions (minimum 2 - respect the correct syntax)
ABCD 20 CDEF 00 BABA 22
Forbidden to use the same color several times
Find solution(s)
See also: Combination N Choose K



ANSWERS TO QUESTIONS (FAQ)

You can edit this FAQ section, review it or improve it!


WHAT IS MASTERMIND? (DEFINITION)

Mastermind is a board game based on deduction where the player must discover a
combination of colors with a minimum of guesswork. The game is generally played
with 2 players with asymmetric functions: one is an encoder, the other is a
decoder. The encoder records a secret color combination that his opponent must
decode by proposing combinations himself. The encoder must respond by indicating
whether one or more colors are correctly or incorrectly placed. If the decoder
finds the combination of the encoder, the game ends.

You can edit this FAQ section, review it or improve it!


HOW TO USE THE MASTERMIND SOLVER (SYNTAX TO USE)?

The Mastermind solver is configurable in size (number of colored pawns in the
solution code) and in choices (number of possible colors/items) depending on the
kind of Mastermind game to be resolved by the player.

In its original version, a mastermind has generally 4 pegs/slots among 6 colours
for each attempt, the player receives 2 clues/numbers: the number of correct
colors' positions and the number of incorrect colors' positions.

The dCode solver uses an easy syntax to describe the combinations proposals and
to deduce the possible solutions. For a N sized combination to guess (N = number
of items to find), each proposal must contain N letters followed by 2 digits
indicating the clues obtained (number of colors well and badly placed). Separate
each proposition with a line break.

Each letter represents a color of your choice, it is advisable to use the
initial letter of the color (but beware of duplicates: do not put B for both
Black and Blue ! Prefer to replace Blue with C (for Cyan).

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 Black and in position 4: Y
for Yellow
Digits 2 and 0 correspond respectively to 2 pegs in the correct position and 0
in wrong position.

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

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

Example: Yellow,Blank,Blank,Blank (0 well placed, 1 bad placed) is written: Y---
01 (with - = joker)

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

You can edit this FAQ section, review it or improve it!


WHAT IS THE OPTIMAL STRATEGY TO PLAY MASTERMIND?

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 puzzle 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).

You can edit this FAQ section, review it or improve it!


WHAT IS THE HARDEST COMBINATION TO GUESS AT MASTERMIND?

Mathematically, if the strategy of the code-breaker (guessing player) is known
then there are indeed more or less difficult combinations, but as indicated
(above), using the optimal strategy of Donald Knuth then no combination is
really difficult and all solutions can be found in 5 steps or less. Always
mathematically, if the player's strategy is not known, then there is no
combination more difficult than another.

For information, using this type of algorithm, the best combinations (the most
difficult combinations to solve) are 1221, 2354, 3311, 4524, 5656, 6643.

However, not all players reason with mathematical algorithms, it is possible to
imagine harder to find combinations by trapping the human brain.

— Novice players often forget that the combination can have the same color
several times, using 2 or 3 times the same element in the combination can make
the game more difficult.

— If the combinations are made of numbers or letters, use large numbers or
letters at the end of the alphabet in priority, because the algorithms and the
players will often start by trying 1122 and not 5566 (and if it does, use mid
range digits).

— If the players have agreed, a variant authorizes one or more empty spaces in
the combination.

You can edit this FAQ section, review it or improve it!


WHAT ARE MASTERMIND VARIANTS?

The best known variant is to use words to guess. The game, sometimes called
Masterword then becomes much more complicated because the number of possible
combinations increases exponentially.

A variant (which needs a players agreement before setting the game) is to allow
a blank (a space without peg / color).

The Mastermind is often used as a puzzle in video games, such as in Old School
RuneScape (OSRS) where a Mastermind makes players sweat (Fremennik Exiles).

You can edit this FAQ section, review it or improve it!


WHO INVENTED MASTERMIND GAME?

The board game Mastermind credits Mordecai Meirovitz as author in 1971.

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SOURCE CODE

dCode retains ownership of the "Mastermind Solver" source code. Except explicit
open source licence (indicated Creative Commons / free), the "Mastermind Solver"
algorithm, the applet or snippet (converter, solver, encryption / decryption,
encoding / decoding, ciphering / deciphering, translator), or the "Mastermind
Solver" functions (calculate, convert, solve, decrypt / encrypt, decipher /
cipher, decode / encode, translate) written in any informatic language (Python,
Java, PHP, C#, Javascript, Matlab, etc.) and all data download, script, or API
access for "Mastermind Solver" are not public, same for offline use on PC,
mobile, tablet, iPhone or Android app!
Reminder : dCode is free to use.


CITE DCODE

The copy-paste of the page "Mastermind Solver" or any of its results, is allowed
as long as you cite dCode!
Cite as source (bibliography):
Mastermind Solver on dCode.fr [online website], retrieved on 2023-02-23,
https://www.dcode.fr/mastermind-solver


NEED HELP ?

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Feedback and suggestions are welcome so that dCode offers the best 'Mastermind
Solver' tool for free! Thank you!

Summary
 * Mastermind game solver
 * What is Mastermind? (Definition)
 * How to use the Mastermind solver (syntax to use)?
 * What is the optimal strategy to play Mastermind?
 * What is the hardest combination to guess at Mastermind?
 * What are Mastermind variants?
 * Who invented Mastermind game?

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 * Combination N Choose K
 * Set Solver
 * Wordle Solver
 * Boggle Solver 4x4
 * Popotamo Solver
 * Wheel of Fortune
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Keywords
mastermind, master, mind, mordecai, meirovitz, peg, slot, code, game,
combination, masterword
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