Thursday, July 26, 2012

Bulls and Cows Mastermind ® Superhirn ® Codebreaker ®

This is my personal and private place where I put my personal notes to all essential links I could find to any information regarding this wonderful game. Thanks for your interest. Please try to help find missing links.

Mastermind ®
Original design by Mordecai Meirowitz (1970) [1]
Various retail names: Mastermind, Superhirn, Supercode, Variabolo, Senha and many others
Note that the names are trademarks.

Logic game (game of deduction)
Number guessing game (by process of elimination)
Color code or word guessing game
2 players

History. back to index

The exact year when the number guessing game Bulls and Cows was invented is not known. "Bulls and Cows has been played as a paper-and-pencil game for a century or more. I first played a computer version in 1968 on Titan, the Cambridge University Atlas" (John Francis, 2010 [1]).
Original features: paper-and-pencil game, number code

A similar word guessing game "Jotto was invented in 1955 by Morton M. Rosenfeld and marketed by his New York-based Jotto Corp." ( [2])
Jotto sheet [3]
New features: word code

"The first computer implementations of Bulls and Cows were the MOO program written by Dr. Frank King at Cambridge in 1968, a version for the TSS/8 time sharing system written by J.S. Felton, and a 1970 version written for the Multics system at MIT by Jerrold Grochow. The game was introduced to a wider audience in the 'Computer Recreations' column of the Apr-Jun 1971 issue of  'Software, Practice & Experience' " (John Francis, 2010) [1]
New features: 1-player vs. computer, mainframe computer game, keyboard
But: very limited access to mainframes, nowadays obsolete

"Mastermind was invented in 1970-71 by Mordecai Meirowitz, an Israeli Postmaster / Telecommunications expert. His idea was at first turned down by many of the leading toy companies, but he persisted, and took it to the International Toy Fair at Nuremberg in February 1971, where he showed it to a small English company, Invicta Plastics Ltd. The small Leicester based company bought up the entire intellectual property rights to the game, and under the guidance of its founder Mr. Edward Jones-Fenleigh, refined it, and released it in 1971-72. It was an immediate hit, and went on to win the first ever Game of the Year Award in 1973."[4]
New features: board game, color code

In 1976, Ronald Samson et al., Leicester, filed a US patent about a game that is known as "Grand Mastermind" (US Patent 4059274) [5][5a]. In 1978, Mordechai Meirovitz filed a patent about a Mastermind game for 4 players known as "Mastermind 44" (US Patent 4241923) [6][6a].
New features: color and shape code, 4 players

Remark: As far as I know no patent has been filed about the original Mastermind game. The name, as it is a trademark, is protected. The special design of a game is an invention and might be protected by copyright laws. Due to so-called prior art the game idea itself about guessing numbers or codes, basically the old "Bulls and Cows" cannot be protected by copyright laws. In my opinion the invention of colored pegs used as game indicators might be copyrighted, but I disagree that this implies its graphical adaption by some computer games, since virtual indicators displayed by a computer do not perform the same way like physical ones do, meaning such invention of physical objects does not bear virtual objects. On the other hand some of the computer games actually clone the design of the original board game as exactly as possible, and with due deference.

In 1977 or 1978, at a time when pocket calculators had become popular for some years, the game was amongst the first electronic handheld games.
Superhirn electronic (Parker, 1977?/1978?)
 New features: handheld computer game

"Video games had been first programmed on university-based computers in the 1950s, but the general public couldn't play them until they began appearing as coin-operated games in the 1960s." [7] "The Atari 2600 -or the Atari Video Computer System (VCS) as it was initially marketed and sold- opened up worlds of game play for its owners and their friends when it was introduced in 1977"[7]. The number guessing video game "Codebreaker" was introduced 1978 by Sears/Atari for the Atari 2600[8]. In 1981, I wrote an APL program running on a BS2000 mainframe which was doing pretty much the same thing. In 1983 Atari home computers came out with BASIC on-board and it became easy to write a similar computer game program.
Atari 2600 (1977) [8]
New features: home video game

With the evolution of PC hardware and software booming since the mid-1980s programmers and designers have been enabled to drastically improve game performance and graphics design. In the 2000s, games with limited memory requirements had a renaissance being appropriate to and used on mobile phones.
New features: PC game/ Online game/ Smartphone app

  • [1] John Francis (2010). "Strategies for playing MOO, or “Bulls and Cows”" (pdf)
  • [4] Toby Nelson (2000). A Brief History of the Master MindTM Board Game
  • [7]

How to playback to index

2 Players
Bulls and Cows (Mastermind/variants) is a game for 2 players. A code (e.g. "4222") is secretly set by the codesetter (player or computer). The codebreaker (player) has to find out this code with as least trials as possible. In order to succeed the codebreaker makes a guess and the codesetter compares guess with code. The result of that comparison is given as specific hints. The game is over if either the code is cracked, all agreed tries are done or the player gives up. There is an uncommon game rule where the codesetter is allowed to select another code (from the possible codes left at that time) during the game; it is not examined if or how the game gets more difficult that way.

It is most important that the codebreaker can create (paper, board, mind/memory) or watch a list of all previous guesses and hints at any time during the whole game. (Only in simple games there are known strategies where the player only needs to remember the same codes for every game [cf. 12 coins problem])

Code specifications.
The specifications of the code are set before the game starts. The code is a sequence (or a pattern) of objects. Most common objects are: numbers (e.g. "4222"), colors, shapes, symbols, characters etc. or a combination of these.
The length of this sequence may vary for each game, originally 4 digits (Bulls and Cows/Mastermind), most common now are: 3,4,5,6,8,10 digits.
The number of available different numbers/colors (etc.) to be placed within the sequence may vary for each game, originally 6 colors (Mastermind) most common now are: 4,5,6,8,10 colors (etc.) and 26 characters. Common limitations to set the code are: no duplicates allowed.
In word codes only words are allowed that are common words of a language or listed in a dictionary agreed on by the players before the game starts.

Guess specifications.
The specifications of a valid guess are set before the game starts. Length of sequence and available objects are the same as the code, but some varieties are possible, e.g. blank spaces might be allowed or not, duplicates might be allowed even if the code must not have. Game difficulty increases rapidly if only a consistant guess is allowed (every guess must be a possible candidate for the secret code in consistance with all hints from the previous guesses), but this is the best strategy to find the code as fast as possible. Note that if a valid word has to be found then the guess does not necessarily have to be too a word.

Hint specifications.
Hints may be indicated by any appropriate method (e.g. colors, pegs, text). There are 3 basic types of hints:
a) color (etc.) in code, in correct position (black peg/ bull)
b) color (etc.) in code, but in wrong position (white peg/ cow)
c)  - color (etc.) not in code (no peg/ empty space)

In some variants more hints exist:
d) [applies only to colors and shapes code games:] a color/symbol is placed on the correct position but the correct symbol has the wrong color or vice versa. (blue peg)
e) [applies only to 2D/3D versions (e.g.Supermind):] see

Very important: The hints must never be given for a specific digit of the code nor in an order other than specified before the game starts (commonly the order is: black peg-white peg-space). If there are duplicates in the guess, then there must be only one hint per digit of code (see example below)

(You can find more examples within the images of the "online games" section of this post)
Bulls and Cows (, 2009)

In the image above there was set a code of 4 digits ("1234"). The game was completed after 4 guesses ("1122", etc.). "1122": "1" at position 1 is correctly placed, 1 bull. "2" at position 3 is wrongly placed, 1 cow. On the right side there are the respective hints for each guess. Note that the hints might not be in order, e.g. the 2nd digit is cow instead of space. Note that there is no 2nd cow for the "2" at position 4 of the guess since the code position of the "2" in "1234" has already been checked. For experts: In this example guess no.2 as well as no.3 do not represent a guess that is consistent with the hints given with guess no.1.

Another example:[1]

  • 1-All four elements are correct - the mark is four black pegs. All of the following examples refer to this combination.
  • 2-Only the white rectangle is correct - one black peg.
  • 3-The white rectangle is right, but in the wrong position - one white peg.
  • 4-The colour white is right in the first position, the shape hexagon is right in the fourth position - two blues.
  • 5-The white rectangle is in the right place and gets a black; the yellow circle is in the wrong place and gets a white; the blue triangle attracts a blue peg because the colour is right.

Links: good introduction video how to

Strategy for real people back to index

  • Basics
  • Word code game
  • Color code game 
  • Links
Your strategies should consider different game scenarios:
  • Codesetter allways sets a random code
  • Codesetter reacts to the codebreaker's strategy
Different game sets might require different strategies.
  • Level of difficulty
  • Dictionary based game sets
Just to illustrate how the level of difficulty can change:
  • 6 colors at 4 digits: 64 = 1,296 possible combinations (duplicates allowed) [original Mastermind]
  • 10 numbers at 5 digits: 105=100,000 (duplicates allowed)
  • 26 characters at 5 digits: 265=11,881,376 (that's why only valid words are allowed as code) 
Word code games

Superhirn Codewort (Parker, 1972)

  • It is not allways the best strategy to start guessing with a valid word and hope to be lucky as shown in the image above. Another strategy goes like this:

  • First find out the quantity of vowels / consonants, e.g. "aeiou". Next start to find consonants, frequent first. The guesses shown above for sure are not optimal, it will depend on the language which guesses might be better than others. In the examples above I just went through the alphabet, and it seems to work at least not badly.
  • Check here for other Jotto rules and strategies. 

Color code games:
  • first try to find all colors, then try to find the right places
  • start with 2 different duplicates: e.g. "1122" or "222777"
  • start with 1 color, e.g. "222222", you get as result how many times it is in the code, then continue with next color until all colors are found, then concentrate on sorting. Example:
First guess gives us 2 blue pegs, so we continue with them and fill with next color red.

  • Now, same strategy, but while searching for the rest of the colors we already start sorting the colors that are already found. Example:
Since the 2nd guess had no hits, the two blue pegs have been shifted to the right to find their correct places
Cf. this approach with the following computer strategies:

Board Gamesback to index
Original features: 2 players, color code

Mastermind, newer version [1]

Grand Mastermind, 1974
New features: colors and shapes code. You have to guess 4 symbols + 4colors (adds up to 8 digits).

Word Mastermind, 1972

  • Invicta Toys and Games Limited
  • List and hundreds of images of most board games ever published plus additional information to each main version
  • e-s-g.euCollection of images of many mastermind versions and variants
  • Collection of images of many mastermind versions
  • latest versions and videos

Electronic Gamesback to index
New feature: Handheld computer, LED display

Superhirn electronic (Parker, 1978?)
But: still the list of hints must be done manually

Invicta (1977)


Video Games
New Feature: Home computer system, TV display, automated hint list
But: Programs only run on specific computer hardware (nowadays some of these games have been emulated for modern operating systems)

Codebreaker (Sears/Atari, 1978)


PC Gamesback to index
New Features: Games for various operating systems, mouse, improved graphics and design
But: Programs only run with the specific operating system they were made for.

Homemade version for MS-DOS, 1985
New Features: Consistancy check (guesses that cannot be the code are indicated/rejected), counter of combinations left to be the code, learning mode
But: MS-DOS didnt support mouse (actually a keyboard can be more comfortable to just enter numbers) Note that MS-DOS programs are still running on modern MS-Windows systems.

win3.0 game

MindsEye, MS-Win, 2003-2012 (,)
Features: up to 15 colors

Supermind, MS-Windows, 2005-2010 [2]
New Features: 2D code geometry and different hint logic

A 3D version might be interesting.

 Bulls n' Cows, MS-Win., 2009 (
New Features: Computer as codebreaker

MS-Win. 2011 (
Features: source code is available, computer as codebreaker

  • (online+pc versions)

Online Gamesback to index
New Features: Browsergame, independant from specific hardware/OS
But: keyboard not supported, sometimes special plugin/player needed (shockwave/flash,java etc)

Color code (

Word code (

Signs code ( Review: excellent mouse feeling 

Colors and shapes ( 3D version available

Color code features up to 15 digits and 10 colors, excellent mouse feeling

color code ( feature: consistancy check (checks if guess is consistant to previous hints)

Ghislain Costagliola

  • More than 200 online games listed and linked, most of them playable (swf/js/java/other), basically color code games, occasionally updated (online+pc versions) online online

 Online Highscores and 2 Players versionsback to index
New Features: Online game competitions
  • 2 players

Logelix (, 2012)
New Features: 2 player online internet game version

 Computer codebreaker back to index
New Features: Computer is solving

Smartphone Appsback to index
New Features: use with smartphone
But: use only with smartphone, Android or other OS

Color code ( 

Word code (

Word code ( (Jibber Jabber By Sqrrl, 2011) (Maize, 2009)

Links: android

Other Formats back to index


Disclaimer: All of my blogs and posts are my private and personal online notebooks and my private opinion to be discussed with my friends only. No information is meant for the public and I do not take any liability for any content for any reason at any time. Warning: many links are "clickable" and your software might direct you to and display content other than mine without warning.

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