Name: 猜数字 - Classic 4 digits bulls and cows game
Rating: 4.8 (4 reviews)
Author: Jasonluo

猜数字（又称 Bulls and Cows ）是一种古老的的密码破译类益智类小游戏，起源于20世纪中期，一般由两个人或多人玩，也可以由一个人和电脑玩。

先解释标准规则，再介绍几种变体。
通常由两个人玩，一方出数字，一方猜。出数字的人要想好一个没有重复数字的4个数，不能让猜的人知道。猜的人就可以开始猜。每猜一个数字，出数者就要根据这个数字给出几A几B，其中A前面的数字表示位置正确的数的个数，而B前的数字表示数字正确而位置不对的数的个数。
如正确答案为 5234，而猜的人猜 5346，则是 1A2B，其中有一个5的位置对了，记为1A，而3和4这两个数字对了，而位置没对，因此记为 2B，合起来就是 1A2B。
接着猜的人再根据出题者的几A几B继续猜，直到猜中（即 4A0B）为止。
猜数字游戏通常设有猜测次数的上限。根据计算机测算，如果采用严谨的猜测策略，任何数字最多7次就可猜出（即达到 4A0B）。值得注意的是，在有些地方把次数上限定义为最多几次猜测以后就可以肯定数字是几，但这时或还需要再猜一次才能得到 4A0B 的结果。
标准的猜数字游戏由10个数码（0-9）和4个数位组成。可以通过变化数码或数位来丰富游戏。例如，可以使用9个数码玩4个数位的游戏。
猜数字游戏的一种变体允许重复的数码。这种规则的游戏被称为 Mastermind。其规则大致为：
除了上面的规则外，如果有出现重复的数字，则重复的数字每个也只能算一次，且以最优的结果为准。例如，如正确答案为5543，猜的人猜5255，则在这里不能认为猜测的第一个5对正确答案第二个，根据最优结果为准的原理和每个数字只能有一次的规则，两个比较后应该为1A1B，第一个5位子正确，记为1A；猜测数字中的第三个5或第四个5和答案的第二个5匹配，只能记为1B。当然，如果有猜5267中的第一个5不能与答案中的第二个5匹配，因此只能记作1A0B。

猜数字 - Classic 4 digits bulls and cows game

Bulls and Cows (also known as Cows and Bulls or Pigs and Bulls) is a code-breaking mind or paper and pencil game for two or more players. The game is played in turns by two opponents who aim to decipher the other's secret code by trial and error.

Bulls and Cows predates the commercially marketed board game version, Mastermind and the word-based version predates the hit word game Wordle. A version known as MOO was widely available for early mainframe computers, Unix and Multics systems, among others.

The numerical version
The numerical version of the game is usually played with 4 digits, but can be played with any number of digits.

On a sheet of paper, the players each write a 4-digit secret number. The digits must be all different. Then, in turn, the players try to guess their opponent's number who gives the number of matches. The digits of the number guessed also must all be different. If the matching digits are in their right positions, they are "bulls", if in different positions, they are "cows". Example:

Secret number: 4271
Opponent's try: 1234
Answer: 1 bull and 2 cows. (The bull is "2", the cows are "4" and "1".)
The first player to reveal the other's secret number wins the game.

The game may also be played by two teams of players, with the team members discussing their strategy before selecting a move.

Computer versions of the game started appearing on mainframes in the 1970s. The first known version was written by Frank King at the Cambridge Computer Laboratory sometime before the summer of 1970.[1] This version ran on Cambridge's multi-user operating system on their Titan machine. It became so popular the administrators had to introduce systems to prevent it from clogging the system.[2] In 1972, the original Cambridge MOO was ported to the Multics operating system at MIT,[1] and early Unix at AT&T.[3]

A version called BASIC MOO was published in the DECUS Program Library for PDP computers and another was available through the DEC Users Society, both dating from 1971.[4][5] A version written by Lane Hauck in the language FOCAL for the PDP-8 later served as the basis for the handheld game Comp IV by Milton Bradley.[6][7]

These programs maintained a league table of players' scores, and protecting the integrity of this league table became a popular case study for researchers into computer security.[8]

It is proved that any number can be solved within seven turns. The average minimal game length is 26274/5040 ≈ 5.21 turns.[9][10]

ref: https://en.wikipedia.org/wiki/Bulls_and_Cows