## Bulls and Cows

Posted on: October 31st, 2013 by

Here is a description from Wikipedia on Bulls and cows:
"Bulls and Cows (also known as Cows and Bulls or Pigs and Bulls or Bulls and Cleots) is an old code-breaking paper and pencil game for two players, predating the similar commercially marketed board game Mastermind.
It is a game with numbers that may date back a century or more. It is played by two opponents. The game can also be played with 3 digits instead of 4.
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. If the matching digits are on their right positions, they are "bulls", if on 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 one to reveal the other's secret number wins the game. As the "first one to try" has a logical advantage, on every game the "first" player changes. In some places, the winner of the previous game will play "second". Sometimes, if the "first" player finds the number, the "second" has one more move to make and if he also succeeds, the result is even."

The puzzle: Design an algorithm that the computer can use to solve the bulls and cows puzzle in as few moves as possible.

- via n1b-algo