The bulls and cows game is a code-breaking game designed for two or more players. Each player chooses a secret code of 4 digits from 0-9. The digits must be all different. The goal of the game is for each player to guess the other player's secret code. The players in turn present their guesses to the opponents. The opponents respond by telling the players: 1. The number of bulls, i.e. the number of matching digits in their right positions, and 2. The number of cows, i.e. the number of matching digits but in different positions. For example, if the computer's secret code is 4281, the match responses for the following guesses are shown as follows: