# Bulls and Cows

## Introduction

Bulls and Cows is an old code-breaking mind or paper and pencil game for two or more players, predating the commercially marketed board game Mastermind.

## How to Play

Bulls and Cows is a 2 player game. One player thinks of a number, while the other player tries to guess it.

- The number to be guessed must be a 4 digit number, using only digits from 1 - 9, each digit atmost once. e.g. 1234 is valid, 0123 is not valid, 9877 is not valid, 9876 is valid.
- For every guess that the player makes, he gets 2 values - the number of bulls and the number of cows. 1 bull means the guess contains and the target number have 1 digit in common, and in the correct position. 1 cow means the guess and the target have 1 digit in common, but not in correct position. e.g. Let the target be 1234. Guessing 4321 will give 0 bulls and 4 cows. 3241 will give 1 bull and 3 cows. 4 bulls means you have won the game!
- The player gets 7 chances to correctly guess the entire number.

P.S. If you still have doubts about the rules, check it over here: https://en.wikipedia.org/wiki/Bulls_and_Cows

## Play it yourself

Try the game vs computer. Copy the following code to a local or online editor and run it.

```
import java.util.*;
class Main {
public static void main(String args[]) {
final String target = getNum();
System.out.println("COWS AND BULLS:");
Scanner in = new Scanner(System.in);
for (int i = 1; i <= 7; i++) {
System.out.print(i+". ");
String guess = in.next();
int feedback = feedback(target, guess);
System.out.println(guess+" - "+(feedback/10)+" bulls, "+(feedback%10)+" cows");
if (feedback == 40) {System.out.println("CONGRATULATIONS! YOU WIN!"); return;}
}
System.out.println("You have run out of moves. The number was - "+target);
}
static String getNum() {
ArrayList<String> possib = new ArrayList<String>();
for (int a = 1; a <= 9; a++) {
for (int b = 1; b <= 9; b++) {
if (b == a) continue;
for (int c = 1; c <= 9; c++) {
if (c == b || c == a) continue;
for (int d = 1; d <= 9; d++) {
if (d == a || d == b || d == c) continue;
String cnt = ""+a+b+c+d;
possib.add(cnt);
}
}
}
}
String guess = possib.get((int)(Math.random() * possib.size()));
return guess;
}
static int feedback(String ans,String guess) {
int bulls = 0, cows = 0;
for (int i = 0; i < guess.length(); i++) {
int ind = ans.indexOf(guess.charAt(i));
if (ind == i) bulls++;
else if (ind >= 0) cows++;
}
return bulls * 10 + cows;
}
}
```

## Solving Bulls and Cows

Think of a number, and give correct feedback while the computer tries to solve it. Copy the following code to a local or online editor and run it.

```
import java.util.*;
class Main {
static ArrayList<String> possib = new ArrayList<String>();
public static void main(String args[]) {
System.out.println("COWS AND BULLS SOLVER:");
init();
Scanner in = new Scanner(System.in);
while (possib.size() > 1) {
String guess = possib.get((int)(Math.random() * possib.size()));
System.out.print(guess+" ");
int bulls = in.nextInt();
int cows = in.nextInt();
for (int j = 0; j < possib.size(); j++)
if (!check(possib.get(j),guess,cows,bulls)) {
possib.remove(j);
j--;
}
}
for (int j = 0; j < possib.size(); j++)
System.out.println(possib.get(j));
}
static void init() {
for (int a = 1; a <= 9; a++) {
for (int b = 1; b <= 9; b++) {
if (b == a) continue;
for (int c = 1; c <= 9; c++) {
if (c == b || c == a) continue;
for (int d = 1; d <= 9; d++) {
if (d == a || d == b || d == c) continue;
String cnt = ""+a+b+c+d;
possib.add(cnt);
}
}
}
}
}
static boolean check(String ans,String guess,int cows,int bulls) {
for (int i = 0; i < guess.length(); i++) {
int ind = ans.indexOf(guess.charAt(i));
if (ind == i) bulls--;
else if (ind >= 0) cows--;
}
return (cows == 0) && (bulls == 0);
}
}
```

## Algorithm

The algorithm used is a simple brute force which runs every guess against all possible target numbers, and guesses a random number from all possible guesses. Now try and solve this wonderful problem suggested by @player_one: https://www.codingame.com/training/expert/bulls-and-cows