How to play BULLS AND COWS
Set up
Players
Bulls and Cows is a 1 vs. 1 game so two players are needed, from 7 years old and up.
What you need to play
A pencil and a sheet of paper for each player.
Who’s first?
The player with the least experience goes first.
Goal of the game
What you need to do to win
The first person to guess the number the other person has thought of wins.
BULLS AND COWS rules: game development
What you need to do to win
The first person to guess the number the other person has thought of wins.
Choice of numbers
Each player secretly writes down a different 4-digit number.
Proposal
The player whose turn it is tries to guess the opponent’s number by saying four digits that must be different from each other.
Bulls and cows
The opponent responds by giving a certain number of Bulls and Cows:
# BULLS = number of digits guessed and placed correctly
# COWS = number of digits guessed, but not in the correct place.
Example 1
Secret number = 5408
Proposed = 3261
Outcome = 0 toros, 0 vacas
Example 2
Secret number = 3284
Proposed = 3548
Result = 1 bull, 2 cows
Example 3:
Secret number = 2169
Proposed = 4379
Result = 1 bull, 0 cows
Example 4:
Secret number = 8642
Proposed = 8624
Result = 2 bulls, 2 cows
Next turns
Players take turns guessing and receiving feedback in the form of bulls and cows.
Game over – who takes the crown??
And the winner is…
The game ends when one of the players guesses the other player’s number to become the winner.
Tips to play BULLS AND COWS
Tip 1 – Time per shift
If a player takes too long to make a guess, it will be convenient to agree on a maximum time per turn. If you overshoot that time, you lose your turn.
Tip 2 – Review
At the end of the game the loser should check that the bulls and cows given by the opponent to his proposals were correct. What if they’re not? If not, the win is forfeited and the other player takes the victory.
Tip 3 – Longer games
You can play with more or less digits. The more digits, the longer the games go on.
Tricks and strategies to win at BULLS AND COWS
Trick 1 – Discard template
Use some kind of template to cross out, after each turn, the numbers that definitely can’t be in certain positions. So you don’t have to memorize everything.
Example of a discard template
Number 1
1 2 3 4 5
6 7 8 9 0
Number 2
1 2 3 4 5
6 7 8 9 0
Number 3
1 2 3 4 5
6 7 8 9 0
Number 4
1 2 3 4 5
6 7 8 9 0
Example
If we propose the number 1234 and we are told 0 bulls and 0 cows, then we know that none of these numbers can be in the secret number. We can cross out those numbers:
Number 1
1 2 3 4 5
6 7 8 9 0
Number 2
1 2 3 4 5
6 7 8 9 0
Number 3
1 2 3 4 5
6 7 8 9 0
Number 4
1 2 3 4 5
6 7 8 9 0
If we then propose the number 5678 and we are told 0 bulls and 2 cows then we know, because we have 0 bulls, that the first digit is NOT a 5, the second is NOT a 6…..
Number 1
1 2 3 4 5
6 7 8 9 0
Number 2
1 2 3 4 5
6 7 8 9 0
Number 3
1 2 3 4 5
6 7 8 9 0
Number 4
1 2 3 4 5
6 7 8 9 0
Moreover, since after saying 12345678 we have only been told 2 cows, we know that the other two digits must surely be the two we have not yet tried: 9 and 0.
So in the following proposals we always have to say a 9, a 0 (even though we don’t know their exact positions yet) and some of the ones that are still free in our staff.
Trick 2 – Setting numbers
When you have 4 cows, all you have to do is order the numbers. But don’t just do it on a whim!
Example
Let’s suppose that luck is on our side and in our first proposal we throw the number 6789 and we get 0 bulls and 4 cows.
Trick 2 – Setting numbers
When you have 4 cows, all you have to do is order the numbers. But don’t just do it on a whim!
We know then that the correct numbers are those: 6,7,8,9 so we can cross out all the others:
Number 1
1 2 3 4 5
6 7 8 9 0
Number 2
1 2 3 4 5
6 7 8 9 0
Number 3
1 2 3 4 5
6 7 8 9 0
Number 4
1 2 3 4 5
6 7 8 9 0
and also, since we have 0 bulls, we know that none of them is in its correct position and we can cross out as well:
Number 1
1 2 3 4 5
6 7 8 9 0
Number 2
1 2 3 4 5
6 7 8 9 0
Number 3
1 2 3 4 5
6 7 8 9 0
Number 4
1 2 3 4 5
6 7 8 9 0
Now all that remains is to place those 6,7,8,9 in their position.
But that’s all we say! Figure it out yourself. That’s part of the fun!: think about what is the best proposal at each moment to minimize the number of attempts to guess the opponent’s number and therefore your chances of winning. Don’t propose random numbers!
Trick 3 – Watch your opponent’s game
The winning strategy starts from the moment the secret number is chosen.
If your opponent always tries 1234 then don’t go writing a secret number with those four digits because on the first try you are giving him 4 cows and maybe even some bull!
