How to Play Bulls and Cows

By Jaques of London · Est. 1795 · Updated 2026-08-17

Bulls and Cows is a two-player code-breaking game played with nothing more than paper and a pen. One player sets a secret four-digit number and the other tries to crack it through a series of logical guesses, using the bull and cow clues returned after each attempt to narrow down the possibilities.

Its appeal is straightforward: it demands pure deductive reasoning, costs nothing to play, and fits into any setting from a kitchen table to a long car journey. A single game typically lasts ten to twenty minutes, making it easy to play several rounds in one sitting.

A little history

The origins of Bulls and Cows are unclear. It is traditionally described as an old pencil-and-paper game, and references to it appear in recreational mathematics literature from at least the mid-twentieth century. It became more widely known after being implemented as one of the earliest computer games in the 1960s and 1970s, which helped standardise the four-digit, no-repeated-digits format now considered the classic form of the game.

Setting up

1. Each player takes a sheet of paper and a pen.
2. Both players independently and secretly write down a 4-digit number. No digit may be repeated within the number (for example, 1234 is valid; 1123 is not).
3. The leading digit may be any digit from 1 to 9. A number beginning with 0 is not permitted in the standard game, as this would effectively make it a 3-digit code.
4. Each player draws two columns on their paper, headed 'Guess' and 'Result', to record the guesses made against them and the clues they return.
5. Decide who goes first, by any agreed method such as a coin toss.

How to play

1. Players alternate turns. On your turn, announce a 4-digit guess (with no repeated digits) aimed at cracking your opponent's secret number.
2. Your opponent checks your guess against their secret number and responds with the count of bulls and cows. A bull means a digit is correct and in the correct position. A cow means a digit appears in the secret number but is in a different position.
3. Example: secret number is 4271, guess is 1234. The digit 2 is in position three in the guess and position two in the secret, so it scores one cow. The digit 4 is in position one in the guess and position one in the secret, so it scores one bull. No other digits match, giving a result of '1 bull, 1 cow'.
4. Both players record each guess and the result on their own sheet. You are responsible for tracking all clues you have received in order to refine your future guesses.
5. Your opponent then takes their turn, guessing your secret number, and you return the bull and cow count to them in the same way.
6. Play continues in strict alternation. Neither player may change their secret number once the game has begun.
7. A guess of four bulls (announced as '4 bulls' or 'Bull') means the guesser has identified the exact number and wins the game immediately.
8. If both players score four bulls on the same round, the game is a draw. Agree before play whether draws are replayed.

Winning and scoring

The first player to guess their opponent's secret number exactly, receiving a response of 4 bulls, wins the game. There is no point scoring in the standard game: it is a win or a loss. If both players crack each other's number on the same round, the result is a draw. For a longer contest, players can agree to play a fixed number of rounds and award one point per win, with the highest score over those rounds determining the overall winner.

The fine points

The most common dispute involves whether a guess must follow its own no-repeated-digits rule. The standard ruling is yes: any guess containing a repeated digit is invalid and the turn is forfeited or the player is asked to re-guess, depending on what the players have agreed before the game starts. Settle this point before play begins.

A second dispute arises when a player returns an incorrect bull or cow count, whether accidentally or not. The standard ruling is that a miscount, once discovered, results in the offending player replaying the round from the most recent confirmed correct count, or in casual play, replaying the whole game. For fairness, both players should double-check each result before it is recorded. If a player guesses the same number twice, there is no penalty in the standard rules, but the wasted turn is its own punishment.

How to win more often

• Open with a guess that spreads four different digits across a wide range, such as 1234 or 1357. This immediately gives you information about four of the ten possible digits.
• Keep a written note of every digit confirmed as a cow or bull. Equally important, note every digit that has been entirely eliminated, as this shrinks the search space quickly.
• If a guess returns zero bulls and zero cows, all four digits in that guess are absent from the secret number. This is among the most valuable results you can receive: act on it by avoiding those digits entirely in future guesses.
• When you have identified the correct digits but are unsure of their order, cycle them through different positions systematically rather than guessing at random. This guarantees you resolve the arrangement in the fewest possible turns.
• Be aware that your opponent is watching your guesses. Avoid accidentally revealing the structure of your own secret number through guesses that are too obviously derived from it.

Variations

5-Digit Bulls and Cows

Players choose a 5-digit secret number with no repeated digits, including the possibility of 0 in any position (some versions allow 0 as a leading digit here, increasing the pool). The additional digit significantly increases the number of possible codes and extends the average game length, making this a good choice for experienced players looking for a stiffer challenge.

Word Bulls and Cows

Instead of a number, each player secretly selects a four-letter word with no repeated letters. Guesses must also be real words. Bulls and cows are awarded on the same basis: a bull for a correct letter in the correct position, a cow for a correct letter in the wrong position. This variant rewards vocabulary as well as logic and is particularly popular with younger players.

Three Strikes

A turn-based variant in which each player is allowed a maximum of ten guesses to crack the opponent's number. If neither player has succeeded after ten rounds, the player who got closest (fewest guesses needed, or most bulls achieved on their final attempt) wins. This format rewards efficiency and adds a time pressure that the open-ended standard game lacks.

Team Play

For four or more players, split into two teams. Each team confers privately to set a single secret number and to agree on guesses. One spokesperson from each team announces each guess and receives the clue. Team discussion between turns is permitted; discussion during the opponent's turn is not. This format introduces a collaborative element and works well as a group activity with younger participants.

Bulls and Cows: frequently asked questions