Bulls and Cows rules

Bulls and Cows was played on paper long before computers, and in the 1970s this number-guessing game became one of the first computer games. The rules fit in a couple of lines, but guessing fast takes real reasoning.

The secret number

A four-digit number with all digits different. It may start with zero, so 0123 and 0987 count too. There are 5040 such numbers: any of the 10 digits can go first, any of the remaining 9 second, then 8 and 7.

How the game answers

You enter a number with four different digits, and the game compares it with the secret and gives two counts:

• 🐂 bulls: how many digits are in the secret number and in the same positions;
• 🐄 cows: how many digits are in the secret number, but in other positions.

The game does not say which digits turned out to be bulls or cows. That is the whole puzzle. For an easier start, choose easy difficulty: there every digit is colored.

Examples

Say the secret is 4271. Here is how the game answers different guesses:

• 12341 bull 2 cows🐂🐄🐄1 bull and 2 cowsthe 2 is in place, the 1 and the 4 are in the number but elsewhere
• 5689nothing0 bulls and 0 cowsno shared digits: all four can be crossed out
• 42703 bulls🐂🐂🐂3 bulls and 0 cows4, 2, and 7 in place, no 0 in the number
• 17424 cows🐄🐄🐄🐄0 bulls and 4 cowsall digits right, but none in its place
• 42714 bulls🐂🐂🐂🐂4 bulls and 0 cowsfour bulls, solved

Note: the answer “3 bulls and 1 cow” never happens. If three digits are in place and the fourth is in the number, the only free position left is its own, so it is a bull too.

Guesses

You get 25 guesses on normal difficulty and unlimited guesses on easy. After the game, the move review shows how many options each guess ruled out.

Difficulty levels

You choose the difficulty above the keypad before your first guess, and it stays until the game ends. The daily number always starts on normal, and the other modes remember your last choice.

• Easy. Besides bulls and cows, every digit is colored: green is in the right position, yellow is in the number but elsewhere, gray is not in the number. The options counter and the move review take the colors into account. These games do not count toward stats or streaks.
• Normal. The classic rules: only the number of bulls and cows, 25 guesses to solve it.

Digit notes

The “Notebook” button opens a grid: digits on top, positions 1 to 4 on the left. Tapping a digit crosses it out, a second tap marks it as definitely in the number, a third clears the mark. On a computer keyboard, Shift plus a digit does the same. The cells under the digits are a scratchpad: the first tap puts “?”, the digit could be here, the second puts “×”, it is not here, the third clears the cell. When an answer leaves no doubt, the game adds the marks itself: after 0 bulls and 0 cows it crosses out all four digits, and if bulls and cows add up to four, it marks those digits and crosses out the rest. On easy, the marks follow the colors.

Modes

• Daily number: one number for everyone, new every day at midnight UTC. Only the daily number counts toward stats and streaks, when played on normal difficulty.
• Practice: a random number, as many games in a row as you like.
• Play with a friend: pick a number and send a link.
• Archive: past daily numbers.

FAQ

What is a bull and what is a cow?

A bull means a digit is in the secret number and in the right position. A cow means the digit is in the number, but in a different position.

Can the number start with zero?

Yes. The secret can be any number with four different digits, including 0123 or 0987. There are 5040 such numbers.

Does the game tell you which digits are right?

On normal difficulty, no: you only learn how many bulls and cows there are, and the rest is up to your reasoning. On easy, every digit is colored: green is in the right position, yellow is in the number, gray is not in it.

How many guesses do you get?

25 on normal difficulty, unlimited on easy. An experienced player usually needs five to seven.

What difficulty levels are there?

Easy: digits are colored, and games do not count toward your stats. Normal: bulls and cows only, 25 guesses. You choose the level before your first guess.

When does a new daily number come out?

Every day at midnight UTC. The number is the same for everyone, which makes it easy to compare results.

Where are my stats stored?

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