Bulls and Cows

How to play Bulls and Cows

• Bulls and Cows is a code-breaking game: you guess a secret number. The secret number is made of different digits from 0 to 9 (with 4 digits, something like 5072), and no digit appears twice.
• Pick your digits and tap OK. Your guess is compared with the secret number, and you get a count of bulls and cows. A bull is a right digit in the right place. A cow is a digit that is in the secret number but in a different place.
• Get every digit as a bull (4 bulls with 4 digits) to win. The fewer guesses you need, the better.

In the example above, 1 is in the right place, so it is a bull. 3 is in the secret number but in a different place, so it is a cow. You are not told which digit is which.

• Tap a digit under Notes to cycle it through × (not in the number) → ○ (in the number) → blank. Your notes also show on the number keys.
• Stuck? Tap Hint to see how many numbers still fit all your clues. Digits that are certain get marked in your notes.
• Choose 3, 4 or 5 digits. New to the game? Start with 3. The daily puzzle is one puzzle for each length every day, the same for everyone. New ones arrive at midnight Japan time (15:00 UTC).
• On a computer, type digits on the keyboard, press Backspace to delete and Enter to guess. If you close the page, your game is saved so you can pick up where you left off.

Playing against the CPU

• In vs CPU mode, you and the CPU each choose a secret number and take turns guessing each other’s. The first to guess the other’s number wins.
• You guess first. If you get it, the CPU still gets the same number of turns, and if it gets yours too, the game is a draw.
• The CPU has three levels. With 4 digits, Easy needs about 9 guesses on average, Normal about 7 to 8, and Hard about 5.

Playing with a friend (2 players and online)

• 2 players mode is for two people sharing one phone or computer. Player 1 chooses a number first while Player 2 looks away, then hands the device to Player 2, who chooses theirs. Both numbers stay hidden.
• Take turns guessing, starting with Player 1. Bulls and cows are counted for you. After checking the result and making notes, tap “Pass to Player 2” (or “Pass to Player 1”) to switch. Each player has their own notes.
• The first to guess the other’s number wins. If Player 1 gets it, Player 2 still gets the same number of turns, and if Player 2 gets it too, it’s a draw.
• To play a friend who isn’t nearby, choose Online, tap “Create a match link” and send the link to your friend in any messaging app. When they open it, you each play on your own phone or computer. No sign-up needed. Choose the number of digits before you create the link.
• Once you have both chosen a number, take turns guessing, just like a match against the CPU. The person who created the link goes first in the first match, and the first turn alternates with each “Rematch”. Tapping “Quit” in the middle of a match counts as giving up. During a match, your number stays on your device: your device scores your friend’s guesses, and your friend sees your number only when the match is over.
• The link works until 12 hours after the last move. If you close the page, open the same link again to continue.
• To set a puzzle for a friend, tap “Challenge”, choose a number and tap “Send link” (“Copy link” on a computer). Whoever opens the link tries to guess your number, and can send you their result. If your friend is right next to you, choose a number, tap “Let them guess here” and hand them the device.

Tips: how to win at Bulls and Cows

• Start with two guesses that share no digits. With 4 digits, try 0123 and then 4567. The bulls plus cows of each guess tell you how many secret digits it contains, and any that are still missing must be 8 or 9.
• 0 bulls and 0 cows is good news. It rules out every digit in that guess at once. Mark them × in your notes.
• Only guess numbers that fit every clue. Check each new guess against all your earlier results. A guess that could be the answer might win right away, and if not, it still narrows things down.
• Watch the bulls. Bulls tell you about positions. If moving a digit turns a cow into a bull, you have found where it belongs.

There are 5,040 possible 4-digit secret numbers, but with careful reasoning you can find any of them in seven guesses or fewer, and in about five on average.

About Bulls and Cows

Bulls and Cows (also called Cows and Bulls) is an old pencil-and-paper code-breaking game for two players. In Japan the same game is known as Hit & Blow, with hits for bulls and blows for cows. The board game Mastermind, which came later, uses colored pegs in place of digits and works in a similar way. This game follows the classic rules and is not affiliated with the makers of Mastermind (a trademark of its owner). For another number puzzle, try Cryptarithm, where each letter hides a digit.