Question 1

How do you play 5-Digit Bulls and Cows?

Accepted Answer

A secret code of 5 digits is hidden. You guess, and each guess is scored: one bull for every digit that is correct and in the right position, and one cow for every digit that is in the code but in the wrong position. No digit repeats — every one in the code is different. You have 12 guesses.

Question 2

Is this free? Do I need an account?

Accepted Answer

Free, no account, nothing installed. Everything runs in your browser.

Question 3

How many codes are there?

Accepted Answer

30,240. 10 choices for the first position, 9 for the second, and so on — repeats are not allowed. That figure is worth knowing because it is what the score is narrowing down, and the counter on screen shows you how far you have got.

Question 4

What does the "possible" counter mean?

Accepted Answer

How many codes are still consistent with every score you have been given. It is computed the way you would compute it: a candidate survives if scoring each of your past guesses *against that candidate* reproduces the score you actually got. It never looks at the real code, so it gives nothing away that you could not work out — and watching it fall from thousands to a handful is the moment the game explains itself.

Question 5

What is the difference between a bull and a cow?

Accepted Answer

A bull means right digit, right position. A cow means that digit is in the code but you have put it somewhere else. The scores are not told to you in order — you learn *how many* of each, never which position produced them, and that is the whole game.

Question 6

Can the same position produce both?

Accepted Answer

No. Each position in your guess earns at most one mark, and each digit in the secret can only be claimed once. If your guess has three of a digit and the code has one, you get one mark for it, not three. This is where most implementations of this game go wrong.

Question 7

Can the total ever be more than the code length?

Accepted Answer

Never. bulls plus cows can be at most 5, because between them they are counting digits in a code that only has 5. If you ever see more, something is broken.

Question 8

What is a good first guess?

Accepted Answer

Something that spends its digits widely rather than one that feels lucky. Using 5 different digits is forced here anyway, so pick a spread and start from the middle of the range. The opening guess is for information, not for a hit.

Question 9

Should I ever guess a code I know is wrong?

Accepted Answer

Often, and it is the real skill. If several candidates remain and they differ in ways one guess could test simultaneously, spending a turn on a code that cannot be right will usually cut the field faster than gambling on one of them. Deduction games reward information over hope.

Question 10

What does the Suggest button do?

Accepted Answer

It fills in a code that is consistent with everything on the board so far — one of the ones still in the counter. It is deliberately not the mathematically optimal choice: an optimal suggestion is one you cannot justify from the rows in front of you, and on a game whose whole appeal is working it out, a hint you can follow beats a hint you cannot.

Question 11

Is this the same as Mastermind?

Accepted Answer

Bulls and Cows is the older game and Mastermind is its commercial, coloured version from 1970. Mechanically they are the same puzzle: a hidden sequence, scored by exact matches and misplaced matches. The differences are the alphabet and whether repeats are allowed — which is exactly how this site models them, as one engine with different settings.

Question 12

How few guesses does it take with perfect play?

Accepted Answer

For standard Mastermind — four pegs, six colours — five guesses always suffice, a result Donald Knuth proved in 1977 by working out the strategy that minimises the worst case. Most people take six or seven, which is a perfectly good game.

Question 13

Can I play if I cannot tell the colours apart?

Accepted Answer

Yes. Every peg carries a letter as well as a colour, and the score marks are a filled circle for an exact match and a ring for a misplaced one — a shape difference, not a shade one. Mastermind is the worst case in this whole site for colour vision, because its classic palette pairs a red with a green and the colour is the entire content of a move.

Question 14

Can I undo a guess?

Accepted Answer

You can take pegs back before you submit, but not after. A guess you can withdraw is not a guess, and the score you were given is information you now have.

Question 15

Can I replay the same code?

Accepted Answer

Yes. Every game has a number and the same number always hides the same code, so you can hand someone the link and race them on identical information.

Question 16

Does the game ever lie or change the code?

Accepted Answer

No. The code is fixed when the game starts, from the game number, and every score is computed against it. Some implementations of this puzzle cheat by moving the answer to whatever is hardest — this one does not, and you can prove it by replaying the same number.

Question 17

What happens if I run out of guesses?

Accepted Answer

The code is shown. There is no penalty and no streak to lose — the next game is one button away.

Question 18

Is there a time limit?

Accepted Answer

None. This is a thinking game, and a clock on it would change what it rewards.

Question 19

Can I play on a phone?

Accepted Answer

Yes, and the layout is built around the thing that actually matters here: seeing your history. The board grows to 12 rows and all of it stays reachable, because a deduction game where you cannot review your earlier guesses is not a deduction game. The digit buttons are 56 pixels, which fits comfortably since there are only 10 of them.

Question 20

What other code-breaking games are here?

Accepted Answer

One engine runs all of them: Bulls and Cows, Mastermind, Super Mastermind, 5-Digit Bulls and Cows. Code length, alphabet size and whether repeats are allowed are three numbers, and each game is a point in that space.

Question 21

Where did this game come from?

Accepted Answer

Bulls and Cows is a pencil-and-paper game that predates computing — it was played with numbers long before it had a board — and it became one of the first games written for early mainframes. Mastermind added coloured pegs and sold tens of millions of sets in the 1970s. The puzzle underneath has not changed in a century.