Narrowing the hidden number faster
You narrow the hidden number faster by choosing each guess for what its answer can teach you, not for its chance of being right. Every reply rules candidates out, and the quick rounds are the ones where each guess is built so that its two counts — digits right, digits in the right position — can be traced back to a cause.
The hidden number falls fastest when every guess is chosen for what its answer will tell you, rather than for its chance of being right. Each reply from Bulls & Cows — how many digits are right, and how many of them sit in the right position — removes possibilities, and a strong round is one where every guess is built so that its two counts can be traced back to a cause. The rules and the three modes have their own guide; this piece picks up where that one stops: what to do with the answers once you have a few of them, and how to pick the next guess so that it cuts away as much as possible. The rules guide is at /blog/how-to-play-bulls-and-cows/
Think in candidates, not in guesses
At the start of a round the hidden number could be any member of a large set of candidates, and the round is over when that set has one member left. Seen that way, a guess is not an attempt at the answer; it is a question put to the set, and the two counts that come back are a filter. Any candidate that would not have produced exactly those counts is gone, and it stays gone for the rest of the round. The practical test is simple and worth making automatic: before you commit to a number, ask whether it could still be the hidden one — whether, if it were, every guess you have already made would have come back with the counts it actually got. If the answer is no, entering it spends a turn purely on information. That is sometimes a good trade early in a round and almost never a good one late, when a consistent guess can both teach you something and win.
What each answer rules out
Some replies say more than they appear to. The table below lists the patterns worth recognising at a glance, and the move each of them points to.
| What comes back | What it tells you | What to do next |
|---|---|---|
| No correct digits | None of the digits you entered is in the hidden number. | Strike them all from your notes; later they can serve as known blanks. |
| Correct digits, none in position | Some of your digits belong, and every digit you entered is out of the place you tried it in. | Keep the digits, move each one, and never put any of them back in that same slot. |
| Correct digits, some in position | The guess mixes digits that are already home with digits that are misplaced. | Change one thing at a time, so the next answer can say which is which. |
| All digits correct | Composition is solved; only the order remains. | Stop testing new digits and spend every remaining guess on arrangement. |
The second row is the one players misread most often. A guess with several correct digits and nothing in position feels like a failure, but it has told you two separate things at once: which digits to keep, and a set of places where each of them cannot go. Written down, that second half becomes a list of exclusions for every position, and exclusions are how arrangement gets solved without trial and error.
Use a ruled-out digit as a blank
The zero answer in the first row hands you a tool as well as a deletion. A digit you know is absent contributes nothing to either count, wherever you put it. Place one in a guess and that slot goes quiet: whatever comes back is a statement about the other digits only. This is how you make answers attributable without waiting for luck. Suppose you already know which digits belong but not where one of them goes. Fill the rest of the guess with digits you know are absent, place the doubtful digit in a single slot, and the in-position count becomes a plain yes or no for that slot. It costs a turn, but it is a turn whose answer cannot be misread — which is more than can be said for a hopeful guess that changes everything at once.
Settle positions with swaps
Once composition is known, swapping two digits is the cleanest way to learn about arrangement. The correct-digit count cannot change, because the same digits are still in the guess, so all of the information lands on the in-position count. If it rises, the swap put at least one of the two digits where it belongs. If it falls, at least one of them was already home and you have just moved it away — put it back and try a different pair. Swapping digits you have already fixed wastes the turn; swap the ones still in doubt, and check your exclusion list so that neither digit lands in a slot it has already been ruled out of.
Choosing the next guess
- Check it against every earlier answer, not only the last one. A guess that contradicts an old reply is information-only, and should be entered as that on purpose rather than by accident.
- Early, favour coverage; late, favour guesses that could win. The first attempts are for finding out which digits are in play, the last ones for landing the number.
- Skip any guess whose answer you can already predict. If your notes say what the counts will be, the turn teaches you nothing.
- Change one variable per turn when you need a clean reading: one digit in, one digit out, or one pair swapped.
- Keep two lists: the digits known to be in, known to be out and still unknown; and, for each position, the digits already excluded from it.
Reading two answers together
The biggest gains come from pairs of guesses rather than from single ones. Take two attempts that share most of their digits and differ in one. If the correct-digit count moved between them, the change belongs to the digit that was swapped in or out — up means the newcomer is in the number, down means the one you dropped was. If the count stayed the same, either both digits belong or neither does, and one further guess that pairs either of them with known blanks decides which. The same comparison works for arrangement: two guesses with identical digits in different orders differ only in their in-position counts, and the difference points at the slots that changed. Played this way, each new guess is chosen to settle a question the earlier ones left open, and it is that habit, more than any clever opening, that makes rounds shorter.
Where to practise it
Bulls & Cows puts three modes in front of this loop. Single player sets you against an AI opponent, the two-player mode finds you another person through Game Center, and the menu also has a training entry. The reasoning above does not change between them, because the answers are the same two counts in every mode; what changes is who is sitting opposite you. Game Center leaderboards are included, so a round you are proud of can be posted rather than only remembered.
Getting the game
Bulls & Cows: IQ Game is free on the App Store, with version 1.7.5 live since 8 August 2026, and it is available in thirteen languages. It is iOS-only; on Android, the same guess-and-answer core lives in Codex Numbers, whose page is at /games/codex-numbers/ — while the store link for Bulls & Cows, its screenshots and the version currently live are on the game page at /games/bulls-and-cows/