NumGrid vs Bulls and Cows
Before Mastermind. Before Wordle. Before NumGrid. There was Bulls and Cows — a pencil-and-paper number deduction game schoolchildren played in the 19th century. It is the direct genetic ancestor of every modern deduction puzzle, including this one.
The original game
The rules are spartan. Player A picks a 4-digit secret number with no repeated digits. Player B guesses a 4-digit number. Player A returns two numbers:
- Bulls — count of digits in the correct position.
- Cows — count of digits present in the secret but in the wrong position.
A correct guess returns 4 bulls. Play continues until B solves it; the score is the number of guesses used. With 5,040 valid 4-digit no-repeat codes, optimal play averages about 5-6 guesses. The game is playable on a single sheet of paper and has been the go-to long-car-ride number game for over a century.
How NumGrid evolves the format
NumGrid takes the deduction loop and updates it for the daily-puzzle era:
- 5 digits instead of 4. Larger search space (100,000 vs 5,040) but offset by richer feedback and free hints.
- Digits can repeat. The answer might contain two 3s or three 0s; this adds expressive range and forces you to read feedback more carefully.
- Per-position feedback. Each digit in your guess gets its own color — green (right digit, right spot), yellow (right digit, wrong spot), gray (not in answer). The Bulls and Cows counts told you how many; NumGrid tells you which.
- Two free hints every day. The digit sum (0-45) and parity (odd/even) of the answer are revealed before you guess. This collapses 100,000 candidates to roughly 1,000-3,000.
- One puzzle per day, shared with the world. The daily-puzzle structure adds the social and collection dynamics that paper-and-pencil could never provide.
The strategic upshot
Bulls and Cows is a memory + deduction game. Because the feedback is anonymous, you have to track hypotheses in your head: “If position 1 is the bull, then position 2 must be a cow that…” The cognitive load is high. Solvers benefit from writing candidate lists.
NumGrid is a constraint-narrowing game. The per-position feedback collapses ambiguity fast. The free hints make the first guess strategic rather than blind. You can solve NumGrid in your head; you usually cannot solve Bulls and Cows in your head past turn 2.
Try it old school
If NumGrid feels too easy, play it Bulls and Cows-style: ignore the digit sum and parity hints, ignore the green/yellow/gray, and only count how many digits are right (bulls) and how many are present but misplaced (cows). With those self-imposed constraints, NumGrid becomes considerably harder — and the historical lineage of the game becomes obvious.
The lineage in one paragraph
Bulls and Cows (19th century, paper) → Mastermind (1971, plastic pegs, anonymized feedback) → Wordle (2021, letters, positional feedback) → Nerdle / Numberle (2022, digits, positional feedback) → NumGrid (2026, digits + free hints, daily). Each step adds either expressive structure, feedback richness, or social distribution.
FAQ
What is Bulls and Cows?
Bulls and Cows is a paper-and-pencil deduction game dating to at least the 19th century. One player picks a 4-digit secret number with no repeated digits. The opponent guesses, and feedback comes as two counts: bulls (correct digit in correct position) and cows (correct digit in wrong position). It is the direct ancestor of Mastermind (1971) and the conceptual ancestor of NumGrid (2026).
How is NumGrid different from Bulls and Cows?
Three big differences. (1) NumGrid uses 5 digits, Bulls and Cows uses 4. (2) NumGrid allows repeated digits in the answer; classical Bulls and Cows does not. (3) NumGrid gives per-position feedback (green/yellow/gray attached to each digit you guessed) and two free hints (digit sum, parity); Bulls and Cows gives only the anonymous bulls/cows counts.
Is Bulls and Cows harder than NumGrid?
Yes, per puzzle. The anonymous feedback in Bulls and Cows makes deduction harder. But Bulls and Cows has a smaller search space (5,040 codes with no repeats vs NumGrid's 100,000) so an expert can still solve it in about 5-7 guesses on average. NumGrid feels easier because the free hints and per-position feedback narrow the space much faster.
Why is the game called Bulls and Cows?
No definitive origin, but most accounts trace the cattle metaphor to British schoolboys of the late 1800s: a "bull" is a direct hit (correct digit, correct slot), a "cow" is partial credit (correct digit, wrong slot). The metaphor stuck because the imagery makes the abstract feedback memorable for children.
Want to feel the 150-year evolution in your head? Start here: play today’s NumGrid puzzle →
Related reading: NumGrid vs Mastermind for the 1971 board-game version, or How to play NumGrid for the rules in two minutes.