Bulls & Cows — Teachers’ Guide

Bulls & Cows is a classic number-deduction game (a predecessor to Mastermind). Students use feedback — bulls (right digit, right place) and cows (right digit, wrong place) — to infer a secret 4-digit code. It’s a natural fit for reasoning, patterns, and efficient search.

Curriculum Links

• Logical reasoning and argumentation
• Number sense and place value
• Combinatorics and search strategies
• Data interpretation (using feedback to guide choices)

Classroom Setup Options

How to Play (Quick)

1. Enter a 4-digit guess with no repeated digits (unless a mode allows repeats).
2. Read the feedback: Bulls (right digit, right place) and Cows (right digit, wrong place).
3. Eliminate impossibilities and refine your next guess.
4. Reach 4 Bulls to win.

Effective Solving Strategies

• Cover more ground early: Start with four distinct digits (e.g., 1 2 3 4) to maximise information.
• Eliminate digits fast: A 0-Bull/0-Cow result removes those digits entirely.
• Localise positions: With 2 Cows, rotate those digits to test positions systematically.
• Control variables: Near the end, change only one or two digits per guess so feedback is clear.
• Record attempts: Keep a simple grid of digits/positions; the attempts table in the UI helps.
• In Bull Rush: Use all five clues together — they’re designed to narrow to a single consistent code.

Teach with Pencil & Paper

Bulls & Cows works beautifully as an unplugged classroom activity — no devices required. Students can work in pairs or small groups to practise logic and deduction.

1. Choose a secret number: One student writes a 4-digit number with all unique digits (no repeats).
2. Make a guess: The other student writes a guess — also 4 unique digits.
3. Give feedback: The “host” counts Bulls (right digit, right place) and Cows (right digit, wrong place) and tells the guesser.
4. Refine and repeat: Students keep guessing, using feedback to eliminate possibilities, until they reach 4 Bulls.

Tip: Provide a simple tracking grid so students can mark which digits/positions are still possible.

Generate Custom Puzzles with Haystack

Haystack lets you create your own Bulls & Cows-style challenges in seconds — perfect for tailored practice, extension work, or quick bell-ringers.

• Pick a difficulty: Choose from Easy, Medium, or Hard. Each setting balances digits and number of given clues to tune the challenge.
• One-click share: Each generated puzzle has a unique link you can paste into your LMS, slide deck, or email.
• Play or print: Students can solve online (with keypad and attempts table) or you can print the generated clue set for a no-tech activity.
• Classroom ideas: Assign different groups different difficulties; compare strategies; have students design “fair” puzzles and swap.

Suggestion: Start the class with an Easy puzzle for confidence, then move to Medium or Hard for deeper reasoning.

Under the Hood: How Bull Rush Builds a Unique Daily Puzzle

Bull Rush ensures every learner sees the same daily challenge and, with careful reasoning, can deduce one unique answer:

• Daily seed: The date acts like a recipe — it produces the same 4-digit secret (no repeated digits) for everyone that day.
• Clue creation: The game tests sets of five example guesses and keeps them only if those five lines, taken together, leave exactly one possible solution in the whole search space.
• Uniqueness check: If more than one code fits, the set is rejected and a new set is tried — until there’s a single provable solution.
• Persistence: A small local record lets students revisit that day’s puzzle and see the same clues and result.

Classroom win: two different classes (or home and school) can discuss the same logical puzzle and compare strategies.

History

Bulls & Cows began as a pen-and-paper code-breaking pastime whose exact origin is murky but is often traced to at least the early 20th century. It spread under different names—“Bulls and Cows” in English, быки и коровы across the USSR, and “Hit & Blow” in Japan—and the core idea (counting correct digits in the right place vs. the wrong place) predates the commercial board game Mastermind by decades. Word-based cousins such as Jotto (1955) show how the same deduction loop migrated between numbers and letters.

The game jumped to computers in the late 1960s as MOO: a version on Cambridge University’s Titan (1968) inspired early ports for Multics (1970), Unix, and DEC systems, making it a fixture on timesharing computers. Around the same era, a lighter three-digit variant, Bagels (with “fermi/pico/bagels” feedback), circulated widely and appeared in 101 BASIC Computer Games (1973), helping cement the mechanic in programming culture and classroom labs.

Mastermind (1970) reframed the pencil-and-paper logic into pegs and colors and went on to sell widely, popularizing the idea for mass audiences. Since then, Bulls & Cows has persisted in classrooms, puzzle books, and apps—its deductive template echoing in TV formats like Lingo and, more recently, daily word-puzzle phenoms.

References (APA)

• Bulls and cows. (2025, August 16). Wikipedia. Retrieved October 14, 2025.
• Grochow, J. M. (1972). Comment: MOO in Multics. Software: Practice and Experience, 2(3), 303–304.
• AT&T. (1983). MOO(6): Guessing game [Unix System V manual page].
• Ahl, D. H. (1973). 101 BASIC computer games. Digital Equipment Corporation.
• Mastermind (board game). (2025, September 26). Wikipedia. Retrieved October 14, 2025.
• Jotto. (n.d.). Wikipedia. Retrieved October 14, 2025.
• Lingo (American game show). (2025, August 11). Wikipedia. Retrieved October 14, 2025.
• Ritchie, D. (2001). Ken, Unix, and games. ICGA Journal, 24(2), 67–70.

Pico • Fermi • Bagels

Pico • Fermi • Bagels is a three-digit version of the Bulls & Cows logic puzzle that became a staple of early computer labs and classrooms. Players try to discover a secret number using only feedback that tells them how close each guess is:

• 🎯 Fermi — a correct digit in the correct place
• 🟡 Pico — a correct digit, but in the wrong place
• 🥯 Bagels — none of the digits appear at all

The name comes from a playful mix of references: “Pico” and “Fermi” were borrowed from scientific prefixes and physicists (the “pico-” scale and Nobel laureate Enrico Fermi), while “Bagels” was added for humor to mean “zero — nothing there.” The term appeared in early programming books such as 101 BASIC Computer Games (1973), where it was used to teach loops, logic, and conditionals in beginner code.

Because the numbers are short and distinct, Pico • Fermi • Bagels is ideal for classroom warm-ups in reasoning and elimination. Students can play together on the board, use printed grids, or solve the daily online challenge to compare strategies.

Connect & Motivate

Encourage sharing results (emoji grids) and checking the global leaderboard to see how they compare with players around the world.