Guess the Formula
You're shown a table of x → y pairs — your job is to identify which of four formulas generated the data. Study the numbers, spot the pattern (linear, quadratic, exponential, modulo?), and select the correct formula before time runs out. On Medium and Hard difficulties you can also 'probe' additional x values to gather more evidence.
How to Play Guess the Formula
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Choose Settings
Select Easy (linear only, 5 pairs), Medium (more formula types, 4 pairs), or Hard (all types, 3 pairs). Pick 10-Round Arcade or Survival mode.
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Study the x → y Table
A table of input-output pairs appears. Analyze the pattern — does y grow linearly? Quadratically? Does it involve absolute values or modular arithmetic?
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Probe for More Data (Medium/Hard)
Not sure? Enter an x value in the probe box and see the corresponding y. Use this to test a hypothesis — e.g. probe x=0 to find the y-intercept, or x=-1 to test for absolute value behavior.
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Select the Formula
Click the formula (or press 1–4) that matches all the data points. Correct answers earn 10 base points plus a speed bonus. See the explanation after each round.
Key Features
7 Formula Categories
Linear (y = ax + b), quadratic (y = x² + b), absolute value (y = |x| + b), cubic (y = x³), modulo (y = x mod n), floor division (y = ⌊x/n⌋), and exponential (y = 2^x or 3^x) — a diverse range of function families.
Probe Feature for Extra Evidence
On Medium and Hard, test additional x values to gather more data before committing to an answer. Use 3–4 free probes per question to distinguish between similar-looking formulas.
Plausible Distractors
Wrong choices are never random — they're always from the same formula family as the correct answer (e.g. if the answer is y = 2x + 3, distractors might be y = 2x + 1 and y = 3x + 3), making the game genuinely challenging.
Difficulty Scales Pairs Shown
Easy shows 5 x→y pairs (linear only), Medium shows 4 pairs, Hard shows just 3 pairs across all formula types — requiring maximum deductive reasoning with minimal data.
What is Guess the Formula?
Guess the Formula is a math deduction puzzle where you analyze input-output data pairs and identify the hidden rule that generated them. It's essentially reverse-engineering a mathematical function — a skill at the heart of algebra, data science, and scientific reasoning. Given that y = 4 when x = 1, y = 7 when x = 2, and y = 10 when x = 3, can you deduce that y = 3x + 1? The game covers linear through exponential functions, making it a compelling challenge for algebra students through adults who love math puzzles.
Why Play Guess the Formula?
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Builds Function Intuition
Repeatedly analyzing x→y tables builds an intuitive feel for function families — you'll start to recognize a quadratic growth pattern or an absolute value V-shape at a glance.
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Great Algebra Supplement
Perfect companion to any algebra or pre-calculus course covering function types. It makes abstract function concepts (slope, vertex, modulo) tangible through active deduction.
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The Probe Mechanic Teaches Scientific Thinking
Designing test inputs to distinguish between hypotheses is exactly how scientists and engineers think. The probe feature turns the game into a miniature scientific inquiry.
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From Linear to Exponential
The formula pool spans a broad range — from simple y = ax + b (accessible for middle schoolers) through cubic and exponential functions, keeping it relevant through high school and beyond.
Frequently Asked Questions
What formula types can appear in the game?
Linear (y = ax + b), quadratic (y = x² + b), absolute value (y = |x + a| + b), cubic (y = x³ + b), modulo (y = x mod n), floor division (y = ⌊x/n⌋), exponential base 2 (y = 2^x), and exponential base 3 (y = 3^x). Easy mode limits to linear; Hard mode unlocks all.
How do I use the probe feature?
On Medium and Hard, a 'Test a value' input field appears. Enter any x value and see what y the hidden formula produces. Use this to test hypotheses — for example, probe x=0 to find the constant, or probe x=−2 to check for absolute value symmetry. You get 3–4 free probes per question.
Why are wrong choices plausible?
Distractors are always from the same formula family as the correct answer. If the answer is y = 2x + 5, you might see y = 2x + 3, y = 3x + 5, and y = 2x − 1 as wrong choices. This prevents guessing by formula type alone.
How is the speed bonus calculated?
You earn up to +50 extra points for answering quickly. A 30-second countdown runs per question; answering in the first few seconds earns near the full bonus. The bonus decreases linearly as time passes.
What keyboard shortcuts are available?
Press 1, 2, 3, or 4 to select a formula choice. Press Enter or Space to confirm. Tab moves focus between the probe input and other controls. This makes the game fully keyboard-accessible.