Back of Envelope

Tackle wild 'how many?' questions by breaking each into factors you can guess, then multiply them into a single back-of-the-envelope estimate.

How to play

Each question is a Fermi estimation puzzle — a quantity too big to know exactly. Enter a guess for each contributing factor and the game chains them into your total estimate. You're scored on how close you land measured in orders of magnitude, not exact digits. Optionally wager a question to double your points if you finish within 10x — or zero it if you miss.

• Build the answer factor by factor; each one multiplies into the total.
• Landing within an order of magnitude is the real target.
• A breakdown shows how each of your factor guesses compared to reality.

Controls

• Desktop: type each factor into its number field, toggle Wager, then click Submit.
• Phone & tablet: type with the numeric keypad and tap Submit — fully touch-friendly.

Game modes

• Daily: a shared seeded set of questions.
• Practice: fresh randomized questions each round.

Tips & strategy

• Round each factor to a clean power of ten; small errors cancel out across the chain.
• Only wager when every factor feels solid — one wild guess can blow the 10x band.

What you'll learn

Back of Envelope is an estimation game built on Fermi problems and order-of-magnitude reasoning.

• Skills: estimation, Fermi problems, order-of-magnitude reasoning
• Best for: roughly grades 7–12 (ages 12+)
• For parents & teachers: estimating big quantities from little.

About Back of Envelope

Back of Envelope is an estimation game built on Fermi problems and order-of-magnitude reasoning. It's an original free browser game built for PlayPendium.

A free, original browser game on PlayPendium — no download, no install. Browse all games →