The Power of Doubling

Exponential beats everything

An interactive lesson with 7 steps, about 6 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• Doubling $n$ times multiplies by $2^n$; it starts slowly, then explodes.
• $2^{10} \approx 10^3$: every 10 doublings is about a thousandfold.
• Halving $n$ times multiplies by $2^{-n}$.

Steps

1. Grains on a chessboard
2. A million grains
3. The last square
4. Lily pads
5. More than all the rest
6. Ten doublings, a thousand
7. Halving