Patterns Can Lie

Test before you trust

An interactive lesson with 6 steps, about 5 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• Points on a circle: 1, 2, 4, 8, 16, then 31. Patterns can break.
• Handshakes among $n$ people: $\frac{n(n-1)}{2}$, backed by a reason.
• A pattern is a conjecture until it is proved.

Steps

1. Points on a circle
2. Six points
3. The surprise
4. Handshakes
5. The next term
6. A famous near miss