The Collatz Conjecture

A simple rule nobody understands

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

• Collatz: halve evens, triple odds and add 1. Does every number reach 1?
• Paths rise and fall unpredictably: 27 takes 111 steps.
• Verified for enormous numbers, but still unproved.

Steps

1. Half or triple plus one
2. Hailstone numbers
3. Count the steps
4. Starting from 6
5. Nine’s journey
6. Is it proved?