Number Patterns and the Collatz Conjecture
Class 6 Maths · Chapter 3: Number Play · NCERT Ganita Prakash section 3.9–3.10
Learn
When numbers come in a pattern, look for pairs before adding one by one: 20 + 20 + 45 + 45 + 30 + 30 = 2 × (20 + 45 + 30) = 190.
2 × 95 = 190
The Collatz rule: if a number is even, take half; if it is odd, multiply by 3 and add 1. Keep going.
The mathematician Lothar Collatz asked in 1937: does this rule always reach 1, whatever number you start with? Computers have checked huge numbers and they all reach 1, but nobody has proved it. It is still an unsolved problem!
Try your favourite numbers. Does each one reach 1?
Remember
- Collatz: even → half; odd → 3 × n + 1.
- A conjecture is a guess that nobody has proved or disproved yet.
Quick check
Collatz rule: what comes after 7?
- 14
- 22
- 21
- 3
Answer
22. 7 is odd: 3 × 7 + 1 = 22.
Think about it
Why does the Collatz rule always reach 1 for the powers of 2 (1, 2, 4, 8, 16 …)?
One answer
They are all even, and half of a power of 2 is the power before it: 16 → 8 → 4 → 2 → 1.
Practice
Practise with fresh questions at three levels (easy, medium, hard), some answered hands-on, with hints and worked answers. Get 4 of your last 5 right to finish the topic.