Class 6 Mathematics | The Amazing Collatz Conjecture – A Math Mystery! #eduvictors

Class 6 Maths | The Amazing Collatz Conjecture – A Math Mystery! 

What is the Collatz Conjecture?

Have you ever played with numbers and discovered an intriguing pattern? The Collatz Conjecture (also known as the 3n + 1 problem) is a renowned unsolved mathematical puzzle that even the brightest mathematicians have yet to solve!

Here’s how it works:

1. Start with any positive whole number (like 5, 12, or 20).

2. If the number is even, divide it by 2.

3. If the number is odd, multiply it by 3 and add 1.

4. Repeat the steps with the new number.

No matter what number you start with, you’ll always end up reaching 1! Or at least, that’s what mathematicians think happens—but nobody has proven it for every number yet!

Let’s Try It!

Example 1: Start with 6

6 is even → 6 ÷ 2 = 3

3 is odd → 3 × 3 + 1 = 10

10 is even → 10 ÷ 2 = 5

5 is odd → 5 × 3 + 1 = 16

16 is even → 16 ÷ 2 = 8

8 is even → 8 ÷ 2 = 4

4 is even → 4 ÷ 2 = 2

2 is even → 2 ÷ 2 = 1

We reached 1

Example 2: Start with 7

Can you work it out? Try it yourself!

Answer: 

Collatz sequence for 7:

7 -> 22 -> 11 -> 34 -> 17 -> 52 -> 26 -> 13 -> 40 -> 20 -> 10 -> 5 -> 16 -> 8 -> 4 -> 2 -> 1

Length: 17 steps

Why is This a Mystery?

Mathematicians have tested billions of numbers, and they all eventually reach 1. But nobody knows if every number follows this rule. Maybe there’s a huge number out there that never reaches 1—we just haven’t found it yet!

Fun Exercises to Try

Find the sequence

Start with 10. How many steps does it take to reach 1?

Answer:

Collatz sequence for 10:

10 -> 5 -> 16 -> 8 -> 4 -> 2 -> 1

Length: 7 steps

Conclusion

The Collatz Conjecture is a simple but unsolved math problem. It shows that even easy-looking puzzles can be super tricky! Maybe one day, you will be the mathematician who solves this mystery!