The Collatz Conjecture

Let's play with numbers!

So first, think of a number. Any number will do.

Thought of it? If it is even then divide it by 2.

And if it is odd, then multiply it by 3 and then add 1 to it.

Now, repeat this process with the number you get until the end.

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Finished? Now tell me, what number do you get?

Is it 1? Surprising, isn't it?

If you do these two operations with any number, then at the end of the road, you will always get 1.

This is what we called the Collatz conjecture.

It is named after mathematician Lothar Collatz, who introduced the idea in 1937.

Do you think that all numbers follow this rule? If yes, is there a proof?

We all know that in mathematics, a statement without proof is not believed to be true even if it seems a truth. You never know when a rule or theorem become false.

Unfortunately, no one has ever proved this conjecture yet.

Although in September 2019, news broke regarding progress on this 82-year-old question, thanks to prolific mathematician Terence Tao. And while the story of Tao's breakthrough is promising, the problem isn't fully solved yet.

Also, this conjecture has been verified for numbers less than 2^68. 2^68! Do you know how unimaginably high this number is? It is approximately 300 quintillion.

So, do you think you can prove it? Do try it. Even if you fail, it will definitely improve your thinking and problem solving abilities.