What exactly is Collatz Conjecture?

This is a problem that is simply stated, easily understood, and all too inviting. Just pick a number, any number: If the number is even, cut it in half; if it’s odd, triple it and add 1. Take that new number and repeat the process, again and again. If you keep this up, you’ll eventually get stuck in a loop. At least at present, we think that happens.

Take 10 for example 10 is even, so we cut it in half to get 5. Since 5 is odd, we triple it and add 1. Now we have 16, which is even, so we halve it to get 8, then halve that to get 4, then halve it again to get 2, and once more to get 1. Since 1 is odd, we triple it and add 1. Now we’re back at 4, and we know where this goes: 4 goes to 2 which goes to 1 which goes to 4, and so on

The conjecture is named after Lothar Collatz, who introduced the idea in 1937, two years after receiving his doctorate.

Lothar Collatz likely posed the eponymous conjecture in the 1930s. The problem sounds like a party trick

This problem is easy to understand, think and try to solve it. It is endless to solve whether number it is true as it is tested for 2^68 and if you really want to test if it is correct then try it after 200 Quadrillion no.

After we do the required steps then after we end in a loop that we get 1 and as that is odd so 3 x 1 + 1 = 4, So. it again 4 and then 2 then 1 and again 4. This loop never ends.

“This is a really dangerous problem. People become obsessed with it and it really is impossible,” said Jeffrey Lagarias, a mathematician at the University of Michigan and an expert on the Collatz conjecture.

 

This is what it really looks like

On September 8, Terence Tao posted a proof showing that — at the very least — the Collatz conjecture is “almost” true for “almost” all numbers. While Tao’s result is not a full proof of the conjecture, it is a major advance on a problem that doesn’t give up its secrets easily.