Question

What is Collatz conjecture?Is Collatz conjecture always true? What so special about 3x+1 ? ​

Answer 1

Answer:

Step-by-step explanation:

The Collatz Conjecture is one of the most intreging of all the possible simple statements in mathematics.

Simply put it says

• if a number is even, divide by 2
• If a number is odd, multiply by 3 and add1. or 3x + 1
• The result will always wind up in a loop. Neat huh!!! Where you wind up going over the same numbers over and over. You can't escape the loop.

Try 5

• It's odd so triple it and add 1. You get 16
• 16 is even. Divide by 2. You get 8
• 8 is even. Divide by 2. You get 4
• 4 is even. Divide by 2. You get 2
• 2 is even. Divide by 2. You get 1
• 1 is odd. Triple it and add 1. You get 4. You can see you wind up doing 4 2 1 forever. The Collatz conjecture has not been proved, but every number up to 2^68 has been shown to go to this loop eventually.

Try another one -- 15. On the 16th move it goes from 4 to 2 to 1 and then keeps on repeating those 3 digits.

• Take 15
• It's odd. Triple it and add 1. That gives 46.
• 46 is even. Divide by 2
• 23 which is odd. Triple it and add 1  = 70
• 70 is even. Divide by 2. 35
• 35 is odd. Triple and add 1.  106  which is even
• 53 which is odd.  Triple it and add 1. You get 160
• 160 is even. Divide by 2. You get 80
• 80 is even Divide by 2. You get 40
• 40 is even. Divide by 2. You get 20
• 20 is even. Divide by 2. You get 10
• 10 is even. Divide by 2. You get 5
• 5 is odd. Triple it and add 1. You get 16
• 16 is even. Divide by 2. You get 8
• 8 is even. Divide by 2. You get 4
• 4 is even. Divide by 2.. You get 2.
• 2 is even. Divide by 2. You get 1
• 1 is odd and you are in the loop because you get 4 which you have already done.