What rule is used to receive number 1

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The discussion centers on the mathematical process of reducing a positive integer "n" to the number 1 using specific rules. If "n" is even, the next number is calculated as n / 2. If "n" is odd, the next number can be either 3n + 1 or 3n - 1. The consensus is that this process will always lead to the number 1, as demonstrated through the example starting with 20, which sequentially reduces to 1. The underlying rule is based on the Collatz conjecture, which posits that all positive integers will eventually reach 1 through this iterative process.

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anre
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On the board is written the number of positive integer "n". In next step we write a new number. If n is even, then we write the number n / 2. If n is odd, then select the 3n + 1 or 3n-1 and write on the blackboard. Can we get the number 1 (always) after many steps ? and why? What rule is used ?
For example:
20 (n / 2)
10 (n / 2)
5 (3n + 1)
16 (n / 2)
8 (n / 2)
4 (n / 2)
2 (n / 2)
1
 
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Not sure. but I know I have to find LCD
 
This problem has been discussed recently in https://driven2services.com/staging/mh/index.php?threads/16219/.
 

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