MHB What rule is used to receive number 1

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The discussion revolves around a mathematical process applied to a positive integer "n" where if n is even, it is halved, and if odd, either 3n + 1 or 3n - 1 is chosen. Participants question whether this process will always lead to the number 1 after multiple iterations. The conversation references the Collatz conjecture, which posits that all positive integers will eventually reach 1 through this method. Examples illustrate the steps taken from various starting points. The consensus is that while the conjecture remains unproven, it has been observed to hold true for many integers.
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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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This problem has been discussed recently in https://driven2services.com/staging/mh/index.php?threads/16219/.
 

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