- Take any number
- if it is even, halve it;
- if it is odd, multiply it by 3 and add 1 and then halve it.
- repeat these operations until you reach the number 1.

For example, starting with the number 5:

5 is odd; 5 x 3 = 15; add 1 : 16

16 ÷ 2 = 8 (step 1)

8 is even; halve it : 4 (step 2)

4 is even; halve it : 2 (step 3)

2 is even; halve it: 1, and stop. (step 4)

Taking it for granted that we will always reach the number 1 in the end, is there a connection between the number of steps required to reach the number 1 and the number we started with? Here, if S(n) stands for the number of steps when we start with n, S(5) = 4.

(Taken from Dozenal Review no. *32)