Start with any natural number. If it is even, divide by two, if odd, multiply by three and add one. Repeat the same method on the new number, and the one after that, so on. Eventually you should reach one, no matter what number you started with.
eg. 6 -> 3-> 10 -> 5 -> 16 -> 8 -> 4 -> 2 -> 1
How can you prove that this is true?