Start with any positive integer \(n\). Then each term is obtained from the previous term as follows: if the previous term is even, the next term is one half the previous term. Otherwise, the next term is 3 times the previous term plus 1. The conjecture is that no matter what value of \(n\), the sequence will always reach 1.
For example, starting with \(n = 12\):
You get the sequence: \(12, 6, 3, 10, 5, 16, 8, 4, 2, 1\). (10 steps)