Peter Hickman wrote: > Problem is that from the quiz it states that you either get a 1 or an > infinite loop and that an unhappy number is "obvious". Which is a sign > that something has not been explained clearly. Given that the Wolfram > page was clearer than the quiz at to what constitutes happy don't be > surprised if some people go off down the wrong path. As I understand the Wolfram article, an unhappy number never hits 1 as a result, whereas a happy number eventually hits 1: "Unhappy numbers have eventually periodic sequences of s(sub)i which never reach 1." The quiz item emphasizes a criterion that is only mentioned in passing on the Wolfram page, that is, there are degrees of happiness, and a number that has many happy predecessors is, umm, more happy. So a relatively large number that eventually results in 1, but with a lot of steps along the way (therefore more happy ancestors), is happier. -- Paul Lutus http://www.arachnoid.com