Paul Lutus wrote:
> 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:

What you have described here is the halting problem. Good luck with that.

> "Unhappy numbers have eventually periodic sequences of s(sub)i which never
> reach 1."

And what stops it from being a 1x10^50 length period, or any arbitrary 
length?

> 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.

And what the quiz neglected to mention is that there is an easy test for 
unhappy number, which the mathworld page enumerates:

	Iterating this sum-of-squared-digits map always eventually
	reaches one of the 10 numbers 0, 1, 4, 16, 20, 37, 42, 58, 89,
	or 145 (Sloane's A039943; Porges 1945).

So if you hit one of those unhappy numbers you know you're in an unhappy 
loop.