Basically, the challenges I most enjoy are those that are... well... most challenging. Wait, no. Not climbing Nuptse. More those which need skills I have, and then of those, they which need hidden skills I have. Like mastering perl, for some degree of mastering (yes, most of those who present me something as a challenge regard perl as something obscure, not enterprise ready, write-only etc.), or gut thinking.

Gut thinking? Yes. That vegetative apparatus is as complex as the brain, and perceiving the interaction of both is exciting. I've perceived that introducing myself to SunOS4.1.3 UNIX. There are no explanations, there are just references. I ate manpage after manpage, and followed each SEE ALSO and then each SEE ALSO there. None of that made sense. But somehow ruminating over all that, things fell into place. I don't know which is greater, the actual knowledge of details or the unconscious big picture.

So, over the time, I have a belly of knowledge which can't be realized but on demand.

The most enjoyable challenge is a broken system which I don't know, infested with a heisenbug - solve that.

P.S.: well, the above written applies to the realm of computers and programming. Elsewhere:

Entzieh dich nicht dem einzigen Geschäfte
vor dem dich schaudert; dieses ist das deine.
Nicht anders sagt das Leben was es meine,
und schnell zerwirft das Chaos deine Kräfte.

Do not elude the only single task
which makes you shiver; it's yours by rigour.
Life only then responds to what you ask
but chaos quickly will disperse your vigour.

Hugo v. Hoffmannsthal, translation shmem

Enjoying that challenge is already mastering it... ;-)