• Combining tools. That can be the combination of a few shell command, or it can be the integration of a blog system into my offline CMS.
• Logical puzzles and riddles like Sudoku or Nonogram both manually and by program
• Quickly coming up with solutions to data munging problems that make all non-perl-programmers gasp
• Solving tricky logic problems with programs
• Making seemingly simple things really useful. For example I maintain (and mostly wrote) the IRC logs for #perl6 and #parrot, and it features far more details than you might see at first, each of which added after a feature request. Not only URLs are turned into links, but also stuff like S03 into S03, revision numbers into links to the appropriate changesets etc. This is mostly not challenging from the programming point of view, the real challenge is to identify what's useful

I'm sure that there are many more that just don't cross my mind right now. Basically everything that makes me think, and that has visible results.

In other words, I like finding problems that require me to think about things in new ways. This is not the same as "I like to learn new things". I am just as happy learning how to solve an old problem in a new way as I outlined in Necessity is the mother of invention. It isn't necessarily important to me that my new knowledge be useful to myself or anyone else. If it has practical application, great.

In addition to finding problems that force me to think about things in a new way, I also enjoy working on problems that I believe are probably beyond my capabilities. I don't know how far I can go until I push myself. Even if I fail, I tend to learn new things along the way and I am happy with that.

The beginning is fun -- I'm faced with a problem or a challenge, I turn a couple of solutions around in my head, drink coffee, try a few pieces of sample code and eventually watch it morph into a solution.

One of my favourites was a mod_perl requester that talked through a pipe to a daemon, making requests. The daemon would spawn an instance of a Big Honking Application for a particular document, get it to do something, pass the result back through the pipe, and keep the child process around for 60 seconds in case another request for the same document came through. Doing a watch on the process tree while the thing was being used was totally awesome, and very satisfying.

Yes, it was all Perl.

Oh, you think there's no programming angle? Actually there is. An important thing for creating a good dinner is time management. All ingredients should be ready at the same time, and if the guests babysitter has to leave at 11, appetisers shouldn't be served at 10.

And we all know many programmers (and other IT people) don't excel in time management. So, if you want to improve your time management (or, in general, resource management; your stove only holds so many pans, the size of the oven is limited, etc), go cook!

There are challenges at different levels. You mention "building infrastructure". Some of the stuff I have enjoyed doing most is of that sort, although more often tool building than library building. It is especially satisfying when everyone on the team uses the result every day and it works so well that it has pretty much disappeared into the woodwork.

Finding elegant solutions to problems of any size. For example, I enjoy challenges related to golf. Not golfing code to obscurity, but golfing it to a point of elegance where it is clean, succinct and clear. Many answers to PerlMonks questions include fragments of that nature. Not always the main part of the answer, but often a clean way of setting up the preconditions for the core part of the answer.

Grand Father's comment resonates a lot. There is something very satisfying about making a solution elegant and balanced (two quite subjective terms), the type of design solution or little code paragraph that just makes you grin...
Pancho

I think most 'programmers' enjoy the same thing. However it is always constrained to some extent by the business for which they work.

Part of the point of programming is solving puzzles.
Just like life.
But we all know, not all puzzles are equal.
Just like... anyway you get the point.

Who doesn't like to make their life easier and more enjoyable. Who wants to repeat the same laborious solution to the same problem over and over again? That's what machines are for!

My favourite challenge is: how much can I get paid whilst not actually having to sit at a desk using a computer? Sadly I am not very good at that particular challenge. I'm still here.

Who doesn't like to make their life easier and more enjoyable. Who wants to repeat the same laborious solution to the same problem over and over again? That's what machines are for!

Based on some of the code and methodology of my coworkers, I'd have to say that this is much rarer than you think. Most of my coworkers are just as happy to hardcode logic in their systems over and over again, which, of course, means solving the same bugs over and over again. Refactoring, data-driven design, or even decent object-oriented style, tooling ... it's all just simply beyond their desire. "No time for it." I keep telling them they don't have time not to do it, but they just don't listen.

So I'm sure they'd love to have an easier life... but they're not willing to work for it. Yet ... it's a challenge I enjoy.

One thing I like is designing interfaces, either user or application programmer. I like balancing useability with power, whittling things down until there is an elegant, simple, and coherent interface that is nonetheless capable of doing everything required of it.

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... ;-)

Well, as of lately, I like any challenge that I am able to solve.

Delving further into my preferences will show I am fond of doing as much as I can to automate anything. Be it a small script to automate a web survey to get me coupons, to a program that downloads all the newest web comics. And so on.

Outside programming I am fond of Cross Sums puzzles and of mazes. When I was a kid, I drew a lot of mazes and was surprised how many people found that hard to do. I don't have the vocabulary for crosswords or the patience for logic problems.

The programming projects I find most enjoyable are web site scraping scripts. I was surprised to find what I would have guessed a mundane task so enjoyable.