Strongly suggest against 'most complex way to light an LED' approach.
Good applied engineering is all about the simplest/cheapest/best way to do a job.
If the simplest is a 9v battery and a 470 ohm resistor, then why should I be interested in something more complex? Especially if it's my company's resources and profit margin at stake?
The point is not to make a clock, the point is that to show that you can make something useful, rather than just something weird to show you can do it. The closer to "production" quality you can make it, the better you'll be able to show yourself off.
I'd go further. Maybe show that you have:
* Defined a problem, requirement or need
* Surveyed how others have done it
* Evaluated the shortcomings of these approaches or an extra feature you'd like
* Designed and constructed something that offers some benefit (eg simpler, cheaper, better) based on what was learned above
Let's take the 9v battery/resistor/LED approach as an example, pick it apart and see if we can make it better. This isn't hard as it has many problems. Eg 9v batteries are too expensive. The 20mA's LED current may be too high. The LED might not be bright enough. The resistor may dissipate (waste) current. The upshot after all this refinement may be a bright LED torch that runs nearly forever on an AA battery (maybe using an efficient switching regulator and better LEDs).
I wouldn't necessarily suggest an LED torch as a project, but this approach is more useful than designing a convoluted way to do the same thing without regards to simplicity or efficiency.
Another possibility is to find a circuit that someone's already done, build it and make it better/cheaper/simpler. Then document it (preferably as you go along). It might not be as 'creative' as starting something from scratch. But it doesn't need to be to be worthwhile if there's some other benefit.
Read here about 'Madman Muntz'. The engineer who made his millions from snipping out unnecessary parts in TVs.
http://en.wikipedia.org/wiki/Madman_Muntz