You think you are an expert? How does this work (UPDATED with solution):

[Lightages]

Instead of making us search for the answer, why not provide it in your post here too!

[Wartex]

Official solution:

You crafty SOB! I knew the coil was around the LED, assuming it was really thin wire, but he went even further and filed a channel around the LED to hide it. The generator and all components fit in the battery connector - battery was unmodified just like he said.

[vk6zgo]

My head hurts!

VK6ZGO

[johnwa]

I saw this a while ago, and managed to come up with an equivalent circuit, but I only got as far as building it up on a breadboard. (I had seen the solution for two switches and lights a while ago.) I hadn't really looked into the physical constraints on component size - I presumed that there was just a chip inductor across the third LED - but the necessary values may not actually be available that small. Winding the coil round the LED is a neat trick!

I thought this puzzle was quite a nice exercise - it is not so much about the solution itself, as seeing if you can figure it out for yourself. Perhaps we should have some electronic related puzzles here on the forum for people to think about. Something along the lines of what they used to publish in 'Electronics Australia'?

John