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