Yup.... sure enough, the cap would work just fine. Man, this is a devious little puzzle.
Now I want to make one of these, put it in a nice Lexan box and confuse others. I have the pars laying around in the junk pile. I'll probably use neon bulbs instead of incandescents just too keep the contraption small.
I'm going to laugh if my professor puts this as a bonus question on a test in my Circuit Analysis & Design class.
I have seen some lamp designs that have a full wave rectifier and cap to reduce flicker but I honestly haven't had a noticeable flicker issue with incandescent lamps. The filament never has time to cool durning the tiny amount of time the voltage drops to zero in the sine wave.
How is it possible that a little circuit like this is so hard to understand? It's probably because I have never seen anything so weird! Is this a purely theoretical circuit or was a commercial design based on it?