jeez! What a load of crap concepts about electricity.
RedShoe, Listen me:
First, you don't need 120 volts to turn 40 LEDs ON. OK?
Second, what I have understood from your question is you want to turn on 40 LEDs and have only 9 volts power source.
Best thing you can do is, connect 3 LEDs in series and make one circuit .. Similarly, make 12 more circuits each consisting of 3 LEDs.
OK, you have 13 circuits with 39 LEDs now. Connect all 'circuits' in parallel and then connect that to 9 volt source. The remaining one LED can be connected directly to 9 volt source via 1k ohm resister.
I am an Electronics Engineer, and I think my input should have weight.
Let me know if you want to reduce the weight of 9 volt source or need any other setup to make this shit work.
