The first circuit I remember was in school, more or less try an error putting together 4.5 V batteries, lamps and switches. We somehow ended up in funny version that used 2 batteries, 2 lamps and a single, single simple switch in a way that either one or the other lamp was active. It took me very long to find out how this could work and for this reason I still remember.
Probably this is still a nice puzzle for the beginners.
In simple switch, you mean a classic SPST switch?
2 Voltage sources, 2 lamps, a single spst switch, that either state turns only one lamp. that's the puzzle?
When I was about 10 our house was extended and a new hallway got a light switch at each end such that, of course, flipping the switch at either end would flip the state of the lights. That was fascinating!
You can do it using two SPDT switches and two conductors between the switches (and a 3rd that goes to the actual lamps), but I noticed the switches being installed were actually DPDT.
I sat down with pencil and paper and figured out that with DPTP switches you can actually generalise this to an arbitrary N switches! I wired this up with 4 or 5 as yet not installed switches and a 6V lantern battery and torch bulb and demonstrated to the electrician that flipping any of the switches flipped the bulb state. He was stunned :-)
I don't know if I've ever seen N>2 in the wild, so this result may not be well known.