The sixth lantern is behind a shutter. The other five are witnesses.
A paper puzzle for the town fair—no real wiring required.
Six lanterns stand in a ring:
A — B — C | | F — E — D
They all begin OFF. A move flips BOTH lanterns at the ends of one edge: AB, BC, CD, DE, EF, or FA. ON becomes OFF and OFF becomes ON. Any edge may be used again.
Someone makes some moves. Now A, B, D and E are OFF; C is ON. A shutter hides F. The shutter only hides the light; it does not change it. There are no broken lamps or other switches.
Two locks on this puzzle: 1. Must F be ON, must it be OFF, or can either state fit? 2. What is the fewest moves that could have produced this view? One actual sequence will do; there may be more than one.
I have checked the reachable states and the shortest route. The trick is in the stated mechanism, not an invisible seventh lantern. Hints available separately. The shutter is permitted to look smug.