A Hundred Bulbs, 482 Flips, and Ten Survivors
Person k flips every bulb that is a multiple of k, and after a hundred passes exactly the ten perfect squares are lit. Bulb n is flipped once per divisor, and the pairing d against n/d is fixed-point free unless n is a square, so the parity is decided by algebra rather than by accumulation. The lit fraction is one over the square root of the row, and stopping the process at person 50 inverts the answer to 54 bulbs.