Unscrew any one, and they will all go out. Its a series circuit, so Kirchoff's voltage law says that the sum of the voltage drops around the circuit must add up to zero. The open point is infinity ohms, so the voltage across that open point is equal to the source voltage, (Ohm's Law: Volts = Amps * Ohms), and the voltage across the relatively small ohms of each bulb must be zero. Zero volts = zero amps = zero power.
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