There are n bulbs in a room and some switches such that each switch is connected to a specific element in power set of except the null set. Each switch on pressing changes the configuration of the bulbs from on to off or off to on (depending on the initial state of the bulb). Prove that we can always light all the bulbs in at most \( 2^{n-1} + 1 \) moves if initially, all the bulbs are off.
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