I think the OP was saying "what if the original solutions posted in this thread were used for <insert really large number here> bulbs?". The solutions posted near the top of the thread relied on walking the list numerous times, which is infeasible if the list is super large. The elegance in finding the mathematical property for the bulbs being on is that it does
Feel the white light, the light within
Be your own disciple, fan the sparks of will
For all of us waiting, your kingdom will come
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