"Perhaps you've heard of Thompson's Lamp. This is an IDEAL lamp, capable of INFINITE switching SPEED and using electricity that travels at INFINITE SPEED."
Is it pedantic of me to point out that this is an IDEAL lamp, i.e. one which only
exists as an idea, and one which, because of its transcendence of the speed of light, can never exist in our universe?
Therefore, there are probably many fanciful or mathematical answers which work within one ideal, abstract, mathematical model of the situation or another. These models must all be incorrect models of known reality however.
I'm with Hal. The question doesn't mean anything about the real world.
This just means I'm too lazy to try to figure it out, but sometimes that's the right answer.