I had one of these brainteaser questions in an interview once, and I liked my mathematician friend’s answer to it the best. Q: Given infinite setup time and infinite money, how would you fill the inside of a 747 with ping pong balls as quickly as possible? A: Define the inside of the plane as the exterior. Now, by definition, all ping pong balls are inside the plane. QED.
I use my infinite resources to become benevolent dictator of Earth.
With my endless wealth I prevent climate change, provide the basic needs of every person on the planet, educate the world, and set up a global system of sustainable reproduction. I have infinite resources so I assume it's not eugenics or something dystopian, but more a collective human understanding of responsibility. Finally, with our future ensured, I dedicate as many of the world's top minds as possible to preserving my own life at any cost.
Once I have achieved immortality, likely by transplanting my mind into a robot body that can be updated over time so I remain the most advanced being on the planet, I steer the course of human history far into the future. All human suffering is ended. We all work as one to better ourselves. We spend decades, centuries, millennia improving not only our society, but our technology for inserting ping pong balls into 747s.
Under my kind leadership as an immortal god-king of increasingly sophisticated artificial intelligence, humanity becomes the dominant species in a surprisingly crowded universe. With each new species we meet, we find new allies in our advancement. Entire galaxies unite under my rule and never-ending resources, each furthering my transcendence of life and the speed at which we can put small plastic balls into extremely archaic public transportation.
Finally, at the far end of time, when there is nothing left to learn, no secret of the universe left unknown to me—I am now a single bio-mechanical entity composed of all intelligent life in existence—my setup is complete. Using technology so advanced that it cannot be described by words we have so far invented, technology so unimaginable it exceeds the power we ascribe to magic, I fill the plane. It is instantaneous. There is no time during which the plane is being filled. There is only before and after it was filled.
The creator of the universe descends on its final moments. The being sees the plane. It weeps for the beauty its children have created.