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In a moment I will ask you a puzzle and its a pretty hard puzzle actually. But before I do, I want to lead with a spoiler, which is the fact that the way were going to solve this involves the use of complex numbers. And once you hear it you will agree that that seems absurd given that the puzzle is going to be purely a discrete question. It only asks about whole numbers and their sums, theres not a whiff of the imaginary or even continuity anywhere on the horizon. Its certainly not the only time that complex numbers are unreasonably useful for discrete math to borrow a phrase. The more famous example that I could bring up would be how the modern way that mathematicians understand prime numbers, you know questions about how theyre distributed their density at certain regions things like that, well it involves studying specially designed functions whose inputs and outputs are complex numbers. Some of you may know that this is what the famous Riemann hy