Is it possible to synthesis a global solution from a bunch of local ones? Consider this question in the context of Diophantine Equations. The answer in the degree 1 case starts us on a journey through modular arithmetic to Hensel's creation, the p-adic numbers -- enabling us to define "locally". Historically, the answer in the degree 2 case, the Hasse-Minkowski Theorem, legitimized the use of p-adic numbers. All this sets the stage for the degree 3 case where local solvability DOES NOT imply global solvability. We will mention Selmer's beautiful example, 3x³+4y³+5z³ = 0 , but focus on Reichardt's example 2x² = 1-17y⁴ . Elementary methods allow us to prove that this is locally solvable, but not globally solvable. The only puzzle is "What is inherently global about the 'not globally solvable' argument?"