Closed-Form Solution for a Zigzag Number Spiral

This article tackles a mathematical puzzle involving an infinite grid of numbers arranged in a spiral pattern that reverses direction at each grid edge. By analyzing patterns along the spiral's edges and diagonal, the author derives a closed-form expression, (f(m, n) = (max(m, n))^2 - max(m, n) + 1 + (-1)^{max(m, n)} (m - n)), to calculate the number at any position (m, n) in the grid. The article meticulously details the derivation, including analysis of edge and diagonal numbers, and the process of transforming a piecewise function into a single closed-form expression.