A deep dive into magic squares: from ancient roots in China and India to modern theory. We unpack odd, singly-even, and doubly-even orders, classic construction methods (De La Loubere / Siamese), pandiagonal patterns, and Euler's Greek-Latin superposition, plus bordering and other variants like multiplicative and multi-magic squares. We'll also discuss key limitations (why 2×2 is impossible and where Euler's method fails) and highlight open questions in this timeless combinatorial world.

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