Great discussion here — I found the insight about there being only eight valid 3×3 magic squares for the numbers 1-9 very helpful. That fact really simplifies the problem by turning it into a fixed comparison set. On a somewhat different note, while I was reading this I reflected on how the same principles of user-experience and efficient logic apply across tech domains. For example, I recently checked out the Black Hole Music APK — an Android app that emphasises smooth UI, ad-free listening, and high-quality audio. It reminded me that whether you’re solving a coding puzzle like designing a magic square or building a music app, attention to detail, performance, and clarity make the difference.

Thanks for sharing all these approaches — they’re really helpful for understanding both the math and the implementation side of algorithmic challenges!