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Yes, Windows 8.1 runs on a Mac
As I've pointed out elsewhere, there's a big difference between PCs designed for Windows 7 and those made for Windows 8 and 8.1. Nothing shows off those differences like Mac hardware. Apple released a Boot Camp update a few months ago that allows Windows 8 to be properly installed on a Mac. I did that on a Mac Mini just to see for myself.
The more common scenario, of course, is to run Windows on Apple's MacBook Air and MacBook Pro. Still, I can't imagine myself doing that. The keyboard differences alone drive me nuts, and I can't go back to a portable PC (even a beautiful one like a MacBook) without a touchscreen.