Well, the Buridan's ass paradox is a pretty simple one. Basically, it goes like this:
Suppose there is an ass that is both hungry and thirsty, to an equal degree. There is a pile of hay to one side and a trough of water to the other side. Neither takes more effort to reach. Since the ass is equally hungry and thirsty, then there is no rational reason for him to turn one way instead of the other. The unfortunate conclusion is that the ass neither eats nor drinks and eventually dies of a combination of hunger & thirst.
Whelp. There's one ass that won't be carrying any more Buridans. *rimshot*
Anyway, I hate to rain on your parade, but it would a trivial undertaking for God to simply use the Many Worlds Interpretation of quantum mechanics to regenerate the limb from the body in one bifurcation of the Cosmos, and regenerate the body from the limb in another.
This is similar to (although not the same as) the timing and deadlock issues we see with electronic components and computer programs that are by nature deterministic. When the circuitry cannot reliably determine the appropriate course of action it halts. For example, in the case of an input voltage exactly halfway between a 1 and a 0, the comparator may not reliably determine the appropriate state.
So in other words, Captain Kirk could talk God to death:
Kirk: Almighty God--you would agree with me that a cat has--one more tail--than no cat, would you not?
God: WORK-ING! *rattling SFX, blinking lights* YES.
Kirk: Would! You agree that--no cat has eight tails?
God: WORK-ING! *rattling SFX, blinking lights* YES.
Kirk: Therefore--eeeevery cat! Has! Nine tails!
God: *rattling SFX, blinking lights, sparks, curliques of smoke* ERR-OR! ERR-OR! DOES NOT COMPUTE! DOES NOT COMPUUUUUUUUTE! *explodes*
Spock: *raises eyebrow* Fascinating.
McCoy: Dammit Jim! I'm a doctor, not a theologian, but...God is dead, Jim.
Spock: An accurate assessment, more eloquently stated by Nietsche.
McCoy: Oh, shut up, you pointy-eared hobgoblin!