Slim - you are correct the maths problem analogy is not a perfect match.
I wasn't trying to nit-pick your analogy to death, but I think that specific analogy was approaching the subject from a bad angle. My problem isn't with analogies, it's with the point the analogies are trying to support--that there might be some justification for needless suffering that we humans miss due to imperfect knowledge.
Your answer seems to make sense if we apply it in a very vague way, as you do in your parenting analogy. But I think you're asking this argument to do wayyyyyyy more work than it is able to do. It's like saying "There exists a woman who is the best mother ever to have lived," but we learn that for years she has kept her children locked in closets with rusty buckets to relieve themselves, and are fed only moldy bread crusts. That is not at all congruent with the title of Most Perfect Mother, and we find it impossible to wave it away by saying, "Maybe she has a good reason that we just can't fathom."
... given that we may not know everything about the situation, and given the possibility that a supreme being may have greater understanding of the situation than we do, it is at least possible that God is acting both from a position of power and goodness in creating the world and sustaining the world in the way in which he does.
I think we know enough. A problem for believers is that God's OmniMax properties are not unimportant or secondary properties. It's not as if we think one of the properties of the Most Perfect Mother is she's right-handed, but we see her writing with her left hand and we think their must be some unknown reason she's doing it this time. God isn't rather smart, sort of powerful, and pretty nice--He's the embodiment of those qualities. They are His basic, defining characteristics. The fact that we don't see these fundamental qualities reflected in His creation cannot be dismissed with "Mysterious Ways."
Actually I was going out of my way not to proof text. That's why I talk about God's inscrutability as a "dominant theme" of the Bible rather than incontrovertible teaching.
But I think it's what you've done. We have some verses saying God has revealed Himself to mankind and wants a relationship with us, and other verses saying he's not fully comprehensible. You haven't tried to reconcile these verses, you've just ignored the former in favor of the latter.
Furthermore, I don't think God's inscrutability is a theme of the Bible at all, let alone a dominant one. It only really comes up when believers are asked about contradictions between God's supposed qualities and evidence to the contrary.
I can't actually think of any scriptures that claim God is perfectly intelligible to humans, but modesty requires I don't rule out the possibility. Do you know of any? What I do know, and I've shown above, is that many parts of the Bible indicate that humans can't hope to fully understand God and why he does things the way he does. So to say that the God of the Bible doesn't exist because we can't account for his actions in terms of goodness ignores a large part of what the Bible has to say about God's inscrutability.
I think you've set an unreasonably low bar for yourself. God doesn't need to be "perfectly" intelligible or "fully" comprehensible. Again, we're talking about God's defining characteristics. We're not saying the Most Perfect Mother isn't "perfectly" understood because we don't know why she always wears a striped scarf, we're saying her actions are so obviously bad that we can confidently say she's not the Most Perfect Mother.
Actually I consider myself agnostic, tending toward atheist.
Apologies, I did not know that. Still, I'm not sure it changes my answer. If you were asked what the Christian God was like, I think you'd answer the same way.
...The human mind, even in a universe without a divine being, is surely not the perfect judge of all that does or can exist. We are living in an age where human reason has been elevated almost to the level of Godlike status. That's why arguments that involve relying on human reason as the arbiter of what can exist go unchallenged. It's the dominant ideology of our time.
Now I think you've set the bar unreasonably high. We don't need to be "the perfect judge." Again, we're not talking about some minor attribute, we're talking about the defining characteristics of people's concept of God. When it comes to God's omniscience, omnipotence, or omnibenevolence, believers do not say "I can't commit to that because He's inscrutable." If God is "scrutable" enough to be called Omni-whatever, then he's "scrutable" enough that the obvious contradictions between these claims and what we see in the world cannot be waved away.