Problem or Question

Dudes,

What are the conceptual differences between "a question" and "a problem"?

Please also give me some examples.
更新: Hmm,
Quaere is just a question in another form. So, let me put it this way:

When a kid wonders - "When I grow up, would I be pretty? Would I be rich?"

Are these questions or problems? Or could they be both?
更新 2: Or,
When a government wonders - "how do I provide enough housing to the poors."

Is it a question or a problem? or both.

Could you also elaborate on these?
更新 3: Oh,
The reason why I asked for your help is:

In Taiwanese, they both are commonly translated into "[noun] 問題"but why does the language called English need 2 different words for the same concept?
更新 4: 我真的不認為"困難度"可以用來分辯!
例如:
is there a God?是一個困難的問題(question )而不是一個問題(problem)
1+1=?是一個問題(question )也是一個問題(problem)
我丟掉了20元!不是一個問題(question )但是是一個問題(problem)
更新 5: 而且,我的問題是在於中翻英

例:
阿義有健康問題。。。這個"問題"要翻成question or a problem? or either?
更新 6: I appreciate Mr. Pony pointed out to me that:

1. "question" typically is to request the transfer of information (ie. from a person possesses it to another who does not.) while

2. "problem" typically requires unspecified action(s) or transformation of information as the solution.
更新 7: So, I tend to choose him as the best answer.

Please speak up today, should you have any objection .
Thanks!
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