I imagine the calendar date is near the winter solstice in the Northern Hemisphere and I would think the time would be whatever puts as much of China/India in the dark as possible, but that's just a wild guess.
Are people being facetious or is the question worded poorly?
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I think your question is well worded, but it's a question that is difficult.
If you try to re-word it, you might make it clearer why you are asking.
For example, do you want the Sun to be visible by a minimum without any warning? Whichever hemisphere has a minimum population (excluding North and South)? Are you writing a story about a solar flare? Does it matter if they are actively looking? Is the event powerful enough to affect those indoors and asleep? Do you need verification of the numbers (count mobile phones, but some have more phones per head)?
Brigalow Bloke
You are correct. Most of the world's population lives between Northern Japan south to Java and west to Pakistan. When it's midnight in eastern India it's night in all that region too, Including Australia.
digquickly
well, ..., I'd go with night!
Anonymous
Hmm! Every night!
Anonymous
Usually during my vacation.