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I don't know why you wanted to know year before month or day, I use dd/mm/yyyy sometime I didn't even use yyyy just dd/mm because day change most frequent then month then year
YYYY-MM-DD is best when programming because it's unambiguous and it makes sorting easier. For humans DD-MM-YYYY is indeed the most sensible.
Most sensible is a matter of opinion
If you're talking dd/mm then mm/dd makes more sense, like a clock.