As well as the leap year stuff people have mentioned, there was something else that I've got a vague memory of (from an old SciAm article, IIRC, which was about using March as the first month for calculations) which pointed out that if you use March as 0, you can multiple the month number by (I forget exactly what but it was around 30.4ish?) and, if you round the fraction up, you get the day number of the start of that month and it all works out correctly for the right 31-30-31 etc sequence.
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As well as the leap year stuff people have mentioned, there was something else that I've got a vague memory of (from an old SciAm article, IIRC, which was about using March as the first month for calculations) which pointed out that if you use March as 0, you can multiple the month number by (I forget exactly what but it was around 30.4ish?) and, if you round the fraction up, you get the day number of the start of that month and it all works out correctly for the right 31-30-31 etc sequence.