My (intuitive) solution was to divide 365 by 12. This leaves 30 days per month, with 5 days left over. A reasonable split would be 7 months of 30 days, and 5 months of 31 days. Regarding the ordering of the months, I considered 2 ways. The first would be to place the 5 odd months at an end of the calendar (either the front or the back). However, after some consideration, I felt that this method, while being easy to remember, seemed unsymmetric, and might leave the halves of the calender unbalanced. My second idea was to alternate the long and short months. The last 3 months would be short.
The resulting calender would be : 31, 30, 31, 30, 31, 30, 31, 30, 31, 30, 30, 30.
Evidently, this is quite different from the current form of the calendar. The current calendar has 7 months with 31 days, 5 months with 30 days, and 1 month with 29 days. This is clearly an arbitary arrangement of days. This leads me to the conclusion that the calender was not created and imposed at a single moment in history by a single planner or authority, but rather the result of a series of incremental changes.
Here's how I hypothesise the calendar came about (based on pure speculation alone):
Original creator : Let's make a 365 day calendar with 12 months ! The calendar should be symmetric around the center.
Result : 31, 30, 31, 30, 31, 30, 30, 31, 30, 31, 30, 31
Problems : 366 day calendar.
Solution : Borrow 1 day from some random month.
Result : 31, 29, 31, 30, 31, 30, 30, 31, 30, 31, 30, 31
After some time : Hey let's make this month longer ! For no reason !
Result : 31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31
Problems : 366 days again ! You clown !
Solution : Pick on the loser month with 29 days. Easier to recall which month is odd.
Result : Existing calendar.
Of course, the previous speculation was utter nonsense. However, I do believe that the present calendar was slowly morphed from a predecessor calendar slowly. The gradual changes were implemented such that the newer calendars would be minimally different from the earlier calendars. In other words, if they added a day to another month, and needed to remove a day from an existing month, the best candiate would be a month which was already an oddity.
Perhaps that is why February is such a 'loser' month. It's at least 2 whole days shorter than everyone else, and even at it's best it's still shorter by 1 day. It must have been the victim of multiple 'shortenings' !