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Regarding day of the week, this simple trick/observation seems surprisingly unknown (called Doomsday Rule: http://en.wikipedia.org/wiki/Doomsday_rule).

In any year, 4/4, 6/6, 8/8, 10/10, 12/12 fall on the same day, so do 9/5, 5/9, 7/11, 11/7 (mnemonic: 9-to-5, 7-11). If you know what day that is for the year (Friday for 2014, Sat for 2015), you can quickly calculate the day of the week for many of the days.

Jan/Feb/Mar require a little bit thought, but with practice reasonably quick.




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