I've seen questions about calculating the exact weekdays on a given day, such as the AMC few years ago asking for the weekday that Charles Dicken's birth.
For example, yesterday's Sunday, August 4, 2013. On 1958, the Billboard Hot 100 was published for the first time in history. How do I calculate the weekday for that day, August 4, 1958?
How can we tell exactly what day would it be on a given day, calculated without calculator/electronic aids in a timely manner?
For example, if 8/4/2013 is a Sunday, then 8/4/2014 would be a Monday, 8/4/2015 is a Tuesday, and 8/4/2016 would be a Thursday (because it's a leap year). Then let $0=$ Sunday, $1=$ Monday, etc, mod 7; do the adding and subtracting.
Or, here's a more "non-mathematical" way.