Artificial intelligent assistant

Calculate the exact weekday of a given date. 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**?

1. 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.

2. Or, here's a more "non-mathematical" way.

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