Which day was it?

Algebra Level 3

\[\begin{cases} f = \left \lfloor \frac{14 - m}{12} \right \rfloor \\ x = d + y - f + \left \lfloor \frac{31(m + 12f -2)}{12} \right \rfloor + \left \lfloor \frac{y}{4} \right \rfloor - \left \lfloor \frac{y}{100} \right \rfloor + \left \lfloor \frac{y}{400} \right \rfloor \\ W(x) = x - 7 \left \lfloor \frac{x}{7} \right \rfloor + 1 \end{cases}\]

The equations above are the formula used to find the week day of any date on a calendar, where \(d\), \(m\), \(y\) are date, month, and year respectively. For example, February 29, 2016, can be represented as 29/2/2016 for \(d\), \(m\), & \(y\).

The function \(W(x)\) will then result in values of 1-7 for Sunday to Saturday respectively.

Which day of the week was July 4, 1776 (America's Independence Day)?

Bonus: Try plug in your birthday and see which day it was!


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