Question

What was the day of the week on 16th July, 1776?

• A. Saturday
• B. Tuesday
• C. Sunday
• D. Saturday
• E.

Hint:

To calculate the day of the week for a historical date, you can use Zeller's formula or an online day calculator tool.

Answer 1

The Correct Option is B

To determine the day of the week for 16th July 1776, we apply Zeller's Congruence for the Gregorian calendar: \[ h = \left(q + \left\lfloor \frac{13(m+1)}{5} \right\rfloor + K + \left\lfloor \frac{K}{4} \right\rfloor + \left\lfloor \frac{J}{4} \right\rfloor + 5J \right) \mod 7 \] where: \begin{itemize} \item \( h \) = day of the week (0 = Saturday, 1 = Sunday, ..., 6 = Friday) \item \( q \) = day of the month (16) \item \( m \) = month (March = 3, April = 4, ..., January = 13, February = 14) \item \( K \) = last two digits of the year (\( 1776 \mod 100 = 76 \)) \item \( J \) = century (\( \text{floor}(1776 / 100) = 17 \)) \end{itemize} Step 1: Assign Values For July, the month value is \( m = 7 \), and no year adjustment is needed. Step 2: Substitute Values into the Formula \[ h = \left(16 + \left\lfloor \frac{13(7+1)}{5} \right\rfloor + 76 + \left\lfloor \frac{76}{4} \right\rfloor + \left\lfloor \frac{17}{4} \right\rfloor + 5(17) \right) \mod 7 \] Step 3: Compute Individual Terms \begin{itemize} \item \( \left\lfloor \frac{13(7+1)}{5} \right\rfloor = \left\lfloor \frac{104}{5} \right\rfloor = 20 \) \item \( \left\lfloor \frac{76}{4} \right\rfloor = 19 \) \item \( \left\lfloor \frac{17}{4} \right\rfloor = 4 \) \item \( 5(17) = 85 \) \end{itemize} Step 4: Compute the Final Value of \( h \) \[ h = (16 + 20 + 76 + 19 + 4 + 85) \mod 7 \] \[ h = 220 \mod 7 \] \[ h = 3 \] Step 5: Interpret the Result The value \( h = 3 \) corresponds to: \begin{itemize} \item 0 = Saturday \item 1 = Sunday \item 2 = Monday \item 3 = Tuesday \end{itemize} Final Answer: The 16th of July 1776 fell on a Tuesday. \[ \boxed{B} \]