Question

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

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

Answer 1

The Correct Option is B

Zeller's Congruence for Determining the Day of the Week 

We will use Zeller’s Congruence to determine the day of the week. The formula for the Gregorian calendar is:

$h = q + \frac{13(m + 1)}{5} + \frac{K}{4} + \frac{J}{4} + 5J \mod 7$

Where:

• h = day of the week (0 = Saturday, 1 = Sunday, 2 = Monday, ..., 6 = Friday)
• q = day of the month (e.g., 16)
• m = month (3 = March, 4 = April, ..., 14 = February)
• K = year of the century (year mod 100)
• J = zero-based century (floor(year / 100))

Step 1: Adjust the Month and Year

For July, the month value m = 7. No adjustment to the year is needed.

Step 2: Assign Values

• q = 16 (day of the month)
• m = 7 (July)
• Year = 1776
• K = 76 (1776 mod 100)
• J = 17 (floor(1776 / 100))

Step 3: Plug Values into Zeller’s Congruence

$h = 16 + \frac{13(7 + 1)}{5} + \frac{76}{4} + \frac{17}{4} + 5(17) \mod 7$

Calculate each term:

• $\frac{13(7 + 1)}{5}$ = $\frac{104}{5} = 20$
• $\frac{76}{4}$ = 19
• $\frac{17}{4}$ = 4
• $5(17)$ = 85

Now, substitute these values:

$h = (16 + 20 + 76 + 19 + 4 + 85) \mod 7$

$h = (220) \mod 7$

$h = 220 \mod 7 = 3$

Step 4: Interpret the Result

• h = 3 corresponds to:
  • 0 = Saturday
  • 1 = Sunday
  • 2 = Monday
  • 3 = Tuesday

Final Answer: 16th July 1776 was a Tuesday.