Question

On what dates of $\text{July 1776}$ did Sundays fall ?

• A. 7th, 14th, 21st and 28th
• B. 3rd, 10th, 17th and 24th
• C. 2nd, 9th, 16th and 23th
• D. 5th, 12th, 19th and 26th

Answer 1

Answer: (A)

7th, 14th, 21st and 28th

First, we shall find out what day was $\text{1 July 1776}$.
$1600$ years have $0$ odd days.
$100$ years have $5$ odd days.
$75$ years comprise of $18$ leap years and $57$ ordinary years.
So, the number of odd days in $\text{75 years}=18\times 2+57=93=\text{13 weeks, 2 odd days}$.
Thus, $\text{1775}$ years have $(0+5+2)=\text{7 odd days}$. So, $0$ odd days.
In $\text{1776, till 1 July}$, the number of odd days is calculated as follows
Month January February March April May June July
Days $3129313031301$
$\text{183 days}=\text{26 weeks + 1 day}=\text{1 odd day}$.
So, $\text{1 July 1776}$ was Monday, and hence the first Sunday in $\text{July 1776}$ was on the 7th.
The other Sundays in $\text{July 1776}$ were $\text{14th, 21st and 28th}$.