What was the first day of the year 1731?
Show answer & explanation
Correct answer: A
Explanation
Odd days in 1600 years:
Number of odd days in 1600 years = 0
Odd days in the next 100 years (up to the year 1700):
Number of odd days in 100 years = 5
From the year 1701 to 1730 (30 complete years):
Leap years in these 30 years: 30/4 = 7 leap years (1704, 08, 12, 16, 20, 24, 28)
Ordinary years: 30 - 7 = 23 ordinary years
Total odd days = (7 x 2) + (23 x 1) = 14 + 23 = 37
Remainder upon dividing by 7: 37/7 = 2 odd days
The first day of the year 1731 (January 1st):
We need to add the odd days up to January 1, 1731, which is simply 1.
Sum of total odd days: 0 (1600) + 5 (1700) + 2 (1730) + 1 (1) = 8. Now, upon dividing 8 by 7, the remainder is 1.
Day Codes:
0 = Sunday
1 = Monday
2 = Tuesday ... etc.
Since the remainder is 1, January 1, 1731, was a Monday.
Correct Answer = Monday