What was the day of the week on 23rd August 1977?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → Tuesday
Count the odd days (days left over after whole weeks) from the start of the calendar up to the date; 0 odd days means Sunday, 1 Monday, 2 Tuesday, 3 Wednesday, 4 Thursday, 5 Friday, 6 Saturday. 23rd August 1977 comes after 1976 complete years and part of 1977.
1600 years: 0 odd days (every 400 years give 0)
Next 300 years (1601 to 1900): 1 odd day
1901 to 1976: 76 years with 19 leap years (1904, 1908, …, 1976) and 57 ordinary years: \(19\times2+57\times1=95\) odd days
\(95=13\times7+4\), so 4 odd days
1977 up to 23 August: January to July give \(3+0+3+2+3+2+3=16\) odd days, that is 2 (1977 is not a leap year, so February gives 0), and 23 days of August give 2: \(2+2=4\) odd days
Total \(=0+1+4+4=9=7+2\), that is 2 odd days
2 odd days means Tuesday