What was the day of the week on 16th June 1998?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → Tuesday
The weekday repeats every 7 days, so only the odd days, the days left over after whole weeks, move it forward. An ordinary year has 1 odd day and a leap year 2; every 400 years have 0 odd days. Counting the odd days from the start of the calendar up to the given date, 0 odd days is Sunday, 1 is Monday, 2 is Tuesday and so on.
The years before 1998 (up to 31 December 1997):
1600 years: 0 odd days
The next 300 years (to 1900): 1 odd day
1901 to 1997 (97 years, 24 of them leap years): \(73\times1+24\times2=121\) odd days, and \(121=17\times7+2\), so 2 odd days
Total: \(0+1+2=3\) odd days
1 January to 16 June 1998 (1998 is not a leap year):
January 31 days: 3 odd days; February 28 days: 0
March 31: 3; April 30: 2; May 31: 3
June 1 to 16: 16 days, 2 odd days
Total: \(3+0+3+2+3+2=13\) odd days, that is, 6 odd days
Odd days in all \(=3+6=9\), which leaves 2 after a full week, so 16 June 1998 was a Tuesday.