On what dates of July, 2001 did Thursday fall?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 5th, 12th, 19th, 26th
The day of the week is found by counting odd days (days left over after complete weeks) from the start of the calendar: 0 odd days = Sunday, 1 = Monday, ..., 6 = Saturday.
Up to 31 December 2000:
Every 400 years have 0 odd days, so 2000 years have 0 odd days
1 January to 30 June 2001 (2001 is not a leap year):
January 31 days (3 odd days), February 28 (0), March 31 (3), April 30 (2), May 31 (3), June 30 (2)
Total \(=3+0+3+2+3+2=13\) odd days \(=1\) week \(+\ 6\) odd days
The days of July 2001:
6 odd days: 30 June 2001 was a Saturday, so 1 July 2001 was a Sunday
Thursday is 4 days after Sunday, so the first Thursday was 5 July
Adding 7 each time: 5th, 12th, 19th and 26th (the next, 2 August, is outside July)