What was the day of the week on 29th October 1991?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 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. 29th October 1991 comes after 1990 complete years and part of 1991.
1600 years: 0 odd days (every 400 years give 0)
Next 300 years (1601 to 1900): 1 odd day
1901 to 1990: 90 years with 22 leap years (1904, 1908, …, 1988) and 68 ordinary years: \(22\times2+68\times1=112\) odd days
\(112=16\times7\), so 0 odd days
1991 up to 29 October: January to September give \(3+0+3+2+3+2+3+3+2=21\), that is 0, and 29 days of October give 1 (1991 is not a leap year)
Total \(=0+1+0+0+1=2\) odd days
2 odd days means Tuesday