The first day of a century is 1st January of a year ending in 01 (for example, 1st January 2001). On which of the following days of the week can the first day of a century never fall?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → Wednesday
Count odd days from the start of year 1 (0 odd days = Sunday, 1 = Monday, and so on). In the Gregorian calendar 100 years give 5 odd days (76 ordinary years + 24 leap years), and a 400-year cycle gives 0, so the last day of a century can only be one of four weekdays. The first day of the next century is the day after it.
100 years: 5 odd days, last day Friday, so the next century starts on Saturday
200 years: \(2\times5=10=7+3\), 3 odd days, last day Wednesday, next starts on Thursday
300 years: \(3\times5=15=14+1\), 1 odd day, last day Monday, next starts on Tuesday
400 years: \(4\times5+1=21\) (the 400th year is a leap year), 0 odd days, last day Sunday, next starts on Monday
So a century can start only on Monday, Tuesday, Thursday or Saturday; never on Sunday, Wednesday or Friday