What was the day of the week on 4th January 1904?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → Monday
The weekday is found by counting the odd days, the days left over after whole weeks, from the start of the calendar: 0 odd days is Sunday, 1 is Monday, and so on. An ordinary year has 1 odd day and a leap year 2.
The 1903 complete years (4th January 1904 comes after 1903 complete years and 4 days):
1600 years: 0 odd days (every 400 years make whole weeks)
300 years (1601-1900): 5 × 3 = 15 odd days (100 years have 5 odd days)
15 odd days = 2 weeks + 1 odd day
1901, 1902, 1903: three ordinary years, 3 odd days
The days of 1904:
1st to 4th January 1904: 4 odd days
The total:
\(0+1+3+4=8\) odd days
8 = 1 week + 1 odd day, which is Monday
Tip: Worth memorising: 100 years have 5 odd days, 200 years 3, 300 years 1 and 400 years 0, so the last day of every century year can only be a Sunday, Monday, Wednesday or Friday.