What was the day on 10th January, 1951?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → Wednesday
The weekday moves forward only by the odd days, the days left over after whole weeks. An ordinary year has 1 odd day (\(365=52\times7+1\)) and a leap year has 2. Counting starts from 1 January of year 1, with 0 odd days standing for Sunday, 1 for Monday, and so on.
The 1950 complete years before 1951:
1600 years: 0 odd days (every 400 years give 0)
300 years: 1 odd day (every 100 years give 5, so 300 years give 15, that is 2 weeks and 1 day)
50 years (1901 to 1950): 12 leap years and 38 ordinary years, so \(12\times2+38=62\) odd days, that is 8 weeks and 6 odd days
Total for 1950 years: \(0+1+6=7\), that is 0 odd days
The days of 1951 up to 10 January:
10 days = 1 week and 3 odd days
Total: \(0+3=3\) odd days, which stands for Wednesday