What was the day of the week on 4th January 1904?

Monday

The correct answer is Option (2) → Monday

To find the day of the week on 4th January 1904, we can use the concept of "odd days" or a calendar calculation.

Step-by-Step Calculation

1. Break down the years:
• We need to find the days up to 31st December 1903 first.
• 1600 years have 0 odd days.
• 300 years (from 1601 to 1900) have 1 odd day.
• Now, we look at the years from 1901 to 1903:
• All 3 years are ordinary years ($3 \times 1 = \mathbf{3 \text{ odd days}}$).
2. Add days for the year 1904:
• We only need to look at January: 4 days.
• Total odd days = $0 (\text{from 1600}) + 1 (\text{from 300 years}) + 3 (\text{from 3 years}) + 4 (\text{days in Jan})$
• Total $= 8 \text{ days}$.
3. Find the remainder:
• $8 \div 7$ leaves a remainder of 1.

Mapping the Remainder to the Day

• 0 = Sunday
• 1 = Monday
• 2 = Tuesday
• 3 = Wednesday

Since the remainder is 1, the day was Monday.