Question

2000 January 1st was Saturday. What was the day in 1900 January 1st ?

• A. Saturday
• B. Sunday
• C. Monday
• D. Tuesday

Answer 1

Answer:

C. Monday

January 1st, 1900 was a Monday.

1. Calculate Year Difference

Find the total number of years between January 1st, 1900 and January 1st, 2000:
$\text{Difference} = 2000 - 1900 = 100 \text{ years}$

2. Count Leap Years

Count the number of leap years in this 100-year interval.

• A standard century contains $24$ leap years.

• Year 2000 is a century year divisible by 400, making it a leap year.

• Year 1900 is a century year not divisible by 400, so it is a normal year.

• Because the target date is January 1st, 2000, the extra leap day (February 29, 2000) has not occurred yet within this range.

• Total leap years counted:
  $\text{Leap Years} = 24$

3. Calculate Odd Days

Every normal year has $1$ odd day and every leap year has $2$ odd days:
$\text{Total Odd Days} = (76 \times 1) + (24 \times 2) = 124 \text{ days}$

Reduce this number by dividing by $7$ to find the remainder:
$124 \div 7 = 17 \text{ weeks with a remainder of } 5 \text{ odd days}$

4. Count Backward

Since we are moving backward in time from 2000 to 1900, subtract the $5$ odd days from Saturday
$\text{Saturday} - 5 \text{ days} = \text{Monday}$