Question

4 January 1999 which day by age calculation

Answer 1

Answer:

Monday

Explanation:

The year 1999 can be split as,

1999 = 1600 + 300 + 98 + 1

Since 1600 is a century and is a multiple of 400, it has 0 odd days.

[Note : Days remaining in a month or a year not as a week are called odd days. An ordinary year has 52 weeks and 1 odd day, while a leap year has 52 weeks and 2 odd days.]

The 300 years (from 1601 to 1900) contain 228 ordinary years and 72 leap years (1700, 1800, 1900 are not leap years! Centuries should be divisible by 400 for being leap years).  

Since an ordinary year has 1 odd day and a leap year has 2 odd days, the total no. of odd days in the 300 years is (1 × 228) + (2 × 72) = 372 ≡ 1 (mod 7). $\quad$

I.e., only 1 odd day.

Now consider those 98 years (from 1901 to 1998). They contain 74 ordinary years and 24 leap years. Hence the total no. of odd days in the 98 years is (1 × 74) + (2 × 24) = 122 ≡ 3.

I.e., 3 odd days.

Now, with the 4 days of January 1999, we have to add all the odd days, thus,

0 + 1 + 3 + 4 = 8 ≡ 1

The first day after Sunday is nothing but Monday.

Hence Monday is the answer.