Given Data

1. Target date: 15 August 1947.

Question

What day of the week was 15 August 1947?

Answer

Friday.

Solution

1. Step 1: Count odd days for 1946 completed years:
2. 1600 years = 0 odd days.
3. 300 years = 1 odd day.
4. 46 years = 11 leap years + 35 ordinary years.
5. Odd days in 46 years = (11 × 2) + (35 × 1) = 22 + 35 = 57 ≡ 1 odd day (57 mod 7).
6. Total odd days up to 1946 = 0 + 1 + 1 = 2 odd days.
7. Step 2: Count odd days in 1947 up to 15 August:
8. Jan(3) + Feb(0) + Mar(3) + Apr(2) + May(3) + Jun(2) + Jul(3) + Aug(15 mod 7 = 1)
9. Sum = 3 + 0 + 3 + 2 + 3 + 2 + 3 + 1 = 17 ≡ 3 odd days (17 mod 7).
10. Step 3: Add total odd days = 2 + 3 = 5 odd days.
11. Day code 5 corresponds to Friday.
12. Therefore, 15 August 1947 was a Friday.