What was the day of the week on 15 August 1947?

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Accepted Answer

To determine the day of the week for 15 August 1947, we calculate the total number of odd days from a reference point.

1. **Odd days from 1600 to 1946 (346 years):**  
   - **1600 years contribute 0 odd days** (as 1600 is a leap year).  
   - **300 years (1700–1900)** contribute **1 odd day** (as each century contributes 1 odd day).  
   - **46 years (1901–1946)** include 11 leap years and 35 ordinary years:  
     $$
     	ext{Odd days} = (11 	imes 2) + (35 	imes 1) = 22 + 35 = 57 \, 	ext{odd days}.
     $$  
     Dividing by 7, we get $$57 \mod 7 = 1$$ odd day.

Total odd days up to 1946: $$0 + 1 + 1 = 2$$.

2. **Odd days from January to August 1947:**  
   - January: $$31 \mod 7 = 3$$ odd days.  
   - February: $$28 \mod 7 = 0$$ odd days (1947 is not a leap year).  
   - March: $$31 \mod 7 = 3$$ odd days.  
   - April: $$30 \mod 7 = 2$$ odd days.  
   - May: $$31 \mod 7 = 3$$ odd days.  
   - June: $$30 \mod 7 = 2$$ odd days.  
   - July: $$31 \mod 7 = 3$$ odd days.  
   - Up to **15 August**, there are $$15 \mod 7 = 1$$ odd day.

Total for January to August: $$3 + 0 + 3 + 2 + 3 + 2 + 3 + 1 = 17$$. Dividing by 7, we get $$17 \mod 7 = 3$$ odd days.

3. **Total odd days up to 15 August, 1947:**  
   Adding the contributions: $$2 + 3 = 5$$ odd days.

4. **Day of the week calculation:**  
   Starting from a known reference point (e.g., **1 January, Monday in year zero**), adding **5 odd days** gives:  
   Monday → Tuesday → Wednesday → Thursday → **Friday**.

Thus, the day on **15 August, 1947 was Friday**.

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