Question

What was the day on 15th August, 1947?

Hint:

Important historical dates are often asked with their corresponding days; remembering a few key ones can save time.

Answer 1

Step 1: Understanding the Problem 
We are asked to determine the day of the week for the date 15th August, 1947.

Step 2: Key Formula (Zeller's Congruence)
Zeller's Congruence is a formula used to calculate the day of the week for any given date. The formula is:
\[ h = \left(q + \left\lfloor \frac{13(m+1)}{5} \right\rfloor + K + \left\lfloor \frac{K}{4} \right\rfloor + \left\lfloor \frac{J}{4} \right\rfloor - 2J \right) \mod 7 \] where:

• h is the day of the week (0 = Saturday, 1 = Sunday, 2 = Monday, ..., 6 = Friday).
• q is the day of the month.
• m is the month (March = 3, April = 4, ..., January = 13, February = 14).
• K is the year of the century (i.e., year % 100).
• J is the century (i.e., year / 100).

Step 3: Applying the Formula
We need to determine the values for the date 15th August, 1947. Here are the details:

• Day (q) = 15
• Month (m) = 8 (since August is the 8th month)
• Year = 1947, so K = 47 and J = 19

Now, substitute these values into the formula:
\[ h = \left(15 + \left\lfloor \frac{13(8+1)}{5} \right\rfloor + 47 + \left\lfloor \frac{47}{4} \right\rfloor + \left\lfloor \frac{19}{4} \right\rfloor - 2 \times 19 \right) \mod 7 \] Simplifying step by step: \[ h = \left(15 + \left\lfloor \frac{13 \times 9}{5} \right\rfloor + 47 + \left\lfloor \frac{47}{4} \right\rfloor + \left\lfloor \frac{19}{4} \right\rfloor - 38 \right) \mod 7 \] \[ h = \left(15 + \left\lfloor \frac{117}{5} \right\rfloor + 47 + \left\lfloor 11.75 \right\rfloor + \left\lfloor 4.75 \right\rfloor - 38 \right) \mod 7 \] \[ h = \left(15 + 23 + 47 + 11 + 4 - 38 \right) \mod 7 \] \[ h = \left(62 \right) \mod 7 \] \[ h = 62 \mod 7 = 6 \] Therefore, the value of \( h = 6 \), which corresponds to **Friday**. 

Step 4: Final Answer
The day on 15th August, 1947 was Friday.