What was the day on 26th Jan 1950, when the 1st Republic Day of India was celebrated?

To determine the day of the week for January 26, 1950, we can use Zeller's Congruence, a well-known algorithm for finding the day of the week for any date.

Step 1: Break Down the Problem

We need to identify the components of the date:

• Day (d) = 26
• Month (m) = 1 (January)
• Year (y) = 1950
• Since January and February are considered as the 13th and 14th months of the previous year, we will use:
  • m = 13 (January)
  • y = 1949 (previous year)
• Century (K) = 49 (last two digits of 1949)
• Year of the century (J) = 1 (first two digits of the year)

Step 2: Relevant Concepts

Zeller's formula is given by:

$h = \left( d + \left\lfloor \frac{13(m + 1)}{5} \right\rfloor + K + \left\lfloor \frac{K}{4} \right\rfloor + \left\lfloor \frac{J}{4} \right\rfloor - 2J \right) \mod 7$

Where:

• $h$ is the day of the week (0 = Saturday, 1 = Sunday, 2 = Monday, ..., 6 = Friday)

Step 3: Analysis and Detail

Substituting the values into Zeller's formula:

• $d = 26$
• $m = 13$
• $K = 49$
• $J = 1$

Calculate $h$:

$h = \left( 26 + \left\lfloor \frac{13(14)}{5} \right\rfloor + 49 + \left\lfloor \frac{49}{4} \right\rfloor + \left\lfloor \frac{1}{4} \right\rfloor - 2 \cdot 1 \right) \mod 7$

Calculating each term:

• $\left\lfloor \frac{13(14)}{5} \right\rfloor = \left\lfloor \frac{182}{5} \right\rfloor = 36$
• $\left\lfloor \frac{49}{4} \right\rfloor = 12$
• $\left\lfloor \frac{1}{4} \right\rfloor = 0$

Now substituting these values into the equation:

$h = (26 + 36 + 49 + 12 + 0 - 2) \mod 7 = (121) \mod 7$

Now calculate $121 \mod 7$:

$121 \div 7 = 17 \quad \text{ remainder } 2$

Thus, $h = 2$.

Step 4: Verify and Summarize

Looking at our computed value of $h$:

• $h = 2$ corresponds to Monday.

Final Answer

January 26, 1950, was a Monday.