What was the day of the week on 10thMarch 1996?a)Thursdayb)Fridayc)Sat...
The last two digits of year:96
The last two digits divided by four:24
The given day:10
The code of the month:3
The code of the year:0
Adding all the above;96+24+10+3=133
Dividing 133/7, we obtain 19 weeks I. e 0 odd days.
Hence the day is Sunday as 0 corresponds to Sunday.
What was the day of the week on 10thMarch 1996?a)Thursdayb)Fridayc)Sat...
The Day of the Week on 10th March 1996
To determine the day of the week on 10th March 1996, we can use a method called Zeller's Congruence. Zeller's Congruence is an algorithm devised by Christian Zeller to calculate the day of the week for any given date.
Zeller's Congruence Algorithm:
Zeller's Congruence algorithm uses the following formula:
\[ h = (q + \frac{13(m+1)}{5} + K + \frac{K}{4} + \frac{J}{4} - 2J) \% 7 \]
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 (3 = March, 4 = April, ..., 12 = December) - We subtract 3 from the month value as Zeller's Congruence considers March as the first month of the year.
- K is the year of the century (year % 100)
- J is the zero-based century (actually \(\lfloor year/100 \rfloor)\)
Calculating the Day of the Week for 10th March 1996:
Let's apply Zeller's Congruence to calculate the day of the week for 10th March 1996.
q = 10
m = 3 - 3 = 0
K = 96
J = \(\lfloor \frac{19}{100} \rfloor\) = 19
Substituting the values into the formula:
\[ h = (10 + \frac{13(0+1)}{5} + 96 + \frac{96}{4} + \frac{19}{4} - 2(19)) \% 7 \]
Simplifying the equation:
\[ h = (10 + \frac{13}{5} + 96 + 24 + 4 - 38) \% 7 \]
\[ h = (10 + 2 + 96 + 24 + 4 - 38) \% 7 \]
\[ h = 98 \% 7 \]
\[ h = 0 \]
Therefore, the remainder of 0 indicates that the day of the week for 10th March 1996 is Saturday.
Conclusion:
Hence, the correct answer is option 'c) Saturday'.