Which of the following day could be the 18th October 2050?a)Tuesdayb)F...
From Zeller's Formula
f = k + [13 x m - 1 / 5] + D + [D/4] + [C/4] - 2 x C.
In this case k = 18 (since 18th October)
Month m = 8 (As march = 1, April = 2, May = 3, October = 8)
D is the last two digit of year here D = 50 (As year is 2050)
C is the 1st two digit of century here C = 20 (As year is 1950)
f = 18 + [13 x 8 - 1 / 5] + 50 + [50/4] + [20/4] - 2 x 20.
f = 18 + [103/5] + 50 + [12.5] + [5] - 40.
f = 18 + 20 + 50 + 12 + 5 - 40 = 65.
When divided by 7 we will get remainder 2, hence number of odd days is 2,
So 18th October 2050 is 2 days more than Sunday, i.e Tuesday.
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Which of the following day could be the 18th October 2050?a)Tuesdayb)F...
Explanation:
Identifying the Day:
- To determine the day of 18th October 2050, we can use the concept of the days in a week.
- Knowing the day of the week for a particular date involves using a mathematical formula or an algorithm.
Calculating the Day:
- We can use Zeller's Congruence formula to calculate the day of the week for a given date.
- Zeller's Congruence formula is:
\[ h = (q + \left\lfloor \frac{(13(m+1))}{5} \right\rfloor + K + \left\lfloor \frac{K}{4} \right\rfloor + \left\lfloor \frac{J}{4} \right\rfloor - 2J) \% 7 \]
- 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)
- K is the year of the century (year % 100)
- J is the zero-based century (year / 100)
Applying the Formula:
- For 18th October 2050:
- q = 18, m = 10, K = 50, J = 20
- Substitute these values into the formula and calculate the day of the week.
Identifying the Result:
- After applying the formula, we find that the day corresponding to 18th October 2050 is Tuesday.
Therefore, the correct answer is option 'a) Tuesday'.