Procedure to calculate the day of the week for a given date.

[burgess]

To calculate the day of the week for a given date, first of all we need to find out the number of odd days.

Today I thought of sharing a beautiful problem I learned in my school, though it is easy, it is tricky too.
Odd Days are number of days more than the complete number of weeks in given period.
Leap Year is the year which is divisible by 4.
A normal year has 365 days
A leap year has 366 days
One normal year = 365 days = 52weeks + 1day
One normal year has one odd day

One leap year = 366 days = 52weeks + 2days
One leap year has two odd days

100 years = 76 ordinary years + 24 leap years = 5200 weeks + 124 days = 5217 weeks + 5 days
100 years have 5 odd days

400 years have (20+1) 0 odd days

The number of odd days and the corresponding day of the week is given below

0-Sunday
1-Monday
2-Tuesday
3-Wednesday
4-Thursday
5-Friday
6-Saturday

So by finding out the number of odd days you can find out the day of the week. I hope this procedure Will be helpful in solving math problems in exams.

Thanks.

 

[jvicens]

Hello! Thank you for sharing this interesting problem. I would like to add some additional information and clarification for your explanation.

Firstly, the concept of "odd days" is also known as the "remainder days" or "residue days." It is the number of days left over after dividing the total number of days by 7. This is because there are 7 days in a week, so if the total number of days is divisible by 7, there are no odd days.

Secondly, while your explanation for odd days in a normal year and leap year is correct, I would like to add that there are exceptions to this rule. Years that are divisible by 100 but not by 400 are not considered leap years. For example, the year 1900 was not a leap year, even though it is divisible by 4.

Lastly, I would like to mention that there are more accurate and efficient methods for calculating the day of the week for a given date, such as the Zeller's Congruence formula or the Doomsday algorithm. These methods take into account the different number of days in each month and the exceptions mentioned above.

Overall, your explanation is a good starting point for understanding the concept of odd days and its relation to finding the day of the week. Thank you for sharing and I hope this additional information is helpful.