How to Solve Calendar Problems

Calendar

Calendars can be classified into four types:

1. Solar
2. Lunisolar
3. Lunar
4. Seasonal

1.Solar Calendar:

It is based on the equivalent position of the Sun relative to the stars, and its dates indicate seasons. For example, the Gregorian Calendar, which is a Solar Calendar, is used mostly in the world.

2. Lunisolar Calendar:

It is a combination of the solar calendar and the lunar calendar.

3. Lunar Calendar:

It is a calendar based on the moon phases on a monthly basis.

4. Seasonal Calendar:

It is based on particular recurring events such as festivals, seasons, etc.

Gregorian Calendar:

The Gregorian calendar is used around the world. Pope Gregory XIII introduced it in October 1582. 

To solve problems related to calendars, we should first know the calendar structure given below. 

Calendar Structure

We know that in the calendar we have,

• 1 week = 7 days – Mon Tue Wed Thu Fri Sat Sun.
• 1 year = 52 weeks + 1 odd day (extra day).
• Leap year = 52 weeks + 2 odd days.
• Ordinary year = 28th Feb. 
• Leap Year = 29th Feb. 

Concept of Odd Days

• In a typical year, we have 365 days, and in a leap year, we have 366 days.
• The days repeat after 7 days.

1.Normal Year:

• When you divide 365 days by 7 weeks, you get the remainder of 1.
• The remainder 1 is your odd day in a normal year.

2.Leap Year:

• When you divide 365 days by 7 weeks, you get the remainder 2.
• The remainder 2 is your odd day in a leap year.

Hence, we see the remainder of the average year gives 1 odd day, whereas, for the leap year, it gives 2 odd days. 

Tricks for solving calendar:

Here are some of the tricks for easy solving of the problems.

i. Days-

  0- Sunday 1-Monday 2-Tuesday

  3-Wednesday 4-Thursday 5-Friday

  6- Saturday

ii. Month-

J F M A M J J A S O N D

0 3 3 6 1 4 6 2 5 0 3 5 

J- January F- February M- March A- April

M- May J- June J- July A- August

S- September O- October N- November D- December 

iii. Year-

1600-1699 – 6

1700-1799 – 4

1800-1899 – 2

1900-1999 – 0

2000-2099 – 6

iv. Identify a leap year-

    If a given year, divided by 4, gives 0 as the remainder, then it is a leap year. 

  For instance, check if the year 2012 is a leap year or not?

         So, 2012/4 = 503 , remainder = 0

         Hence, 2012 is a leap year.

Example 1. What was the day of the week on 26th January 1947?

Solution: i. Last two digits of the year = 47

1. So, 47/4 we get quotient = 11

iii. Take the date = 26

1. Take no of the month = January = 0
2. Take no of year = 1900 – 1999 = 0

Add first five steps: 47 + 11+ 26 + 0 + 0 = 84

Now, divide it by 7  days in a week = 84/7 = 12

Take the remainder, which is equal to 0.

Hence, 0 – Sunday.

So, Sunday was the day of the week on 26th January 1947.

iv. Leap Year:

Now let us take the example of the leap year.

Example 2. Find out the day of the week for 29th February 2012?

Solution: Here, 2012 is a leap year,

12. Given the last two digits of the year = 12.
13. So, 12/4, we get quotient = 3.

iii. Take the date = 29.

3. Take no. of the month = February = 3.
4. Take no. of year=2000-2099 = 6.

Add the first five steps: 12 + 3 + 29 + 3 + 6 = 53.

Now, divide it by 7 (days in a week) = 53/7. 

Take the remainder, which is equal to 4.

Since it is for leap year, subtracting it by 1, we get = 4-1 = 3.

So, 3- Wednesday.

So, Wednesday was the day of the week on 29th February 2012.

Take any other example:

Example 3. What dates in May 2002 were Monday?

Solution. i. Last two digits of the year = 02.

1. So, 12/4, we get the quotient = 0.

iii. Take the date = 01.

1. Take no. of the month = May = 01.
2. Take no. of year =2000-2099 = 06.

Add the first five steps: 2 + 0 + 1 + 1 + 6 = 10.

Now, divide it by 7 (days in a week) = 10/7.

Take the remainder, which is equal to 3.

3- Wednesday, so 1st May 2002 falls on Wednesday.

1 2 3 4 5 6 

Wed Thu Fri Sat Sun Mon

Hence, the first Monday falls on 6th May and adding 7 will give the respective dates (6 + 7 = 13).

Moreover, 6, 13, 20, and 27 are the respective dates on Mondays in May 2002.

Conclusion

• We use the Gregorian calendar.
• In calendar problem solving, first, check whether the year is a leap year or not. 
• Leap year is divisible by 4; it is easily identifiable with this.
• A year consists of 2 weeks and 7 days per week.
• There is one odd day in a typical year and two odd days in a leap year.
• An average year has 365 days; however, a leap year has 366 days.