Calendar – Tricks, Units, Questions | How to Solve Calendar Problems?

The calendar helps you to see the dates, weeks, and months. With the guidance of the calendar, we can know that there are 12 months in a year, number of days in a month, number of weeks, etc. Students of 4th Grade can make use of this article to know uses of the calendar, Calendar units, odd days, leap year, non-leap year, examples of calendars, decoded day of the week, the basic structure of the calendar, etc. Know how to solve the calendar problems from here.

Do Refer:

What is a Calendar?

A calendar is a chart or series of pages that show days, weeks, months of a particular year. It gives particular seasonal information.

The list of the topics under the calendar section is as follows,
1. Numbers of days in a week
2. Evaluation of a leap year.
3. Structure of Odd day.
4. Structure of Even day.
5. Evaluation of odd days in a century.
6. Evaluation of non-leap year.
7. Matching the calendars of a month.

Calendar Units

Day: The smallest unit in a calendar is a day. The link with the clock and calendar is 24 hours make a day.
Week: There are seven days a week. A week is the next larger period of time. Weekdays are Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, and Sunday in the sequence that repeats. These names are easy to remember.
Month: The next larger interval or unit in a calendar is a month and finally 12 months make a year. Months are January, February, March, April, May, June, July, August, September, October, November, and December in sequence and repeating over years.
General Concept: No fixed number of weeks or days make a month or year.

  • a month has 4 weeks
  • a month has 30 days
  • a year has 52 weeks
  • a year has 365 days

Basic Structure of a Calendar

1. Ordinary year: Any year which has 365 days is called an ordinary year. Example: 2019 is an ordinary year.
2. Leap Year: Any year which has 366 days is called a leap year. Example: 2020
3. The division of the number 365 by 7 gives the quotient 52 and leaves the remainder 1 which indicates that an ordinary year has 52 weeks and one extra day. This extra day is referred to as an odd day throughout the calendar topics.
4. A leap year has 366 days, the division of the number 366 by 7 gives the quotient 52 and remainder 2. This indicates that a leap year has 52 weeks and 2 extra days. These two extra days are also referred to as odd days.

Decoded Day of the week

Generally, the week begins with Monday and ends with Sunday. Monday to Friday are called weekdays and Saturday, Sunday are called Weekends.

The days of the week are coded as follows,

Code of the day Day
0 Sunday
1 Monday
2 Tuesday
3 Wednesday
4 Thursday
5 Friday
6 Saturday

Example: If today is Monday, what will be the day after 3 days.
Today is Monday
Add 3 days to the given day.
3 days after Monday is Thursday.

Concept of Odd Day

January has 31 days, irrespective of ordinary year or leap year. The division of the number 31 by 7 gives the remainder 3 hence January has 3 odd days. Any month which has 31 days has 3 odd days and any month that has 30 days has 2 odd days. The February month of the ordinary year has 28 days, division of 28 by 7 gives zero as remainder. Hence the number of odd days in February of an ordinary year will have 0 odd days and in the case of leap year, it has 1 odd day as February has 29 days in a leap year.

Month Number of Odd Days
January 3
February 0/1
March 3
April 2
May 3
June 2
July 3
August 3
September 2
October 3
November 2
December 3

Properties of Calendar Elements in Calendar Problems

Properties of a year:

  • There are 2 kinds of years: Leap year and non-leap year.
  • An ordinary year has 365 days and a leap year has 366 days. This extra day appears in February which in a leap year has 29 days instead of 28.

Leap Year Rule:
A year to be a leap year, it must satisfy two conditions.

  • It must be divisible by 4 such as 2016, 5324, and so on. By this rule, every century year should be a leap year.
  • But for a century year to be a leap year, there is a second rule, a century year must be divisible by 400 to be a leap year. 1600, 2000, 2400 are leap years but 1990, 2100, 2200 are not.

Calendar Problems with Solutions

Example 1.
If it is Monday on 1st October 2012, what day will it be on 2nd December 2013?
Till 1st October 2013, it is intervening 1 ordinary year with 365 days and 1 odd day.
So, the weekday on 2nd December 2013 will be Monday.

Example 2.
What was the weekday on 21st June 1354?
The usual calendar starts with 1st January, Monday and the 0th day of January is on Sunday.
The mechanism enables you to get intervening odd days up to say, 31st December 100 AD as exactly 5 and so the weekday will be 6 days after Sunday that is Saturday.
In the 13th century, odd days is 5.
In the first 53 years of the 14th century, 13 leap years and 40 ordinary years contribute to odd days as,
modulo 7(13 × 2 + 40) = modulo 7(66) = 3.
In 1354 (a normal year) upto 21st June, number of days = (31 + 28 + 31 + 30 + 31 + 21) = 172 giving a number of odd days 4.
So, the weekday on 21st June 1354 is Friday.

Example 3.
The calendar for the year 2007 will be the same for the year.
a. 2018
b. 2017
c. 2016
d. 2014
2007 is not a leap year and intervening years starting from 2007 together has 0 days.
2007 – odd days 1,
2008 – a leap year – odd days 2,
2009 – odd days 1,
2010 – odd days 1,
2011 – odd days 1,
2012 – a leap year – odd days 2,
2013 – odd days 1
Up to 2013 odd days are 9 – net 2.
So, 2014 1st January won’t have the same day as 1st January 2007.
2014 – odd days between 1st January 2007 and 1st January 2017 is 6. Add 1 more odd day for 2017 to odd day 7, net 0, to have 1st January 2018 same day as 1st January 2007.
Thus the answer is 2018 option a.

Example 4.
If today is 26th January 2021 Tuesday, what will be the day 350 days from now?
a. Monday
b. Tuesday
c. Wednesday
d. Thursday
350 days from today is 50 complete weeks with 0 odd days.
Today being Tuesday, 350 days from today will also be Tuesday.
Thus the correct answer is option B.

Example 5.
If yesterday was Monday, tomorrow will be
a. Tuesday
b. Wednesday
c. Thursday
d. Friday
Solution: Tuesday
So, the answer is option a.

FAQs on Calendar

1. What if the formula of the calendar?

1 ordinary year = 365 days = (52 weeks + 1 day)
1 ordinary year has 1 odd day.
1 leap year has 2 odd days = (76 × 1 + 24 × 2) odd days = 124 odd days

2. Is 2000 leap year or not?

The year 2000 was a leap year, for example, but the years 1700, 1800, and 1900 were not. The next time a leap year will be skipped is the year 2100.

3. Which two months in a year have the same calendar?

April and July months will have the same calendar.

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