Calendars

Prerequisites

Division with remainder — the whole method is “divide by 7 and keep the remainder”.
The number of days in each month (the knuckle method works).
Series and Analogies and Puzzles come earlier in General Mental Ability; this page is independent of them.

The Hook: Which Day Was the State Born?

Connect

Chhattisgarh came into being on 1 November 2000, the date celebrated every year as Rajyotsava (राज्योत्सव). Few people remember which day of the week that was.

It was a Wednesday — and by the end of this page you will be able to work that out with nothing but a pencil, in under a minute.

The question this page answers: given any date, how do you find its day of the week — and how do you move from a known day to an unknown one across months and years?

Why it matters for CGPSC: calendar (कैलेंडर) questions in Prelims Paper II are almost pure method. Once you know odd days and the leap-year rule, every question is a short remainder calculation.

Odd Days: The Only Idea You Need

A week has 7 days, so only the remainder after dividing by 7 affects the day of the week. That remainder is called the number of odd days (विषम दिन).

Period	Days	Odd days
1 ordinary year	365 = 52 weeks + 1 day	1
1 leap year	366 = 52 weeks + 2 days	2
Month of 31 days	4 weeks + 3 days	3
Month of 30 days	4 weeks + 2 days	2
February (ordinary / leap)	28 / 29 days	0 / 1

Leap years

$$\boxed{\text{Non-century year: leap if divisible by 4} \qquad \text{Century year: leap only if divisible by 400}}$$

2024 and 2028 are leap years; 2026 is not.
2000 was a leap year (divisible by 400); 1900 was not, and 2100 will not be (divisible by 100 but not by 400).

Odd days in centuries

Years	Leap years in them	Odd days
100	24	5
200	48	3
300	72	1
400	97	0

So every complete block of 400 years contributes 0 odd days, which is why 1600, 2000 and 2400 all “reset” the count.

Day codes

Total odd days, counted from the start of year 1, give the day directly:

Odd days	0	1	2	3	4	5	6
Day	Sunday	Monday	Tuesday	Wednesday	Thursday	Friday	Saturday

Finding the Day for Any Date

Split the date into three parts, find the odd days in each, add, and divide by 7:

Complete years before the given year (use 400-year blocks, the century table, then the remaining years).
Complete months of the given year before the given month.
Days of the given month.

Worked example: 1 November 2000 (Chhattisgarh Rajyotsava)

Complete years = 1999 = 1600 + 300 + 99.

1600 years → 0 odd days; 300 years → 1 odd day.
99 years contain 24 leap years and 75 ordinary years: $ 24\times 2 + 75 = 123 $; $ 123 \div 7 $ leaves 4.
Years total: $ 0 + 1 + 4 = 5 $.

Months of 2000 before November (2000 is a leap year): Jan 31, Feb 29, Mar 31, Apr 30, May 31, Jun 30, Jul 31, Aug 31, Sep 30, Oct 31 = 305 days; $ 305 \div 7 $ leaves 4.

Days: 1.

Total $ = 5 + 4 + 1 = 10 $; $ 10 \div 7 $ leaves 3 → Wednesday.

Worked example: 15 August 1947

Complete years = 1946 = 1600 + 300 + 46. The 46 years contain 11 leap years: $ 11\times 2 + 35 = 57 $ → 1. Years total $ = 0 + 1 + 1 = 2 $.

Jan–Jul 1947 (ordinary year): $ 31 + 28 + 31 + 30 + 31 + 30 + 31 = 212 $ → 2.

Days: 15 → 1.

Total $ = 2 + 2 + 1 = 5 $ → Friday.

Moving From a Known Day

Most CSAT calendar questions give you one day and ask for another. Count odd days between the two dates and shift.

Situation	Shift
Same date, next year (no 29 February in between)	+1 day
Same date, next year (29 February in between)	+2 days
$ N $ days later	$ N \div 7 $, keep the remainder

Worked examples

1 January 2026 was a Thursday. 2026 is an ordinary year, so 1 January 2027 is a Friday. Going back, 2025 was also ordinary, so 1 January 2025 was a Wednesday.
Today is Tuesday. What day will it be after 100 days? $ 100 = 14\times 7 + 2 $, so 2 days ahead → Thursday.
What day comes 61 days after a Tuesday? $ 61 = 8\times 7 + 5 $ → Tuesday + 5 = Sunday.

Where the extra day sits

Moving one year forward picks up the extra day only if a 29 February lies between the two dates. From 10 January 2024 to 10 January 2025 it does (+2); from 10 March 2024 to 10 March 2025 it does not (+1); from 10 March 2027 to 10 March 2028 it does (+2). Check which side of 29 February each date lies.

Repeating Calendars

Two years have identical calendars when they start on the same day and are both leap or both ordinary.

Type of year	Calendar repeats after	Example
Leap year	28 years	2024 → 2052
Year just after a leap year (remainder 1 on dividing by 4)	6 years	2025 → 2031
Second or third year after a leap year (remainder 2 or 3)	11 years	2026 → 2037; 2027 → 2038

These gaps hold only when no century non-leap year (like 2100) falls in between; near such a year, count the odd days directly.

Months with the same calendar

Within one year, months that start on the same weekday:

Ordinary year	Leap year
January – October	January – April – July
February – March – November	February – August
April – July	March – November
September – December	September – December

The Doomsday Shortcut

In any year, the dates 4/4, 6/6, 8/8, 10/10, 12/12 and 9/5, 5/9, 7/11, 11/7, along with the last day of February and 14 March, all fall on the same weekday (the year’s “doomsday”).

For 2026, that day is Saturday. So 12 December 2026 is a Saturday, and 25 December 2026 (13 days later) is a Saturday + 6 = Friday.

Use it as a check, not the main method

The doomsday trick is perfect when the question gives you the current year’s days. For historical dates (1947, 1950, 2000), the odd-days method is safer.

Memory Tricks

Anchor these

“1-2, 3-2-0”: ordinary year 1, leap year 2; 31-day month 3, 30-day month 2, February 0 (1 in a leap year).
Centuries: “5-3-1-0” — 100, 200, 300, 400 years.
“Sunday is zero” — 0 Sunday, 1 Monday … 6 Saturday.
Repeat gaps “28 – 6 – 11 – 11” — leap year, then the three years after it.
Doomsday pairs “9 to 5 at the 7-11” — 9/5, 5/9, 7/11, 11/7, plus every even month’s same-number date from April.

Don’t Confuse

This	vs	That
2000 — leap (divisible by 400)		1900, 2100 — not leap (divisible by 100 only)
100 years = 5 odd days		1 ordinary year = 1 odd day
Ordinary-year calendar repeats after 6 or 11 years		Leap-year calendar repeats after 28 years
Ordinary year: January = October		Leap year: January = April = July

Common Mistakes

Trap 1: Counting the given year as complete

For 1 November 2000, the complete years are 1999, not 2000. The months of 2000 are counted separately, and only up to October.

Trap 2: Treating every century year as leap

“Divisible by 4” is not enough for century years. 1900 was not a leap year; options built on “1900 is leap” are a standard trap.

Trap 3: Assuming every calendar repeats after 28 years

Only leap-year calendars wait 28 years. 2026’s calendar comes back in 2037, not 2054.

Practice

Level 1: Foundation

How many odd days are there in a leap year?
Was 1900 a leap year? Was 2000?
How many odd days are there in 300 years?
If today is Monday, what day will it be after 15 days?

Answers

2 (366 = 52 weeks + 2 days).
1900 — no (not divisible by 400); 2000 — yes.
1.
$ 15 = 2\times 7 + 1 $ → Tuesday.

Level 2: Prelims MCQs

Q1. What day of the week was 26 January 1950?

(a) Wednesday (b) Thursday (c) Friday (d) Sunday

Answer: (b) Thursday

Complete years = 1949 = 1600 (0) + 300 (1) + 49 years. The 49 years have 12 leap years: $ 12\times 2 + 37 = 61 $ → 5. Years total $ = 0 + 1 + 5 = 6 $. Days in January: 26 → 5. Total $ = 6 + 5 = 11 $ → 4 → Thursday.

Q2. If 1 January 2026 is a Thursday, what day of the week is 1 January 2027?

(a) Thursday (b) Saturday (c) Friday (d) Wednesday

Answer: (c) Friday

2026 is an ordinary year (not divisible by 4), so it has 1 odd day. Thursday + 1 = Friday. Option (b) wrongly treats 2026 as a leap year.

Q3. The calendar for the year 2026 will next be repeated in the year:

Answer: (d) 2037

2026 is the second year after the leap year 2024, so its calendar repeats after 11 years: 2037. Check by odd days: 2026 to 2036 contain 8 ordinary and 3 leap years, $ 8 + 6 = 14 $ odd days → 0, and 2037 is also an ordinary year.

Q4. Consider the following statements:

A century year is a leap year only if it is divisible by 400.
2000 was a leap year.
1900 was a leap year.

Which of the statements given above is/are correct?

(a) 1 and 2 only (b) 2 only (c) 2 and 3 only (d) 1, 2 and 3

Answer: (a) 1 and 2 only

Statement 1 is the Gregorian rule. 2000 is divisible by 400, so it was a leap year (2 correct). 1900 is divisible by 100 but not by 400, so it was not a leap year (3 wrong).

Q5. Match List I (period) with List II (number of odd days):

List I	List II
A. An ordinary year	1. 1
B. A leap year	2. 2
C. 100 years	3. 3
D. 200 years	4. 5

(a) A-1, B-2, C-3, D-4 (b) A-2, B-1, C-4, D-3 (c) A-1, B-2, C-4, D-3 (d) A-1, B-3, C-4, D-2

Answer: (c) A-1, B-2, C-4, D-3

An ordinary year has 1 odd day and a leap year 2. 100 years (24 leap + 76 ordinary) have $ 48 + 76 = 124 $ → 5 odd days; 200 years have $ 5\times 2 = 10 $ → 3.

Level 3: Speed Drill — Solve in 60 Seconds

Each item should take under 60 seconds. In the reasoning part of Mains Paper IV (GS-II), show the odd-day split (years, months, days) as your working.

How many odd days are there in the year 2024?
What day of the week was 15 August 1947?
1 January 2026 was a Thursday. What day was 1 January 2025?
Which is the next year after 2025 with exactly the same calendar?
Today is Tuesday. What day will it be after 100 days?
12 December 2026 is a Saturday (doomsday). What day is 25 December 2026?
How many leap years are there from 1901 to 2000, both inclusive?

Answers with the method used

2 — 2024 is a leap year.
Friday — $ 2 + 2 + 1 = 5 $ odd days.
Wednesday — 2025 is ordinary, so step back 1 day.
2031 — year after a leap year repeats after 6 years.
Thursday — $ 100 \div 7 $ leaves 2.
Friday — 13 days later = Saturday + 6.
25 — 1904 to 2000 in steps of 4 (2000 counts, being divisible by 400).

Quick Revision Table

Idea	Fact
Odd days	Ordinary year 1, leap year 2; months 3 / 2 / 0 (Feb, 1 if leap)
Leap year	Divisible by 4; century years only if divisible by 400
Centuries	100 → 5, 200 → 3, 300 → 1, 400 → 0
Day codes	0 Sunday, 1 Monday, … 6 Saturday
Any date	Complete years + complete months + days, then $ \div 7 $
Calendar repeat	Leap 28; year after leap 6; other two 11
Doomsday 2026	Saturday (4/4, 6/6, 8/8, 10/10, 12/12 …)
1 Nov 2000	Wednesday (Chhattisgarh formation day)

Key Takeaways

Only the remainder after dividing by 7 matters — that is the number of odd days.
Leap year: divisible by 4, but a century year must be divisible by 400 (2000 yes, 1900 and 2100 no).
Century blocks give 5, 3, 1, 0 odd days for 100, 200, 300, 400 years.
For any date: complete years + complete months + days, then divide by 7 and read the day code (0 = Sunday).
Calendars repeat after 28 years (leap), 6 years (year after a leap) or 11 years (the other two).

What’s Next

Clocks — the other fixed-formula topic of mental ability.
Puzzles — ranking, grid and counting puzzles.
State Formation and Administration — the story behind 1 November 2000.
Basic Numeracy — division and remainders underpin the odd-day method.
General Mental Ability — Quick Revision — the chapter on one page.