Calendar Odd Days Trick for SSC CGL
The calendar odd days trick works like this: odd days are the days left over after removing complete weeks. Add the odd days of the completed centuries, the completed years, the completed months and the given date, divide the total by 7, and read the remainder as the day: 0 = Sunday, 1 = Monday, 2 = Tuesday, 3 = Wednesday, 4 = Thursday, 5 = Friday, 6 = Saturday. An ordinary year has 1 odd day and a leap year has 2.
🔥 Key Exam Takeaway: Learn four numbers: 100 years = 5 odd days, 200 years = 3, 300 years = 1, 400 years = 0. Example: 15 August 1947 → 1600 years (0) + 300 years (1) + 46 years (1) + Jan–Jul (2) + 15 days (1) = 5 → Friday.
Calendar questions are asked in the reasoning section of SSC CGL, CHSL, MTS and CPO, and sometimes in bank exams. Every date and day in this note has been checked against Python's datetime module, and both methods below were tested on every date from 1 January 1600 to 31 December 2399 (Gregorian calendar) with zero errors.
What Are Odd Days in Calendar Reasoning?
A week has 7 days. Any number of days can be written as complete weeks plus a remainder. That remainder (0 to 6) is the number of odd days.
| Period | Total days | Complete weeks + odd days | Odd days |
|---|---|---|---|
| Ordinary year | 365 | 52 weeks + 1 day | 1 |
| Leap year | 366 | 52 weeks + 2 days | 2 |
| 31-day month | 31 | 4 weeks + 3 days | 3 |
| 30-day month | 30 | 4 weeks + 2 days | 2 |
| February (ordinary) | 28 | 4 weeks + 0 days | 0 |
| February (leap) | 29 | 4 weeks + 1 day | 1 |
Odd day number to day of the week:
| Odd days (remainder) | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|---|
| Day | Sunday | Monday | Tuesday | Wednesday | Thursday | Friday | Saturday |
Leap Year Rules for Calendar Questions
| Year type | Rule | Examples |
|---|---|---|
| Normal year | Leap if divisible by 4 | 2024, 2028 are leap; 2026 is not |
| Century year (ends in 00) | Leap only if divisible by 400 | 1600, 2000, 2400 are leap |
| Century year not divisible by 400 | Not leap | 1700, 1800, 1900, 2100 are not leap |
Trap: 1900 and 2100 are not leap years even though they are divisible by 4. In 400 consecutive years there are exactly 97 leap years.
Century Odd Days and Century Codes (Calendar Trick Table)
In 100 years there are 24 leap years and 76 ordinary years: 24 × 2 + 76 × 1 = 124 odd days, and 124 ÷ 7 leaves 5. The 400th year is a leap century year, which adds 1 more, so 400 years have 0 odd days.
| Completed years | Odd days | Meaning |
|---|---|---|
| 100 years | 5 | e.g. years 1 to 100 |
| 200 years | 3 | 10 ÷ 7 leaves 3 |
| 300 years | 1 | 15 ÷ 7 leaves 1 |
| 400 years | 0 | 20 + 1 = 21, leaves 0 |
| 800, 1200, 1600, 2000 years | 0 | Any multiple of 400 |
Century rule: the last day of a century can only be Sunday, Monday, Wednesday or Friday. It can never be Tuesday, Thursday or Saturday. (For example, 31 December 1999 was a Friday and 31 December 2000 was a Sunday.)
Century codes for the month-code method (used in the second trick below):
| Years | 1600–1699 | 1700–1799 | 1800–1899 | 1900–1999 | 2000–2099 | 2100–2199 |
|---|---|---|---|---|---|---|
| Century code | 6 | 4 | 2 | 0 | 6 | 4 |
The codes repeat every 400 years (6, 4, 2, 0).
How to Calculate the Day of Any Date: Odd Days Method (Step by Step)
- Completed centuries: for a date in year Y, take Y − 1 completed years and split them into centuries and remaining years. For 1947 that is 1600 + 300 + 46.
- Odd days of the centuries: use the table (1600 → 0, 300 → 1).
- Odd days of the remaining years: count the leap years among them. Odd days = 2 × (leap years) + 1 × (ordinary years), then take the remainder after dividing by 7.
- Odd days of completed months of the given year (31-day month = 3, 30-day month = 2, February = 0 or 1).
- Add the date itself.
- Total ÷ 7: the remainder gives the day (0 = Sunday … 6 = Saturday).
Worked example: 15 August 1947
| Part | Working | Odd days |
|---|---|---|
| 1600 years | multiple of 400 | 0 |
| 300 years | from the table | 1 |
| 46 years (1901–1946) | 11 leap + 35 ordinary = 22 + 35 = 57 → 57 ÷ 7 leaves 1 | 1 |
| January to July 1947 | 31 + 28 + 31 + 30 + 31 + 30 + 31 = 212 → leaves 2 | 2 |
| 15 August | 15 ÷ 7 leaves 1 | 1 |
| Total | 0 + 1 + 1 + 2 + 1 = 5 | Friday |
Calendar Month Code Trick: Day of the Week in 30 Seconds
This shortcut is faster for dates from 1600 to 2399.
Day number = (date + month code + YY + ⌊YY ÷ 4⌋ + century code) ÷ 7, take the remainder. YY is the last two digits of the year, and ⌊YY ÷ 4⌋ means divide by 4 and drop the remainder. In a leap year, subtract 1 for dates in January and February. Remainder 0 = Sunday, 1 = Monday, … 6 = Saturday.
| Month | Jan | Feb | Mar | Apr | May | Jun | Jul | Aug | Sep | Oct | Nov | Dec |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Month code | 0 | 3 | 3 | 6 | 1 | 4 | 6 | 2 | 5 | 0 | 3 | 5 |
Memory hook: read the codes as three groups, 033 614 625 035.
Example: 15 August 1947 → 15 + 2 + 47 + 11 + 0 = 75 → 75 ÷ 7 leaves 5 → Friday (same answer as the odd days method).
Example with the leap-year correction: 29 February 2028 → 29 + 3 + 28 + 7 + 6 − 1 = 72 → 72 ÷ 7 leaves 2 → Tuesday.
Day-of-Week Shortcut: Same Date Next Year or After N Days
| Question type | Rule |
|---|---|
| Same date, next year | Day moves forward by 1, or by 2 if 29 February falls in between |
| Same date, previous year | Day moves back by 1, or by 2 if 29 February falls in between |
| N days after a known day | Move forward by (N ÷ 7) remainder |
| N days before a known day | Move back by (N ÷ 7) remainder |
| Days between two dates | Count days left in the first month + full months + days in the last month, then ÷ 7 |
| 53 of one weekday in a year | Ordinary year: the day of 1 January occurs 53 times. Leap year: the days of 1 and 2 January occur 53 times each |
Watch the 29 February trap: from 1 March 2027 to 1 March 2028, 29 February 2028 falls in between, so the day moves by 2. But from 1 January 2028 to 1 January 2029, it also falls in between, so that moves by 2 as well. Always ask: "Does 29 February lie inside my interval?"
Repeat Calendar Rule: When Does a Year's Calendar Repeat?
Two years have the same calendar 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, 2028 → 2056 |
| Year after a leap year (Y ÷ 4 leaves 1) | 6 years | 2025 → 2031, 2029 → 2035 |
| Year ÷ 4 leaves 2 | 11 years | 2026 → 2037, 2022 → 2033 |
| Year ÷ 4 leaves 3 | 11 years | 2027 → 2038, 2023 → 2034 |
Exception: the rule assumes no non-leap century year (like 1900 or 2100) falls in between. It is exact for every year from 1901 to 2071. Near 2100 it fails (2096 repeats in 2108, not 2124), so count odd days instead. A quick self-check: the total odd days between the two years must be a multiple of 7.
Calendar Questions for SSC CGL with Solutions
Example 1: Republic Day 1950 by the odd days method
What day was 26 January 1950?
Solution: 1600 years → 0; 300 years → 1; 49 years (1901–1949) have 12 leap years → 24 + 37 = 61 → leaves 5; 26 January → leaves 5. Total = 0 + 1 + 5 + 5 = 11 → leaves 4 → Thursday.
Example 2: 1 January 2000
Solution: 1999 completed years = 1600 + 300 + 99. Odd days: 0 + 1 + (24 leap + 75 ordinary = 123 → leaves 4) = 5. Add 1 for 1 January → 6 → Saturday.
Example 3: Gandhi Jayanti, 2 October 1869
Solution: 1600 → 0; 200 → 3; 68 years (1801–1868) have 17 leap years → 34 + 51 = 85 → leaves 1; January to September 1869 (ordinary year) = 273 days → leaves 0; 2 October → 2. Total = 6 → Saturday.
Example 4: Month-code method for a date in 2027
What day will 26 January 2027 be?
Solution: 26 + 0 (January) + 27 + 6 (⌊27 ÷ 4⌋) + 6 (2000s) = 65 → 65 ÷ 7 leaves 2 → Tuesday. 2027 is not a leap year, so no correction is needed.
Example 5: Same date next year
1 January 2026 was a Thursday. What day will 1 January 2027 be?
Solution: 2026 is an ordinary year, so the day moves by 1 → Friday.
Example 6: Two years ahead across a leap day
16 October 2026 is a Friday. What day will 16 October 2028 be?
Solution: October 2026 → October 2027: no 29 February in between → +1 (Saturday). October 2027 → October 2028: 29 February 2028 is in between → +2. Total +3 → Monday.
Example 7: N days later
16 October 2026 is a Friday. What day is 25 December 2026?
Solution: Days after 16 October: 15 (rest of October) + 30 (November) + 25 (December) = 70 → 70 ÷ 7 leaves 0 → same day → Friday.
Example 8: Gap between two dates in the same year
26 January 2026 was a Monday. What day was 15 August 2026?
Solution: Days from 26 January to 15 August = 5 (rest of January) + 28 + 31 + 30 + 31 + 30 + 31 + 15 = 201 → 201 ÷ 7 leaves 5. Monday + 5 → Saturday.
Example 9: Repeat calendar
Which year will have the same calendar as 2026?
Solution: 2026 ÷ 4 leaves 2, so the calendar repeats after 11 years → 2037. Check: both are ordinary years and both start on a Thursday.
Example 10: 53 weekdays in a year
Which day occurs 53 times in 2026, and which days occur 53 times in 2028?
Solution: 2026 is ordinary and starts on Thursday → 53 Thursdays. 2028 is a leap year and starts on Saturday → 53 Saturdays and 53 Sundays.
Common Mistakes in Calendar Odd Days Questions
| Trap | Correct way |
|---|---|
| Counting the given year as completed | For a date in 1947, count only 1946 completed years |
| Treating 1900 or 2100 as leap | Century years are leap only if divisible by 400 |
| Forgetting the leap-year correction in the month-code method | Subtract 1 for January and February dates of a leap year |
| Adding 2 for every leap year in a "same date next year" question | Add 2 only if 29 February lies in the interval |
| Starting the day table from Monday | In the odd days method, 0 = Sunday |
| Using the 6 / 11 / 28 rule across 2100 | Count odd days when a non-leap century year is in between |
Calendar Odd Days Quick Revision Table
| Item | Value |
|---|---|
| Ordinary year | 1 odd day |
| Leap year | 2 odd days |
| 100 / 200 / 300 / 400 years | 5 / 3 / 1 / 0 odd days |
| 31-day / 30-day month | 3 / 2 odd days |
| February | 0 (ordinary), 1 (leap) |
| Month codes | 0 3 3 6 1 4 6 2 5 0 3 5 |
| Century codes 1600s / 1700s / 1800s / 1900s / 2000s | 6 / 4 / 2 / 0 / 6 |
| Last day of a century | Never Tuesday, Thursday or Saturday |
| Calendar repeats | Leap year 28; Y ÷ 4 leaves 1 → 6; leaves 2 or 3 → 11 |
Calendar Questions with Answers (Practice Set for SSC CGL and CHSL)
Q1. How many odd days are there in the year 2028? Answer: 2. 2028 is divisible by 4 and is not a century year, so it is a leap year.
Q2. How many odd days are there in 800 years? Answer: 0. 800 is a multiple of 400.
Q3. 26 January 2026 was a Monday. What day was 15 August 2026? Answer: Saturday. The gap is 201 days, which leaves 5 odd days; Monday + 5 = Saturday.
Q4. What day of the week was 1 January 2001? Answer: Monday. 2000 completed years have 0 odd days; add 1 for 1 January → 1 → Monday.
Q5. Which year will have the same calendar as 2025? Answer: 2031. 2025 ÷ 4 leaves 1, so it repeats after 6 years. Both 2025 and 2031 start on a Wednesday and are ordinary years.
Q6. 1 March 2027 is a Monday. What day will 1 March 2028 be? Answer: Wednesday. 29 February 2028 lies in between, so the day moves forward by 2.
Q7. What day was 14 November 1889? Answer: Thursday. 1600 → 0; 200 → 3; 88 years (1801–1888) with 22 leap years → 44 + 66 = 110 → leaves 5; January to October 1889 = 304 days → leaves 3; 14 November → 0. Total 11 → leaves 4 → Thursday.
Q8. 16 October 2026 is a Friday. What day will it be 100 days later? Answer: Sunday. 100 ÷ 7 leaves 2; Friday + 2 = Sunday (24 January 2027).
Q9. Is 2100 a leap year? Answer: No. It is a century year that is not divisible by 400.
Q10. Can the last day of a century be a Thursday? Answer: No. The last day of a century can only be a Sunday, Monday, Wednesday or Friday.
Calendar Odd Days FAQs
What is odd days in calendar?
Odd days are the extra days left after taking out complete weeks from a period. An ordinary year has 365 days = 52 weeks + 1 odd day, and a leap year has 2 odd days.
How to calculate odd days in calendar?
Divide the number of days by 7 and take the remainder. For years, count 1 odd day for each ordinary year and 2 for each leap year, then divide the total by 7. For centuries, use 100 years = 5, 200 = 3, 300 = 1, 400 = 0.
How many odd days are there in 100 years?
- A century (not counting a 400-multiple) has 24 leap years and 76 ordinary years, giving 124 odd days, and 124 ÷ 7 leaves 5.
What is the month code trick in calendar reasoning?
Add the date, the month code (0 3 3 6 1 4 6 2 5 0 3 5), the last two digits of the year, those digits ÷ 4 (whole part), and the century code (6 for the 2000s, 0 for the 1900s). Subtract 1 for January or February of a leap year. The remainder after dividing by 7 gives the day, with 0 = Sunday.
After how many years does a calendar repeat?
A leap year's calendar repeats after 28 years. For other years it repeats after 6 years if the year leaves remainder 1 when divided by 4, and after 11 years if it leaves 2 or 3. This holds as long as no non-leap century year falls in between.
Why is 1900 not a leap year?
A century year is a leap year only if it is divisible by 400. 1900 ÷ 400 is not a whole number, so 1900 is an ordinary year, while 2000 is a leap year.
Related topics: revise blood relation questions for SSC CGL, probability questions for bank exams and dice questions for SSC CGL next.
Practice Next
- Take the SSC CGL General Intelligence and Reasoning Sectional Mock Test 01, then Mock Test 02 and Mock Test 03.
- New sectional tests: RRB NTPC General Intelligence and Reasoning Sectional Mock Test 01: CBT 1 Pattern 2026 (30 Questions) and RRB Group D General Intelligence and Reasoning Sectional Mock Test 01: CBT Pattern 2026 (30 Questions).
- New SSC topic test: SSC CGL Calendar, Clock and Mirror Time Mock Test 01: Odd Days, Clock Angles and Mirror Images (15 Questions).
- New SSC topic test: SSC CHSL Calendar and Clock Mock Test 01: Odd Days, Clock Angles and Mirror Time (15 Questions).
- Pair this with the clock topic: Mirror Image Clock Formula.
- Number-based shortcuts that use the same remainder idea: Unit Digit Tricks for SSC CGL and CI and SI Difference Formula for 2, 3 and 4 Years.
- Quant formula sheets: Pipe and Cistern Formula for SSC CGL and Statistics Formulas for SSC CGL.
- Check dates and eligibility in the SSC CGL 2026 notification and the SSC CHSL 2026 notification.
- Browse all study notes.