# Calendars — Find the Day of Any Date with Odd Days

Source: https://skills101.in/learn/reasoning/calendars — Skills101 free tutorial (Logical Reasoning). Updated 2026-11-09.

Calendar questions ask "what day of the week was this date?" The method is **counting odd days** — the days left over after full weeks.

## 1. Leap years

- A year divisible by **4** is a leap year (2024, 2028).
- But a **century** year (1900, 2000) is a leap year only if divisible by **400**.
- So 2000 was a leap year; 1900 and 2100 are **not**.

## 2. Odd days

An **odd day** is a day beyond complete weeks. 8 days = 1 week + **1 odd day**.

![Odd days table: normal year 1, leap year 2, 100 years 5, 200 years 3, 300 years 1, 400 years 0. Odd days 0 to 6 map to Sunday to Saturday](https://skills101.in/learn-img/reasoning/odd-days.svg)

- Normal year = 365 days = 52 weeks + **1** odd day
- Leap year = 366 days = 52 weeks + **2** odd days
- 100 years (24 leap + 76 normal) = 124 days → **5** odd days
- 400 years → **0** odd days (so the calendar repeats every 400 years)

Month odd days (non-leap year): Jan 3, Feb 0, Mar 3, Apr 2, May 3, Jun 2, Jul 3, Aug 3, Sep 2, Oct 3, Nov 2, Dec 3. (In a leap year Feb has 1.)

## 3. Day shifts: the fast method

Most questions give one date and ask about another nearby. Just count odd days between them.

### Example 1
*1 January 2025 was a Wednesday. What day is 1 January 2026?*

2025 is a normal year → +1 odd day → **Thursday**.

### Example 2
*15 August 2024 was a Thursday. What day was 15 August 2025?*

From 15 Aug 2024 to 15 Aug 2025 there is no 29 February in between (it was in Feb 2024, before August) → +1 → **Friday**.

### Example 3
*If 5 March 2023 was a Sunday, what day was 5 March 2024?*

This period includes 29 Feb 2024 → +2 → **Tuesday**.

### Example 4 — within a year
*If 1 March is a Monday, what day is 1 June in the same year?*

Odd days: March 3 + April 2 + May 3 = 8 → 8 mod 7 = 1 → **Tuesday**.

## 4. Day of the week from scratch

Count odd days from 1 January of year 1 (which counts as a Monday). Use the table: 0 = Sunday, 1 = Monday, … 6 = Saturday.

### Example 5
*What day was 26 January 1950?*

- 1600 years → 0 odd days. 300 more (1601–1900) → 1.
- 1901–1949: 49 years with 12 leap years → 49 + 12 = 61 → 61 mod 7 = 5.
- 26 days of January 1950 → 26 mod 7 = 5.
- Total = 0 + 1 + 5 + 5 = 11 → 11 mod 7 = 4 → **Thursday**. ✓ (India's first Republic Day was a Thursday.)

## 5. Same calendar years

Two years have the same calendar if they start on the same day **and** are both leap or both normal.

### Example 6
*Which is the next year with the same calendar as 2023?*

Add up the odd days year by year, starting from 2023, until the running total is a multiple of 7 — and the year you land on is also a normal (non-leap) year like 2023.

| Year | Type | Odd days | Running total |
|---|---|---|---|
| 2023 | normal | 1 | 1 |
| 2024 | leap | 2 | 3 |
| 2025 | normal | 1 | 4 |
| 2026 | normal | 1 | 5 |
| 2027 | normal | 1 | 6 |
| 2028 | leap | 2 | 8 |
| 2029 | normal | 1 | 9 |
| 2030 | normal | 1 | 10 |
| 2031 | normal | 1 | 11 |
| 2032 | leap | 2 | 13 |
| 2033 | normal | 1 | **14** ✓ |

After 2033 the total is 14 (a multiple of 7), so **2034** starts on the same day as 2023, and both are normal years → same calendar.

## Common mistakes

- Calling 1900 or 2100 a leap year.
- Adding 2 for a leap year when 29 February is **not** inside the period.
- Forgetting to reduce totals mod 7.

## Quick recap

- Leap year: divisible by 4; century years only if divisible by 400.
- Normal year → 1 odd day, leap year → 2.
- Count odd days between dates; reduce mod 7; shift the day.
- 0 = Sunday … 6 = Saturday.


Practice quiz and free certificate: https://skills101.in/learn/reasoning/calendars