Find the day of the week for any date: the odd days trick

किसी भी तारीख का दिन निकालें: विषम दिन (ऑड डेज़) ट्रिक

Only the days left over after full weeks (odd days) decide the weekday. Add the odd days of the centuries, the years and the months, take the remainder after dividing by 7, and read the day: 0 = Sunday, 1 = Monday … 6 = Saturday.

पूरे सप्ताहों के बाद बचे दिन (विषम दिन) ही वार तय करते हैं। शताब्दियों, वर्षों और महीनों के विषम दिन जोड़ें, 7 से भाग देकर शेषफल लें और दिन पढ़ें: 0 = रविवार, 1 = सोमवार … 6 = शनिवार।

The numbers to remember

Ordinary year = 365 days = 52 weeks + 1 odd day. Leap year = 366 days = 2 odd days.

A year is a leap year if it divides by 4 — but a century year (1900, 2000) must divide by 400. So 2000 was a leap year and 1900 was not.

Centuries: 100 years = 5 odd days, 200 years = 3, 300 years = 1, 400 years = 0 (so 1600 and 2000 years also give 0).

Months: a 31-day month = 3 odd days, a 30-day month = 2, February = 0 (or 1 in a leap year).

साधारण वर्ष = 1 विषम दिन, लीप वर्ष = 2। शताब्दी वर्ष तभी लीप है जब 400 से विभाज्य हो (2000 लीप, 1900 नहीं)। 100 वर्ष = 5, 200 = 3, 300 = 1, 400 = 0 विषम दिन। 31 दिन का महीना = 3, 30 दिन का = 2, फ़रवरी = 0 (लीप वर्ष में 1)।

Split the date: completed 400-year blocks + completed centuries + completed years + days of the current year up to the date. · तारीख को बाँटें: पूरे 400 वर्ष + पूरी शताब्दियाँ + पूरे वर्ष + चालू वर्ष के दिन।
Odd days from the years = (number of years) + (number of leap years among them). · वर्षों के विषम दिन = वर्षों की संख्या + उनमें लीप वर्षों की संख्या।
Add everything and divide by 7. The remainder gives the day: 0 Sun, 1 Mon, 2 Tue, 3 Wed, 4 Thu, 5 Fri, 6 Sat. · सब जोड़कर 7 से भाग दें; शेषफल: 0 रवि, 1 सोम, 2 मंगल, 3 बुध, 4 गुरु, 5 शुक्र, 6 शनि।

Example What day of the week was 15 August 1947?

1600 years → 0. Next 300 years (1601–1900) → 1. Years 1901–1946: 46 years with 11 leap years → 46 + 11 = 57 → 57 mod 7 = 1. 1947 up to 15 Aug: Jan 3 + Feb 0 + Mar 3 + Apr 2 + May 3 + Jun 2 + Jul 3 + 15 days 1 = 17 → 3. Total 0 + 1 + 1 + 3 = 5 → Friday.

Example What day of the week was 26 January 1950?

1600 → 0, 300 → 1. Years 1901–1949: 49 years with 12 leap years → 61 → 5. 26 January → 26 mod 7 = 5. Total 0 + 1 + 5 + 5 = 11 → 4 → Thursday.

Same date in the next year (the quick shift)

The same date one year later moves forward 1 weekday — or 2 weekdays if 29 February falls in between.

एक वर्ष बाद वही तारीख 1 दिन आगे खिसकती है — और यदि बीच में 29 फ़रवरी आए तो 2 दिन।

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

2025 is not a leap year → +1 → Thursday.

Example 10 March 2023 was a Friday. What day was 10 March 2024?

29 February 2024 falls in between → +2 → Sunday.

Repeating calendars

A year repeats the calendar of an earlier year when both start on the same weekday and both are (or both are not) leap years. Keep adding odd days year by year until the total is a multiple of 7. From 2026: 2026, 2027 (1 each), 2028 (2), 2029–2031 (1 each), 2032 (2), 2033–2035 (1 each), 2036 (2) = 14 = 0 mod 7, so 2037 has the same calendar as 2026.

दो वर्षों का कैलेंडर तब एक जैसा होता है जब दोनों एक ही वार से शुरू हों और दोनों लीप (या दोनों साधारण) हों। विषम दिन जोड़ते जाएँ जब तक योग 7 का गुणज न हो जाए: 2026 का कैलेंडर 2037 में दोहराएगा।

Try it yourself · अभ्यास

What day of the week was 2 October 1869? · 2 अक्टूबर 1869 को कौन-सा दिन था?
Show answer
1600 → 0; 1601–1800 (200 years) → 3; 1801–1868: 68 years + 17 leap = 85 → 1; 1 Jan–2 Oct 1869 = 275 days → 2. Total 6 → Saturday
If 19 October 2026 is a Monday, what day will 19 October 2027 be? · यदि 19 अक्टूबर 2026 सोमवार है, तो 19 अक्टूबर 2027 को कौन-सा दिन होगा?
Show answer
No 29 February in between → +1 → Tuesday
How many odd days are there in 300 years? · 300 वर्षों में कितने विषम दिन होते हैं?
Show answer
1 (300 years = 5 × 3 = 15 → 15 mod 7 = 1)