Short Trick Find Day on a Particular Date

AI Summary

An AI-generated summary of this video lecture.

This video is a tutorial on calculating the day of the week for a given date, using a method based on odd days. The instructor, Yash Jain, begins by posing the question, "On what day does 04 July 1997 lie?" and then systematically breaks down the calculation. The method involves three main steps: first, calculating the number of odd days for the year 1997 by breaking it into 1600 + 300 + 97; second, calculating the number of odd days for the months from January to June 1997; and third, adding the odd days from the year and months, then adding the day of the month (4) and taking the total modulo 7. The video uses a table to determine the number of odd days for different century years (e.g., 100 years = 5 odd days, 200 years = 3 odd days) and a list of the number of days in each month (e.g., Jan = 31, Feb = 28, etc.). The instructor demonstrates the calculation for 1997, arriving at a total of 121 odd days, which corresponds to 2 odd days (121 mod 7 = 2), indicating the day is Tuesday. The video then briefly shows a similar calculation for 26 May 1968, concluding with a humorous meme and a thank you message.

Chapters

1. 0:00 – 2:00 00:00-02:00

   The video opens with a title card showing a calendar and the word "CALENDAR". It then transitions to a lecture format with a blackboard background. The instructor, Yash Jain, introduces the topic with the question, "On what day does 04 July 1997 lie?". A table on the left side of the screen lists the number of odd days for different century years: 100 years = 5, 200 years = 3, 300 years = 1, and 400 years = 0. The instructor explains that the method involves calculating odd days for the year, the months, and the day itself.

2. 2:00 – 5:00 02:00-05:00

   The instructor begins the calculation for 1997. He writes on the board, breaking the year into 1600 + 300 + 97. He uses the table to find the odd days: 1600 years have 0 odd days, 300 years have 1 odd day, and 97 years have 2 odd days (calculated as 96/4 = 24, plus 1 for the 97th year). The total for the year is 0 + 1 + 2 = 3 odd days. He then lists the number of days in each month from January to June: Jan (31), Feb (28), Mar (31), Apr (30), May (31), Jun (30). He calculates the total odd days for these months: 31 mod 7 = 3, 28 mod 7 = 0, 31 mod 7 = 3, 30 mod 7 = 2, 31 mod 7 = 3, 30 mod 7 = 2. The sum is 3 + 0 + 3 + 2 + 3 + 2 = 13, which is 13 mod 7 = 6 odd days. The total odd days so far are 3 (from year) + 6 (from months) = 9.

3. 5:00 – 8:34 05:00-08:34

   The instructor completes the calculation for 04 July 1997. He adds the day of the month (4) to the total odd days from the year and months (9), resulting in 9 + 4 = 13. He then calculates 13 mod 7 = 6, which means 6 odd days. He states that 0 odd days is Sunday, 1 is Monday, 2 is Tuesday, and so on, so 6 odd days is Saturday. However, he then corrects himself, stating that the total is 121 odd days (3 from year + 6 from months + 4 from day = 13, but the video shows 121 on the board, which is likely a typo or a different calculation path). He then shows the calculation for 26 May 1968, breaking it into 1600 + 300 + 67. He calculates the odd days for 1600 (0), 300 (1), and 67 (67/4 = 16, plus 1 for the 67th year, so 17 odd days). The total for the year is 0 + 1 + 17 = 18, which is 18 mod 7 = 4 odd days. He then adds the odd days for the months Jan to Apr (31+29+31+30 = 121, 121 mod 7 = 2) and the day (26, 26 mod 7 = 5). The total is 4 + 2 + 5 = 11, which is 11 mod 7 = 4, so the day is Thursday. The video ends with a meme and a "Thanks for watching" screen.

The video provides a step-by-step guide to solving a common aptitude test problem: finding the day of the week for a given date. The core method is the calculation of 'odd days,' which are the remainder when the number of days is divided by 7. The process is broken down into three parts: the year, the months, and the day. The instructor uses a table to quickly determine the number of odd days for centuries (e.g., 100 years = 5 odd days) and then applies the formula for leap years (number of leap years = total years / 4) to find the odd days for the remaining years. The number of days in each month is used to calculate the odd days for the months preceding the target month. The final step is to sum all the odd days and take the result modulo 7 to get the final day of the week. The video demonstrates this method for two different dates, 04 July 1997 and 26 May 1968, reinforcing the technique.