Question Find Day on a Particular Date

Duration: 5 min

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  1. About Course: About the Course
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AI summary & chapters

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, specifically 14 March 1965. The instructor, Yash Jain, uses a step-by-step method involving the calculation of odd days. The process begins by breaking down the year 1964 into 1600 and 364. The number of odd days for 1600 years is taken as 0, as per the standard rule. For the remaining 364 years, the calculation involves finding the number of leap years and ordinary years. The instructor calculates that 364 years contain 86 leap years and 278 ordinary years, resulting in a total of 400 odd days. This is then reduced to 1 odd day (400 mod 7 = 1). The next step is to calculate the odd days for the months of January and February 1965, which are 31 and 28 days respectively, totaling 59 days, which is 3 odd days (59 mod 7 = 3). Finally, the odd days for the 14 days of March are calculated as 14 mod 7 = 0. The total number of odd days is the sum of all these components: 0 (from 1600) + 1 (from 364 years) + 3 (from Jan-Feb) + 0 (from March) = 4. The instructor then maps this to a day of the week, stating that 0 is Sunday, 1 is Monday, and so on, concluding that 4 corresponds to Thursday. The video uses a digital blackboard with a table of odd days for different century years and a list of month lengths.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video opens with a title card showing a calendar and the word 'CALENDAR'. The main content begins with a question displayed on a digital blackboard: 'On what day does 14 March 1965 lie?'. The instructor, Yash Jain, introduces the problem. A table on the left lists the number of odd days for different century years: 100 years have 5 odd days, 200 have 3, 300 have 1, and 400, 800, 1200, and 1600 have 0 odd days. The instructor begins the calculation by writing '1964 = 1600 + 364' on the board, breaking down the year into a base of 1600 and the remaining 364 years. The instructor explains that 1600 years have 0 odd days, which is a standard rule in this method.

  2. 2:00 – 4:46 02:00-04:46

    The instructor continues the calculation for the 364 years. He explains that 364 years consist of 86 leap years and 278 ordinary years. He calculates the total odd days as (86 * 2) + (278 * 1) = 172 + 278 = 450. He then reduces this to 450 mod 7, which is 1 odd day. Next, he calculates the odd days for the months of January and February 1965, writing 'Jan -> 31' and 'Feb -> 28'. The sum is 59 days, which is 59 mod 7 = 3 odd days. He then calculates the odd days for the 14 days of March, which is 14 mod 7 = 0. The total number of odd days is the sum: 0 (from 1600) + 1 (from 364 years) + 3 (from Jan-Feb) + 0 (from March) = 4. The instructor then states that 0 is Sunday, 1 is Monday, 2 is Tuesday, 3 is Wednesday, and 4 is Thursday. Therefore, 14 March 1965 was a Thursday. The video ends with a 'THANKS FOR WATCHING' screen.

The video presents a complete, step-by-step solution to a classic calendar problem. It demonstrates a systematic method for finding the day of the week for any date by breaking the problem into manageable parts: calculating odd days for centuries, the remaining years, the months, and the days. The core of the method relies on the fact that a non-leap year has 1 odd day and a leap year has 2 odd days. The instructor uses a digital blackboard to clearly show the calculations, referencing a table of odd days for centuries and the number of days in each month. The final answer is derived by summing all the odd days and using a simple mapping to the days of the week, concluding that 14 March 1965 was a Thursday.

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