Short Trick Same Calendar in 2 Years

Duration: 7 min

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AI Summary

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This video is a tutorial on determining which year will have the same calendar as a given year, focusing on the concept of 'odd days'. The instructor first presents a question from an Infosys placement exam asking for the year with the same calendar as 1997. He explains that this requires finding a year with the same day of the week for January 1st and the same leap year status. The method involves calculating the total number of odd days from the given year to subsequent years. The instructor demonstrates this by calculating the odd days for each year from 1997 onwards, using the fact that a normal year contributes 1 odd day and a leap year contributes 2. He systematically adds the odd days for each year, and when the cumulative total is a multiple of 7 (i.e., 0 odd days), the calendar will be the same. The calculation shows that 2003 is the first such year. The video then transitions to a similar problem for the year 2018, where the instructor applies the same method to find that 2029 is the answer. The video concludes with 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 slide with the question: 'The calendar for the year 1997 will be the same for the year' with options A) 2003, B) 2005, C) 2006, D) 2007. The instructor, Yash Jain, begins to explain the concept of 'odd days' and how to determine if two years have the same calendar. He states that for two years to have the same calendar, they must start on the same day of the week and have the same leap year status. He starts the calculation by noting that 1997 is a normal year, contributing 1 odd day, and 1998 is also a normal year, contributing another 1 odd day, making the total 2 odd days from 1997 to 1998.

  2. 2:00 – 5:00 02:00-05:00

    The instructor continues the calculation for the year 1997. He writes on the screen, showing the cumulative odd days for each subsequent year. He calculates that 1999 (a leap year) adds 2 odd days, making the total 4. 2000 (a leap year) adds 2 more, making the total 6. 2001 (normal) adds 1, making the total 7, which is equivalent to 0 odd days. He then calculates 2002 (normal) adds 1, making the total 1. Finally, 2003 (normal) adds 1, making the total 2. He explains that since the total odd days from 1997 to 2003 is 2, the calendar will not be the same. He then circles the year 2003 and continues the calculation, showing that 2004 (leap) adds 2, making the total 4, and 2005 (normal) adds 1, making the total 5. He continues this process, and the on-screen text shows the calculation for 2006 and 2007. The instructor explains that the year with a total of 0 odd days will have the same calendar. He then circles the year 2003 as the answer, but the calculation shows a total of 2 odd days, which is not 0. The instructor then circles the year 2003 again, indicating it is the answer.

  3. 5:00 – 7:08 05:00-07:08

    The video transitions to a new question: 'The calendar for the year 2018 will be the same for the year' with options A) 2023, B) 2027, C) 2029, D) 2022. The instructor begins the calculation for 2018. He writes on the screen, showing the cumulative odd days for each subsequent year. He calculates that 2019 (normal) adds 1 odd day, making the total 1. 2020 (leap) adds 2, making the total 3. 2021 (normal) adds 1, making the total 4. 2022 (normal) adds 1, making the total 5. 2023 (normal) adds 1, making the total 6. 2024 (leap) adds 2, making the total 8, which is equivalent to 1 odd day. 2025 (normal) adds 1, making the total 2. 2026 (normal) adds 1, making the total 3. 2027 (normal) adds 1, making the total 4. 2028 (leap) adds 2, making the total 6. 2029 (normal) adds 1, making the total 7, which is equivalent to 0 odd days. The instructor circles the year 2029 as the answer. The video ends with a 'THANKS FOR WATCHING' screen.

The video provides a step-by-step tutorial on solving a common type of calendar problem found in placement exams. The core concept is the calculation of 'odd days' to determine if two years have the same calendar. The method involves summing the odd days from the given year to each subsequent year until the total is a multiple of 7 (i.e., 0 odd days). The instructor demonstrates this method for two different years, 1997 and 2018, showing the detailed arithmetic on a digital blackboard. The key insight is that a normal year contributes 1 odd day and a leap year contributes 2. The video effectively uses visual aids, such as the on-screen text and handwritten calculations, to guide the viewer through the logical process, making it a clear and practical guide for students preparing for competitive exams.