There were 12 friends A, B, C, D, E, F, G, H, I, J, K, & L. In the year 1996, A celebrated his birthday on January 11 and it was Thursday. B celebrated his birthday on February 20, which was a Tuesday and C, D, E, F, G, H and I, celebrated on April 05 (Friday), May 05 (Sunday), June 05 (Wednesday), July 05 (Friday), August 05 (Monday), September 05 (Thursday) and October 05 (Saturday) respectively. J, K and L celebrated their birthday on November 15 (Friday), March 15, (Friday) and December 15 (Sunday) respectively. Before the year 2025, when will all of them celebrate their birthdays again on the same day as they did in 1996? (Note:- DO NOT include spaces in your answer)
To determine the next year when all friends' birthdays will fall on the same day of the week as they did in 1996, we need to consider the pattern of the Gregorian calendar and leap years. Here's a step-by-step process to solve the problem: 1. Identifying Key Information: - A's birthday on January 11 was a Thursday in 1996. - B's birthday on February 20 was a Tuesday in 1996. - The other friends' birthdays and their respective weekdays in 1996 are provided. 2. Analyzing the Days of the Week in 1996: - 1996 is a leap year. In a leap year, February has 29 days. - Days of the week repeat every 7 days. 3. Finding the Cycle of Repetition: - The calendar for a non-leap year repeats itself every 6 or 11 years. For a leap year, the repetition cycle is different. - The complete pattern of day and date repeats every 28 years for the Gregorian calendar, accounting for the leap year cycle. 4. Calculating the Next Same Day: - Add 28 years to 1996 to determine when the same day-date combination will occur again. \( 1996 + 28 = 2024 \) Thus, all friends will celebrate their birthdays on the same day of the week as in 1996 in the year 2024
