When Does Your Birthday Fall on the Day You Were Born?Date: 02/20/2004 at 23:35:16 From: Peggy Lee Gazay Subject: This is just something I'm curious about! I'm curious how many years pass before your birthday falls on the day of the week you were born? Date: 02/21/2004 at 12:01:09 From: Doctor Rob Subject: Re: This is just something I'm curious about! Thanks for writing to Ask Dr. Math, Peggy Lee! Your question is made a lot harder by leap years, but let's wait on that for a moment and just think about a 365 day year. Since a week has 7 days, 52 weeks covers 52*7 or 364 days, leaving one day left out. That means that ordinarily your birthday day shifts by one day each year. If it was on a Tuesday this year, it will be on Wednesday next year. Since a leap year adds an extra day, your birthday day will jump two days during a leap year. If it was on Tuesday this year, it will jump to Thursday next year. So the answer to your question really depends on how the leap years fall in relation to the year of your birth. Since 14 September 1752, when the Gregorian calendar was adopted by English-speaking countries, this is how it works: The answer is either 5, 6, 7, 11, or 12 years. Let a 29th of February be called a leap day. If you are born on a leap day, consider the 1st of March to be your birthday in nonleap years. If there is a leap day before your first birthday and between your fourth and fifth birthdays, it will be 5 years. If there is a leap day before your first birthday but not between your fourth and fifth birthdays, it will be 6 years. If there is a leap day between your fourth and fifth birthdays but not before your first birthday, it will be 6 years. If there is a leap day between your first and second birthdays, your fifth and sixth birthdays, and your ninth and tenth birthdays, it will be 11 years. If there is a leap day between your first and second birthdays but not between your ninth and tenth birthdays, it will be 12 years. If there is a leap day between your first and second birthdays but not between your fifth and sixth birthdays, it will be 6 years. If there is a leap day between your fifth and sixth birthdays but not between your first and second birthdays, it will be 6 years. If there is a leap day between your second and fourth birthdays, it will be 6 years. If there is no leap day before your seventh birthday, it will be 7 years. This list should cover all cases. Feel free to reply if I can help further with this question. - Doctor Rob, The Math Forum http://mathforum.org/dr.math/ |
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