intend my birthday dropped on a Sunday. What is the maximum number of years ns may need to wait till mine birthday falls on a Sunday again?

My intuition claims 11 years:

At the earliest, the next Sunday is in 6 year time. Reason: before I deserve to encounter one more Sunday, there have to be at least one leap year. (7 - 1 = 6).

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Suppose by negative luck, 6 years later is a leap year (my birthday would certainly skip Sunday and also fall on a Monday). Native this point, before I can encounter the next Sunday, there must be another leap year. There are two leap years involved, so the next Sunday is in 5 year time. (7 - 1 - 1 = 5)

6 + 5 = 11

Is 11 the exactly answer? If yes, I would appreciate an explanation an ext rigorous 보다 the above. If no, you re welcome teach.

I am likewise looking because that exceptional cases where the over reasoning might be faulty.

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edited Feb 11 "20 in ~ 9:59
Flux
asked Feb 11 "20 in ~ 9:23

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## 2 answers 2

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Assuming the one is not born top top February 29, climate the complying with possibilities have the right to occur:

The day of the week repeats ~ 5 years. For example, in march 1, 2015, and March 1, 2020, are both Sundays.The work of the mainly repeats ~ 6 years. Because that example, April 1, 2012, and April 1, 2018, space both Sundays.The work of the week repeats after 7 years. This instance can only happen for dates from in march 1 in a year ending with "96" come February 28 the following year finishing with "97". Because that example, march 1, 1896, and also March 1, 1903, are both Sundays, since 1900 was not a leap year.The day of the week repeats ~ 11 years. For example, October 1, 2006, and also October 1, 2017, room both Sundays.The work of the week repeats ~ 12 years. This situation can only happen for dates within the last decade of a century. For example, October 1, 2090, and also October 1, 2102, space both Sundays, with the skipped leap year below being 2100.

Hence, the maximum is 12 years (for dates other 보다 February 29). The course, one could replace Sunday with any type of other work of the week and the same feasible gaps in between occurrences would still occur.

For February 29, the job of the week have the right to only repeat after ~ 12, 28, or 40 years. The 12-year gap can only occur for leap years ending with "92" or "96", when the 40-year void can only take place for leap years ending with "72", "76", "80", "84", or "88".

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Hence, the maximum for February 29 is 40 years. For example, February 29, 2088, and February 29, 2128, room both Sundays, with the skipped leap year here again gift 2100.

By the way, it transforms out the the 40-year void can take place for leap year with any type of dominical letter:

AG: 1888 and 1928BA: 1684 and also 1724, 1780 and also 1820, or 1876 and 1916CB: 1672 and 1712DC: 1688 and 1728, 1784 and also 1824, or 1880 and also 1920ED: 1676 and also 1716, or 1772 and 1812FE: 1788 and 1828, or 1884 and also 1924GF: 1680 and 1720, 1776 and 1816, or 1872 and also 1912