# Turkey and Birthday Cake


Since my birthday is on November 22nd, it occasionally falls on the same day as Thanksgiving, which is always the [fourth Thursday of each November](https://en.wikipedia.org/wiki/Thanksgiving_(United_States)). Due to some quirks of the Gregorian calendar and leap years, there isn't a great pattern to the years when the 22nd falls on a Thursday.<!--more-->

Taking leap years out of consideration, you'd expect that Thanksgiving would be on a Thursday once in every 7 years (because `365 % 7 == 1`, so each year Thanksgiving day shifts by 1 weekday until it rolls over).

Adding in leap years, things become more involved. Leap years add an extra day 4 years, which messes up the clean "one weekday shifted per year" recurrence. (Not to mention the added craziness of when you add in the '100 and 400 divisible' [leap year exceptions](https://en.wikipedia.org/wiki/Leap_year#Algorithm)).

This has been something that I've been mildly curious about for a while, so I wrote a small script to generate the dates in my (approximate) lifetime on which my birthday and Thanksgiving coincide:

* 2001 - 5th birthday
* 2007 - 11th birthday (6 year gap)
* 2012 - 16th birthday (5 year gap)
* 2018 - 22nd birthday (6 year gap)
* 2029 - 33rd birthday (11 year gap)
* 2035 - 39th birthday (6 year gap)
* 2040 - 44th birthday (5 year gap)
* 2046 - 50th birthday (6 year gap)
* 2057 - 61st birthday (11 year gap)
* 2063 - 67th birthday (6 year gap)
* 2068 - 72nd birthday (5 year gap)
* 2074 - 78th birthday (6 year gap)
* 2085 - 89th birthday (11 year gap)
* 2091 - 95th birthday (6 year gap)

It appears that as a basic rule, there's this `6-5-6-11` year 'Thanksgiving Gap' cycle between coincidences. The *average* gap in my lifetime ends up being ~6.92 years, so in the end, the 7 year rule-of-thumb still holds reasonably well. Extrapolating out another 5000 years yields an average gap of ~6.89 years, so it doesn't appear that the sequence converges to 7 (which is to be expected because of the aforementioned special leap year exceptions).

Then, I began to think about other November birthdays that have this same characteristic. It turns out that birthdays between Nov. 22 and Nov. 28 have a similar Thanksgiving periodicity.

* Nov. 22: 6.89 years
* Nov. 23: 7.14 years
* Nov. 24: 6.90 years
* Nov. 25: 7.13 years
* Nov. 26: 6.90 years
* Nov. 27: 7.01 years
* Nov. 28: 7.03 years

Huh. Lucky me. November 22 seams to be the 'luckiest' date for Thanksgiving coincidences (at least between the years 1996 and 6996).

Taking this to it's logical conclusion, I decided to find which birth day+year combinations would yield the most and least Thanksgiving coincidences. I considered a life expectancy of 78 years, and calculated the lifetime coincidence count. 

* The luckiest date/year combinations turned out to be **Nov 22** of 1913, 1914, 1915, 1916, 1917, 1941, 1942, 1943, 1944, 1945, 1969, 1970, 1971, 1972, 1973, 1997, 1998, 1999, or 2000 with **11** coincidences.[^1]
* The unluckiest dates/years were **Nov 23** of 2035, 2063, and 2091 with only **8** coincidences[^2]

[^1]: These are just the 20th century maximum coincidence years, the full list is much longer.

[^2]: Again, an abbreviated list. Interestingly, no date in the 20th century had this low a coincidence rate, so I picked the results from the 21st century.

So, just another quirk of the Gregorian calendar and the way we 'schedule' Holidays.

Happy Thanksgiving! (Also, the [obligatory xkcd](https://www.xkcd.com/1514/))

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*Parts of this post were inspired by Scott Forbes' ["How often does my birthday fall on Thanksgiving?"](http://scottforbes.net/2010/07/07/how-often-does-my-birthday-fall-on-thanksgiving/)*