Three Day Chag

This year, Rosh Hashanah falls on Thursday/Friday. When this happens, the holiday becomes what is colloquially known as a "three day chag" -- the two days of the holiday are immediately followed by Shabbat (this of course is something of a misnomer, but oh well). Moreover, because the two days of Rosh Hashanah fall on the same days of the week as the first days of Sukkot and the two days of Shemini Atzeret, those holidays also create "three day chags."

It was pointed out to me that it seems like every year for the past few years has been a three day chag. So, I took a look at how common they are, and made some plots.

This shows the day of the week on which the first day of Rosh Hashanah occurs from 1980 to 2040. Rosh Hashanah can fall on Monday, Tuesday, Thursday, or Saturday. The three day chag years are those which fall on Thursday, highlighted in red:

Looking at this, it's clear that there have indeed been an unusually high number of three day chag years recently. From 2010-2014, all but one year were three day chags. However, a large gap is coming up -- from 2015-2023, there will be only one. Interestingly, we are in the middle of a long gap of weekend chag years, in which the first day of Rosh Hashanah is Saturday. The last one was in 2009, and we don't have another until 2020.

What about the other chagim?

The same question can be asked of the other chagim. The first day of Pesach can be Sunday, Tuesday, Thursday, or Saturday. That means that the first days of Pesach can form a three day chag from either direction, i.e. after Shabbat or before Shabbat. The last days of Pesach cannot form a three day chag. Here is a similar plot to the one above, although slightly different -- here I am showing which chagim occur as a three day chag, for all of the two day chagim of the year. Light blue indicates a Thursday/Friday chag, while dark blue indicates a Sunday/Monday chag:

Just to be clear, the line labeled here "Rosh Hashanah" is the same as the line labeled "Thursday" in the previous plot (i.e., those years in which Rosh Hashanah falls as a three day chag). We are in the middle of a long gap in three day chags around Pesach, in either direction. One perhaps surprising result from this plot is that it seems that there are no years that do not have a three day chag. This is only true because I did this based on the Gregorian calendar. If you divide the years based on the Hebrew calendar, then years without a three day chag do occur, e.g. 5777 (2016-2017) will be such a year.