Tenth of Tevet on January 1

I am an avid student of the Jewish calendar.  The mathematics of the calendar have always fascinated me.  This week someone asked if I remember the last time the 10th of Tevet came out on January 1.

I said I didn't. It turns out that the last time was 1939 and before that 1920.   That's why I didn't remember.(I'm not that old).  If math bores you I'm afraid it doesn't get too much more interesting than that.  But I think its fascinating that those two years and our new year of 2015 all have something in common.  All three of them are the eighteenth year of the nineteen year cycle of leap years.  As you know there are 7 leap years every 19 years and each year will come out approximately to plus or minus one day on the same secular solar date.  Thus the fourth year of the cycle will come out on the same solar date as the fourth year nineteen years later ( The plus or minus one day relates to the length of that year which is another topic).  So January 1 comes out in the eighteenth year on the 9, 10 or 11 of Tevet every nineteen years.  This holds true for about 250 to 350 years depending on where we are in the Gregorian calendar.  Then the Gregorian goes ahead one day in 2100, 2200 and 2300.  Thus the first time the 10th of Tevet came out on January 1 was in 1863 and the last time will be shortly after 2200 at which time the Gregorian will go ahead by one day so that never again in the eighteenth year will 10 Tevet come out on January 1.  The latest date for Tevet on January 1 will be Tevet 9.  As an aside from 2100 to 2200 the twelfth year of the cycle will shift backwards so that it too can have a date of Tevet 10 on January 1 2102.   The twelfth year then will hold that position for a few hundred years.

Fascinating.