Ok, I'm going to break character here and ask a question:
The day that just ended (in addition to being Mission Accomplished Day) was both MJS's 28th birthday (on the secular calendar) and the 28th day of the omer.
Puzzle for anyone who wants to figure it out: What is the maximum number of times that this confluence can occur in a person's lifetime? (Obviously, only the first 49 years of one's life are germane.)
Bonus question: A secular date actually spans two days of the omer. (MJS's 28th birthday was in fact both the 28th and 29th days of the omer.) Answer the question again taking this into account.
[Of course, this can only happen once in your lifetime for your Hebrew birthday. But in the era before the fixed calendar, it could have happened twice for people born in Iyar, and as many as thrice for people born in the first few days of Sivan.]
I believe I've established an upper bound. If a person has their Xth birthday on day X of the omer (for X in [1..25]), and this happens in year 19 of the 19-year cycle, then they may have as many as 8 more birthdays (for a total of 9) fall on the "right" omer day.
ReplyDeleteStill working on it...
No, wait, sorry, I misread my calculations. Starting on year 8 instead of year 19 is better. It may give as many as 10 birthdays, but requires starting with an X in [1..22].
ReplyDeletemy *Hebrew* birthday is the 29th day of the ‘omer... does that count? ;)
ReplyDeleteHappy belated birthday, and happy Pesach Sheni! This was addressed in the post -- it may count, but you only turn(ed) 29 once.
ReplyDeleteI figured it out for MJS (born May 1, 1979, so his birthday is always during the omer). It happened on his 7th, 13th, 16th, 25th, and 28th birthdays. Sorry, this was the last time. :(
ReplyDeleteAfter running a simulation, I'm almost certain that the answer to the initial problem is 6 times. This happens in several different ways. For example, if you first have a birthday that matches the omer day in year 3 of a 19-year cycle, on a gregorian leap year, and the molad of the Tishrei after that is at 11:00pm exactly on a Saturday, then you'll match up 5 more times after that (assuming you started out young enough).
ReplyDeleteThis doesn't consider the case of a "weird non-leap-year" like 1900 or 2100, but I think I've covered all my other bases.
I haven't yet written a program to expand those results and tell me exactly which subsequent birthdays match up, or exactly what the year structures of the relevant years are, but I might do that next. Also might try the bonus problem.