Goldilocks
Today you are!
It is all spelled out in Rambam Kidddush Hachodesh 7 wit hmefarshim there as well as end of hilchos Rosh chodesh in OC
first Tuesday- it is more common and a bit easier
The time between one molad and the next is 29 days 12 hours and 793 chalakim ( a chelek is 1/1080 of an hour which equal 3 and 1/3 seconds)
Since 28 days is 4 full weeks One month’s molad will occur 1 day 12 hours and 793 chalakim later in the week.
A regular year is of course 12 months, if you multiple 1 day 12 hours 793 by chalakim and remove full weeks)
You end up wit h4 days 8 hours 876 chalakim
Thus for example the molad Of Tishrei 5781 Was Thursday 20 hours 701 chalakim
If you add 4 days 8 hours 876 Chalaikm
you get molad tishrei 5782 which was Tuesday 5 hours 497 chalakim
Rosh Hashana 5781 was pushed off to Shabbos, since Molad occured after 18 hours (noon) and cant be Friday becasue Lo Adu Rosh
Rosh Hashana of this year 5782 was not pushed off and was on Tuesday, the day of the molad
However if the molad occurs on a tuesday after 9 hrs 204 chalakim (G”T”RD gimmel is 3 for tues tes 9 for 9 hours 204 chalakim) Then Rosh Hashana That year would be Tuesday
The next molad occurs 4 days 8 hours 876 Chalaikm later in the week Whci his Shabbos, 18 hours 0 chalaikm. This is molad Zaken pushed to Sunday then Pushed to Monday Because of the first 2 dechuyos)
A Year that begins on Tuesday and whose final day is Sunday is 356 days long this is too long (options are 354 if all months alternate 29/30, 353 if bot h chesvan Kislev have 29 and 355 if both have 30)
So we push off Rosh Hashana from Tuesday thursday
The monday Dechiya is rarer still, in fact it will not occur again until after 6000
The idea is the same except it comesu p after leap years
the difference between molad Tishrei before a leap year and after is 13 x (1-12-793) = 5 days 21 hrs 589 Chalakim
As mentioned Molad tishrei 5782 was Tuesday 5 hours 497 chalakim
NExt Year’s molad tishrei 5782 will be Monday 3 hrs 6 chalakim
However if Molad of year after leap year is on Monday 15 hrs 589 chalakim or later
The previous years’ molad was 5 days 21 hrs 589 Chalakim earlier whci his Tuesday 18 hours.
That Rosh hashana gets pushed off because molad zaken then lo adu Rosh to Thursday. If we keep the year after leap year on Monday the year is 382 days long this is too short options for leap year are 383 384 385 (regular year + 30) so we push off the year after leap year to tuesday
hope this helps