When is 40 years before the destruction of the 2nd Temple?

Question

We read in the Jerusalem Talmud:

"Forty years before the destruction of the Temple, the western light went out, the crimson thread remained crimson, and the lot for the Lord always came up in the left hand. They would close the gates of the Temple by night and get up in the morning and find them wide open" (Jacob Neusner, The Yerushalmi, p.156-157).

A similar passage in the Babylonian Talmud states:

"Our rabbis taught: During the last forty years before the destruction of the Temple the lot ['For the Lord'] did not come up in the right hand; nor did the crimson-colored strap become white; nor did the western most light shine; and the doors of the Hekel [Temple] would open by themselves" (Soncino version, Yoma 39b).

The 2nd Temple was destroyed in 70 CE August on Tisha B'Av. So when is 40 years before it? Was it 30 CE or 31 CE? Those who favor 31 CE say that Jews generally count the first year as well.

Answer 1

עבודה זרה ט ע"ב records that the year 4231 לבה״ע (*not accounting for שנת תוהו which adds 1) was THREE years later than "FOUR HUNDRED years after the Temple's destruction", which means that the destruction of the Temple must have occurred in 4231 - 403 years = 3828 לבה״ע.

​אמר רבי חנינא: "אחר ארבע מאות לחורבן הבית, אם יאמר לך אדם 'קח שדה שוה אלף דינרים בדינר אחד'—לא תקח!" במתניתא תנא: "אחר ארבעת אלפים ומאתים ושלשים ואחת שנה לבריאת עולם, אם יאמר לך אדם 'קח לך שדה שוה אלף דינרים בדינר אחד'—אל תקח!" מאי בינייהו? איכא בינייהו תלת שנין דמתניתא טפיא תלת שני׃

*However, the Jewish calendar actually begins almost a full year BEFORE the creation of Man, because אדם הראשון is considered to have been created on 1st Tishri of Year 2, the first five of the ששת ימי בראשית being deemed as the last five days of Ellul of Year 1 - known as the Void Year (שנת תוהו, because all but its last six days were before anything existed) - following the principle "יום אחד בשנה חשוב שנה" (e.g. ראש השנה ב ע"ב, נידה מה ע"א).

And Hebrew dates exceed the corresponding civil dates by 3760 years for dates between the beginning of January and the end of אלול (the difference is 3761 years from the beginning of תשרי to the end of December), so it follows that the Temple was destroyed in the summer of 3828 + 1 − 3760 years = 69 CE. And 40 years before that would have been 3789 by our calendar or 29 CE.