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The Halacha is that you are not allowed to count people. But you could count noses, or shirts, or left shoes, or ... (source: Magen Avraham O.C. 156 - 4th wide line of right column here).
The Sefer Chazoinim which was printed in the late 16th century includes 327 Piyutim for Shabbos, Yom Tov, and Rosh Hashana. Thanks to Seridei Shira for this information.
Even Sapir volume 2 - page 224 says that the Sefer Hoshea from Trei Asar spans a period of 327 years from Uziyahu Hamelech until the year Alexander Mokdon arrived. ספר הושע ספר שנים עשר נביאים שלש מאות ועשרים ושבע שנים מן עוזיהו המלך עד השנה שבא אלכסנדר מוקדון
As pointed out by many meforshim, the food in the teivah was provided miraculously. Rabbi Sorotzkin in Oznayim Latorah 6:21 (answer 3) says It is known that the Ark's provisions were insufficient to sustain its passengers for even a week, and only Hashem's blessing caused the food to last the entire year of the flood. Similarly, he says that after they ...
There are at most 325 days on which work is permitted per year, for those who live in Israel. This occurs in a leap year starting on Shabbos, where Cheshvan and Kislev each have 30 days. 385 days in the year - 55 Shabbasos - 8 days of Yom Tov + 3 days of Yom Tov and Shabbos, which were double counted: Rosh Hashanah, ...
107 is the number of "folk sayings" (אמרי אינשי) that appear in the gemora Bavli, as listed in this sefer.
The gemora in Sotah 13a says that 36 crowns were hung on the coffin of Ya’akov by the kings of various nations.
The source of the Rambam is the Mishna, Rosh Hashana 2:7, and Rav Ovadia MiBartenura explains (based on the combination of Rav Pappa and Rav Nachman Bar Yitzchak's opinions in the Gemara Rosh Hashana 24a) that the declaration is structured according to the verses in Vayikra 23 2 and 44. In verse 44, Moshe declares the holidays, and thus the start of the ...
See this article which related this question to the Atzeres Hatefila event. (I'm unfamiliar with what this event is or when it occurred. I just noticed the article as it relates to answering your question.) Excerpt: Prior to the event, the question was raised whether the bracha can be recited if unable to ascertain whether there truly are 600,000 in ...
In the Tur Yoreh Deah, Siman 168 is missing. See also: What happened to Siman 168? (I saw Double AA's comment there, and gave Shmuel Brin a whole day to come post this, but he never did, even though i saw that he logged on since then...)
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