Who knows eighteen?
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Eighteen are the minimum (or according to Rambam, the absolute) number of days in a woman's cycle, according to the original Torah law: seven of niddah (Lev. 15:19), and eleven of zivah (based either on Lev. 15:25, or an unwritten halachah le-Moshe mi-Sinai - Talmud, Niddah 72b-73a).
Shemona Asar was the number of berachot in the Shemona Esrei, before the addition of Birkas HaMinim." (Berachot 28b)
Eighteen is the value (in maneh) of the linen clothing that the Kohen Gadol wore for his first entry into the Holy of Holies each Yom Kippur, according to the majority opinion (Yoma 34b).
Eighteen are the years before one gets hitched. (Ben Shemonah Esrei LiChupah: Avos 5:21)
There are eighteen sins for which the punishment is misa bide shamayim but for which one can get lashes. Source: Rambam, Sanhedrin 19.
18 are the instances of prayer in the Torah, as enumerated by Rav Saadya Gaon in the introduction to his Siddur: Gen 20:17, 25:21, 32:10, Exo 8:8, 8:26, 9:33, 10:18, 15:1, 32:11, 33:13, 34:9, Num 11:2, 12:13, 14:13, 21:7, 21:17, 27:16, Deu 3:23.
He also mentions that there are 18 days the Torah sanctified as Moadim: 7 for Pesach, 1 each for Shavuot, Rosh haShana, and Yom Kippurim, and 8 for Sukkot.
18 things were enacted at this day (Mishna Shabbat 1, 4)
וְאֵלּוּ מִן הַהֲלָכוֹת שֶׁאָמְרוּ בַעֲלִיַּת חֲנַנְיָה בֶן חִזְקִיָּה בֶן גֻּרְיוֹן כְּשֶׁעָלוּ לְבַקְּרוֹ. נִמְנוּ וְרַבּוּ בֵּית שַׁמַּאי עַל בֵּית הִלֵּל, וּשְׁמֹנָה עָשָׂר דְּבָרִים גָּזְרוּ בוֹ בַיּוֹם:
Eighteen are the rows of R. Elazar Ben Azaria's beard that turned white.
Lag B'Omer is on 18 Iyur
Eighteen is the age at which one should finish learning the entire Talmud according to one opinion (15 to start learning (Pirkei Avos), and it is a machlokes (in kiddushin I think) if it takes 3 or 5 years to complete it).
Sichon's (the King of the Emorites) thigh bones were eighteen cubits long (Midrash Tanchuma, Buber ed., Devarim appendix 7)
18 is the gematriya of chai