Two variants of the number 11 in the Torah was developed by Rabbi David Slotkin and Gary Lelonek on Shabbat Naso and Devarim 5784
Many cultures have developed their number system from base ten, likely derived from using hands to count. 11 and 12 have their own distinctive names connected to the number ten. In English and German, 13 starts the pattern of the name of the number with the suffix teen. With the twenties and forward, all numbers follow the same numbering system of twenty with the single digit number. The etymology for the English/German numbering system is from a set of 10 with either 1 or 2 extra. Eleven means one remaining after ten have been counted (from the Old English word enleofan "one left"), and twelve means two remaining after ten have been counted (two left [after 10]).
https://www.etymonline.com/word/twelve
In the Torah, there are two names for the number 11. All mentions of the number 11 in the Chumash are אַחַ֨ד עָשָׂ֥ר except for the four times עַשְׁתֵּֽי־עָשָׂ֥ר is used;
- The 11 curtains of the Mishkan (Exodus 26:7-9 & 36:14-15).
- The 11th day of gifts from the princes for the Mishkan (Numbers 7:72).
- The third day of Sukkot Musaf offering of 11 bulls (Numbers 29:20).
- The 11th month of the year. (Deuteronomy 1:1-3)
אֵ֣לֶּה הַדְּבָרִ֗ים אֲשֶׁ֨ר דִּבֶּ֤ר מֹשֶׁה֙ אֶל־כָּל־יִשְׂרָאֵ֔ל בְּעֵ֖בֶר הַיַּרְדֵּ֑ן בַּמִּדְבָּ֡ר בָּֽעֲרָבָה֩ מ֨וֹל ס֜וּף בֵּֽין־פָּארָ֧ן וּבֵֽין־תֹּ֛פֶל וְלָבָ֥ן וַחֲצֵרֹ֖ת וְדִ֥י זָהָֽב׃ אַחַ֨ד עָשָׂ֥ר יוֹם֙ מֵֽחֹרֵ֔ב דֶּ֖רֶךְ הַר־שֵׂעִ֑יר עַ֖ד קָדֵ֥שׁ בַּרְנֵֽעַ׃ וַיְהִי֙ בְּאַרְבָּעִ֣ים שָׁנָ֔ה בְּעַשְׁתֵּֽי־עָשָׂ֥ר חֹ֖דֶשׁ בְּאֶחָ֣ד לַחֹ֑דֶשׁ דִּבֶּ֤ר מֹשֶׁה֙ אֶל־בְּנֵ֣י יִשְׂרָאֵ֔ל כְּ֠כֹל אֲשֶׁ֨ר צִוָּ֧ה ה׳ אֹת֖וֹ אֲלֵהֶֽם׃
THESE are the words which Moshe spoke to all Yisra᾽el on the other side of the Yarden, in the wilderness over against Suf, between Paran, and Tofel, and Lavan, and Ḥażerot, and Di-zahav. It is eleven days’ journey from Ḥorev by the way of mount Se῾ir to Qadesh-barnea. And it came to pass in the fortieth year, in the eleventh month, on the first day of the month, that Moshe spoke to the children of Yisra᾽el, according to all that the Lord had given him in commandment to them;
In verses 2 and 3, the number 11 is written in two different ways: verse 2 is אַחַ֨ד עָשָׂ֥ר, and verse 3 is עַשְׁתֵּֽי־עָשָׂ֥ר. In verse 2, 11 refers to the 11-day journey between Chorev and Kadesh Barnea. Verse 3's 11 refers to the 11th month.
Rabbi David Slotkin explains that the incidence of the עשתי עשר in the Torah is found when 11 is in a series followed by 12. When 11 is a count it is written אַחַ֨ד עָשָׂ֥ר.
In Deuteronomy 1:2, 11 refers to the absolute number of the 11-day journey between Chorev and Kadesh Barnea. Verse 3's 11 refers to the 11th month, which is part of a series of 12 months. Since 12 follows 11, you refer to 11 as 12-1.
וְעָשִׂ֙יתָ֙ יְרִיעֹ֣ת עִזִּ֔ים לְאֹ֖הֶל עַל־הַמִּשְׁכָּ֑ן עַשְׁתֵּי־עֶשְׂרֵ֥ה יְרִיעֹ֖ת תַּעֲשֶׂ֥ה אֹתָֽם׃ אֹ֣רֶךְ ׀ הַיְרִיעָ֣ה הָֽאַחַ֗ת שְׁלֹשִׁים֙ בָּֽאַמָּ֔ה וְרֹ֙חַב֙ אַרְבַּ֣ע בָּאַמָּ֔ה הַיְרִיעָ֖ה הָאֶחָ֑ת מִדָּ֣ה אַחַ֔ת לְעַשְׁתֵּ֥י עֶשְׂרֵ֖ה יְרִיעֹֽת׃ וְחִבַּרְתָּ֞ אֶת־חֲמֵ֤שׁ הַיְרִיעֹת֙ לְבָ֔ד וְאֶת־שֵׁ֥שׁ הַיְרִיעֹ֖ת לְבָ֑ד וְכָפַלְתָּ֙ אֶת־הַיְרִיעָ֣ה הַשִּׁשִּׁ֔ית אֶל־מ֖וּל פְּנֵ֥י הָאֹֽהֶל׃
You shall then make cloths of goats’ hair for a tent over the tabernacle; make the cloths eleven in number. The length of each cloth shall be thirty cubits, and the width of each cloth shall be four cubits, the eleven cloths to have the same measurements. Join five of the cloths by themselves, and the other six cloths by themselves; and fold over the sixth cloth at the front of the tent.
The 11 curtains of the tabernacle. 5 were connected together and the other 6 were connected together. The sixth curtain was "doubled" toward the entrance.
אל מול פני האהל. חֲצִי רָחְבָּה הָיָה תָלוּי וְכָפוּל עַל הַמָּסָךְ שֶׁבַּמִּזְרָח כְּנֶגֶד הַפֶּתַח, דּוֹמֶה לְכַלָּה צְנוּעָה הַמְכֻסָּה בְּצָעִיף עַל פָּנֶיהָ:
אל מול פני האהל OPPOSITE THE FRONT OF THE TENT; half of its breadth (two cubits) hung down, being doubled, over the screen which was on the east side before the entrance, whereby the Tabernacle gained the appearance of a modest bride who has her face covered by a veil.
Since the 11 curtains appeared to be part of a series of 12 curtains, the version of 11 in the verse is עַשְׁתֵּי־עֶשְׂרֵ֥ה.
In the Katzar version of Ibn Ezra, he comments on this verse that the grammar of the word eleven עַשְׁתֵּי־עֶשְׂרֵ֥ה is in the grammar book. Allan Benyowitz's footnote says the grammar book is Sefer Tzachot (Book of the Clarity of Language) p. 41.2
וַיַּ֙עַשׂ֙ יְרִיעֹ֣ת עִזִּ֔ים לְאֹ֖הֶל עַל־הַמִּשְׁכָּ֑ן עַשְׁתֵּֽי־עֶשְׂרֵ֥ה יְרִיעֹ֖ת עָשָׂ֥ה אֹתָֽם׃ אֹ֜רֶךְ הַיְרִיעָ֣ה הָאַחַ֗ת שְׁלֹשִׁים֙ בָּֽאַמָּ֔ה וְאַרְבַּ֣ע אַמּ֔וֹת רֹ֖חַב הַיְרִיעָ֣ה הָאֶחָ֑ת מִדָּ֣ה אַחַ֔ת לְעַשְׁתֵּ֥י עֶשְׂרֵ֖ה יְרִיעֹֽת׃
The second reference to the crutains with the same version of the number 11.
בְּיוֹם֙ עַשְׁתֵּ֣י עָשָׂ֣ר י֔וֹם נָשִׂ֖יא לִבְנֵ֣י אָשֵׁ֑ר פַּגְעִיאֵ֖ל בֶּן־עָכְרָֽן׃
On the eleventh day Pag῾i᾽el the son of ῾Okhran, prince of the children of Asher, offered:
The 11th day of the consecration of the tabernacle. This is part of a series which ended with the 12th day.
ביום עשתי עשר יום. כבר בארתי בספר מאזנים למה השתנה זה המספר וטעם עשתי. כמו עשתנותיו מה שיולידו מחשבותיו כאילו העשר הוליד והוא סוד גדול. ויאמר רבי יונה הספרדי כי פירושו על שתי עשר והטעם החשבון שהוא קודם ממנו והנה טעה שתי טעיות גדולות. האחד כי חשבון שנים עשר הוא על אחד עשר הפך דבורו והעד הנאמן מבן עשרים שנה ומעלה. והטעות השנית כי אילו היה על שתי היה ראוי שיאמר עשני עשר ולא עשתי עשר כי עשתי לשון נקבה רק עשתי מלה אחת:
ON THE ELEVENTH DAY. I have already explained in the book מאזנים why this number עשתי עשר (eleven), differs [from the other numbers]. *[The word for eleven in our verse is "ashte asar" and not "achad (1) asar (10)."] The meaning of עשתי is similar to the word עשתנותיו (his thoughts) (Ps. 146:4). עשתנותיו refers to 'that which a person’s thoughts give birth to,' as if the number 'ten' gave birth to [eleven, etc.]. This is a great secret. *[According to I.E., “Ten is the foundation of all sums, for all sums that follow ten are made up of a part or parts of ten, or come into being by doubling ten, multiplying ten, or a combination of the two” (The Secret of the Torah, translated by Rabbi Norman Strickman, 2021 p. 129).]
Now, רבי יונה הספרדי *[Jonah ibn Janach, the eleventh-century grammarian.] says that עשתי עשר is short for על שתי עשר, whose meaning is 'the number that precedes twelve.' Behold, רבי יונה made two great mistakes. Firstly, contrary to his words, the number twelve is above (al) the number eleven, the opposite of what he tried to prove. *[In other words, the number above 12 is 13. The word al means above, not before. Hence if עשתי עשר is short for על שתי עשר, then its meaning is, not before 12 but beyond 12.] The conclusive proof is from twenty years old and upward (ומעלה) (Num. 1:3). *[ומעלה and על come from the same root. We therefore see that על means upward or beyond, not before.] His second mistake is that if the word עשתי is short for על שתי, then the text should have read עשני עשר, *[Because the masculine version for 12 is שני עשר], not עשתי עשר, since עשתי is feminine. *[According to Rabbi Jonah, עשתי is short for על שתי. but שתי עשר is feminine and the word it modifies, יוֹם is masculine. Why would Scripture employ a feminine?] Rather, עשתי is just one word [not a contraction].
וּבַיּ֧וֹם הַשְּׁלִישִׁ֛י פָּרִ֥ים עַשְׁתֵּי־עָשָׂ֖ר אֵילִ֣ם שְׁנָ֑יִם כְּבָשִׂ֧ים בְּנֵי־שָׁנָ֛ה אַרְבָּעָ֥ה עָשָׂ֖ר תְּמִימִֽם׃
And on the third day eleven bullocks, two rams, fourteen lambs of the first year without blemish;
On the third day of Sukkot, 11 bulls were brought as part of the collection of sacrifices for the musaf offering. This is part of a descending sequence. On the first day of Sukkot, there were 13 cows; on the second day, 12; and now, on the third day, 11. Therefore, the version of 11 is עַשְׁתֵּי־עָשָׂ֖ר .
וַיַּחֲלֹ֥ם עוֹד֙ חֲל֣וֹם אַחֵ֔ר וַיְסַפֵּ֥ר אֹת֖וֹ לְאֶחָ֑יו וַיֹּ֗אמֶר הִנֵּ֨ה חָלַ֤מְתִּֽי חֲלוֹם֙ ע֔וֹד וְהִנֵּ֧ה הַשֶּׁ֣מֶשׁ וְהַיָּרֵ֗חַ וְאַחַ֤ד עָשָׂר֙ כּֽוֹכָבִ֔ים מִֽשְׁתַּחֲוִ֖ים לִֽי׃
In Yosef's dreams, the number 11 represents an absolute count and is not part of a series. Therefore the version אַחַ֤ד עָשָׂר֙ is employed.
אמר חזקיה מניין שכל המוסיף גורע שנאמר (בראשית ג, ג) אמר אלהים לא תאכלו ממנו ולא תגעו בו רב משרשיא אמר מהכא (שמות כה, י) אמתים וחצי ארכו רב אשי אמר (שמות כו, ז) עשתי עשרה יריעות
Ḥizkiyya says: From where is it derived that anyone who adds, subtracts? It is derived from a verse, as it is stated that Eve said: “God has said: You shall not eat of it, neither shall you touch it” (Genesis 3:3), whereas God had actually rendered prohibited only eating from the tree but not touching it, as it is stated: “But of the Tree of Knowledge of good and evil, you shall not eat of it” (Genesis 2:17). Because Eve added that there was a prohibition against touching the tree, the snake showed her that touching it does not cause her to die, and she consequently sinned by eating from it as well. Rav Mesharshiyya says that the idea that one who adds, subtracts can also be proven from here: “Two cubits [amatayim] and a half shall be its length” (Exodus 25:10). Without the letter alef at the beginning of the word amatayim, it would be read matayim, which would mean two hundred cubits. The addition of the alef therefore reduces this term to only two cubits. Rav Ashi says another example: In the verse: “Eleven [ashtei esrei] curtains” (Exodus 26:7), without the letter ayin at the beginning of the phrase it would read shtei esrei, twelve. Therefore, the additional letter ayin reduces the amount from twelve to eleven.