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There's a story that Rabbi Chaim of Volozhin once asked the Vilna Gaon if he should wear Rabbenu Tam tefillin, to which the Gaon replied that to cover all doubts one would have to wear 64 pairs a day.

Does anyone have a source for this or knows how the Gaon arrived at that number?

Also, why would it not be 4 factorial?

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  • How do you get 4 factorial?
    – Noach MiFrankfurt
    Dec 15, 2016 at 14:35
  • the order of parchment is not the only area of disagreement, take the Shimisha Rabbah wotj regards to soze of the batim
    – sam
    Dec 15, 2016 at 16:18
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    @Nic There's also the Machloket how to spell "totafot". And Afatzim there is about the content of the Dyo, not how to cure the leather, which is another Machloket. 99.99% of the Tefillin on the market today are completely Pasul accd to the Rambam bc of that one.
    – Double AA ♦
    Dec 15, 2016 at 16:19
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    related judaism.stackexchange.com/q/12772/759
    – Double AA ♦
    Dec 15, 2016 at 16:52
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    @NoachMiFrankfurt while it was in the original wording, I don't think adding "why not 4 factorial" really makes sense in the current version.
    – Nic
    Dec 15, 2016 at 17:16

2 Answers 2

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A source for this is in הלכות הגר"א ומנהגיו.

מצאתי כתוב פעם אחת שאל הגאון רבי חיים מוולזין זצ"ל לרבינו למה אינו מניח תפילין דרבינו תם, והשיב למה מניח הוא, שהבין משאלתו שמניחם, א"ל כדי לצאת ספק ב' הדיעות, השיבו א"כ צריך להניח ס"ד זוגות תפילין דהיינו ב' שיטות של רש"י ורבינו תם ושיטה ג' שהוא של הראב"ד בהלכות תפילין דס"ל כרבינו תם דהויות באמצע, אלא דרבינו תם ס"ל דברייתא קמייתא משמאל המניח, והראב"ד ס"ל דברייתא קמייתא מימין קדש והיה כי יביאך ואחר כך והיה אם שמוע משמאל המניח , וברייתא דמיתנא איפכא בקורא, עוד יש להמציא שיטה חדשה היינו כדעת הראב"ד דברייתא קמייתא מימין המניח אך סדר הפרשיות כדעת רש"י, דהיינו קדש והיה כי יביאך שמע והיה אם שמוע דהיינו ד' זוגות, ועוד יש מחלוקת הפוסקים אי הפרשיות יהיו עומדין או מונחין הרי ח' זוגות, עוד יש מחלוקת הפוסקים אם לכתוב במקום שער או בשר הרי ט"ו זוגות, עוד יש מחלוקת הרמב"ם ורא "ש בפתוחות וסתומות הרי ל"ב זוגות ועוד יש מחלוקת בעשיית הדיו, הרי הוא שיש להניח ס"ד זוגות

My translation would be:

I found written that the once the Gaon Rabbi Chaim of Volozhin asked Rabeinu [the Gaon] why he doesn't wear Rabeinu Tam's tefillin, and he [the Gaon] answered "Why do you wear them?". He [Rabbi Chaim] answered "to fulfill the mitzvah according to both (Rashi and R"T's) systems. He [the Gaon] answered him that if so, he should be wearing 64 pairs of tefillin: The two systems (best translation of שיטה I have) of Rashi and R' Tam, a third system of the R"avad who holds like R'Tam that the two והיה paragraphs should be in the middle, but that the first of the two והיה should be on the right instead of on the left. In addition, one would need to create a new system that holds the והיה order as the R"avad, but uses Rashi for the full ordering. This makes four systems so far. And then there is a dispute if the orientation of parashas should be placed vertical or horizontal. And there is another dispute if the writing should be on the hair side of the skin or the meat side. This makes 16 pair (of systems) and there is a dispute of the R"osh and the R"ambam regarding leaving space when a "stuma" paragraph (i.e. one that finishes in the middle of a row) is written -- 32 systems. And there is a dispute in the making the ink, so there are 64 different systems (for writing tefillin).

To clarify:

  • Rashi / R'Tam = 2 options for general ordering of the parashas.
  • R"avad / Rambam = 2 options for ordering the two והיה parashas.
  • Orientation = 2 options for orienting the klaf in the boxes.
  • Klaf = 2 options for deciding which side of the skin to write on.
  • R"osh / Rambam = 2 options for adding space after "stumot".
  • ink = 2 options for making the ink.

All together, we have 2*2*2*2*2*2 = 64 different exclusive ways to create tefillin.

Edit: As noted by @Double-AA, there are further disputes that can increase this number by further factors of two if one was so inclined.

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  • To list some additional machlokot, the Shimushah Rabbah holds by yet another order. Further, as mentioned in the comments elsewhere, the way in which the klaf and leather were tanned is a machloket (Tosefot/Rambam). There are different shittot for forming the letters (Beit Yosef/Ari/old Yekkisch/Sephardi [I'm discounting Alter Rebbe k'tav, as the Gr"A had him under cherem]).
    – Noach MiFrankfurt
    Dec 15, 2016 at 17:23
  • [cont'd.] The knots also have multiple shittot, see links and discussion here: judaism.stackexchange.com/q/75260/4504
    – Noach MiFrankfurt
    Dec 15, 2016 at 17:24
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    @Noach The Shimusha order isn't meakev according to the link, nor is the form of the letters accd to anyone
    – Double AA ♦
    Dec 15, 2016 at 17:29
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R. Asher Ashkenazi, a disciple of R. Chaim of Volozhin, records the story a little differently. He writes that R. Chaim made the following argument to his teacher, the Vilna Gaon:

You only wear Rashi tefillin because you wear tefillin all day. Since Rashi tefillin is the main one, every moment of wearing Rabbeinu Tam tefillin is a wasted moment where you could have been wearing Rashi tefillin. But I anyway spend many hours not wearing tefillin at all, so why shouldn't I put on Rabbeinu Tam tefillin in order to fulfill the mitzvah according to all opinions.

R. Ashkenazi writes that the Vilna Gaon responded to R. Chaim by saying that if he really wants to fulfill all the opinions he would have to put on 24 pairs of tefillin. The conclusion of 24 was explained as follows:

In addition to the dispute between Rashi and Rabbeinu Tam there is also the opinion of R. Hai Gaon that is the reverse of Rabbeinu Tam. This brings us to 3 permutations. Then there is the dispute about the petuchot u'stumot which brings us up to 6 permutations. Then there is the dispute about whether the words should be written on the flesh side of the parchment which brings us up to 12 permutations. Finally there is the dispute whether the parshiot should be standing up or lying down which brings us up to 24 permutations.

Orchot Chaim (Keter Rosh) # 13

תפילין דרבינו תם שאל מרבו הגר"א ז"ל מו"ר אינו מניח תפילין דרבינו תם כדי שלא לבטל אף רגע מתפילין ושל רש"י עיקר אבל אני שבלאו הכי הנני מבטל כמה שעות מתפילין מה בכך אם אניח איזה שעות ביום ואצא ידי חובת תפילין לכל הדעות

השיבו כשתרצה לצאת לכל הדיעות תצטרך להניח כ"ד זוגות והיכן מצינו כ"ד חילוקי דעות בתפילין אמר לו דוק ותשכח ואסיק על דעתו דדעת רב האי גאון היא כרבינו תם רק להיפך מימין לשמאל הרי ג' זוגות מחלוקת בפתוחות וסתומות הרי ששה זוגות מחלוקת אם לכותבן בקלף במקום בשר הרי י"ב מחלוקת אם להניח הפרשיות מעומדות או מונחות הרי כ"ד זוגות

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  • "whether the words should be written on the flesh side of the parchment" That's imprecise. Everyone agrees tefillin is written on the flesh side. The machloket is if the flesh side of the hide or the hair side of the hide is to be tanned into klaf. Whichever you pick you then write on the flesh side of that.
    – Double AA ♦
    Mar 12, 2021 at 3:15

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