The Torah commands in the Book of Vayikra (22:32), "Ve’nikdashti Be’toch Beneh Yisrael" – "I shall be proclaimed sacred among Beneh Yisrael." The Sages understood this verse as implying that "Debarim She’bi’kdusha" – prayers which pronounce G-d’s glory – may be recited only "among Beneh Yisrael," meaning, in the presence of a quorum, defined as ten men.
We find in the Talmud two different approaches to explain how the "Be’toch Beneh Yisrael" indicates that specifically ten people are needed. According to one approach in the Gemara, this is inferred from the word "Toch" which appears here ("Be’toch") and also in reference to the story of Korah’s revolt, when G-d commanded Moshe and Aharon, "Hibadelu Mi’toch Ha’eda Ha’zot" – "Separate from this congregation." The word "Eda" in this verse appears also in a different verse, in reference to the ten spies who spoke negatively about the Land of Israel, when G-d said to Moshe, "Ad Matai La’eda Ha’ra’a Ha’zot" – "Until when will there be this evil congregation?" The word "Eda" thus refers to a group of ten, and so the word "Toch," which is mentioned both in the context of Korah’s uprising and in the command of "Ve’nikdashti," is associated with a group of ten. Hence, the Gemara understood that "Debarim She’bi’kdusha" require a quorum of at least ten.
The Talmud Yerushalmi (Berachot 7:3) brings this approach, but also a different approach, noting that the word "Be’toch" is used in reference to Yosef’s ten brothers who came to Egypt to purchase grain ("Be’toch Ha’ba’im"). Thus, when the Torah commands, "Ve’nikdashti Be’toch Beneh Yisrael," it refers to a group of at least ten people.
Hacham Ovadia Yosef, in his Yabia Omer, suggests that the practical difference between these two sources might be the possibility of counting a minor as one of the ten men in the quorum. If the basis for defining "Be’toch Beneh Yisrael" as a group of ten is the story of Yosef’s brothers, then we might require specifically ten adult males, just as Yosef’s brothers were ten adult males when they came to Egypt. But if the basis for this Halacha is Korah’s uprising, then we might include even minors, since minors were included in Korah’s revolt.
(Incidentally, Rabbenu Bahya, in his Torah commentary to Parashat Emor, cites an opinion that the Gemara did not, in fact, suggest deriving the concept of Minyan from Korah’s revolt, which consisted of evil men. This would be a very peculiar way of establishing the lofty concept of a Minyan, and so this opinion claims that this statement in the Gemara was the result of a "Ta’ut Sofer" – a scribal error, and in truth, according to all views, the source is Yosef’s brothers’ arrival in Egypt.)
The issue of whether a minor can be counted toward a Minyan is mentioned already by the Gemara in Masechet Berachot (chapter 7), where Rabbi Yehoshua Ben Levi is cited as ruling that a minor can count as the tenth man to make a Minyan for a Zimun. Tosafot (commentaries by Medieval French and German scholars) show that Rabbi Yehoshua Ben Levi’s statement was intended also with regard to a Minyan for "Debarim She’bi’kdusha." Accordingly, Tosafot cite Rabbenu Tam (France, 1100-1171) as ruling that a minor can be counted towards a Minyan, following the ruling of Rabbi Yehoshua Ben Levi. Tosafot add that some people had the practice of giving the minor a Humash to hold as a condition for him to be counted as the tenth person, but Rabbenu Tam called this practice a "Minhag Shetut" – "silly custom," as it unnecessary for the minor to hold a Humash.
Significantly, however, one of Rabbenu Tam’s students, the Ri (Rabbenu Yishak of Dampierre), attested that Rabbenu Tam did not follow this ruling as a practical matter. Although he maintained that in principle, a child may count as the tenth person for a Minyan, he himself did not actually rely on this lenient position.
The Shuhan Aruch (Orah Haim 55) brings Rabbenu Tam’s lenient opinion, and then writes, "Ve’en Nirin Dibrehem" – this view does not seem correct. Quite clearly, then, the Shulhan Aruch did not accept this lenient ruling, and maintained that a child may not count towards a Minyan. We may assume that the Shulhan Aruch would not allow this even under extenuating circumstances, such as in a small community where ten adult males are not often present in the synagogue. Even under such conditions, the Shulhan Aruch would not permit counting a minor towards a Minyan.
Among Ashkenazic Poskim, this issue is subject to some controversy. The Rama (Rav Moshe Isserles of Cracow, 1530-1572), in his glosses to the Shulhan Aruch, writes that some had the practice to count a minor as the tenth person of a Minyan, and the Magen Abraham (Rav Abraham Gombiner, 1633-1683) adds that in his time this practice was commonly followed. On the opposite extreme, the Lebush (Rav Mordechai Yoffe, 1530-1612) writes that he never saw anyone allow this practice, and he strongly insists that it not be followed. In between these two extremes, the Shulhan Aruch Ha’Rav (Rav Schneur Zalman of Liadi, the founding Rebbe of Lubavitch, 1745-1813) writes that under extenuating circumstances, a minor may be counted towards a Minyan.
For Sepharadim, however, the Shulhan Aruch’s ruling is very clear, that a minor may not be counted towards a Minyan.
There were those who supported the lenient position in light of a responsum of Rav Yaakob of Marvege (France, 13th century), one of the Tosafists. Rav Yaakob of Marvege had the practice of going to sleep with a Halachic question in his mind, and the answer would then come to him in a dream. He would wake up the next morning and record the response. These responses were collected into a work entitled "She’elot U’teshubot Min Ha’Shamayim" – "Questions and Answers From the Heavens." One question he asked was whether a child may count for a Minyan, and the response he received was the verse in Tehillim, "Ha’ketanim Im Ha’gedolim; Yosef Hashem Alechem" – "Young and old together; may Hashem increase your numbers." Rav Yaakob understood this to mean that if a youngster joins adults as part of a Minyan, this brings blessing – meaning, this is acceptable. Some argued that as this response was given from the heavens, it is authoritative.
Hacham Ovadia, however, notes that many authorities did not regard these rulings of Rav Yaakob of Marvege as authoritative. He cites the Shiboleh Ha’leket (Rav Sidkiya Ben Abraham, Italy, 13th century) as remarking, "We are not beholden to this Sadik’s dreams, nor to his interpretations." Although Rav Yaakob of Marvege was certainly a righteous man, the principle of "Lo Ba’shamayim Hi" (the Torah "is not in the heavens") establishes that Halacha is determined through the scholarship of the Torah sages, and not through any sort of prophetic or quasi prophetic revelation. As such, we are not bound by the rulings found in Rav Yaakob of Marvege’s responsa. Indeed, there are number of rulings in his work which Sephardic practice clearly does not follow. For example, he ruled (based on his dreams) that the Beracha of "She’hehiyanu" should be recited before even the morning Megila reading on Purim, whereas our practice is to recite this Beracha only at the nighttime reading. He also ruled that women should recite a Beracha before performing a Misva from which they are exempt, whereas we follow the Shulhan Aruch’s ruling that women do not recite a Beracha in such a case. As such, we have no basis on which to rely on his lenient ruling that minors may be counted toward a Minyan, in opposition to the ruling of the Shulhan Aruch.
The question arises as to whether a Sepharadi may pray with a Minyan of Ashkenazim that relies on the lenient position and counts a minor as the tenth person in the Minyan. Lubavitch Hasidim, for example, who follow the rulings of the Shulhan Aruch Ha’Rav, permit counting a minor for a Minyan under extenuating circumstances. May a Sepharadi participate in such a Minyan?
Hacham Bension Abba Shaul (Israel, 1924-1998), in Or Le’sion (vol. 2, p. 45), writes that since there are opinions who allow counting a minor toward a Minyan, one may participate in a Minyan that relies on this opinion. Hacham Ovadia, however, in his critique of Or Le’sion, disagrees. He notes that this very question was already addressed by the Maharam Me’Rutenberg (Germany, 1215-1293), and he ruled unequivocally that one must not participate in a Minyan that counts a minor as one of the ten men, as in his view, there is no basis for such a practice. The Maharam Me’Rutenberg pointed to the fact that Rabbenu Tam himself, the Rishon who permitted this practice, did not follow it as a practical matter. Hacham Ovadia also cites a responsum written by Rashi in which Rashi wrote that this practice may not be followed under any circumstances. Therefore, Hacham Ovadia ruled that one may not participate in such a Minyan.
(This debate might also relate to a different dispute between Hacham Bension and Hacham Ovadia, as to whether one may answer "Amen" to a Beracha if one follows the view that this Beracha is not warranted. For example, Ashkenazim recite a Beracha on Hallel on Rosh Hodesh, whereas Sepharadim follow the view that this Beracha is not required, and thus it constitutes a Beracha Le’batala – a Beracha recited in vain. Hacham Bension maintained that a Sepharadi may nevertheless answer "Amen" to this Beracha, since it is recited according to Ashkenazic tradition, whereas Hacham Ovadia maintained that it would be forbidden for a Sepharadi to answer "Amen" to this Beracha. According to Hacham Ovadia, if one follows the opinion that a certain Beracha constitutes a "Beracha Le’batala," then he may not answer "Amen" to that Beracha. Conceivably, this applies also to the Berachot in the Hazzan’s repetition of the Amida in a Minyan comprised of nine adults and one minor.)
Summary: A minor may not be counted toward a Minyan, even if there are nine adult males. Some Ashkenazic communities allow relying on a minor as the tenth person under extenuating circumstances, but a Sepharadi may not participate in such a Minyan.
