How Many People are Needed for a Minyan?

In this previous post we discussed the issue of Pores Al Shma. We mentioned that according to Rashi the mishna is basically saying that for kaddish and kedusha you need 10 people. The gemara there in Megillah 23b explains that the pshat in the mishna is that all things classified as "davar shebikdusha" need 10 people for a minyan.

Interestingly there is a Meseches Sofrim (10:7) which at first glance seems to argue with this gemara in Megillah. Here are some excerpts from that Meseches Sofrim:

And one does not say Kaddish and Borchu with less than 10... Our Rabbis in the west say... with seven... [as it says] bifroa peraos etc... and some say even six... And in a place where there are nine or 10 that already heard either Borchu or Kaddish and after tefillah one of these gets up and says Borchu or Kaddish and they answer after him he is yotzei. And the Chachamim were already mesaken for the Chazanim that after geulah they say Yehi Shem Hashem Mevorach... and after this Borchu in order to be motzee those that haven't heard because R' Yochanan said "Halvei that a person should daven all day". And the people of the west and east have a custom to say it after Oseh Shalom in the three tefillos of shemoneh esrai as a gezairah fro those who have just entered and a gezairah for those leaving and even after krias hatorah...

The Rishonim in Megillah mention this Meseches Sofrim. Some say that the Rabbis of the West argued with our gemara and actually required less than 10 for a minyan. Others say that the Meseches Sofrim doesn't mean to say that you need 6 or 7 for a minyan, but only means that you need 6 or 7 who have not yet davened to be a part of the minyan.

In Iggros Moshe O.C. 1:28 Rav Moshe mentions using the concept of Rubo K'kulo when it comes to minyanim. He says that obviously the rule of Rubo K'kulo does not apply to shiurim. So, if you need a minyan of 10 people you can't say that with 6 you have a minyan because of rubo k'kulo. However, he says that if 6 of the 10 have not yet davened you can apply rubo k'kulo and say that you have an "entire" minyan of people who are chayav in davening.

We find the idea of rubo k'kulo applied here in the words of the Ran on Daf 3a in Dapei Harif of Megillah as well. The issue being dealt with there is that we know R' Assi holds that 10 are needed for krias megillah. So the rishonim are bothered how come in this mishna of pores al shma we don't list krias megillah as something that needs 10 people (according to R' Assi)? It is especially difficult to say that this was left out since this list is in a Mishna that is in Meseches Megillah. Certainly Krias Megillah itself should make the list! It is difficult to say that the mishna is lav davka. The Ran there explains (following the shitah of the Milchamos there; see also Baal HaMaor) that the Mishna is only listing things that are Chovas Tzibbur. This means that if you have a tzibbur who are all still chayav to hear or recite one of the things in the mishna the chiyuv is chas on the tzibbur as a whole. When it comes to krias megillah it is not a chovas tzibbur. Rather, it is a chovas yachid (every yachid needs to hear the megillah) that should be done in front of 10 people due to pirsumei nissa. This is why Krias Megillah is not in the Mishna.

It comes out that according to the Ramban krias hatorah (which is also in the Mishna in Megillah) is a chovas yachid. This would mean that if one does not go to minyan on a Monday or Thursday the chiyuv to hear krias hatorah would never be chal on him. I heard, however, that Rav Chaim Soloveitchik was machmir for the opinion that krias hatorah is a chovas yachid. Therefore, he was very makpid to hear leining on Mondays and Thursdays - even if it meant jumping off trains (I don't know if they were moving).