Shulchan Aruch, Orach Chayim 124:4, in my own, loose translation:

When the leader repeats the amida (sh'mone esre), the congregation should be quiet, pay attention to the benedictions that the leader recites, and respond "amen". If there are fewer than nine paying attention to his benedictions, his benedictions are nearly in vain. Therefore, everyone should treat himself as if there were not nine besides for him and pay attention to the benediction of the leader.

Normally, women and minors don't count toward a minyan, a quorum of ten required for various things, especially d'varim shebikdusha, matters of holiness. (One minor may count, as outlined somewhere else in Shulchan Aruch, but let's ignore that fact for simplicity.) I wonder whether the same is true here, for the following two reasons:

  • The Shulchan Aruch doesn't say explicitly that they need to be adult males.
  • This sounds to me like a "someone has to be listening" thing rather than like a "we need a minyan here" thing. For example, the Aruch Hashulchan (:9) paraphrases the Taz (:2) to the effect that the necessary nine cannot include someone whose ears are stuffed up so he cannot hear, even though he counts toward a minyan.

Do women count toward this quorum of nine listeners? Do minors?

  • I read this question as women/**mirrors**. Like can you set up a couple of mirrors to reflect one person's image many times to make a minyan. – Daniel Feb 1 '16 at 17:57

Ba'er Hetev note #8 says that one who isn't listening is not included as part of the minyan, and this includes even one who is a pike'ach. The term pike'ach refers to someone who is deaf but can speak (vs. a cherish who can neither hear nor speak.)

So, I'm focusing mainly on your 2nd bulleted item, here and making some logical conclusions:

  • It is already understood that a minyan must be present to do the Amidah repetition.
    • The definition of minyan means 10 men over Bar Mitzvah and does not include women.
    • From Ba'er Hetev's comment, I think that you can make a logical conclusion. He's basically stating that someone who isn't listening essentially is excluded from the minyan. It's not merely, that there's a minyan around and people aren't paying attention. If there's no minyan, which by definition means men only, the fact that women are there and are listening, it seems doesn't help the situation at all. You need at least 10 men who are actively listening to keep the minyan going.

Keep in mind that this is just one opinion. In a previous note, Ba'er Hetev discusses those people who learn during the repetition, but are aware of the ending of the bracha happening, so they can answer "Amen". It seems that such people are still considered valid "listeners".

I assume that the mentioning of the pike'ach is to prove that it doesn't require mere awareness that the chazzan is making a bracha and you have some mere idea and understanding of when he reaches the end. Other than the learning situation mentioned above, which seems to be a special situation, one must be actively listening to what the chazzan is saying.

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