The Shulchan Aruch Siman 55 says that if one of the Minyan is in middle of Shemona Esrei, he is still counted as part of the ten. The Mishna Berura says that as long as 6 are not in middle of Shemona esrei, the other 4 are Mitztaref (counted as being part of the minyan)

 

BUT...

 

The problem is, that this Halacha is said regarding saying Kadish or a different Davar Sh'Bekedusha, that only requires ten people to be together, but not necessarily 10 people "answering"

 

The question is if this Halacha applies to Chazaras HaShatz as well?

 

The Shulchan Aruch HaRav (Siman 55:7) says explicitly that this only works for Kadish and Barchu etc. but  for Chazaras HaShatz, anything less than 9 answering is a Bracha L'Vatalah. The Kaf HaChaim Paskens like this as well as do many other Poskim.

 

Some Poskim maintain that the opinion of the  Maharil  was to indeed allow even Chazaras HaShatz with only 6 people of the 10 answering. (The Maharil does not say this clearly, rather they deduce that this is what he would have held. The reasoning and proofs that apply to and against  this opinion is too lengthy a discussion for this email)

 

Rav Shlomo Zalmen Auerbach Zatzal  maintained that even if the Maharil was lenient,  the Shulchan Aruch wasn't and he paskened that for Kadish and Barchu 6 is enough, while for Chazaras HaShatz  nine people answering is required.

 

Some Poskim allow the starting of Chazaras HaShatz with only 6 people answering, B'Sha'as HaDchak- in extreme situations, but not as a rule to be relied on daily.

 

For Halacha L'Maaseh please consult your Rav, and do not rely on what any Shliach Tzibbur "was told" to do by someone who may not know the real Halacha.