We have Halacha that at least 6 people need to be fasting in order to read the Torah in a fast day. However, let's say there are 10 people and 5 are definitely fasting and one who accidentally ate (the other four aren't fasting at all). Can they read the Torah?
Inspired by You accidentally broke your fast. Now what?
Chasam sofer implies you can rely on 3 fasters for leining vayechal - in a comunity where 10 fasters are present in another shul - bedieved in the minian. This is the amount needed to be called up to the torah, as only fasters may be called up to the torah and there would have not been leining were it not for the fast. This would applies during mincha any day, and shacharis sunday, tuesday, wednesday and friday (however monday and thureday morning even though its better to call up fasters he has a right to tell them they could have leined the normal weekly parsha so he can be called up). the chassam Sofer compares this case in teshuva orach chaim siman 157 to a zimun, where we don't make a non participating cohein mechubad to be mezamein if he is not eating with them (i.e hes eating separately from them) so too a non fasting cohein goes out the room if not fasting since the torah reading was specifically induced on that day for the fast. even though if one calls up a non faster (who's oneis for health reasons) by mistake we allow him proceed to bless the torah, we still need 3 Fasters who could have been called up. The chasam sofer also says tisha ba'av is a yom tov so even on a non leining day if its not nidche (delayed) one can call up a non faster (also since hes wearing slippers and doing other forms of aveilus so is included in the fast).
However Aneinu in the repetition of amida as a separate brocho requires 10 fasters according to shulchan oruch and some poskim allow only 7 or 6 (NOT LESS)in a town with another shul where there are 10 fasters since we include them as one community.
