The gemoro seems to conclude here that on the morning of a taanis which falls on Monday or Thursday you lein Parshas Hashovua
L'Maaseh we don't, as the ran and others explain
However, in the Aliba D'Hilchoso in the back of the new gemoros, it seems to conclude that if there weren't 6 fasters at your minyan you would yes lein parshas Hahovua
In Actuality, what would one do in such a case, and its not so far fetched, for example, a minyan in a nursing home
Chag Kosher V'Sameach
The conclusion of most of the Acharonim is that six people fasting is required in order to read Vayechal on a Ta'anis, and if there are less than six people, on a regular morning there is no Keri'as Ha'Torah and on Monday and Thursday we read the Parshas ha'Shavu'a. This is the view of the Yeshu'os Yakov, Sdei Chemed, Kaf ha'Chayim (119:27), Chelkas Yakov (3:69), and Igros Moshe (Orach Chayim 4:113), Minchas Yitzchak (1:65), and Yechaveh Da'as (1:79).
A minority of Poskim follow the ruling of the Chasam Sofer (Teshuvos, Orach Chayim 157) who maintains that on a fast day we read Vayechal even if only three people are fasting and they are called to the Torah. This opinion is based on the Me'iri (Megilah 2b) and is also the opinion of the Aruch ha'Shulchan (Orach Chayim 566:7).
sorry but could you also be more specific on the chelkas yaakov - what does 3:69 mean I only see one chelek orach chaim
also cant find yechaveh daas
(I am using hebrewbooks.org)
Since Sefer Yechaveh Da'as is still being sold commercially, you won't find it on Hebrewbooks. Nonetheless, I checked the responsa project and found that he maintains that it is enough to have six people fasting.
The Chelkas Yakov I quoted is based on the notation in an old edition. The Teshuvah can be found in Orach Chayim 215, and he says similarly that six fasting men are required, and if not we read the normal Parshah.
and if there are less than 6? what do u do then?
According to these Poskim, we read the Parshah of that week on Monday and Thursday. If it is not Monday and Thursday, we omit Keri'as ha'Torah.