Query (Rebbi Yirmeyah): Do synagogues and study halls require checking?

Question: Why would they require checking?

Answer: Since Chametz is brought there for the meals celebrating (Shabbos and) the new moon [and the leap years].

Question: It is therefore obvious that they would require checking?!

Clarification: His doubt is as to whether they should be checked by candlelight at night even though they are very brightly lit in the daytime.

Query (Rebbi Yosa): Must one check the courtyards in Yerushalayim in which they would eat the loaves of the Toda offering and the wafers of the Nazir?

Answer: No, since they would anyway be checked in order to burn any remains of korbanos left there.

Objection (Rebbi Zecharia): A Nidah must shampoo and comb [to be permitted to her husband] and a Kohen's wife need not [in order to eat Terumah- since she regularly immerses, she is careful]. But a Kohen's wife who is a Nidah must shampoo and comb in order to keep all Nidos alike. Similarly this courtyard (as well as synagogues and study halls) should require checking in order to keep all cases alike!

Rebuttal (Beraisa): A Kohen's wife who is a Nidah must shampoo and comb since she has not immersed for seven days, but when not a Nidah she immerses daily so she need not do so [but it is not for the reason of keeping all Nidos alike]!

Objection (Rebbi Mana): A shomeres yom keneged yom must also shampoo and comb [even though she immersed the day before](so it must be for the reason of keeping all Nidos alike)!