THE CONTRADICTORY LOCATIONS OF THE LISHKAS HATELAIM
R. Ada b. R. Yitzhok resolved the contradiction by explaining that the Lishkah was very long and appeared differently to one who might enter from the two directions.
He also taught that it is further likely that the Lishkah was primarily in the SW.
There is an apparent contradiction between Mishnayos regarding the Lechem ha'Panim.
This contradiction is resolved by differing perspectives, one to the right and one to the left.
By positioning the Lishkas ha'Telaim at the SW, its position coincides with the resolution of the Mishnayos regarding the Lechem ha'Panim.
Question: How can we identify the position of the Lishkah from the left, given that we always turn to the right?
Answer: This is not a turning; it is only a calculation of a location.
THE KOHEN GADOL GOING FIRST
He offers first by selecting which Korbanos he will offer.
He takes first by designating the Korbanos he will eat.
He takes one (of two) Chalos on Shavuos.
He takes four or five Chalos from the weekly Lechem ha'Panim.
Rebbi taught that he always takes five, representing half.
Question: The Mishnah ends up switching authors in the middle!?
First clause: His taking one (of two) Chalos- Rebbi.
Second clause: He takes four or five- Rabanan.
Third clause: He takes five- Rebbi.
Answer: The first and second clauses are Rabanan (who hold he takes less than half) but they also concur that we don't give the Kohen Gadol broken loaves (hence one of two loaves on Shavuos).