(Mishnah): On the first day of Sukos, they brought 13 bulls, two rams and one goat.

There remained 14 lambs (that were brought each day of Sukos) to be brought by the eight remaining Mishmaros (of the 24 that had not been used for the 13+2+1 above) -

On the 1st day, (of the 8 remaining Mishmaros) - 6 Mishmaros brought two lambs each and the last two Mishmaros brought 1 lambs each.

On the 2nd day (when 12 bulls were brought, so it was 12+2+1=15, with 9 Mishmaros remaining) - 5 Mishmaros brought two lambs each and the last 4 Mishmaros brought 1 lamb each.

On the 3rd day (when 11 bulls were brought, so it was 11+2+1=14, with 10 Mishmaros remaining) - 4 Mishmaros brought two lambs each and the last 6 Mishmaros brought 1 lamb each.

On the 4th day (when 10 bulls were brought, so it was 10+2+1=13, with 11 Mishmaros remaining) - 3 Mishmaros brought two lambs each and the last 8 Mishmaros brought 1 lamb each.

On the 5th day (when 9 bulls were brought, so it was 9+2+1=12, with 12 Mishmaros remaining) - 2 Mishmaros brought two lambs each and the last 10 Mishmaros brought 1 lamb each.

On the 6th day (when 8 bulls were brought, so it was 8+2+1=11, with 13 Mishmaros remaining) - 1 Mishmar brought two lambs and the last 12 Mishmaros brought 1 lamb each.

On the 7th day, (when 7 bulls were brought, so it was 7+2+1=10, with 14 Mishmaros remaining) all of the Mishmaros were equal in that they brought one lamb.

On the 8th day (when they brought 1 bull, 1 ram and 7 lambs), they returned to the regular lottery of the festivals (in order to select the Mishmaros that would merit bringing the sacrifices). They said that whoever had already sacrificed bulls would not sacrifice them tomorrow; rather, they would take turns in rotation.

(Gemara - Beraisa): All of the Mishmaros in the Temple would sacrifice a bull three times, except for the last two Mishmaros who would only sacrifice a bull twice.

Query (R. Elazar): Do we continue the rotation of Mishmaros during the next festival (meaning that on Pesach, the last two Mishmaros will sacrifice the two bulls)?

R. Yosa: Our Mishnah says not - "On the eight day, they returned to the regular lottery of the festivals" - meaning that they would not sacrifice without a lottery.

This query is only relevant to the opinion of R. Noson, who said in a Beraisa that on the eighth day there was no lottery (and the one bull of the day would be brought by one of the last two Mishmaros). (The Gemara dos not answer.)

R. Yochanan - Beraisa: Shemini Atzeres (the 8th day of Sukos) is a separate festival, has a separate lottery, has its own blessing of Shehecheyanu and has different sacrifices -

It is a separate festival - as R. Avin quoted from the House of Acha - The Pasuk about all of the days of Sukos begins with "and on the day..."; but in reference to the 8th day, the Pasuk says "On the day", without connecting it to previous days. This teaches that it is a separate festival.

It has a separate lottery - as R. Yosa said - our Mishnah teaches, "on the eighth day they returned to the regular lottery of the festivals.

Blessing - as R. Ila said - this refers to the blessing of Shehecheyanu.

The sacrifice - Shemini Atzeres had different sacrifices - a bull and a ram are brought.