(Mishnah - R. Meir): Monetary cases require three judges; cases of theft and wounds (hitting someone) require three judges. Cases of damage, half-damage, double payment (of a thief), payment of four or five (if he slaughtered or sold a Kosher Behemah) require three.

Rape or enticement of a virgin Na'arah (a girl less than six months after becoming Bas Mitzvah), and Motzi Shem Ra (one who claimed that his Kalah was not a virgin) require three judges;

Chachamim say, 23 are needed for Motzi Shem Ra, for sometimes it is a capital case.

Cases of lashes require three;

R. Yishmael says, they require 23.

R. Meir says, three judges are needed for Ibur Chodesh or Ibur Shanah (to add a day to the month or a month to the year);

R. Shimon ben Gamliel says, we begin Ibur Shanah with three, we deliberate with five, and the verdict is with seven;

If three judges gave a verdict to make an Ibur Shanah, it is Me'uberes.

R. Shimon says, three judges are needed for Semichah of judges (leaning on a Korban for a mistake of the Great Sanhedrin; alternatively, ordination), and for the Eglah Arufah (a calf beheaded for atonement when a murdered corpse is found);

R. Yehudah says, five are needed.

Three judges are needed for Chalitzah, Mi'un, redemption of Ma'aser Sheni or Neta Reva'i whose value is not known, or of Hekdesh, and Erchin ha'Metaltelim (this will be explained);

R. Yehudah says, one of them must be a Kohen;

Redemption of land or a person needs a Kohen and nine other people.

Capital cases require 23 judges;

If an animal slept with a man or woman, 23 judges are needed - "v'Haragta Es ha'Ishah v'Es ha'Behemah" (if it slept with a woman), "v'Es ha'Behemah Taharogu" (if it slept with a man);

An animal that is stoned (e.g. for killing a Yisrael) requires 23 judges - "ha'Shor Yisakel v'Gam Be'alav Yumas" - the animal is killed like its owner (would be killed if he was Chayav Misah).

Twenty-three judges are needed to kill a wolf, lion, bear, leopard, Bardelus (panther?), or snake;

R. Eliezer says, anyone who kills one of these (without Beis Din) did a Mitzvah;

R. Akiva says, 23 judges are needed.

Seventy-one judges are needed to judge a Shevet (tribe) (this will be explained), a false Navi, or a Kohen Gadol;

Seventy-one judges are needed to decide to go to an optional war;

Seventy-one judges are needed to add to Yerushalayim or the Azaros (courtyards of the Mikdash);

Seventy-one judges are needed to establish a Sanhedrin for a Shevet;

Seventy-one judges are needed to make an Ir ha'Nidachas (a city destroyed because its majority served idolatry);

We do not make an Ir ha'Nidachas near the border of Eretz Yisrael. We do not make three of them (even not near the border), but we may make one or two.

The Great Sanhedrin has 71 judges. A small Sanhedrin has 23;

We learn (about a Great Sanhedrin) from "Esfah Li Shiv'im Ish", and Moshe was the head;

R. Yehudah says, there are only 70.

We learn about a small Sanhedrin from "v'Shaftu ha'Edah... v'Hitzilu ha'Edah" - there is an Edah (congregation) Mechayev (incriminating), and an Edah Mezakeh (vindicating);

Question: What is the source that an Edah is (at least) 10?

Answer: "La'Edah ha'Ra'ah ha'Zos" refers to the 10 Meraglim other than Yehoshua and Kalev.

Question: This teaches only 20 judges. How do we learn another three?

Answer: "Lo Siheyeh Acharei Rabim Lera'os", but you may follow a majority to acquit;

Question: What do we learn from "Acharei Rabim Lehatos"?

Answer: We follow a majority to convict, but it is different from the majority to acquit. A majority of one (judge who decides to acquit) suffices to acquit, but we need a majority of two to convict.

(In order to convict against an Edah that acquits, 12 judges must convict.) W do not make a Beis Din with an even number of judges, therefore, 23 are required.

Question: How many people must there be in a city to qualify it to have a Sanhedrin?

Answer #1: It needs 120 (23 judges, 69 Talmidim,... - 17b).

Answer #2 (R. Nechemyah): It needs 230, corresponding to judges of 10 (i.e. each judge on the Sanhedrin could be a judge over 10 people of the city).

(Gemara) Question: Cases of theft or wounds are monetary cases! (Why are they listed separately?)

Answer #1 (R. Avahu): The Mishnah teaches monetary cases, then gives examples, i.e. theft and wounds;

It omits admissions and loans (witnesses heard Reuven admit that he owes Shimon, or they saw a loan).

The Mishnah had to teach monetary cases, and also theft or wounds.

Had it taught only monetary cases, one might have thought that this includes admissions and loans. Therefore, it had to teach theft and wounds, to exclude admissions and loans;

Had it taught only theft and wounds, one might have thought that the same applies to admissions and loans, and the Tana taught theft and wounds because regarding them the Torah taught about three judges.

Regarding (a watchman suspected of) theft, it says "v'Nikrav... El ha'Elohim." (This means Mumchim (expert judges), and it is written three times in the Parshah.)

Reasoning teaches that wounds are like theft. Striking a person is like striking his money.

Question: The Mishnah teaches monetary cases, and gives theft and wounds for examples. Why were admissions and loans omitted?

Suggestion: Admissions and loans do not require three judges.

Rejection: R. Avahu taught that all agree that if two judged a monetary case, the verdict is invalid!

Answer: They were omitted because admissions and loans do not require Mumchim.

Question: Does R. Avahu say that Eruv Parshiyos (words in a Parshah teach about a different Parshah) applies here?

If it does (i.e. "Ki Hu Zeh... ha'Elohim" written here really applies to loans), we should require Mumchim also for admissions and loans!

If Eruv Parshiyos does not apply here, admissions and loans should not require three judges!

Answer: Really, Eruv Parshiyos applies here. The reason we do not require Mumchim is similar to R. Chanina's teaching;

(R. Chanina): Mid'Oraisa, we must interrogate witnesses for monetary cases just like for capital cases - "Mishpat Echad Yihyeh Lachem."

It is an enactment not to interrogate witnesses in monetary cases, lest this discourage loans (people would be afraid to lend, lest the witnesses err and be disqualified. Similarly, the need for Mumchim discourages loans, for it makes it hard for lenders to collect.)