The new year for kings & festivals: First of Nisan.

The new year for Ma'aser Behemah:

(Tana Kama): First of Elul.

(R. Elazar & R. Shimon): First of Tishrei.

The new year for counting years, Shemittah, Yovelos, Orlah and Ma'aser Yerek: First of Tishrei.

The new year for trees:

(Beis Shammai): First of Shevat.

(Beis Hillel): Fifteenth Shevat.

Question: What is the relevance of the new year for kings?

Answer: In order to discern that a contract is pre-dated (and thus invalid).

First Beraisa: When a king is appointed on the 29th of Adar, that day counts as the first year of his reign.

This teaches that the new year for kings is the first of Nisan.

It also teaches that one day can count as a year.

But when a king is appointed on the first of Nisan, it is not counted as a year until the following Nisan.

Question: This is obvious!

Answer: It is needed to teach that when the king was selected in Adar (but not yet coronated), it is not counted as his first year.

Second Beraisa: If a king died and was succeeded in Adar, that year is counted for both kings.

Question: This is obvious!

Answer: It is needed to teach that one year can count for two kings.

If a king died and was succeeded in Nisan, that year is counted for both kings.

Question: This is obvious!

It is needed to teach that one day can count as a whole year (for the deceased king) even when it is at the beginning of the year.

If a king died in Adar and was succeeded by the new king in Nisan, the first year is counted for the first (deceased) king and the second year is counted for the second (new) king.

Question: This is obvious!

Answer: It is needed to teach that even in a case when the second king was already selected in Adar, and he is the son of the first king, nevertheless he counts his first year from Nisan. when he is coronated.

Source #1 (R. Yochanan): The new year for kings is learned from a verse (Melachim I 6,1) that connects the years of King Shlomo's reign to the years from the Exodus, which itself is counted from Nisan.

Question: How do we know that the years from the Exodus are counted from Nisan and not from Tishrei?

Answer: The Torah's considering Aharon's death in Av (Bamidbar 33, 38) and Moshe's subsequent speech in Shevat (Devarim 1,3) as being in the same (40th) year, shows that the year cannot begin from Tishrei.

Question: How do we know that the year of Moshe's speech is being counted from the Exodus and not from the building of the Mishkan which was a year later?

Answer (based on Rav Papa's statement later): The identical phrase (Gezeirah Shava) of "the fortieth year" in each verse shows that they are both being counted from the Exodus.

Question: How do we know that Moshe's speech was subsequent to Aharon's death? Perhaps it was before his death!.

Answer: Moshe's speech was after Sichon's death (Devarim 1,4) and when Aharon died Sichon was still alive.This can be proven as follows

The verse (Bamidbar 21,1) states that "the Cana'ani King Arad heard" (that Aharon died) and he attacked Israel.

The previous verse (Bamidbar 20,29) states that Israel "saw that ("ki") Aharon died" is understood as "they feared (attack) because Aharon died."

This is in accordance with Resh Lakish's teaching that "ki" can only mean 'if," "perhaps," "rather," and "because" (in this case, it means "because") and not "that".

Question: We need to know about Sichon, but the verse speaks of Arad and not Sichon!

Answer: Sichon, Arad and Cana'an are all the same person. He was named "Sichon" because he was as wild as a foal ("Siach"); "Cana'an" was his kingdom; and "Arad" was his name; alternatively, he was named "Arad" because he was as wild as a wild ass ("Arod"); "Cana'an" was his kingdom; and "Sichon" was his name.