1) WHEN MUST THE NAZIR SHAVE?
OPINIONS: The Mishnah records a dispute among Tana'im with regard to when a Nazir must shave at the end of his Nezirus. Rebbi Yehudah maintains that the Nazir shaves after he offers his Korban Shelamim. Rebbi Elazar maintains that he shaves after he offers his Korban Chatas, because a Chatas is always offered before an Olah or Shelamim, and it is logical that the shaving is done immediately after the first Korban is offered (see BARTENURA).
The Mishnah records the reason for Rebbi Elazar's view, but not the reason for Rebbi Yehudah's. What is the reason for Rebbi Yehudah's view that a Nazir shaves after he offers his Korban Shelamim?
The Gemara explains that Rebbi Yehudah derives the requirement for a Nazir to shave after he offers the Korban Shelamim from the verse which states, "The Nazir shall shave at the entrance of the Ohel Mo'ed" (Bamidbar 6:18). The words "at the entrance of the Ohel Mo'ed" teach that the Nazir must shave after he offers the Korban Shelamim, since the Korban Shelamim is the only Korban for which the verse mentions "the entrance of the Ohel Mo'ed" -- "He shall slaughter it at the entrance of the Ohel Mo'ed" (Vayikra 3:2).
According to Rebbi Yehudah, at what point in the order of the Nazir's Korbanos is the Shelamim offered? If Rebbi Yehudah agrees with Rebbi Elazar's logical assertion that the Nazir should shave immediately after the first Korban is offered, and he maintains that the Nazir shaves after the Korban Shelamim, does this imply that he maintains that the Korban Shelamim is offered first?
(a) TOSFOS (DH Tiglachas) writes that Rebbi Yehudah indeed maintains that the Nazir's Korban Shelamim is offered before his Chatas and his Olah, despite the fact that in all other situations of multiple Korbanos the Chatas is offered first.
Tosfos understands that since Rebbi Yehudah maintains that the Tiglachas is performed after the Shelamim is offered, it must be that the Shelamim is the first Korban offered. What is the logic behind this assertion? The fact that the Tiglachas is performed after the Shelamim does not seem to be a logical reason to assume that the Shelamim is offered first. Similarly, why is it so obvious to Rebbi Elazar that the Torah requires that the Tiglachas be performed after the first Korban?
The answer is as follows. The law is that once any one of the Nazir's Korbanos is offered, the Nazir's Taharah process begins and he may shave. Accordingly, the Korban which is offered first is the most important one. Rebbi Elazar follows the ordinary rule which states that a Chatas is offered first. Rebbi Yehudah derives from the Gezeiras ha'Kasuv -- which teaches that the offering of the Shelamim enables the Tiglachas to be performed -- that the Shelamim is offered first. (This may be the intention of the Mefarash on the Mishnah (DH sheha'Chatas) when he writes that Rebbi Elazar maintains that the Chatas of a Nazir is offered first "in order that the Nazir should shave upon offering it.")
(b) The RAMBAM (Hilchos Nazir 8:2) writes that the Nazir offers his Chatas first, and he shaves only after he offers the Shelamim -- which is offered last. The KESEF MISHNEH asks that the Rambam's ruling is problematic, as he seems to rule unlike either of the two Tana'im.
The LECHEM MISHNEH (ibid.) explains that the Rambam rules like Rebbi Yehudah. He understands that Rebbi Yehudah agrees that the Korban Shelamim is offered last, but nevertheless derives from the verse that the Nazir shaves after he offers the Korban Shelamim. Rebbi Elazar, in contrast, maintains that since the Chatas has the privilege of always being offered first, the Torah presumably prefers that the Nazir shave after he offers the Chatas.
The explanation of the Rambam has an advantage over that of Tosfos in that it answers Tosfos' question: if Rebbi Yehudah maintains that the Nazir offers the Korban Shelamim first and that he shaves after he offers the Korban Shelamim, why does he imply in the Mishnah that the Nazir offers the Chatas first? According to the Rambam, Rebbi Yehudah indeed maintains that the Chatas is offered first.

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2) WHEN DOES THE NAZIR PLACE HIS HAIR IN THE FIRE?
QUESTION: The Tana Kama of the Mishnah teaches that when a Nazir who concludes his Nezirus in Taharah performs the Tiglachas in the Beis ha'Mikdash, his hair is placed in the fire beneath the pot in which the Zero'a of the Shelamim is cooked. When the Tiglachas is performed outside of the Beis ha'Mikdash, his hair is not placed beneath the pot of the Zero'a. When a Nazir who became Tamei shaves as part of the Taharah process, his hair is never placed in the fire, regardless of where the Tiglachas is performed. Rebbi Meir disagrees and states that the Nazir's hair is placed in the fire in every case except for that of a Nazir Tamei who shaves outside of the Beis ha'Mikdash.
The Gemara quotes a Beraisa which explains these opinions in more detail. Rebbi Meir maintains that the reason why the hair of a Nazir Tamei is not placed in the fire is that it must be buried. Rebbi Yehudah maintains that the hair of a Nazir Tahor is always placed in the fire, and the hair of a Nazir Tamei is never placed in the fire, regardless of where the Tiglachas is performed. The Chachamim maintain that only hair of a Nazir Tahor who shaves in the Beis ha'Mikdash is placed in the fire, since his Tiglachas was performed in the prescribed manner (in the Beis ha'Mikdash).
The RAMBAM (Hilchos Nazir 8:3) rules that, l'Chatchilah, the Tiglachas of a Nazir Tahor is performed in the Ezras Nashim section of the Beis ha'Mikdash, but even if it was performed elsewhere the hair is placed in the fire. Whose opinion does the Rambam follow?
ANSWERS:
(a) The KESEF MISHNEH writes that the Rambam rules like Rebbi Yehudah, as is evident from his words later when he writes that the hair of a Nazir Tamei is not placed in the fire.
The Kesef Mishneh is perplexed by the Rambam's ruling. The Mishnah explicitly follows the view of the Chachamim in the Beraisa. Why does the Rambam not rule like the Chachamim in the Mishnah, whose opinion is the majority?
(b) The LECHEM MISHNEH explains that the Rambam indeed rules like the majority opinion. Both Rebbi Yehudah and the Chachamim maintain that the hair of a Nazir Tamei is not placed in the fire. Rebbi Meir maintains that it is placed in the fire if the Tiglachas was performed in the Beis ha'Mikdash. The Rambam rules like the majority who maintain that the Nazir Tamei's hair is not placed in the fire.
In the case of a Nazir Tahor, however, both Rebbi Meir and Rebbi Yehudah maintain that the hair is always placed in the fire, while the Chachamim differentiate between a Tiglachas performed in the Beis ha'Mikdash and one performed outside of the Beis ha'Mikdash. The opinion of the Chachamim, therefore, is a minority opinion. The Rambam rules in this matter like Rebbi Meir and Rebbi Yehudah, the majority opinion. (Y. Montrose)