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1)

(a) Both Rebbi Yehudah and Rebbi Shimon learns from "Al Mitzcho" - that that is where the Tzitz must be worn.

(b) Rebbi Shimon learns from "Al Metzach ve'Nasa" - that the Tzitz atones only as long as it is fit to be worn (i.e. when it is not broken).

(c) Rebbi Shimon does not consider the extra 'Vav' redundent - in his opinion, it is a regular manner of speech.

(a) Rebbi Meir obligates the Kohen who prepared the Parah Adumah to be sprinkled with the ashes of all the cows that had been used to date on *each of the seven days* that he was separated from his house. According to Rebbi Yossi, he was only sprinkled on the *third and the seventh* days.

(b) We try to explain that Rebbi Meir holds 'Tum'ah *Dechuyah* Hi be'Tzibur', and Rebbi Yossi, "Hutrah*.

(c) Rebbi Meir holds 'Tum'ah *Dechuyah* Hi be'Tzibur - therefore, the purification had to be done properly, and, since, on each day there was a Safek whether the Kohen Gadol required Haza'ah or not, it was necessary to sprinkle him every day. But according to Rebbi Yossi, who holds 'Tum'ah *Hutrah* Hi be'Tzibur' - the need to sprinkle him was no more than a Ma'alah de'Rabbanan, and Chazal did not require more than the two (necessary) Haza'os on the third and the seventh days.

(d) If Rebbi Yossi held 'Tum'ah hi be'Tzibur' the Gemara retorts, then he would not have required Haza'ah at all!

(a) We conclude that in fact, both Tana'im hold 'Tum'ah Dechuyah Hi be'Tzibur': - Rebbi Meir holds 'Tevilah bi'Zemanah Mitzvah' (and we are comparing Haza'ah to Tevilah), in which case it was necessary to sprinkle the Kohen Gadol on each day that may have been his third day or his seventh days; Rebbi Yossi holds 'Tevilah bi'Zemanah La'av Mitzvah', so it sufficed to sprinkle him on one of the days which might be the third day, and then four days later.

(b) Rebbi Yossi permits someone who has the Name of Hashem written on his skin to Tovel without the need to tie a string around it - because, since he holds 'Tevilah bi'Zemanah Mitzvah', we are afraid that if we require that he ties a string around the Name of Hashem, he may not find a piece of string and will postpone the Tevilah; whereas the Rabbanan hold 'Tevilah bi'Zemanah La'av Mitzvah', and therefore required him to tie a string around it (should he not find a string yoday, then he will Tovel tomorrow).

(c) The reason that Rebbi Yossi does not require the Kohen who prepared the Parah Adumah to be sprinkled every day (in spite of the fact that he holds 'Tevilah bi'Zemanah Mitzvah') - is because he does not compare Haza'ah to Tevilah in this regard.

(a) We learn from the juxtaposition of "ve'Ibadtem es Shemam" to "Lo Sa'asun Kein la'Hashem Elokeichem" - that it is forbidden to erase the Name of Hashem.

(b) Rebbi Meir and Rebbi Yossi argue whether they sprinkled the Kohen Gadol on all *seven* days or only on *two*, both with regard to the Kohen who prepared the cow and the Kohen Gadol on Yom Kipur.
Rebbi Chanina S'gan ha'Kohanim holds like Rebbi Meir by the Kohen who prepares the Parah Adumah, but like Rebbi Yossi by the Kohen Gadol on Yom Kipur.

(c) In fact, the Gemara concludes, he does not compare Haza'ah to Tevilah (like Rebbi Yossi). Nevertheless, he requires Haza'ah on each of the seven days by the Kohen who prepares the Parah - because of a Ma'alah de'Rabbanan.

5)

(a) According to the Beraisa, the only practical difference between the Kohen who separates the cow, whose separation was for Taharah purposes, and the Kohen Gadol, who separated for additional Kedushah (according to the Tana of the Beraisa currently under discussion) - is that as far the latter is concerned, the Hafrashah also served to remind his to be humble as well as keeping him away from anything that led to lightheadedness.

(b) The author of this Beraisa cannot be Rebbi Chanina S'gan ha'Kohanim, because according to him, there was another difference between the two Hafrashos - namely, that the one was sprinkled *seven* times (in fact, he was only sprinkled five or six times, as we shall soon see) the other *twice*.

(a) The problem with sprinkling him on the *fourth* day, according to Rebbi Meir (who says that the Kohen had to be sprinkled every day of the seven days of Hafrashah) - is that there was really no reason to do so, seeing as it could neither be the third day (after Tevilah) nor the fifth day after the first Haza'ah (as is the seventh after the fourth).

(b) Rebbi Meir cannot have meant that the Kohen Gadol is literally sprinkled on each of the seven days - because Haza'ah on Shabbos is anyway forbidden (mi'de'Rabbanan - as we learnt in Pesachim on 65a). Consequently, 'every day' is not literal because it precludes Shabbos, in which case, we can go a little further and say that it also precludes the fourth day.

(c) As a result of this, we separate the Kohen Gadol on Yom Kipur on the third of Tishri (seeing as we have no choice in choosing the date on which Yom Kipur is to fall that year), and if the fourth day of the Hafrashah does not fall on Shabbos (in which case there will be *two* days that year on which the Kohen Gadol is not sprinkled - so be it. But as far as the Kohen who prepares the Parah Adumah is concerned, we will make sure that he begins his Hafrashah on Wednesday, so that the fourth day falls on Shabbos, and there will only be *one* day on which he is not sprinkled.

(a) Initially, the room designated for the Hafrashah of the Kohen Gadol was called 'Lishkas Belavti' - meaning the Room of the Princes.

(b) They change its name to 'Lishkas Farhedrin' - because the Kohanim Gedolim, (who, having obtained their positions by means of bribery, were unworthy incumbents of the position, and) who used to (therefore) invariably die on the first Yom Kipur after taking office, would, immediately following their appointment, rebuild it, to perpetuate their names. So they named it after the officers (some say of the market-ministers) whom the king tended to change year by year - who were called 'Farhedrin'.

(a) Chazal obligated bakers to give from the produce that they purchased from Amei ha'Aretz - Terumas Ma'aser (from the Ma'aser Rishon, which they separated but kept themselves) and Chalah.

(b) They did not obligate them to give ...

1. ... Terumah Gedolah - because (since they knew that it carried with it a Chiyuv Misah) all the Amei-ha'Aretz used to give it, so there was no reason to decree on the purchaser.
2. ... Ma'aser Rishon and Ma'aser Ani - since these are purely monetary considerations, and in money-matters we say 'ha'Motzi me'Chaveiro, Alav ha'Re'ayah' (the onus is on the claimant to prove that the seller had not already given them before selling the crops).

(c) Strictly speaking, the bakers should have been obligated to take Ma'aser Sheini to Yerushalayim (just like everybody else). However, Chazal relieved them of the obligation, to make up for the Farhedrin, who used to beat them and force them to sell their confectionery cheaply (perhaps to help them pay for the new rooms that they used to build in the Beis-Hamikdash).

(d) This is perfectly justifiable - because the whole Takanah of Demai is purely mi'de'Rabbanan (since the majority of Amei-ha'Aretz used to give Ma'asros anyway). So Chazal reserved the right to waive it whenever they see fit.