Question: This falls far short of the total - because if one deducts from the six hundred thousand the six hundred officers of thousands from the total, one will not be left with six thousand officers of the hundreds? And if one then deducts them from the total, there will not remain twelve thousand officers of fifty? And certainly, if one then deducts them ... , there will not remain sixty thousand officers of tens?

Answer #1: There are some who answer that perhaps all the officers were over the age of sixty (and the Gemara says in 'Yesh Nochlin' that whoever was under twenty and over sixty was not included in the six hundred thousand). And as far as the officers of ten are concerned, it doesn't matter even if they were under sixty and included in those who were counted, since each one was an officer of nine and he was the tenth.

Answer #2: Whilst others suggest that the Gemara is concerned with the officers - i.e. that initially, they counted the officers of ten. The most important of whom were appointed as officers of fifty. Out of them, they then appointed officers of hundreds and the most important of them, as officers of hundreds.

Clarification: In other words, why does the Tana see fit to mention 'Dan' (that the Kohen Gadol is permitted to judge)? To which the Gemara replies that he needed to mention 'Danin Oso' (since we might otherwise thought, that, due to his greatness, he cannot be judged), and he mentions 'Dan' because of 'Danin'). On this, the Gemara then asks that this too, is obvious (because since he is permitted to judge, it is obvious that he is able to be judged), due to the Pasuk "Hiskosheshu ve'Koshu", as the Gemara explains.

Implied Question: Why does the Gemara not answer that the Tana needed to mention 'Danin', because we would otherwise have thought that he cannot be judged, and therefore he cannot judge either?

Answer: because then it would have sufficed to write 'Dan', and from there we would have known 'Danin'.

Question: The Kashya remains however, that regarding Melech, why does the Tana not just say 'Lo Danin', and we will know automaticaly that Eino Dan, due to "Hiskosheshu ve'Koshu"?

Answer #1: Certainly by a Kohen Gadol, having learned 'Dan', to add 'Danin Oso' was superfluous; Whereas by Melech, one cannot ask why the Tana inserts 'Lo Dan', since he learns it before 'Lo Danin Oso'.

Answer #2: Furthermore, having learned 'Kohen Gadol Dan ve'Danin Oso', he balances this by writing with regard to Melech 'Lo Dan ve'Lo Danin Oso'.

Implied Question: Why then, does the Gemara omit this entire discussion?

Answer: Because it takes for granted that the Tana learns the Seifa to balance the Reisha (So Tosfos found in the name of the Rebbe, R. Troysh).

Refutation: R. Troysh's explanation however, is unnecessary. It is quite obvious that once it is necessary to mention 'Dan' or 'Danin' by Kohen Gadol, or 'Lo Danin' or 'Lo Dan' by Melech, the Kashya as to why the Tana adds 'Danin Oso' by Melech, and 'Lo Dan' by Melech is inappropriate. This is because, once one of them teaches us a Chidush, it is natural for the Tana to mention the other one.

Proof: A proof for this lies in the fact that the Gemara asks here 'P'shita?' meaning why the need to mention 'Danin Oso'. To which it answers that he needs to mention 'Danin Oso', on account of which he mentions 'Dan'.

Implied Question: One cannot ask why the Gemara does not answer that the Mishnah needs to mention 'Dan' and 'Danin Oso' (even if there would be no other Chidush), because had it not mentioned either, we would have thought that a Kohen Gadol cannot be judged (as we explained earlier), in which case, he cannot judge either (due to "Hiskosheshu ve'Koshu").

Answer: Because we could just as well say the opposite - that had it not mentioned either, we would have thought that since there is no reason for him not to be able to judge, he must be able to be judged too (for the same reason)!

Question: Why did Rebbi learn 'Kohen Gadol' immediately after the first Perek?

Answer: Because having taught some of the Dinim of a Kohen Gadol in the first Perek, the Beraisa concludes the topic with which it is dealing before switching to the Dinim of a king, who is superior in eminence to a king, following which he goes back to the Kohen Gadol.

Clarification: This speaks specifically where a. they did not appoint another Kohen Gadol before his Din was finalized and b. there was neither a Mashuach she'Avar (a deputy who once stood in for the Kohen Gadol on Yom Kipur) nor a Kohen Mashu'ach Milchamah at the time the murderer's Din was finalized (since of the latter two, the former frees the murderer unanimously, whilst the latter is subject to a Machlokes between R. Yehudah and the Rabbanan in 'Horiyos').

Question (Part 1): Why does the Gemara not establish our Mishnah with regard to testifying on having seen the new moon, something that a Kohen Gadol is certainly permitted to do - because when it comes to an Isur, we have a principle 'Ein Chochmah ve'Ein Tevunah ... Neged Hash-m, as we have learned in Perek Shevu'as ha'Eidus regarding a Talmid-Chacham.

Question (Part 2): Because when we say that Kavod ha'Beri'os' overrides a Lo Sa'aseh, that pertains specifically to money issues, but not Isurim, as we have already explained (see Aruch la'Ner).

Answer #1: The answer is that 'Meid' implies across the board, irrespective of whether it is for Isur or for Mamon, just like 'Melech Lo Me'id', which incorporates matters of Mamon.

Answer #2: Alternatively 'Me'id pertains specifically to Mamon, just like 'Melech Lo Me'id', which must be talking about Mamon, because if it is a matter of Isur, we will apply the principle 'Ein Chochmah ve'Ein Tevunah ... '.

Question: Why do we not establish our Mishnah ('Melech Lo Dan ... ') by the kings of Yisrael, and the Mishnah which says 'Dan ... ', by the kings of Beis David (about whom we will learn shortly 'Dan ... ')?

Answer: It is logical to establish the entire Mishnah by Malchei Yisrael, just like 'Melech Lo Dan ... ').

Question #1: Why did the Gemara not rather ask from our Mishnah - 'Melech Lo Dan'?

Question #2: Furthermore, what is the Chidush of 'Ein Moshivin ... ', in view of our Mishnah?

Answer #1: We would otherwise have restricted the Mishnah's prohibition to the king judging on his own, which we would have forbidden as a result of the fact that he cannot be judged (on account of 'Hiskosheshu ve'Koshu"), but to judge as a member of Sanhedrin would have been permitted, seeing as the rulings are not issued by him alone (So it appears to Mori ha'Ran).

Question: The Gemara established the Sugya about judging a prince. But how is it possible for a king to be judging his own son?

Answer: To be sure, the Gemara knew full well that the king did not come to judge, only to sit in on the proceedings, but even that, it seems, is forbidden.

Answer #2 (to first question). This also explains why the Gemara did not ask our Mishnah 'Melech Lo Dan'?

Explanation #1: Rashi explains that this is due to the fact that the Kohen Gadol required Tevilah.

Refutation: This is not correct however, since it is implied in the Gemara in Yoma that would heat up a kettle of hot water on Yom Kipur.

Explanation #2: The reason therefore appears to be because of the coldness of the floor, on which the Kohen served all day barefoot.

Explanation #1: Rashi explains that the cold and the heat of the year are determined by the months - so that if the year would not be a leap-year, then the cold weather that would have occurred in Mar-Cheshvan, will now occur in Tishri.

Refutation: The problem with this is why the Kohen Gadol needs to be perturbed by the leap-year, seeing as the point of a leap-year is bring the 'sun months' in line with the 'moon-months', and to turn mar-Cheshvan into Tishri. And the reason for this is so that the autumn solstice falls in Tishri, for some of Chag ha'Succos to fall in the new solstice. Just like in most years, when the new solstice falls in the month of Tishri.

Explanation #2: Tosfos therefore explain that the Gemara is speaking in a case where they are discussing a leap-year on account of Pesach falling in the spring or so that the fruit of the trees should be ripe for Bikurim. Because then, the cold of the forthcoming Tishri will be different than that of other years, inasmuch as the temperature in Tishri will resemble that of a regular Mar-Cheshvan.

Proof: This is borne out by the fact that the Gemara now asks from the three 'Roei Bakar' - implying that the fruit and the cold coincide, since one of the cowhands gave the reason as 'Peiros', whilst one of remaining two gave it as the cold weather (see Tosfos ha'Rosh).