1) THE INCREASE IN THE NUMBER OF "MISHMAROS"
QUESTION: The Gemara says that originally there were 16 Batei Avos -- 8 from the family of Elazar and 8 from the family of Isamar. In the times of David ha'Melech, the family of Elazar increased significantly, and the 8 family groups of Elazar were divided into 16 Batei Avos, for a total of 24 (16 from Elazar and 8 from Isamar). The Gemara asks what the source is that the family of Elazar doubled. Perhaps it was the family of Isamar which doubled. The Gemara proves that the family of Isamar remained the same from the verse, "One Beis Av was apportioned to Elazar, and apportioned, apportioned to Isamar" (Divrei ha'Yamim I 24:6).
What is the Gemara's proof from this verse? The verse implies that twice as many Batei Av were apportioned to Isamar than to Elazar, the opposite of what the Gemara is trying to prove. How does the verse imply that Elazar had twice as many Batei Avos as Isamar?
(a) RASHI explains that the words "apportioned, apportioned" mean that the number of Mishmaros that had been apportioned previously to Isamar remained and nothing more was added.
(b) Some explain that the verse refers to the lottery which was conducted in order to determine the new order of the Mishmaros, now that eight additional Mishmaros were added. How many lots were included in the lottery? To represent the 16 Batei Avos of Elazar, 16 lots were included. How many lots were included to represent the 8 Batei Avos of Isamar? If only 8 lots would have been put in the lottery for the 8 Batei Avos of Isamar, the Batei Avos of Elazar would have a far greater chance of being chosen first. Therefore, they wrote each one of the Batei Avos of Isamar on two lots in order to make the lottery fair and equal.
That is what the verse means when it says "apportioned, apportioned to Isamar" -- the repetition of the word "apportioned" refers to the two lots that were written for each of the Batei Avos of Isamar, since they had half as many Batei Avos.
The NACHALAS DAVID in HAVEN B'MIKRA (at the end of Nachalas David) cites this explanation but rejects it for several reasons. First, the Gemara cites the verse to prove that the number of Batei Avos of Isamar did not double. According to this explanation, however, perhaps they did double -- from four to eight. Second, the verse itself does not read well according to this explanation. The verse refers to the people themselves and mentions nothing about the lots. Third, it is not logical to suggest that they made two lots for one Mishmar in order to double their chances in the lottery. What would happen if both lots of the same Mishmar were selected? It obviously would have to be discarded, and thus the lottery itself would have become less meaningful.
(c) The NACHALAS DAVID suggests an original explanation which is consistent with the straightforward meaning of the verse and which conforms with the Gemara perfectly. He explains that since Elazar was older than Isamar, it was decided that the a Mishmar from the family of Elazar would serve first. That Mishmar would be followed immediately by one from Isamar (so as not to leave him too far behind Elazar). Therefore, in order to determine the order of the Mishmaros, they made two separate boxes and conducted two separate lotteries: one for the family of Elazar and one for the family of Isamar. Elazar drew the first one and Isamar the second, and they continued to draw lots in an alternating manner, first Elazar and then Isamar.
The increase of the family of Elazar from 8 Mishmaros to 16 meant that each family group became divided into two families. Consequently, it was decided that the spin-off from the family group would always serve immediately after the first half of the original family group served, because it would not be fair to have the spin-off serve at an entirely different time than the first half of that family (since they used to serve together as one Mishmar). Therefore, when they drew lots to determine the order of the Mishmaros from Elazar's family, they drew only 8 lots for the original 8 Mishmaros. The spin-off family groups would serve immediately after the original Mishmar from which they came.
They placed into a box 8 lots, representing the original 8 Mishmaros of Elazar, in order to determine the order of all 16 Mishmaros of Elazar (the lottery determined the order of the original Mishmaros, each of which was followed by its spin-off group). A lot was first chosen from Elazar's box to determine which of his Mishmaros would be first (and second, the spin-off Mishmar). Then, the first lot from Isamar's box was chosen to determine which Mishmar from Isamar would serve first, after the first two Mishmaros of Elazar.
However, it emerged that the drawing of one lot from Elazar's box determined the order of two Mishmaros (the original Mishmar and its spin-off). If they subsequently chose only one lot from Isamar's box, Isamar would have only one Mishmar following Elazar's two Mishmaros, and thus Isamar would not be on an equal standing with Elazar. Therefore, after they chose one lot from Elazar's box, they chose two lots, and thus two Mishmaros, from Isamar's box. Then, one lot was chosen again from Elazar's box (which determined their third and fourth Mishmaros), and then two lots were again chosen from Isamar's box to determine their third and fourth Mishmaros. This process continued until the fourth lot was chosen from the box of Elazar (which determined the seventh and eighth Mishmaros of Elazar) and the seventh and eighth lots were chosen from the box of Isamar (which determined the seventh and eighth Mishmaros of Isamar). After that, there remained no Mishmaros from the family of Isamar to choose (since they had only eight), and there were still eight Mishmaros from Elazar which remained to be chosen (by selecting four lots). Thus, the final four lots were all chosen from Elazar's box.
This is subtly and succinctly expressed by the verse. In the lottery which selected the order of the Mishmaros of Elazar, one lot was chosen to determine two Mishmaros -- the original Mishmar and its spin-off. Afterwards, two lots were chosen from the Mishmaros of Isamar to select two Mishmaros ("apportioned, apportioned").
Further support for this explanation is found in the verses which list the Mishmaros of the families of Elazar and Isamar. Whenever the verses list the Mishmaros, each verse randomly lists one, two, or three Mishmaros. Here, however, each verse lists exactly two Mishmaros. Why do the verses here list the Mishmaros in this specific manner? The answer is that the verses are listing them the way they were chosen by the lots, two at a time.
The Nachalas David uses this approach to explain a cryptic statement in the Yerushalmi. The Yerushalmi here (Ta'anis 4:2) states that the seventeenth Mishmar was called "Chezir" because it served at the point at which the cycle "returned" ("Chazar") to the family of Elazar. All of the commentators are at a loss to explain the intent of the Yerushalmi.
The VILNA GA'ON in Divrei ha'Yamim explains that the Yerushalmi alludes to the Gemara here which says that they added another 8 Mishmaros to Elazar. Since there originally was a total of only 16 Mishmaros (8 from Elazar and 8 from Isamar), the fact that there was a seventeenth Mishmar indicated that new Mishmaros had been added. The Vilna Ga'on's explanation, however, is not consistent with the wording of the Yerushalmi. According to his explanation, the Yerushalmi should say that the seventeenth Mishmar was called "Chezir" because "it hints that" 8 Mishmaros were added from Elazar. There is no indication that the seventeenth Mishmar itself was from Elazar. What does the Yerushalmi mean when it says that "the cycle returned to Elazar"?
According to the explanation of the Nachalas David, the intent of the Yerushalmi is clear. After the sixteenth Mishmar was chosen by the lottery (8 from Elazar and 8 from Isamar), no more lots were drawn for the lottery of Isamar (because there were no more Mishmaros to choose from Isamar), and thus "the cycle" of drawing lots "returned to Elazar" -- all of the remaining lots were drawn from the lottery of the Mishmaros of Elazar!

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2) DIVIDING A VERSE IN THE TORAH
QUESTION: Rav and Shmuel argue about how five verses are to be divided between two people during the Torah reading when each person must read at least three verses. Rav says that they repeat a verse: the first person reads the first three verses, and the second person repeats the last verse that the first person read and continues with the last two verses. Shmuel says that they split a verse: the first person reads the first two verses and half of the third, and the second person reads the second half of the third verse and the last two verses.
The Gemara explains that Rav disagrees with Shmuel because he rules that "any verse which Moshe Rabeinu did not divide, we are not permitted to divide." This principle is generally understood to mean that whenever a verse from the Torah is read or quoted, it must be read in its entirety. Since the Halachah follows the opinion of Rav with regard to how to divide five verses between two people (SHULCHAN ARUCH OC 423:2), the Halachah should also follow Rav with regard to dividing any verse: whenever a verse is read it must be read in its entirety.
In practice, however, many incomplete verses from Tanach are recited in various contexts. The following are some examples of such instances:
1. In the Hagadah of Pesach, several verses are quoted but not in their entirety: Devarim 6:3 in the paragraph, "Said Rebbi Elazar ben Azaryah"; Devarim 6:20 in the paragraph, "The wise son"; Shemos 12:16 in the paragraph, "The wicked son"; Shemos 1:22 in the paragraph, "And our labor"; Shemos 3:9 in the paragraph, "And our oppression"; Divrei ha'Yamim I 21:16 in the paragraph, "And with an outstretched arm"; the second half of Devarim 6:21, "Avadim Hayinu" ("... we were slaves") is quoted as the opening phrase for the paragraph of Avadim Hayinu and the first words of that verse, "v'Amarta l'Vincha..." ("And you shall say to your son...") are omitted.
2. In the Kidush of Shabbos night, only the second half of Bereishis 1:31 ("va'Yehi Erev va'Yehi Voker Yom ha'Shishi") is recited.
3. In the Kidush of Shabbos morning, many have the practice not to say the entire paragraph of "Zachor Es Yom ha'Shabbos," and yet they nevertheless say the last words of the paragraph, "Al Ken Berach Hash-m Es Yom ha'Shabbos va'Yekadshehu," which is an incomplete verse from Shemos 20:11.
4. When the Chazan returns the Sefer Torah to its place after Keri'as ha'Torah, he says, "Yehalelu Es Shem Hash-m Ki Nisgav Shemo Levado," the first half of Tehilim 148:13. The congregation recites after him, "Hodo Al Eretz v'Shamayim," the second half of that verse. Why is the congregation permitted to recite an incomplete verse? (See RAV JOSEPH PEARLMAN's comprehensive discussion of this topic in HA'MEIR, 5753).