1) SPEAKING TO THE JEWISH PEOPLE ON THE DAY OF THEIR ARRIVAL AT HAR SINAI
QUESTION: The Gemara says that when the Beraisa mentions that the "third day" was also the third of the month (3 Sivan) and the third day of the week (Tuesday), it refers to the third day on which Moshe Rabeinu spoke to the Jewish people in preparation for Kabalas ha'Torah, when he told them of the punishments and rewards that awaited them. Since that day was the third of the month, the first day, on which he began to tell them of the punishments and rewards, must have been the first of Sivan, the day they arrived at Har Sinai.
This seems to contradict the Gemara earlier (86b) which states that on the day of their arrival at Har Sinai, Moshe did not speak to them at all because they were exhausted from traveling. How are we to reconcile these two statements of the Gemara?
ANSWER: The MAHARSHA answers that on the first day at Har Sinai, Moshe did not tell the people anything that Hash-m had told him. This is what the Gemara earlier means. Rather, he merely spoke to them his own words of preparation for receiving the Torah.

87b----------------------------------------87b

2) THE JEWS TRAVELING ON SHABBOS IN THE DESERT
QUESTION: Rava and Rav Acha bar Yakov argue whether the Jewish people arrived at Har Sinai the same day they left Refidim or on a different day. The Gemara explains their argument. According to Rava, although the Jews were commanded at Marah to fulfill the Mitzvah of Shabbos, the prohibition of Techumin (traveling beyond a certain distance on Shabbos) was not included in that commandment, and thus the Jews were permitted to travel on Shabbos. Since they traveled on Shabbos, they were able to leave Refidim earlier in order to arrive at Har Sinai on Sunday. According to Rav Acha bar Yakov, all of the Mitzvos of Shabbos were included in the commandment at Marah, including the prohibition of Techumin. Consequently, the Jews were unable to travel on Shabbos, so they must have left after Shabbos, on Sunday. Consequently, they arrived at Har Sinai on the same day (Sunday) that they left Refidim.
However, it should have been forbidden for them to travel on Shabbos for other reasons, such as Hotza'ah (carrying into Reshus ha'Rabim) and Mechamer (making their animals carry)! How could they travel if they were transgressing other Mitzvos of Shabbos which were commanded at Marah?
ANSWERS:
(a) TOSFOS (DH a'Techumin) says that the Gemara does not mean that the only Mitzvah of Shabbos that the Jews did not receive at Marah was Techumin. The prohibition of Hotza'ah was also not commanded at that time.
(b) The RITVA explains that they did not have to carry anything because they placed it all on animals to carry. Even though Mechamer (having an animal do Melachah) is also forbidden, the Ritva explains that they had not yet been taught the laws of Mechamer, just as they had not yet been taught the laws of Techumin. When the Gemara says that the prohibition of Techumin was not included in the commandment at Marah, it means that any prohibition like Techumin was not included. That is, any prohibition which is a Lav (and not a Chiyuv Misah) like Techumin, such as Mechamer, was not included in the commandment at Marah.
(c) The CHASAM SOFER explains that even though Hotza'ah was forbidden, they put their belongings on animals (as the Ritva explains). This did not necessitate transgression of the Melachah of Mechamer, because their animals could have started to walk before the onset of Shabbos without stopping (and making a Hanachah) until after Shabbos departed (see Shabbos 153b).
Others ask, however, how did they take down their tents on Shabbos? Taking down a tent involves the Melachah of Setiras Ohel? The PNEI YEHOSHUA suggests that they could have taken down their tents with a Shinuy, such as by having two people take down one tent.

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