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When did the Jewish people first begin counting the Omer?
The Rishonim state a tradition that when we were told in Egypt that we would receive the Torah we became exceptionally excited to the point that we began counting down the days until Matan Torah. This eventually became known as the Mitzvah of Sefiras HaOmer. Nevertheless, from the legal aspect of the Torah in which the counting of Sefira is dependent on the Omer offering, the Mitzvah to count Sefira did not begin until after the Jewish people entered into Eretz Yisrael and were able to bring the Omer on the 16th of Nissan of that year.
 Ran Pesachim 28a; Chinuch Emor Mitzvah 273 “We were commanded to count starting from the day after we left Mitzrayim until the day we receive the Torah to show our anticipation and excitement for receiving the Torah.”
 Ran Pesachim 28a
 Ran ibid; To note that the Ran states that the Jewish people were told that the Torah would be given on the 50th day of their count, while in truth the Torah given on the 52nd day after they left Mitzrayim which was the 51st day of the Omer and not the 50th. [See Admur 494/1] Vetzaruch Iyun!
 See Yalkut Shimoni Parshas Behar that the Mitzvah of the Omer only began on the 16th of Nissan, after entering Eretz Yisrael.