Hadrash Ve-Haiyun by the Reisha Rav, HaGoan Rav Aaron Levine Elucidated and Adapted by Efraim Levine

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All the persons who are coming with Yaakov to mitzrayim -- his own descendants, aside from the wives of Yaakov's sons were 66 persons in all.

And Yosef's sons who were born to him in mitzrayim numbered two persons. All the people of Yaakov household who are coming to mitzrayim were seventy. (Bereishis 45:26-27)

Rashi here notes the obvious difficulty with the calculation. First the posuk tells us that the family who left mitzrayim totaled 66. We are then informed of another three in mitzrayim, i.e., Yosef and his two sons. Finally we are told that the total equals 70. But 66 + 3 = 69 not 70? Rashi quoting the Gemara answers that Yocheved was born between the walls. She was number 70.

 The Tosfos Yom Tov (Nazir 5) writes that one is allowed to offer an alternative answer to a Gemara's question as long as one does not draw practical halachic conclusions based on his interpretation. With this permit, let us suggest an alternative approach.

 First, let us note that the Gemara's calculation does not include Yaakov and his three wives (Rachel died years before). However, Yosef and his sons are listed even though they were already in mitzrayim and were not descending to mitzrayim now. In addition, the Gemara introduces a new person of whom there is no mention, i.e., Yocheved.

 Perhaps there is a simpler explanation. There were 66 members of Yaakov's family plus Yaakov and his three wives for a total of 70. The posuk is not counting Yosef and his sons because they were already in mitzrayim and it cannot be said of them "who are coming," i.e., in the present tense. This fits well into the simple translation of the posuk. The posuk, when recording the sum of 66, refers to all the persons as Yaakov's "descendents." The word "descendents" implies to the exclusion of himself and his wives. Later, when the posuk records the total of 70, it does not mention this word. It simply says "all the people of Yaakov's household," which can be interpreted as including Yaakov and his wives. The posuk in between informs us that, in addition, Yaakov had a son and two grandchildren. But they are not included in the calculation since they already settled in mitzrayim. The calculation includes only the new arrivals as the posuk reads "who are coming" i.e., in the present tense to the exclusion of those who have already come, i.e., Yosef and his sons.

 Let us now analyze the difference between the Gemara's calculation and ours. According to the Gemara, Yosef and his sons are listed but not Yaakov and his wives. In addition, we do list Yocheved. According to our explanation we omit Yosef and his sons but do include Yaakov and his wives and most importantly we make no mention of Yocheved. The key difference here is Yocheved. The Gemara is forced to invent Yocheved but according to us this is unnecessary.

Why didn't the Gemara choose our approach? Does it not seem simpler? Does it not fit well into the posuk?

 At first glance, we are tempted to suggest that according to the Gemara, Yocheved was only included as an afterthought. Because the calculation was one short, we were forced to introduce her in order to fill the gap. By stating she was born between the walls, it reconciles the discrepancy between the two numbers. However, we can no longer suggest that Yocheved was just an afterthought because we easily could have made the other calculation without her. Obviously chazal felt that it was necessary to include her. Chazal's calculation started with her in mind and from there they worked backwards. But why was Yocheved so important?

 Let us explain. First, a mother is symbol of a beginning or the source of something. Second, Yocheved was the mother of Moshe who was the redeemer of Klal Yisroel. Putting these two together, Yocheved is a symbol for the source for our redemption.

 In the next posuk we find that Yaakov sent Yehuda to mitzrayim to prepare a proper Torah environment to receive Klal Yisroel. Why was this necessary? Why couldn't Yaakov's sons establish a Torah environment when they arrived? The answer is that it would be too late. When entering a danger zone, the protection must already be in place. Only then is it possible to overcome the difficulties.

 Taking all these ideas together we can suggest the following. When Klal Yisroel entered mitzrayim they were entering into Galus. For them to survive, it was necessary that they enter with their source of redemption. Yocheved symbolized that source. Chazal were thus compelled to find her. They found her hidden in the discrepancy between 69 and 70.

 If we go a step further, we may suggest that the birth of Yocheved between the walls foreshadows the actual geulah 210 years later. Yocheved, the symbol of our source of redemption, was born as Klal Yisroel entered into Galus. We mentioned that it is vital to enter a danger zone prepared. The birth of Yocheved symbolizes that Klal Yisroel entered galus prepared with geulah. But let us note that this preparation came at the very last possible moment, just as they entered the walls of mitzrayim. This foreshadowed the actual geulah where chazal tell us that had it been delayed one more moment it would have been too late; we would have sunk to the fiftieth level of defilement where it would have been impossible for us to be redeemed.

 In conclusion, we have two possible calculations for the number 70. By contrasting the two we learn that chazal's starting point was to include Yocheved and then work backwards. Yocheved symbolized our source of geulah and her birth between the walls, i.e., at the last possible moment, foreshadowed our actual redemption that also took place at the last possible moment.