"Aseres Yemei Teshuva" Math Problem?

A talk by the Lubavitcher Rebbe, 6 Tishrei, 5747 · October 9, 1986.

The Novi Yeshaya declares: "Seek Hashem when He can be found, call to Him when He is near." The Gemara explains: "This refers to the Ten Days of Repentance between Rosh Hashanah and Yom Kippur."

Torah is precise. Why does the Gemara speak of ten days "between" Rosh Hashanah and Yom Kippur, when in fact there are only seven?

Even while they share the general theme of repentance, Rosh Hashanah and Yom Kippur each contain a unique quality. Rosh Hashanah is a day of coronation of Hashem as our King. In the process of recommitting ourselves as His subjects, we also repent "out of love" -- which is why the liturgy does not mention anything negative. Yom Kippur is a day which, on its own, brings atonement for sins; at the same time, it is also the culmination of the journey of repentance that began ten days earlier, on Rosh Hashanah.

On the one hand, they each have their own special quality; on the other, they share the overarching theme of the Ten Days of Repentance.

From the Living Torah program,Volume 105, Program 419.