number - How did Avrohom learn that nine doesn't work?

The Midrash says (Bereshis Rabbah 49:13 quoted in Rashi Genesis 18:32) that Abraham stopped asking HaShem to save Sodom in the merit of less than 10 people because Noah and his family who were 8 people weren't able to save the world. The question is that from Noah we only see that 8 doesn't work, but not that anything less than 10 doesn't work. So why didn't Avraham daven for the merit of nine people?

Answer

The Chumash Shai LeMorah brings the Be'er Mayim Chaim (A commentary on Rashi written by the Maharal of Prague's brother, R' Chaim of Friedberg) says that once G-d agreed to save the 5 cities if there were 45 righteous people, Avraham understood that G-d was willing to be complete the quorum in order to save the city. (as Rashi 18:28 explains).

Once Avraham understood this, when he asked G-d to spare 3 cities in the merit of 30 righteous people (2 for the sake of 20, etc.) (Rashi 18:29), he was asking G-d to save 3 cities even if there were only 27 righteous individuals, relying on G-d to complete the quorum in each of the 3 cities.

So when Avraham was asking G-d to save 1 city if there were 10 righteous people to be found, he was asking G-d to save the city even if there were only 9 righteous people in the city, with G-d Himself counted as the 10th. (Of course, if there would be 10 without counting G-d, that would work too)

Now we can understand why Rashi jumps from 10 people to 8 people, since asking 10 was also asking 9. This also clarifies why Avraham went from 50 to 45, but went from 40 to 30 to 20 to 10, since 40 includes 36, etc.