Verse Ex19-01 describing the Jews arrival at Sinai, where they received the Torah, states: In the third month after the children of Israel were gone forth out of the land of Egypt, the same day came they into the wilderness of Sinai. Verse Nu10-11a describing the departure of the Jews from Sinai, states: And it came to pass in the second year, in the second month, on the twentieth day of the month, that the cloud was taken up from over the tabernacle of the testimony. Based on these two verses Rashi infers The Jews stayed at Sinai for a little under a year. [The table below shows they stayed for 11 months 3 weeks)] The spreadsheet below shows the computations that led to Rashi's conclusion.

Source	Arrival	Place	Year	Month	Day
Ex19-01	Arrival	Mount Sinai	Year 0	Month 3	Day 1
Nu10-11a	Departure	Mount Sinai	Year 1	Month 2	Day 20
Logic	Duration	Mount Sinai	0	11 months	19 days

Sermonic Points: The Torah was received at Sinai. But you can't learn a whole new law code in one day. There are in fact 293 paragraphs in the Torah. Moses, at the orders of God, taught the people one paragraph a day. Saturdays were used for review. Hence the whole Torah was reviewed in 293 days (one for each paragraph) + 49 Saturdays (293/6 = 49) = 344 days = 11 months x 29.5 days per month + 19 days. Here the Torah and Moses show us the proper way to absorb new learning material thru digestable daily learning. This Rashi is the basis of the Page-a-day (DafYomi) Talmud learning project.