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I am aware that Sotah 27b and Rashi do not not regard these verses as self-contradictory, although they point to the apparent contradiction.

The verses in English:

The LORD spoke to Moses in the steppes of Moab at the Jordan near Jericho, saying: Instruct the Israelite people to assign, out of the holdings apportioned to them, towns for the Levites to dwell in; you shall assign to the Levites pasture land around their towns. The towns shall be theirs to dwell in, and the pasture shall be for the cattle they own and all their other beasts.

The town pasture that you are to assign to the Levites shall extend a thousand cubits outside the town wall all around. You shall measure off two thousand cubits outside the town on the east side, two thousand on the south side, two thousand on the west side, and two thousand on the north side, with the town in the centre. That shall be the pasture for their towns.

The apparent contradiction, alluded to in Sotah 27b and Rashi: the pasture area appears to be both 1,000 and 2,000 cubits beyond the city, in every direction, at the same time.

Can someone explain to me why these verses are not self-contradictory? Or is this a mystery in the Torah that we have yet to get to the bottom of?

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Sometimes a picture is clearer than a thousand words. Does this illustration (taken from the Stone Chumash) help build the right mental model for what the Torah describes?

Schema of fields and vineyards

Or, in the words of R Steinsaltz's commentary

An area extending 2000 cubits in each direction was alloted to each city (see Ramban, Ha'amek Davar). One thousand cubits of this extension was the surrounding tract mentioned in verses 2-4. The purpose of the further thousand cubits is not stated here, it probably served as forest land and for various requirements of the city, such as fields and vineyards (see Rashi on verse 4, Sotah 26b, Eruvin 56b). The whole area, 2000 cubits, in all directions is also referred to as the surrounding tract of the city (see Vayikra 25:34, Joshua 21)

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