The neighbor borrowed an extra cow, to make the total number of cows 18.
Then the oldest son got 1/2 of 18 is 9 cows,
the middle son got 1/3 of 18 is 6 cows,
and the youngest son got 1/9 of 18 is 2 cows.
Since 9+6+2 = 17, the cows could be divided among the three brothers in such a way that the borrowed cow was left over,
and could be returned to its owner.
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